diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-06-14 04:25:41 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-14 04:25:41 +0000 |
| commit | 5f7a5c1a81c50807bf1315260f94108dd9a5ac2e (patch) | |
| tree | 6b485c54e2fa2b6c71ec68d89ad143087625d342 | |
| parent | 335db800c7cbaff88eda34d83e23ad808ea42fb8 (diff) | |
| download | open-axiom-5f7a5c1a81c50807bf1315260f94108dd9a5ac2e.tar.gz | |
* Partially revert previous change.
| -rw-r--r-- | src/ChangeLog | 4 | ||||
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/dpolcat.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/lodop.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 644 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1520 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1312 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9036 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31160 |
9 files changed, 21843 insertions, 21843 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index f3890cc8..9406a0da 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,9 @@ 2010-06-13 Gabriel Dos Reis <gdr@cs.tamu.edu> + * Partially revert previous change. + +2010-06-13 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/catdef.spad.pamphlet (DifferentialRing): Now extends DifferentialDomain. (DifferentialExtension): Check parameter for only DifferentialDomain. diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 1ea30684..4c6317f3 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -446,7 +446,7 @@ DifferentialExtension(R:Ring): Category == Ring with D: (%, R -> R, NonNegativeInteger) -> % ++ D(x, deriv, n) differentiate x n times ++ using a derivation which extends deriv on R. - if R has DifferentialDomain R then DifferentialRing + if R has DifferentialRing then DifferentialRing if R has PartialDifferentialRing(Symbol) then PartialDifferentialRing(Symbol) add @@ -457,7 +457,7 @@ DifferentialExtension(R:Ring): Category == Ring with D(x:%, derivation: R -> R, n:NonNegativeInteger) == differentiate(x, derivation, n) - if R has DifferentialDomain R then + if R has DifferentialRing then differentiate x == differentiate(x, differentiate$R) if R has PartialDifferentialRing Symbol then diff --git a/src/algebra/dpolcat.spad.pamphlet b/src/algebra/dpolcat.spad.pamphlet index 65533281..c5da0b47 100644 --- a/src/algebra/dpolcat.spad.pamphlet +++ b/src/algebra/dpolcat.spad.pamphlet @@ -300,7 +300,7 @@ DifferentialPolynomialCategory(R:Ring,S:OrderedSet, ++ separant(p) returns the ++ partial derivative of the differential polynomial p ++ with respect to its leader. - if R has DifferentialDomain R then + if R has DifferentialRing then InnerEvalable(S, R) InnerEvalable(S, $) Evalable $ @@ -394,7 +394,7 @@ DifferentialPolynomialCategory(R:Ring,S:OrderedSet, differentialVariables p == removeDuplicates [variable v for v in variables p] - if R has DifferentialDomain R then + if R has DifferentialRing then makeVariable p == differentiate(p, #1) diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet index d4aba322..3ebad1d2 100644 --- a/src/algebra/lodop.spad.pamphlet +++ b/src/algebra/lodop.spad.pamphlet @@ -86,7 +86,7 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where R: Ring OPRcat == MonogenicLinearOperator(R) with - if P has DifferentialDomain P then DifferentialRing + if P has DifferentialRing then DifferentialRing op: P -> $ ++ op(p) creates a value in $ equal to p in P. po: $ -> P ++ po(q) creates a value in P equal to q in $. diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index c93c135a..80bc4a2e 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2267469 . 3485464570) +(2267397 . 3485478046) (-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 -3636) +(-32 R -1384) ((|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 -1049) (QUOTE (-572))))) @@ -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 -3636 UP UPUP -3163) +(-40 -1384 UP UPUP -2189) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-3783 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-3783 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-3783 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-3783 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) -(-41 R -3636) +((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-2813 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-2813 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-2813 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) +(-41 R -1384) ((|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 (-460))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -438) (|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."))) ((-4454 . T) (-4455 . T)) -((-3783 (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|))))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|))))))) +((-2813 (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|))))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3636) +(-54 |Base| R -1384) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) -(-61 -2402) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +(-61 -2029) ((|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 -2402) +(-62 -2029) ((|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 -2402) +(-63 -2029) ((|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 -2402) +(-64 -2029) ((|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 -2402) +(-65 -2029) ((|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 -2402) +(-66 -2029) ((|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 -2402) +(-67 -2029) ((|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 -2402) +(-68 -2029) ((|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 -2402) +(-69 -2029) ((|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 -2402) +(-70 -2029) ((|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 -2402) +(-71 -2029) ((|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 -2402) +(-72 -2029) ((|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 -2402) +(-73 -2029) ((|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 -2402) +(-74 -2029) ((|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 -2402) +(-77 -2029) ((|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 -2402) +(-78 -2029) ((|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 -2402) +(-79 -2029) ((|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 -2402) +(-80 -2029) ((|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 -2402) +(-81 -2029) ((|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 -2402) +(-82 -2029) ((|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 -2402) +(-83 -2029) ((|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 -2402) +(-84 -2029) ((|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 -2402) +(-85 -2029) ((|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 -2402) +(-86 -2029) ((|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 -2402) +(-87 -2029) ((|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 -2402) +(-88 -2029) ((|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 -2402) +(-89 -2029) ((|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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-3783 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) +((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (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 -3636 UP) +(-116 -1384 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}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-918))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-117 |#1|) (QUOTE (-1033))) (|HasCategory| (-117 |#1|) (QUOTE (-828))) (-3783 (|HasCategory| (-117 |#1|) (QUOTE (-828))) (|HasCategory| (-117 |#1|) (QUOTE (-858)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-1163))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-313))) (|HasCategory| (-117 |#1|) (QUOTE (-553))) (|HasCategory| (-117 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-918))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-117 |#1|) (QUOTE (-1033))) (|HasCategory| (-117 |#1|) (QUOTE (-828))) (-2813 (|HasCategory| (-117 |#1|) (QUOTE (-828))) (|HasCategory| (-117 |#1|) (QUOTE (-858)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-1163))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-313))) (|HasCategory| (-117 |#1|) (QUOTE (-553))) (|HasCategory| (-117 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (|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"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130)))))) (-3783 (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-130) (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111)))) (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130)))))) +((-2813 (-12 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130)))))) (-2813 (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-130) (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111)))) (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4456 "*") . T)) NIL -(-136 |minix| -3436 S T$) +(-136 |minix| -4131 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -3436 R) +(-137 |minix| -4131 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) ((-4454 . T) (-4444 . T) (-4455 . T)) -((-3783 (-12 (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) +((-2813 (-12 (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (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."))) ((-4451 . T)) NIL -(-149 -3636 UP UPUP) +(-149 -1384 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 -3636) +(-159 R -1384) ((|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 (-918))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564)))) (-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})"))) -((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4101 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4447 -2813 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-3559 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . 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}."))) -((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4101 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-836)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1214)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| 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(|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-356))))) +((-4447 -2813 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-3559 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-836)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1214)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4453)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-356))))) (-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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -3636) +(-190 R -1384) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -3636 UP UPUP R) +(-217 -1384 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 -3636 FP) +(-218 -1384 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-3783 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) +((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -3636) +(-221 R -1384) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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}."))) ((-4451 . T)) NIL -(-226 R -3636) +(-226 R -1384) ((|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}."))) -((-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . 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}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-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 @@ -859,7 +859,7 @@ NIL (-232 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -235) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (-233 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) ((-4451 . T)) @@ -892,22 +892,22 @@ 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 -(-241 S -3436 R) +(-241 S -4131 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-801))) (|HasCategory| |#3| (QUOTE (-856))) (|HasAttribute| |#3| (QUOTE -4451)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-734))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (QUOTE (-1111)))) -(-242 -3436 R) +(-242 -4131 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) NIL -(-243 -3436 A B) +(-243 -4131 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 -(-244 -3436 R) +(-244 -4131 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."))) ((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-370))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1060)))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370)))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-801))) (-3783 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-734))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1060)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (-3783 (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE 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(QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) 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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 @@ -927,7 +927,7 @@ NIL (-249 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}"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-250 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 @@ -935,7 +935,7 @@ NIL (-251 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1060)))) (-2813 (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1060)))) (|HasCategory| |#3| (QUOTE (-734))) (-12 (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (LIST (QUOTE -909) (QUOTE (-1188)))))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -1049) (QUOTE (-572))))) (-2813 (|HasCategory| |#3| (QUOTE (-1060))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -1049) (QUOTE (-572)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#3| (QUOTE (-1111)))) (-2813 (|HasAttribute| |#3| (QUOTE -4451)) (-12 (|HasCategory| |#3| (QUOTE (-237))) (|HasCategory| |#3| (QUOTE (-1060)))) (-12 (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (-257 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -235) (|devaluate| |#2|)))) +((|HasCategory| |#2| (QUOTE (-237)))) (-258 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\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|) $ |#2|) "\\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|)) $ |#2|) "\\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|) $ |#2|) "\\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|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\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|)) |#2|) "\\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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) @@ -1007,7 +1007,7 @@ NIL (-269 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"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#3| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#3| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#3| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#3| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#3| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-270 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1052,11 +1052,11 @@ 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 -(-281 R -3636) +(-281 R -1384) ((|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 -(-282 R -3636) +(-282 R -1384) ((|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 @@ -1108,7 +1108,7 @@ 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 -(-295 S R |Mod| -4322 -4086 |exactQuo|) +(-295 S R |Mod| -3635 -1867 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -1130,21 +1130,21 @@ NIL NIL (-300 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-302) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-303 -3636 S) +(-303 -1384 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 -(-304 E -3636) +(-304 E -1384) ((|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 @@ -1192,7 +1192,7 @@ 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 -(-316 -3636) +(-316 -1384) ((|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 @@ -1207,7 +1207,7 @@ NIL (-319 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-1033))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-828))) (-3783 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-828))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-858)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-1163))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -315) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -292) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-313))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-553))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-858))) (-12 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| $ (QUOTE (-146)))) (-3783 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| $ (QUOTE (-146)))))) +((|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-1033))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-828))) (-2813 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-828))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-858)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-1163))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -315) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (LIST (QUOTE -292) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1265) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-313))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-553))) (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-858))) (-12 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| $ (QUOTE (-146)))) (-2813 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1265 |#1| |#2| |#3| |#4|) (QUOTE (-918))) (|HasCategory| $ (QUOTE (-146)))))) (-320 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1218,9 +1218,9 @@ NIL NIL (-322 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."))) -((-4451 -3783 (-3804 (|has| |#1| (-1060)) (|has| |#1| (-647 (-572)))) (-12 (|has| |#1| (-564)) (-3783 (-3804 (|has| |#1| (-1060)) (|has| |#1| (-647 (-572)))) (|has| |#1| (-1060)) (|has| |#1| (-481)))) (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) ((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4452 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(|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 @@ -1231,7 +1231,7 @@ NIL (-325 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1263,12 +1263,12 @@ NIL (-333 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."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) -(-334 S -3636) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +(-334 S -1384) ((|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 (-375)))) -(-335 -3636) +(-335 -1384) ((|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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -1292,15 +1292,15 @@ 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 -(-341 S -3636 UP UPUP R) +(-341 S -1384 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 -(-342 -3636 UP UPUP R) +(-342 -1384 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 -(-343 -3636 UP UPUP R) +(-343 -1384 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 @@ -1320,26 +1320,26 @@ 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 -(-348 S -3636 UP UPUP) +(-348 S -1384 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 (-375))) (|HasCategory| |#2| (QUOTE (-370)))) -(-349 -3636 UP UPUP) +(-349 -1384 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."))) ((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-350 |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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) +((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) (-351 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) (-352 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) (-353 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 @@ -1356,31 +1356,31 @@ 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL -(-357 R UP -3636) +(-357 R UP -1384) ((|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 (-358 |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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) +((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) (-359 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) (-360 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) (-361 |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}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) +((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) (-362 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) -(-363 -3636 GF) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +(-363 -1384 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 @@ -1388,14 +1388,14 @@ 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 -(-365 -3636 FP FPP) +(-365 -1384 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 (-366 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}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) +((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) (-367 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 @@ -1474,7 +1474,7 @@ NIL NIL (-386) ((|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}."))) -((-4437 . T) (-4445 . T) (-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4437 . T) (-4445 . T) (-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-387 |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}."))) @@ -1528,7 +1528,7 @@ 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 -(-400 -3636 UP UPUP R) +(-400 -1384 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 @@ -1552,11 +1552,11 @@ 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 -(-406 -2402 |returnType| -1701 |symbols|) +(-406 -2029 |returnType| -1563 |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 -(-407 -3636 UP) +(-407 -1384 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1578,7 +1578,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4437)) (|HasAttribute| |#1| (QUOTE -4445))) (-412) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-413 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."))) @@ -1591,7 +1591,7 @@ NIL (-415 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."))) ((-4441 -12 (|has| |#1| (-6 -4452)) (|has| |#1| (-460)) (|has| |#1| (-6 -4441))) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-828))) (-3783 (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-858)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836))))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-553))) (-12 (|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-460)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-828))) (-2813 (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-858)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836))))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-836)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-553))) (-12 (|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#1| (QUOTE -4441)) (|HasCategory| |#1| (QUOTE (-460)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-416 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1612,11 +1612,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-421 R -3636 UP A) +(-421 R -1384 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4451 . T)) NIL -(-422 R -3636 UP A |ibasis|) +(-422 R -1384 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 -1049) (|devaluate| |#2|)))) @@ -1635,7 +1635,7 @@ NIL (-426 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."))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -315) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1233))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-460)))) +((|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -315) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1233))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-460)))) (-427 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 @@ -1664,7 +1664,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4454 . T) (-4444 . T) (-4455 . T)) NIL -(-434 R -3636) +(-434 R -1384) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1672,7 +1672,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4441 -12 (|has| |#1| (-6 -4441)) (|has| |#2| (-6 -4441))) (-4448 . T) (-4449 . T) (-4451 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#2| (QUOTE -4441)))) -(-436 R -3636) +(-436 R -1384) ((|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 @@ -1682,17 +1682,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-1123))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-438 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}."))) -((-4451 -3783 (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) ((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-564)) (-4446 |has| |#1| (-564))) +((-4451 -2813 (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) ((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-564)) (-4446 |has| |#1| (-564))) NIL -(-439 R -3636) +(-439 R -1384) ((|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 -(-440 R -3636) +(-440 R -1384) ((|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)))) -(-441 R -3636) +(-441 R -1384) ((|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 @@ -1700,7 +1700,7 @@ 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 -(-443 R -3636 UP) +(-443 R -1384 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 -1049) (QUOTE (-48))))) @@ -1732,7 +1732,7 @@ 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 -(-451 R UP -3636) +(-451 R UP -1384) ((|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 @@ -1779,7 +1779,7 @@ NIL (-462 |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"))) (((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-918))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-918))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) (-463 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1844,7 +1844,7 @@ 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 -(-479 |lv| -3636 R) +(-479 |lv| -1384 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 @@ -1859,11 +1859,11 @@ NIL (-482 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-483 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111)))) (-484 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4455 . T) (-4454 . T)) @@ -1879,7 +1879,7 @@ NIL (-487 |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."))) ((-4454 . T) (-4455 . 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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 @@ -1887,11 +1887,11 @@ NIL (-489 |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 @@ -1899,8 +1899,8 @@ NIL (-492 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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) -(-493 -3636 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +(-493 -1384 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 @@ -1911,7 +1911,7 @@ NIL (-495) ((|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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-3783 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) +((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) (-496 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1936,7 +1936,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-502 -3636 UP |AlExt| |AlPol|) +(-502 -1384 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 @@ -1947,16 +1947,16 @@ NIL (-504 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-505 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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-506 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 -(-507 R UP -3636) +(-507 R UP -1384) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1976,7 +1976,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-512 -3636 |Expon| |VarSet| |DPoly|) +(-512 -1384 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-1188))))) @@ -2027,7 +2027,7 @@ NIL (-524 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-525) ((|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 @@ -2035,15 +2035,15 @@ NIL (-526 |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}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| (-589 |#1|) (QUOTE (-146))) (|HasCategory| (-589 |#1|) (QUOTE (-375)))) (|HasCategory| (-589 |#1|) (QUOTE (-148))) (|HasCategory| (-589 |#1|) (QUOTE (-375))) (|HasCategory| (-589 |#1|) (QUOTE (-146)))) +((-2813 (|HasCategory| (-589 |#1|) (QUOTE (-146))) (|HasCategory| (-589 |#1|) (QUOTE (-375)))) (|HasCategory| (-589 |#1|) (QUOTE (-148))) (|HasCategory| (-589 |#1|) (QUOTE (-375))) (|HasCategory| (-589 |#1|) (QUOTE (-146)))) (-527 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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-528 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."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-529 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 @@ -2055,7 +2055,7 @@ NIL (-531 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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-532) ((|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 @@ -2088,7 +2088,7 @@ 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 -(-540 K -3636 |Par|) +(-540 K -1384 |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 @@ -2112,7 +2112,7 @@ 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 -(-546 K -3636 |Par|) +(-546 K -1384 |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 @@ -2163,12 +2163,12 @@ NIL (-558 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) -(-559 R -3636) +((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +(-559 R -1384) ((|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 -(-560 R0 -3636 UP UPUP R) +(-560 R0 -1384 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 @@ -2178,7 +2178,7 @@ NIL NIL (-562 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."))) -((-4091 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-3548 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-563 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."))) @@ -2188,7 +2188,7 @@ 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."))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL -(-565 R -3636) +(-565 R -1384) ((|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 @@ -2200,7 +2200,7 @@ 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 -(-568 R -3636 L) +(-568 R -1384 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 -664) (|devaluate| |#2|)))) @@ -2208,11 +2208,11 @@ 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 -(-570 -3636 UP UPUP R) +(-570 -1384 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 -(-571 -3636 UP) +(-571 -1384 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 @@ -2224,15 +2224,15 @@ 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 -(-574 R -3636 L) +(-574 R -1384 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 -664) (|devaluate| |#2|)))) -(-575 R -3636) +(-575 R -1384) ((|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 -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1150)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-637))))) -(-576 -3636 UP) +(-576 -1384 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 @@ -2240,27 +2240,27 @@ 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 -(-578 -3636) +(-578 -1384) ((|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 (-579 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."))) -((-4091 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-3548 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-580) ((|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 -(-581 R -3636) +(-581 R -1384) ((|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 -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-290))) (|HasCategory| |#2| (QUOTE (-637))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-290)))) (|HasCategory| |#1| (QUOTE (-564)))) -(-582 -3636 UP) +(-582 -1384 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 -(-583 R -3636) +(-583 R -1384) ((|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 @@ -2292,11 +2292,11 @@ 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 -(-591 R -3636) +(-591 R -1384) ((|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 -(-592 E -3636) +(-592 E -1384) ((|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 @@ -2304,7 +2304,7 @@ 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 -(-594 -3636) +(-594 -1384) ((|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}."))) ((-4449 . T) (-4448 . T)) ((|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-1188))))) @@ -2335,7 +2335,7 @@ NIL (-601 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (-3783 (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) +((-2813 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (-2813 (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (-602 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 @@ -2343,7 +2343,7 @@ NIL (-603 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))) (|HasCategory| (-572) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))) (|HasCategory| (-572) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572)))))) (-604 |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.}"))) (((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -2360,7 +2360,7 @@ 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 -(-608 R -3636 FG) +(-608 R -1384 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 @@ -2371,7 +2371,7 @@ NIL (-610 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-611 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2390,12 +2390,12 @@ NIL NIL (-615 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4451 -3783 (-3804 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) -((-3783 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) +((-4451 -2813 (-2085 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) +((-2813 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-616 |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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-617 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 @@ -2420,7 +2420,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-623 -3636 UP) +(-623 -1384 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2448,7 +2448,7 @@ 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}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-856)))) -(-630 R -3636) +(-630 R -1384) ((|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 @@ -2480,18 +2480,18 @@ 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 -(-638 R -3636) +(-638 R -1384) ((|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 -(-639 |lv| -3636) +(-639 |lv| -1384) ((|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 (-640) ((|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."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-1170) (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-1170) (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111)))) (-641 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2502,8 +2502,8 @@ NIL NIL (-643 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4451 -3783 (-3804 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) -((-3783 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) +((-4451 -2813 (-2085 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) +((-2813 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-644 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 @@ -2515,7 +2515,7 @@ NIL (-646 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 -((-3796 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) +((-2074 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) (-647 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4451 . T)) @@ -2539,7 +2539,7 @@ NIL (-652 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-653 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2551,7 +2551,7 @@ NIL (-655 S) ((|substitute| (($ |#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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-656 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 @@ -2568,7 +2568,7 @@ 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 -(-660 R -3636 L) +(-660 R -1384 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 @@ -2588,11 +2588,11 @@ 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}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) NIL -(-665 -3636 UP) +(-665 -1384 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)))) -(-666 A -3693) +(-666 A -2514) ((|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}}"))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) @@ -2628,11 +2628,11 @@ 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}."))) ((-4455 . T) (-4454 . T)) NIL -(-675 -3636) +(-675 -1384) ((|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 -(-676 -3636 |Row| |Col| M) +(-676 -1384 |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 @@ -2643,7 +2643,7 @@ NIL (-678 |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."))) ((-4451 . T) (-4454 . T) (-4448 . T) (-4449 . T)) -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564))) (-3783 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-679) ((|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 @@ -2663,7 +2663,7 @@ NIL (-683 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 -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-684) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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."))) ((-4454 . T) (-4455 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-698 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 @@ -2728,7 +2728,7 @@ 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 -(-700 S -3636 FLAF FLAS) +(-700 S -1384 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 @@ -2738,8 +2738,8 @@ NIL NIL (-702) ((|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"))) -((-4447 . T) (-4452 |has| (-707) (-370)) (-4446 |has| (-707) (-370)) (-4101 . T) (-4453 |has| (-707) (-6 -4453)) (-4450 |has| (-707) (-6 -4450)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . 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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}."))) ((-4455 . T)) @@ -2752,13 +2752,13 @@ 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.")) 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(|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 (-707) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) 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T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-708 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."))) @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-237))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-721 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-723 R |Mod| -4322 -4086 |exactQuo|) +(-723 R |Mod| -3635 -1867 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4451 . T)) NIL @@ -2832,7 +2832,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4449 . T) (-4448 . T)) NIL -(-726 -3636) +(-726 -1384) ((|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]]}."))) ((-4451 . T)) NIL @@ -2868,7 +2868,7 @@ 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 -(-735 -3636 UP) +(-735 -1384 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 @@ -2887,7 +2887,7 @@ NIL (-739 |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."))) (((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-918))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-918))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) (-740 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3020,11 +3020,11 @@ 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 -(-773 -3636) +(-773 -1384) ((|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 -(-774 P -3636) +(-774 P -1384) ((|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 @@ -3032,7 +3032,7 @@ NIL NIL NIL NIL -(-776 UP -3636) +(-776 UP -1384) ((|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 @@ -3048,7 +3048,7 @@ 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."))) (((-4456 "*") . T)) NIL -(-780 R -3636) +(-780 R -1384) ((|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 @@ -3068,7 +3068,7 @@ 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 -(-785 -3636 |ExtF| |SUEx| |ExtP| |n|) +(-785 -1384 |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 @@ -3083,7 +3083,7 @@ NIL (-788 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE 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(-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-2074 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-2074 (|HasCategory| |#1| (QUOTE (-553)))) (-2074 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-2074 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572))))) (-2074 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-2074 (|HasCategory| |#1| (LIST (QUOTE -1003) (QUOTE (-572))))))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-789 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 @@ -3091,7 +3091,7 @@ NIL (-790 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)}"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4450 |has| |#1| (-370)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-791 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 @@ -3152,23 +3152,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) NIL -(-806 -3783 R OS S) +(-806 -2813 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-807 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (-3783 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (-2813 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (-808) ((|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 -(-809 R -3636 L) +(-809 R -1384 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 -(-810 R -3636) +(-810 R -1384) ((|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 @@ -3176,7 +3176,7 @@ 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 -(-812 R -3636) +(-812 R -1384) ((|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 @@ -3184,11 +3184,11 @@ 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 -(-814 -3636 UP UPUP R) +(-814 -1384 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 -(-815 -3636 UP L LQ) +(-815 -1384 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 @@ -3196,38 +3196,38 @@ 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 -(-817 -3636 UP L LQ) +(-817 -1384 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 -(-818 -3636 UP) +(-818 -1384 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 -(-819 -3636 L UP A LO) +(-819 -1384 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 -(-820 -3636 UP) +(-820 -1384 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)))) -(-821 -3636 LO) +(-821 -1384 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 -(-822 -3636 LODO) +(-822 -1384 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . 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(((-4456 "*") |has| |#2| (-370)) (-4447 |has| |#2| (-370)) (-4452 |has| |#2| (-370)) (-4446 |has| |#2| (-370)) (-4451 . T) (-4449 . T) (-4448 . T)) @@ -3271,7 +3271,7 @@ NIL (-835 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -235) (|devaluate| |#1|)))) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-237)))) (-836) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) NIL @@ -3295,7 +3295,7 @@ NIL (-841 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."))) ((-4451 |has| |#1| (-856))) -((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-3783 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-3783 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) +((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) (-842 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 @@ -3335,12 +3335,12 @@ NIL (-851 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4451 |has| |#1| (-856))) -((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-3783 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-3783 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) +((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) (-852) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-853 -3436 S) +(-853 -4131 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 @@ -3376,11 +3376,11 @@ 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 (-370))) (|HasCategory| |#1| (QUOTE (-564)))) -(-862 R |sigma| -4198) +(-862 R |sigma| -2073) ((|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."))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) -(-863 |x| R |sigma| -4198) +(-863 |x| R |sigma| -2073) ((|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}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-370)))) @@ -3447,15 +3447,15 @@ NIL (-879 |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)."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-878 |#1|) (QUOTE (-918))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-148))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-878 |#1|) (QUOTE (-1033))) (|HasCategory| (-878 |#1|) (QUOTE (-828))) (-3783 (|HasCategory| (-878 |#1|) (QUOTE (-828))) (|HasCategory| (-878 |#1|) (QUOTE (-858)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-1163))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-237))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -878) (|devaluate| |#1|)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (QUOTE (-313))) (|HasCategory| (-878 |#1|) (QUOTE (-553))) (|HasCategory| (-878 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))))) +((|HasCategory| (-878 |#1|) (QUOTE (-918))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-148))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-878 |#1|) (QUOTE (-1033))) (|HasCategory| (-878 |#1|) (QUOTE (-828))) (-2813 (|HasCategory| (-878 |#1|) (QUOTE (-828))) (|HasCategory| (-878 |#1|) (QUOTE (-858)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-1163))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-237))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -878) (|devaluate| |#1|)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (QUOTE (-313))) (|HasCategory| (-878 |#1|) (QUOTE (-553))) (|HasCategory| (-878 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))))) (-880 |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)}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-828))) (-3783 (|HasCategory| |#2| (QUOTE (-828))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-828))) (-2813 (|HasCategory| |#2| (QUOTE (-828))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) (-881 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 (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) (-882) ((|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 @@ -3515,7 +3515,7 @@ NIL (-896 |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 (-3796 (|HasCategory| |#2| (QUOTE (-1060)))) (-3796 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (-3796 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) +((-12 (-2074 (|HasCategory| |#2| (QUOTE (-1060)))) (-2074 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (-2074 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-897 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 @@ -3524,7 +3524,7 @@ 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 -(-899 R -4020) +(-899 R -3608) ((|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 @@ -3548,7 +3548,7 @@ 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 -(-905 UP -3636) +(-905 UP -1384) ((|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 @@ -3571,7 +3571,7 @@ NIL (-910 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 (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-911 |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 @@ -3587,7 +3587,7 @@ NIL (-914 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."))) ((-4451 . T)) -((-3783 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) +((-2813 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) (-915 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 @@ -3608,7 +3608,7 @@ 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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-375)))) -(-920 R0 -3636 UP UPUP R) +(-920 R0 -1384 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 @@ -3636,7 +3636,7 @@ 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 -(-927 -3636) +(-927 -1384) ((|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 @@ -3652,11 +3652,11 @@ 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}."))) (((-4456 "*") . T)) NIL -(-931 -3636 P) +(-931 -1384 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-932 |xx| -3636) +(-932 |xx| -1384) ((|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 @@ -3680,7 +3680,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-938 R -3636) +(-938 R -1384) ((|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 @@ -3692,7 +3692,7 @@ 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 -(-941 S R -3636) +(-941 S R -1384) ((|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 @@ -3712,11 +3712,11 @@ 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 -895) (|devaluate| |#1|)))) -(-946 R -3636 -4020) +(-946 R -1384 -3608) ((|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 -(-947 -4020) +(-947 -3608) ((|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 @@ -3739,7 +3739,7 @@ NIL (-952 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-953 |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 @@ -3764,7 +3764,7 @@ 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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) NIL -(-959 E V R P -3636) +(-959 E V R P -1384) ((|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 @@ -3775,8 +3775,8 @@ NIL (-961 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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-962 E V R P -3636) +((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-962 E V R P -1384) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-460)))) @@ -3799,12 +3799,12 @@ NIL (-967 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-968) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-969 -3636) +(-969 -1384) ((|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 @@ -3819,11 +3819,11 @@ NIL (-972 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}"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4452))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4452))) (-973 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"))) ((-4451 -12 (|has| |#2| (-481)) (|has| |#1| (-481)))) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801)))) (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-858))))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3783 (-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 (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-375)))) (-3783 (-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 (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-858))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801)))) (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-858))))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2813 (-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 (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-375)))) (-2813 (-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 (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-801))))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-858))))) (-974) ((|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 @@ -3912,7 +3912,7 @@ 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 -(-996 K R UP -3636) +(-996 K R UP -1384) ((|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 @@ -3971,11 +3971,11 @@ NIL (-1010 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.}"))) ((-4447 |has| |#1| (-296)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553)))) (-1011 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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-1012 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3984,14 +3984,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1014 -3636 UP UPUP |radicnd| |n|) +(-1014 -1384 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-3783 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-3783 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-3783 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-3783 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) +((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-2813 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-2813 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-2813 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) (-1015 |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."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-3783 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) +((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) (-1016) ((|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 @@ -4024,19 +4024,19 @@ 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}}"))) ((-4447 . T) (-4452 . T) (-4446 . T) (-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4451 . T)) NIL -(-1024 R -3636) +(-1024 R -1384) ((|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 -(-1025 R -3636) +(-1025 R -1384) ((|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 -(-1026 -3636 UP) +(-1026 -1384 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 -(-1027 -3636 UP) +(-1027 -1384 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 @@ -4071,8 +4071,8 @@ NIL (-1035 |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"))) ((-4447 . T) (-4452 . T) (-4446 . T) (-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4451 . T)) -((-3783 (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572))))) -(-1036 -3636 L) +((-2813 (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572))))) +(-1036 -1384 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 @@ -4108,14 +4108,14 @@ 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 -(-1045 -3636 |Expon| |VarSet| |FPol| |LFPol|) +(-1045 -1384 |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"))) (((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-1046) ((|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.}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) (-1047) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4172,7 +4172,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4451 . T)) NIL -(-1061 |xx| -3636) +(-1061 |xx| -1384) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4191,7 +4191,7 @@ NIL (-1065 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4454 . T) (-4449 . T) (-4448 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-3783 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-370)))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#3| (QUOTE (-564))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870))))) +((|HasCategory| |#3| (QUOTE (-174))) (-2813 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-370)))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#3| (QUOTE (-564))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870))))) (-1066 |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 @@ -4227,7 +4227,7 @@ NIL (-1074) ((|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}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) (-1075 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 @@ -4276,11 +4276,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1087 |Base| R -3636) +(-1087 |Base| R -1384) ((|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 -(-1088 |Base| R -3636) +(-1088 |Base| R -1384) ((|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 @@ -4295,7 +4295,7 @@ NIL (-1091 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."))) ((-4447 |has| |#1| (-370)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-356)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-356)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370))))) (-1092 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 @@ -4323,7 +4323,7 @@ NIL (-1098 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"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . 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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 @@ -4383,7 +4383,7 @@ NIL (-1113 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4454 . T) (-4444 . T) (-4455 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-1114 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) 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|#3| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#3| (QUOTE (-1111)))) (|HasAttribute| |#3| (QUOTE -4451)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (-1125 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4436,7 +4436,7 @@ 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 -(-1127 R -3636) +(-1127 R -1384) ((|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 @@ -4475,16 +4475,16 @@ NIL (-1136 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1137 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) (-1138 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}"))) ((-4455 . T) (-4454 . T)) NIL -(-1139 UP -3636) +(-1139 UP -1384) ((|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 @@ -4539,11 +4539,11 @@ NIL (-1152 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))) (-3783 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))))) (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))) (-2813 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))))) (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870))))) (-1153 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4451 . T) (-4443 |has| |#2| (-6 (-4456 "*"))) (-4454 . T) (-4448 . T) (-4449 . T)) -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (-3783 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1154 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4563,7 +4563,7 @@ NIL (-1158 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-1159 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 @@ -4575,7 +4575,7 @@ NIL (-1161 |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."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111)))) (-1162) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4603,7 +4603,7 @@ NIL (-1168 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4455 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-1169) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4455 . T) (-4454 . T)) @@ -4611,11 +4611,11 @@ NIL (-1170) NIL ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) +((-2813 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (-1171 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4454 . T) (-4455 . 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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 @@ -4646,9 +4646,9 @@ NIL NIL (-1179 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1185 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1186 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1187) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4691,7 +4691,7 @@ NIL (-1190 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| (-982) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasAttribute| |#1| (QUOTE -4452))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| (-982) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasAttribute| |#1| (QUOTE -4452))) (-1191) ((|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 @@ -4735,7 +4735,7 @@ NIL (-1201 |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}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-1202 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 @@ -4791,7 +4791,7 @@ NIL (-1215 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4455 . T) (-4454 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (-1216 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4800,7 +4800,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1218 R -3636) +(-1218 R -1384) ((|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 @@ -4808,7 +4808,7 @@ 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 -(-1220 R -3636) +(-1220 R -1384) ((|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 -622) (LIST (QUOTE -901) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -895) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -895) (|devaluate| |#1|))))) @@ -4823,7 +4823,7 @@ NIL (-1223 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) (-1224 |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 @@ -4836,7 +4836,7 @@ 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 (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) -(-1227 -3636) +(-1227 -1384) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) 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the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4939,7 +4939,7 @@ NIL (-1252 |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}"))) (((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4450 |has| |#2| (-370)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-3783 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1253 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 @@ -4955,7 +4955,7 @@ NIL (-1256 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 -909) (QUOTE (-1188)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1123))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3491) (LIST (|devaluate| |#2|) (QUOTE (-1188)))))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1123))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2940) (LIST (|devaluate| |#2|) (QUOTE (-1188)))))) (-1257 |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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -4983,15 +4983,15 @@ NIL (-1263 |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)}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) +((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-1264 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1265 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))}."))) (((-4456 "*") |has| (-1264 |#2| |#3| |#4|) (-174)) (-4447 |has| (-1264 |#2| |#3| |#4|) (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-174))) (-3783 (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-370))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-460))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-564)))) +((|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-174))) (-2813 (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1264 |#2| |#3| |#4|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-370))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-460))) (|HasCategory| (-1264 |#2| |#3| |#4|) (QUOTE (-564)))) (-1266 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5007,7 +5007,7 @@ NIL (-1269 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3270) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3921) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) (-1270 |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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -5015,12 +5015,12 @@ NIL (-1271 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1272 |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 -(-1273 -3636 UP L UTS) +(-1273 -1384 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 (-564)))) @@ -5047,7 +5047,7 @@ NIL (-1279 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."))) ((-4455 . T) (-4454 . T)) -((-3783 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) +((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-1280) ((|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 @@ -5080,7 +5080,7 @@ 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 -(-1288 K R UP -3636) +(-1288 K R UP -1384) ((|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 @@ -5116,11 +5116,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) NIL -(-1297 S -3636) +(-1297 S -1384) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1298 -3636) +(-1298 -1384) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -5180,4 +5180,4 @@ NIL NIL NIL NIL -((-3 NIL 2267449 2267454 2267459 2267464) (-2 NIL 2267429 2267434 2267439 2267444) (-1 NIL 2267409 2267414 2267419 2267424) (0 NIL 2267389 2267394 2267399 2267404) (-1308 "ZMOD.spad" 2267198 2267211 2267327 2267384) (-1307 "ZLINDEP.spad" 2266264 2266275 2267188 2267193) (-1306 "ZDSOLVE.spad" 2256209 2256231 2266254 2266259) (-1305 "YSTREAM.spad" 2255704 2255715 2256199 2256204) (-1304 "YDIAGRAM.spad" 2255338 2255347 2255694 2255699) (-1303 "XRPOLY.spad" 2254558 2254578 2255194 2255263) (-1302 "XPR.spad" 2252353 2252366 2254276 2254375) (-1301 "XPOLY.spad" 2251908 2251919 2252209 2252278) (-1300 "XPOLYC.spad" 2251227 2251243 2251834 2251903) (-1299 "XPBWPOLY.spad" 2249664 2249684 2251007 2251076) (-1298 "XF.spad" 2248127 2248142 2249566 2249659) (-1297 "XF.spad" 2246570 2246587 2248011 2248016) (-1296 "XFALG.spad" 2243618 2243634 2246496 2246565) (-1295 "XEXPPKG.spad" 2242869 2242895 2243608 2243613) (-1294 "XDPOLY.spad" 2242483 2242499 2242725 2242794) (-1293 "XALG.spad" 2242143 2242154 2242439 2242478) (-1292 "WUTSET.spad" 2237982 2237999 2241789 2241816) (-1291 "WP.spad" 2237181 2237225 2237840 2237907) (-1290 "WHILEAST.spad" 2236979 2236988 2237171 2237176) (-1289 "WHEREAST.spad" 2236650 2236659 2236969 2236974) (-1288 "WFFINTBS.spad" 2234313 2234335 2236640 2236645) (-1287 "WEIER.spad" 2232535 2232546 2234303 2234308) (-1286 "VSPACE.spad" 2232208 2232219 2232503 2232530) (-1285 "VSPACE.spad" 2231901 2231914 2232198 2232203) (-1284 "VOID.spad" 2231578 2231587 2231891 2231896) (-1283 "VIEW.spad" 2229258 2229267 2231568 2231573) (-1282 "VIEWDEF.spad" 2224459 2224468 2229248 2229253) (-1281 "VIEW3D.spad" 2208420 2208429 2224449 2224454) (-1280 "VIEW2D.spad" 2196311 2196320 2208410 2208415) (-1279 "VECTOR.spad" 2194985 2194996 2195236 2195263) (-1278 "VECTOR2.spad" 2193624 2193637 2194975 2194980) (-1277 "VECTCAT.spad" 2191528 2191539 2193592 2193619) (-1276 "VECTCAT.spad" 2189239 2189252 2191305 2191310) (-1275 "VARIABLE.spad" 2189019 2189034 2189229 2189234) (-1274 "UTYPE.spad" 2188663 2188672 2189009 2189014) (-1273 "UTSODETL.spad" 2187958 2187982 2188619 2188624) (-1272 "UTSODE.spad" 2186174 2186194 2187948 2187953) (-1271 "UTS.spad" 2180978 2181006 2184641 2184738) (-1270 "UTSCAT.spad" 2178457 2178473 2180876 2180973) (-1269 "UTSCAT.spad" 2175580 2175598 2178001 2178006) (-1268 "UTS2.spad" 2175175 2175210 2175570 2175575) (-1267 "URAGG.spad" 2169848 2169859 2175165 2175170) (-1266 "URAGG.spad" 2164485 2164498 2169804 2169809) (-1265 "UPXSSING.spad" 2162130 2162156 2163566 2163699) (-1264 "UPXS.spad" 2159284 2159312 2160262 2160411) (-1263 "UPXSCONS.spad" 2157043 2157063 2157416 2157565) (-1262 "UPXSCCA.spad" 2155614 2155634 2156889 2157038) (-1261 "UPXSCCA.spad" 2154327 2154349 2155604 2155609) (-1260 "UPXSCAT.spad" 2152916 2152932 2154173 2154322) (-1259 "UPXS2.spad" 2152459 2152512 2152906 2152911) (-1258 "UPSQFREE.spad" 2150873 2150887 2152449 2152454) (-1257 "UPSCAT.spad" 2148660 2148684 2150771 2150868) (-1256 "UPSCAT.spad" 2146153 2146179 2148266 2148271) (-1255 "UPOLYC.spad" 2141193 2141204 2145995 2146148) (-1254 "UPOLYC.spad" 2136125 2136138 2140929 2140934) (-1253 "UPOLYC2.spad" 2135596 2135615 2136115 2136120) (-1252 "UP.spad" 2132795 2132810 2133182 2133335) (-1251 "UPMP.spad" 2131695 2131708 2132785 2132790) (-1250 "UPDIVP.spad" 2131260 2131274 2131685 2131690) (-1249 "UPDECOMP.spad" 2129505 2129519 2131250 2131255) (-1248 "UPCDEN.spad" 2128714 2128730 2129495 2129500) (-1247 "UP2.spad" 2128078 2128099 2128704 2128709) (-1246 "UNISEG.spad" 2127431 2127442 2127997 2128002) (-1245 "UNISEG2.spad" 2126928 2126941 2127387 2127392) (-1244 "UNIFACT.spad" 2126031 2126043 2126918 2126923) (-1243 "ULS.spad" 2116589 2116617 2117676 2118105) (-1242 "ULSCONS.spad" 2108985 2109005 2109355 2109504) (-1241 "ULSCCAT.spad" 2106722 2106742 2108831 2108980) (-1240 "ULSCCAT.spad" 2104567 2104589 2106678 2106683) (-1239 "ULSCAT.spad" 2102799 2102815 2104413 2104562) (-1238 "ULS2.spad" 2102313 2102366 2102789 2102794) (-1237 "UINT8.spad" 2102190 2102199 2102303 2102308) (-1236 "UINT64.spad" 2102066 2102075 2102180 2102185) (-1235 "UINT32.spad" 2101942 2101951 2102056 2102061) (-1234 "UINT16.spad" 2101818 2101827 2101932 2101937) (-1233 "UFD.spad" 2100883 2100892 2101744 2101813) (-1232 "UFD.spad" 2100010 2100021 2100873 2100878) (-1231 "UDVO.spad" 2098891 2098900 2100000 2100005) (-1230 "UDPO.spad" 2096384 2096395 2098847 2098852) (-1229 "TYPE.spad" 2096316 2096325 2096374 2096379) (-1228 "TYPEAST.spad" 2096235 2096244 2096306 2096311) (-1227 "TWOFACT.spad" 2094887 2094902 2096225 2096230) (-1226 "TUPLE.spad" 2094373 2094384 2094786 2094791) (-1225 "TUBETOOL.spad" 2091240 2091249 2094363 2094368) (-1224 "TUBE.spad" 2089887 2089904 2091230 2091235) (-1223 "TS.spad" 2088486 2088502 2089452 2089549) (-1222 "TSETCAT.spad" 2075613 2075630 2088454 2088481) (-1221 "TSETCAT.spad" 2062726 2062745 2075569 2075574) (-1220 "TRMANIP.spad" 2057092 2057109 2062432 2062437) (-1219 "TRIMAT.spad" 2056055 2056080 2057082 2057087) (-1218 "TRIGMNIP.spad" 2054582 2054599 2056045 2056050) (-1217 "TRIGCAT.spad" 2054094 2054103 2054572 2054577) (-1216 "TRIGCAT.spad" 2053604 2053615 2054084 2054089) (-1215 "TREE.spad" 2052179 2052190 2053211 2053238) (-1214 "TRANFUN.spad" 2052018 2052027 2052169 2052174) (-1213 "TRANFUN.spad" 2051855 2051866 2052008 2052013) (-1212 "TOPSP.spad" 2051529 2051538 2051845 2051850) (-1211 "TOOLSIGN.spad" 2051192 2051203 2051519 2051524) (-1210 "TEXTFILE.spad" 2049753 2049762 2051182 2051187) (-1209 "TEX.spad" 2046899 2046908 2049743 2049748) (-1208 "TEX1.spad" 2046455 2046466 2046889 2046894) (-1207 "TEMUTL.spad" 2046010 2046019 2046445 2046450) (-1206 "TBCMPPK.spad" 2044103 2044126 2046000 2046005) (-1205 "TBAGG.spad" 2043153 2043176 2044083 2044098) (-1204 "TBAGG.spad" 2042211 2042236 2043143 2043148) (-1203 "TANEXP.spad" 2041619 2041630 2042201 2042206) (-1202 "TALGOP.spad" 2041343 2041354 2041609 2041614) (-1201 "TABLE.spad" 2039754 2039777 2040024 2040051) (-1200 "TABLEAU.spad" 2039235 2039246 2039744 2039749) (-1199 "TABLBUMP.spad" 2036038 2036049 2039225 2039230) (-1198 "SYSTEM.spad" 2035266 2035275 2036028 2036033) (-1197 "SYSSOLP.spad" 2032749 2032760 2035256 2035261) (-1196 "SYSPTR.spad" 2032648 2032657 2032739 2032744) (-1195 "SYSNNI.spad" 2031830 2031841 2032638 2032643) (-1194 "SYSINT.spad" 2031234 2031245 2031820 2031825) (-1193 "SYNTAX.spad" 2027440 2027449 2031224 2031229) (-1192 "SYMTAB.spad" 2025508 2025517 2027430 2027435) (-1191 "SYMS.spad" 2021531 2021540 2025498 2025503) (-1190 "SYMPOLY.spad" 2020538 2020549 2020620 2020747) (-1189 "SYMFUNC.spad" 2020039 2020050 2020528 2020533) (-1188 "SYMBOL.spad" 2017542 2017551 2020029 2020034) (-1187 "SWITCH.spad" 2014313 2014322 2017532 2017537) (-1186 "SUTS.spad" 2011218 2011246 2012780 2012877) (-1185 "SUPXS.spad" 2008359 2008387 2009350 2009499) (-1184 "SUP.spad" 2005172 2005183 2005945 2006098) (-1183 "SUPFRACF.spad" 2004277 2004295 2005162 2005167) (-1182 "SUP2.spad" 2003669 2003682 2004267 2004272) (-1181 "SUMRF.spad" 2002643 2002654 2003659 2003664) (-1180 "SUMFS.spad" 2002280 2002297 2002633 2002638) (-1179 "SULS.spad" 1992825 1992853 1993925 1994354) (-1178 "SUCHTAST.spad" 1992594 1992603 1992815 1992820) (-1177 "SUCH.spad" 1992276 1992291 1992584 1992589) (-1176 "SUBSPACE.spad" 1984391 1984406 1992266 1992271) (-1175 "SUBRESP.spad" 1983561 1983575 1984347 1984352) (-1174 "STTF.spad" 1979660 1979676 1983551 1983556) (-1173 "STTFNC.spad" 1976128 1976144 1979650 1979655) (-1172 "STTAYLOR.spad" 1968763 1968774 1976009 1976014) (-1171 "STRTBL.spad" 1967268 1967285 1967417 1967444) (-1170 "STRING.spad" 1966677 1966686 1966691 1966718) (-1169 "STRICAT.spad" 1966465 1966474 1966645 1966672) (-1168 "STREAM.spad" 1963383 1963394 1965990 1966005) (-1167 "STREAM3.spad" 1962956 1962971 1963373 1963378) (-1166 "STREAM2.spad" 1962084 1962097 1962946 1962951) (-1165 "STREAM1.spad" 1961790 1961801 1962074 1962079) (-1164 "STINPROD.spad" 1960726 1960742 1961780 1961785) (-1163 "STEP.spad" 1959927 1959936 1960716 1960721) (-1162 "STEPAST.spad" 1959161 1959170 1959917 1959922) (-1161 "STBL.spad" 1957687 1957715 1957854 1957869) (-1160 "STAGG.spad" 1956762 1956773 1957677 1957682) (-1159 "STAGG.spad" 1955835 1955848 1956752 1956757) (-1158 "STACK.spad" 1955192 1955203 1955442 1955469) (-1157 "SREGSET.spad" 1952896 1952913 1954838 1954865) (-1156 "SRDCMPK.spad" 1951457 1951477 1952886 1952891) (-1155 "SRAGG.spad" 1946600 1946609 1951425 1951452) (-1154 "SRAGG.spad" 1941763 1941774 1946590 1946595) (-1153 "SQMATRIX.spad" 1939379 1939397 1940295 1940382) (-1152 "SPLTREE.spad" 1933931 1933944 1938815 1938842) (-1151 "SPLNODE.spad" 1930519 1930532 1933921 1933926) (-1150 "SPFCAT.spad" 1929328 1929337 1930509 1930514) (-1149 "SPECOUT.spad" 1927880 1927889 1929318 1929323) (-1148 "SPADXPT.spad" 1919475 1919484 1927870 1927875) (-1147 "spad-parser.spad" 1918940 1918949 1919465 1919470) (-1146 "SPADAST.spad" 1918641 1918650 1918930 1918935) (-1145 "SPACEC.spad" 1902840 1902851 1918631 1918636) (-1144 "SPACE3.spad" 1902616 1902627 1902830 1902835) (-1143 "SORTPAK.spad" 1902165 1902178 1902572 1902577) (-1142 "SOLVETRA.spad" 1899928 1899939 1902155 1902160) (-1141 "SOLVESER.spad" 1898456 1898467 1899918 1899923) (-1140 "SOLVERAD.spad" 1894482 1894493 1898446 1898451) (-1139 "SOLVEFOR.spad" 1892944 1892962 1894472 1894477) (-1138 "SNTSCAT.spad" 1892544 1892561 1892912 1892939) (-1137 "SMTS.spad" 1890816 1890842 1892109 1892206) (-1136 "SMP.spad" 1888291 1888311 1888681 1888808) (-1135 "SMITH.spad" 1887136 1887161 1888281 1888286) (-1134 "SMATCAT.spad" 1885246 1885276 1887080 1887131) (-1133 "SMATCAT.spad" 1883288 1883320 1885124 1885129) (-1132 "SKAGG.spad" 1882251 1882262 1883256 1883283) (-1131 "SINT.spad" 1881191 1881200 1882117 1882246) (-1130 "SIMPAN.spad" 1880919 1880928 1881181 1881186) (-1129 "SIG.spad" 1880249 1880258 1880909 1880914) (-1128 "SIGNRF.spad" 1879367 1879378 1880239 1880244) (-1127 "SIGNEF.spad" 1878646 1878663 1879357 1879362) (-1126 "SIGAST.spad" 1878031 1878040 1878636 1878641) (-1125 "SHP.spad" 1875959 1875974 1877987 1877992) (-1124 "SHDP.spad" 1865670 1865697 1866179 1866310) (-1123 "SGROUP.spad" 1865278 1865287 1865660 1865665) (-1122 "SGROUP.spad" 1864884 1864895 1865268 1865273) (-1121 "SGCF.spad" 1858023 1858032 1864874 1864879) (-1120 "SFRTCAT.spad" 1856953 1856970 1857991 1858018) (-1119 "SFRGCD.spad" 1856016 1856036 1856943 1856948) (-1118 "SFQCMPK.spad" 1850653 1850673 1856006 1856011) (-1117 "SFORT.spad" 1850092 1850106 1850643 1850648) (-1116 "SEXOF.spad" 1849935 1849975 1850082 1850087) (-1115 "SEX.spad" 1849827 1849836 1849925 1849930) (-1114 "SEXCAT.spad" 1847608 1847648 1849817 1849822) (-1113 "SET.spad" 1845932 1845943 1847029 1847068) (-1112 "SETMN.spad" 1844382 1844399 1845922 1845927) (-1111 "SETCAT.spad" 1843704 1843713 1844372 1844377) (-1110 "SETCAT.spad" 1843024 1843035 1843694 1843699) (-1109 "SETAGG.spad" 1839573 1839584 1843004 1843019) (-1108 "SETAGG.spad" 1836130 1836143 1839563 1839568) (-1107 "SEQAST.spad" 1835833 1835842 1836120 1836125) (-1106 "SEGXCAT.spad" 1834989 1835002 1835823 1835828) (-1105 "SEG.spad" 1834802 1834813 1834908 1834913) (-1104 "SEGCAT.spad" 1833727 1833738 1834792 1834797) (-1103 "SEGBIND.spad" 1833485 1833496 1833674 1833679) (-1102 "SEGBIND2.spad" 1833183 1833196 1833475 1833480) (-1101 "SEGAST.spad" 1832897 1832906 1833173 1833178) (-1100 "SEG2.spad" 1832332 1832345 1832853 1832858) (-1099 "SDVAR.spad" 1831608 1831619 1832322 1832327) (-1098 "SDPOL.spad" 1829034 1829045 1829325 1829452) (-1097 "SCPKG.spad" 1827123 1827134 1829024 1829029) (-1096 "SCOPE.spad" 1826276 1826285 1827113 1827118) (-1095 "SCACHE.spad" 1824972 1824983 1826266 1826271) (-1094 "SASTCAT.spad" 1824881 1824890 1824962 1824967) (-1093 "SAOS.spad" 1824753 1824762 1824871 1824876) (-1092 "SAERFFC.spad" 1824466 1824486 1824743 1824748) (-1091 "SAE.spad" 1822641 1822657 1823252 1823387) (-1090 "SAEFACT.spad" 1822342 1822362 1822631 1822636) (-1089 "RURPK.spad" 1820001 1820017 1822332 1822337) (-1088 "RULESET.spad" 1819454 1819478 1819991 1819996) (-1087 "RULE.spad" 1817694 1817718 1819444 1819449) (-1086 "RULECOLD.spad" 1817546 1817559 1817684 1817689) (-1085 "RTVALUE.spad" 1817281 1817290 1817536 1817541) (-1084 "RSTRCAST.spad" 1816998 1817007 1817271 1817276) (-1083 "RSETGCD.spad" 1813376 1813396 1816988 1816993) (-1082 "RSETCAT.spad" 1803312 1803329 1813344 1813371) (-1081 "RSETCAT.spad" 1793268 1793287 1803302 1803307) (-1080 "RSDCMPK.spad" 1791720 1791740 1793258 1793263) (-1079 "RRCC.spad" 1790104 1790134 1791710 1791715) (-1078 "RRCC.spad" 1788486 1788518 1790094 1790099) (-1077 "RPTAST.spad" 1788188 1788197 1788476 1788481) (-1076 "RPOLCAT.spad" 1767548 1767563 1788056 1788183) (-1075 "RPOLCAT.spad" 1746621 1746638 1767131 1767136) (-1074 "ROUTINE.spad" 1742504 1742513 1745268 1745295) (-1073 "ROMAN.spad" 1741832 1741841 1742370 1742499) (-1072 "ROIRC.spad" 1740912 1740944 1741822 1741827) (-1071 "RNS.spad" 1739815 1739824 1740814 1740907) (-1070 "RNS.spad" 1738804 1738815 1739805 1739810) (-1069 "RNG.spad" 1738539 1738548 1738794 1738799) (-1068 "RNGBIND.spad" 1737699 1737713 1738494 1738499) (-1067 "RMODULE.spad" 1737464 1737475 1737689 1737694) (-1066 "RMCAT2.spad" 1736884 1736941 1737454 1737459) (-1065 "RMATRIX.spad" 1735708 1735727 1736051 1736090) (-1064 "RMATCAT.spad" 1731287 1731318 1735664 1735703) (-1063 "RMATCAT.spad" 1726756 1726789 1731135 1731140) (-1062 "RLINSET.spad" 1726150 1726161 1726746 1726751) (-1061 "RINTERP.spad" 1726038 1726058 1726140 1726145) (-1060 "RING.spad" 1725508 1725517 1726018 1726033) (-1059 "RING.spad" 1724986 1724997 1725498 1725503) (-1058 "RIDIST.spad" 1724378 1724387 1724976 1724981) (-1057 "RGCHAIN.spad" 1722961 1722977 1723863 1723890) (-1056 "RGBCSPC.spad" 1722742 1722754 1722951 1722956) (-1055 "RGBCMDL.spad" 1722272 1722284 1722732 1722737) (-1054 "RF.spad" 1719914 1719925 1722262 1722267) (-1053 "RFFACTOR.spad" 1719376 1719387 1719904 1719909) (-1052 "RFFACT.spad" 1719111 1719123 1719366 1719371) (-1051 "RFDIST.spad" 1718107 1718116 1719101 1719106) (-1050 "RETSOL.spad" 1717526 1717539 1718097 1718102) (-1049 "RETRACT.spad" 1716954 1716965 1717516 1717521) (-1048 "RETRACT.spad" 1716380 1716393 1716944 1716949) (-1047 "RETAST.spad" 1716192 1716201 1716370 1716375) (-1046 "RESULT.spad" 1714252 1714261 1714839 1714866) (-1045 "RESRING.spad" 1713599 1713646 1714190 1714247) (-1044 "RESLATC.spad" 1712923 1712934 1713589 1713594) (-1043 "REPSQ.spad" 1712654 1712665 1712913 1712918) (-1042 "REP.spad" 1710208 1710217 1712644 1712649) (-1041 "REPDB.spad" 1709915 1709926 1710198 1710203) (-1040 "REP2.spad" 1699573 1699584 1709757 1709762) (-1039 "REP1.spad" 1693769 1693780 1699523 1699528) (-1038 "REGSET.spad" 1691566 1691583 1693415 1693442) (-1037 "REF.spad" 1690901 1690912 1691521 1691526) (-1036 "REDORDER.spad" 1690107 1690124 1690891 1690896) (-1035 "RECLOS.spad" 1688890 1688910 1689594 1689687) (-1034 "REALSOLV.spad" 1688030 1688039 1688880 1688885) (-1033 "REAL.spad" 1687902 1687911 1688020 1688025) (-1032 "REAL0Q.spad" 1685200 1685215 1687892 1687897) (-1031 "REAL0.spad" 1682044 1682059 1685190 1685195) (-1030 "RDUCEAST.spad" 1681765 1681774 1682034 1682039) (-1029 "RDIV.spad" 1681420 1681445 1681755 1681760) (-1028 "RDIST.spad" 1680987 1680998 1681410 1681415) (-1027 "RDETRS.spad" 1679851 1679869 1680977 1680982) (-1026 "RDETR.spad" 1677990 1678008 1679841 1679846) (-1025 "RDEEFS.spad" 1677089 1677106 1677980 1677985) (-1024 "RDEEF.spad" 1676099 1676116 1677079 1677084) (-1023 "RCFIELD.spad" 1673285 1673294 1676001 1676094) (-1022 "RCFIELD.spad" 1670557 1670568 1673275 1673280) (-1021 "RCAGG.spad" 1668485 1668496 1670547 1670552) (-1020 "RCAGG.spad" 1666340 1666353 1668404 1668409) (-1019 "RATRET.spad" 1665700 1665711 1666330 1666335) (-1018 "RATFACT.spad" 1665392 1665404 1665690 1665695) (-1017 "RANDSRC.spad" 1664711 1664720 1665382 1665387) (-1016 "RADUTIL.spad" 1664467 1664476 1664701 1664706) (-1015 "RADIX.spad" 1661388 1661402 1662934 1663027) (-1014 "RADFF.spad" 1659801 1659838 1659920 1660076) (-1013 "RADCAT.spad" 1659396 1659405 1659791 1659796) (-1012 "RADCAT.spad" 1658989 1659000 1659386 1659391) (-1011 "QUEUE.spad" 1658337 1658348 1658596 1658623) (-1010 "QUAT.spad" 1656795 1656806 1657138 1657203) (-1009 "QUATCT2.spad" 1656415 1656434 1656785 1656790) (-1008 "QUATCAT.spad" 1654585 1654596 1656345 1656410) (-1007 "QUATCAT.spad" 1652506 1652519 1654268 1654273) (-1006 "QUAGG.spad" 1651333 1651344 1652474 1652501) (-1005 "QQUTAST.spad" 1651101 1651110 1651323 1651328) (-1004 "QFORM.spad" 1650719 1650734 1651091 1651096) (-1003 "QFCAT.spad" 1649421 1649432 1650621 1650714) (-1002 "QFCAT.spad" 1647714 1647727 1648916 1648921) (-1001 "QFCAT2.spad" 1647406 1647423 1647704 1647709) (-1000 "QEQUAT.spad" 1646964 1646973 1647396 1647401) (-999 "QCMPACK.spad" 1641711 1641730 1646954 1646959) (-998 "QALGSET.spad" 1637790 1637822 1641625 1641630) (-997 "QALGSET2.spad" 1635786 1635804 1637780 1637785) (-996 "PWFFINTB.spad" 1633202 1633223 1635776 1635781) (-995 "PUSHVAR.spad" 1632541 1632560 1633192 1633197) (-994 "PTRANFN.spad" 1628669 1628679 1632531 1632536) (-993 "PTPACK.spad" 1625757 1625767 1628659 1628664) (-992 "PTFUNC2.spad" 1625580 1625594 1625747 1625752) (-991 "PTCAT.spad" 1624835 1624845 1625548 1625575) (-990 "PSQFR.spad" 1624142 1624166 1624825 1624830) (-989 "PSEUDLIN.spad" 1623028 1623038 1624132 1624137) (-988 "PSETPK.spad" 1608461 1608477 1622906 1622911) (-987 "PSETCAT.spad" 1602381 1602404 1608441 1608456) (-986 "PSETCAT.spad" 1596275 1596300 1602337 1602342) (-985 "PSCURVE.spad" 1595258 1595266 1596265 1596270) (-984 "PSCAT.spad" 1594041 1594070 1595156 1595253) (-983 "PSCAT.spad" 1592914 1592945 1594031 1594036) (-982 "PRTITION.spad" 1591612 1591620 1592904 1592909) (-981 "PRTDAST.spad" 1591331 1591339 1591602 1591607) (-980 "PRS.spad" 1580893 1580910 1591287 1591292) (-979 "PRQAGG.spad" 1580328 1580338 1580861 1580888) (-978 "PROPLOG.spad" 1579900 1579908 1580318 1580323) (-977 "PROPFUN2.spad" 1579523 1579536 1579890 1579895) (-976 "PROPFUN1.spad" 1578921 1578932 1579513 1579518) (-975 "PROPFRML.spad" 1577489 1577500 1578911 1578916) (-974 "PROPERTY.spad" 1576977 1576985 1577479 1577484) (-973 "PRODUCT.spad" 1574659 1574671 1574943 1574998) (-972 "PR.spad" 1573051 1573063 1573750 1573877) (-971 "PRINT.spad" 1572803 1572811 1573041 1573046) (-970 "PRIMES.spad" 1571056 1571066 1572793 1572798) (-969 "PRIMELT.spad" 1569137 1569151 1571046 1571051) (-968 "PRIMCAT.spad" 1568764 1568772 1569127 1569132) (-967 "PRIMARR.spad" 1567769 1567779 1567947 1567974) (-966 "PRIMARR2.spad" 1566536 1566548 1567759 1567764) (-965 "PREASSOC.spad" 1565918 1565930 1566526 1566531) (-964 "PPCURVE.spad" 1565055 1565063 1565908 1565913) (-963 "PORTNUM.spad" 1564830 1564838 1565045 1565050) (-962 "POLYROOT.spad" 1563679 1563701 1564786 1564791) (-961 "POLY.spad" 1561014 1561024 1561529 1561656) (-960 "POLYLIFT.spad" 1560279 1560302 1561004 1561009) (-959 "POLYCATQ.spad" 1558397 1558419 1560269 1560274) (-958 "POLYCAT.spad" 1551867 1551888 1558265 1558392) (-957 "POLYCAT.spad" 1544675 1544698 1551075 1551080) (-956 "POLY2UP.spad" 1544127 1544141 1544665 1544670) (-955 "POLY2.spad" 1543724 1543736 1544117 1544122) (-954 "POLUTIL.spad" 1542665 1542694 1543680 1543685) (-953 "POLTOPOL.spad" 1541413 1541428 1542655 1542660) (-952 "POINT.spad" 1540251 1540261 1540338 1540365) (-951 "PNTHEORY.spad" 1536953 1536961 1540241 1540246) (-950 "PMTOOLS.spad" 1535728 1535742 1536943 1536948) (-949 "PMSYM.spad" 1535277 1535287 1535718 1535723) (-948 "PMQFCAT.spad" 1534868 1534882 1535267 1535272) (-947 "PMPRED.spad" 1534347 1534361 1534858 1534863) (-946 "PMPREDFS.spad" 1533801 1533823 1534337 1534342) (-945 "PMPLCAT.spad" 1532881 1532899 1533733 1533738) (-944 "PMLSAGG.spad" 1532466 1532480 1532871 1532876) (-943 "PMKERNEL.spad" 1532045 1532057 1532456 1532461) (-942 "PMINS.spad" 1531625 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(-559 "INTAF.spad" 887711 887727 888201 888206) (-558 "INTABL.spad" 886229 886260 886392 886419) (-557 "INT8.spad" 886109 886117 886219 886224) (-556 "INT64.spad" 885988 885996 886099 886104) (-555 "INT32.spad" 885867 885875 885978 885983) (-554 "INT16.spad" 885746 885754 885857 885862) (-553 "INS.spad" 883249 883257 885648 885741) (-552 "INS.spad" 880838 880848 883239 883244) (-551 "INPSIGN.spad" 880286 880299 880828 880833) (-550 "INPRODPF.spad" 879382 879401 880276 880281) (-549 "INPRODFF.spad" 878470 878494 879372 879377) (-548 "INNMFACT.spad" 877445 877462 878460 878465) (-547 "INMODGCD.spad" 876933 876963 877435 877440) (-546 "INFSP.spad" 875230 875252 876923 876928) (-545 "INFPROD0.spad" 874310 874329 875220 875225) (-544 "INFORM.spad" 871509 871517 874300 874305) (-543 "INFORM1.spad" 871134 871144 871499 871504) (-542 "INFINITY.spad" 870686 870694 871124 871129) (-541 "INETCLTS.spad" 870663 870671 870676 870681) (-540 "INEP.spad" 869201 869223 870653 870658) (-539 "INDE.spad" 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487891 487907 494824 494829) (-333 "FARRAY.spad" 486041 486051 487074 487101) (-332 "FAMR.spad" 484177 484189 485939 486036) (-331 "FAMR.spad" 482297 482311 484061 484066) (-330 "FAMONOID.spad" 481965 481975 482251 482256) (-329 "FAMONC.spad" 480261 480273 481955 481960) (-328 "FAGROUP.spad" 479885 479895 480157 480184) (-327 "FACUTIL.spad" 478089 478106 479875 479880) (-326 "FACTFUNC.spad" 477283 477293 478079 478084) (-325 "EXPUPXS.spad" 474116 474139 475415 475564) (-324 "EXPRTUBE.spad" 471404 471412 474106 474111) (-323 "EXPRODE.spad" 468564 468580 471394 471399) (-322 "EXPR.spad" 463839 463849 464553 464960) (-321 "EXPR2UPS.spad" 459961 459974 463829 463834) (-320 "EXPR2.spad" 459666 459678 459951 459956) (-319 "EXPEXPAN.spad" 456606 456631 457238 457331) (-318 "EXIT.spad" 456277 456285 456596 456601) (-317 "EXITAST.spad" 456013 456021 456267 456272) (-316 "EVALCYC.spad" 455473 455487 456003 456008) (-315 "EVALAB.spad" 455045 455055 455463 455468) (-314 "EVALAB.spad" 454615 454627 455035 455040) (-313 "EUCDOM.spad" 452189 452197 454541 454610) (-312 "EUCDOM.spad" 449825 449835 452179 452184) (-311 "ESTOOLS.spad" 441671 441679 449815 449820) (-310 "ESTOOLS2.spad" 441274 441288 441661 441666) (-309 "ESTOOLS1.spad" 440959 440970 441264 441269) (-308 "ES.spad" 433774 433782 440949 440954) (-307 "ES.spad" 426495 426505 433672 433677) (-306 "ESCONT.spad" 423288 423296 426485 426490) (-305 "ESCONT1.spad" 423037 423049 423278 423283) (-304 "ES2.spad" 422542 422558 423027 423032) (-303 "ES1.spad" 422112 422128 422532 422537) (-302 "ERROR.spad" 419439 419447 422102 422107) (-301 "EQTBL.spad" 417911 417933 418120 418147) (-300 "EQ.spad" 412716 412726 415503 415615) (-299 "EQ2.spad" 412434 412446 412706 412711) (-298 "EP.spad" 408760 408770 412424 412429) (-297 "ENV.spad" 407438 407446 408750 408755) (-296 "ENTIRER.spad" 407106 407114 407382 407433) (-295 "EMR.spad" 406394 406435 407032 407101) (-294 "ELTAGG.spad" 404648 404667 406384 406389) (-293 "ELTAGG.spad" 402866 402887 404604 404609) (-292 "ELTAB.spad" 402341 402354 402856 402861) (-291 "ELFUTS.spad" 401728 401747 402331 402336) (-290 "ELEMFUN.spad" 401417 401425 401718 401723) (-289 "ELEMFUN.spad" 401104 401114 401407 401412) (-288 "ELAGG.spad" 399075 399085 401084 401099) (-287 "ELAGG.spad" 396983 396995 398994 398999) (-286 "ELABOR.spad" 396329 396337 396973 396978) (-285 "ELABEXPR.spad" 395261 395269 396319 396324) (-284 "EFUPXS.spad" 392037 392067 395217 395222) (-283 "EFULS.spad" 388873 388896 391993 391998) (-282 "EFSTRUC.spad" 386888 386904 388863 388868) (-281 "EF.spad" 381664 381680 386878 386883) (-280 "EAB.spad" 379940 379948 381654 381659) (-279 "E04UCFA.spad" 379476 379484 379930 379935) (-278 "E04NAFA.spad" 379053 379061 379466 379471) (-277 "E04MBFA.spad" 378633 378641 379043 379048) (-276 "E04JAFA.spad" 378169 378177 378623 378628) (-275 "E04GCFA.spad" 377705 377713 378159 378164) (-274 "E04FDFA.spad" 377241 377249 377695 377700) (-273 "E04DGFA.spad" 376777 376785 377231 377236) (-272 "E04AGNT.spad" 372627 372635 376767 376772) (-271 "DVARCAT.spad" 369316 369326 372617 372622) (-270 "DVARCAT.spad" 366003 366015 369306 369311) (-269 "DSMP.spad" 363470 363484 363775 363902) (-268 "DROPT.spad" 357429 357437 363460 363465) (-267 "DROPT1.spad" 357094 357104 357419 357424) (-266 "DROPT0.spad" 351951 351959 357084 357089) (-265 "DRAWPT.spad" 350124 350132 351941 351946) (-264 "DRAW.spad" 343000 343013 350114 350119) (-263 "DRAWHACK.spad" 342308 342318 342990 342995) (-262 "DRAWCX.spad" 339778 339786 342298 342303) (-261 "DRAWCURV.spad" 339325 339340 339768 339773) (-260 "DRAWCFUN.spad" 328857 328865 339315 339320) (-259 "DQAGG.spad" 327035 327045 328825 328852) (-258 "DPOLCAT.spad" 322384 322400 326903 327030) (-257 "DPOLCAT.spad" 317795 317813 322316 322321) (-256 "DPMO.spad" 310021 310037 310159 310460) (-255 "DPMM.spad" 302260 302278 302385 302686) (-254 "DOMTMPLT.spad" 302031 302039 302250 302255) (-253 "DOMCTOR.spad" 301786 301794 302021 302026) (-252 "DOMAIN.spad" 300873 300881 301776 301781) (-251 "DMP.spad" 298133 298148 298703 298830) (-250 "DLP.spad" 297485 297495 298123 298128) (-249 "DLIST.spad" 296064 296074 296668 296695) (-248 "DLAGG.spad" 294481 294491 296054 296059) (-247 "DIVRING.spad" 294023 294031 294425 294476) (-246 "DIVRING.spad" 293609 293619 294013 294018) (-245 "DISPLAY.spad" 291799 291807 293599 293604) (-244 "DIRPROD.spad" 281379 281395 282019 282150) (-243 "DIRPROD2.spad" 280197 280215 281369 281374) (-242 "DIRPCAT.spad" 279141 279157 280061 280192) (-241 "DIRPCAT.spad" 277814 277832 278736 278741) (-240 "DIOSP.spad" 276639 276647 277804 277809) (-239 "DIOPS.spad" 275635 275645 276619 276634) (-238 "DIOPS.spad" 274605 274617 275591 275596) (-237 "DIFRING.spad" 274211 274219 274585 274600) (-236 "DIFRING.spad" 273825 273835 274201 274206) (-235 "DIFFDOM.spad" 272990 273001 273815 273820) (-234 "DIFFDOM.spad" 272153 272166 272980 272985) (-233 "DIFEXT.spad" 271324 271334 272133 272148) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2267377 2267382 2267387 2267392) (-2 NIL 2267357 2267362 2267367 2267372) (-1 NIL 2267337 2267342 2267347 2267352) (0 NIL 2267317 2267322 2267327 2267332) (-1308 "ZMOD.spad" 2267126 2267139 2267255 2267312) (-1307 "ZLINDEP.spad" 2266192 2266203 2267116 2267121) (-1306 "ZDSOLVE.spad" 2256137 2256159 2266182 2266187) (-1305 "YSTREAM.spad" 2255632 2255643 2256127 2256132) (-1304 "YDIAGRAM.spad" 2255266 2255275 2255622 2255627) (-1303 "XRPOLY.spad" 2254486 2254506 2255122 2255191) (-1302 "XPR.spad" 2252281 2252294 2254204 2254303) (-1301 "XPOLY.spad" 2251836 2251847 2252137 2252206) (-1300 "XPOLYC.spad" 2251155 2251171 2251762 2251831) (-1299 "XPBWPOLY.spad" 2249592 2249612 2250935 2251004) (-1298 "XF.spad" 2248055 2248070 2249494 2249587) (-1297 "XF.spad" 2246498 2246515 2247939 2247944) (-1296 "XFALG.spad" 2243546 2243562 2246424 2246493) (-1295 "XEXPPKG.spad" 2242797 2242823 2243536 2243541) (-1294 "XDPOLY.spad" 2242411 2242427 2242653 2242722) (-1293 "XALG.spad" 2242071 2242082 2242367 2242406) (-1292 "WUTSET.spad" 2237910 2237927 2241717 2241744) (-1291 "WP.spad" 2237109 2237153 2237768 2237835) (-1290 "WHILEAST.spad" 2236907 2236916 2237099 2237104) (-1289 "WHEREAST.spad" 2236578 2236587 2236897 2236902) (-1288 "WFFINTBS.spad" 2234241 2234263 2236568 2236573) (-1287 "WEIER.spad" 2232463 2232474 2234231 2234236) (-1286 "VSPACE.spad" 2232136 2232147 2232431 2232458) (-1285 "VSPACE.spad" 2231829 2231842 2232126 2232131) (-1284 "VOID.spad" 2231506 2231515 2231819 2231824) (-1283 "VIEW.spad" 2229186 2229195 2231496 2231501) (-1282 "VIEWDEF.spad" 2224387 2224396 2229176 2229181) (-1281 "VIEW3D.spad" 2208348 2208357 2224377 2224382) (-1280 "VIEW2D.spad" 2196239 2196248 2208338 2208343) (-1279 "VECTOR.spad" 2194913 2194924 2195164 2195191) (-1278 "VECTOR2.spad" 2193552 2193565 2194903 2194908) (-1277 "VECTCAT.spad" 2191456 2191467 2193520 2193547) (-1276 "VECTCAT.spad" 2189167 2189180 2191233 2191238) (-1275 "VARIABLE.spad" 2188947 2188962 2189157 2189162) (-1274 "UTYPE.spad" 2188591 2188600 2188937 2188942) (-1273 "UTSODETL.spad" 2187886 2187910 2188547 2188552) (-1272 "UTSODE.spad" 2186102 2186122 2187876 2187881) (-1271 "UTS.spad" 2180906 2180934 2184569 2184666) (-1270 "UTSCAT.spad" 2178385 2178401 2180804 2180901) (-1269 "UTSCAT.spad" 2175508 2175526 2177929 2177934) (-1268 "UTS2.spad" 2175103 2175138 2175498 2175503) (-1267 "URAGG.spad" 2169776 2169787 2175093 2175098) (-1266 "URAGG.spad" 2164413 2164426 2169732 2169737) (-1265 "UPXSSING.spad" 2162058 2162084 2163494 2163627) (-1264 "UPXS.spad" 2159212 2159240 2160190 2160339) (-1263 "UPXSCONS.spad" 2156971 2156991 2157344 2157493) (-1262 "UPXSCCA.spad" 2155542 2155562 2156817 2156966) (-1261 "UPXSCCA.spad" 2154255 2154277 2155532 2155537) (-1260 "UPXSCAT.spad" 2152844 2152860 2154101 2154250) (-1259 "UPXS2.spad" 2152387 2152440 2152834 2152839) (-1258 "UPSQFREE.spad" 2150801 2150815 2152377 2152382) (-1257 "UPSCAT.spad" 2148588 2148612 2150699 2150796) (-1256 "UPSCAT.spad" 2146081 2146107 2148194 2148199) (-1255 "UPOLYC.spad" 2141121 2141132 2145923 2146076) (-1254 "UPOLYC.spad" 2136053 2136066 2140857 2140862) (-1253 "UPOLYC2.spad" 2135524 2135543 2136043 2136048) (-1252 "UP.spad" 2132723 2132738 2133110 2133263) (-1251 "UPMP.spad" 2131623 2131636 2132713 2132718) (-1250 "UPDIVP.spad" 2131188 2131202 2131613 2131618) (-1249 "UPDECOMP.spad" 2129433 2129447 2131178 2131183) (-1248 "UPCDEN.spad" 2128642 2128658 2129423 2129428) (-1247 "UP2.spad" 2128006 2128027 2128632 2128637) (-1246 "UNISEG.spad" 2127359 2127370 2127925 2127930) (-1245 "UNISEG2.spad" 2126856 2126869 2127315 2127320) (-1244 "UNIFACT.spad" 2125959 2125971 2126846 2126851) (-1243 "ULS.spad" 2116517 2116545 2117604 2118033) (-1242 "ULSCONS.spad" 2108913 2108933 2109283 2109432) (-1241 "ULSCCAT.spad" 2106650 2106670 2108759 2108908) (-1240 "ULSCCAT.spad" 2104495 2104517 2106606 2106611) (-1239 "ULSCAT.spad" 2102727 2102743 2104341 2104490) (-1238 "ULS2.spad" 2102241 2102294 2102717 2102722) (-1237 "UINT8.spad" 2102118 2102127 2102231 2102236) (-1236 "UINT64.spad" 2101994 2102003 2102108 2102113) (-1235 "UINT32.spad" 2101870 2101879 2101984 2101989) (-1234 "UINT16.spad" 2101746 2101755 2101860 2101865) (-1233 "UFD.spad" 2100811 2100820 2101672 2101741) (-1232 "UFD.spad" 2099938 2099949 2100801 2100806) (-1231 "UDVO.spad" 2098819 2098828 2099928 2099933) (-1230 "UDPO.spad" 2096312 2096323 2098775 2098780) (-1229 "TYPE.spad" 2096244 2096253 2096302 2096307) (-1228 "TYPEAST.spad" 2096163 2096172 2096234 2096239) (-1227 "TWOFACT.spad" 2094815 2094830 2096153 2096158) (-1226 "TUPLE.spad" 2094301 2094312 2094714 2094719) (-1225 "TUBETOOL.spad" 2091168 2091177 2094291 2094296) (-1224 "TUBE.spad" 2089815 2089832 2091158 2091163) (-1223 "TS.spad" 2088414 2088430 2089380 2089477) (-1222 "TSETCAT.spad" 2075541 2075558 2088382 2088409) (-1221 "TSETCAT.spad" 2062654 2062673 2075497 2075502) (-1220 "TRMANIP.spad" 2057020 2057037 2062360 2062365) (-1219 "TRIMAT.spad" 2055983 2056008 2057010 2057015) (-1218 "TRIGMNIP.spad" 2054510 2054527 2055973 2055978) (-1217 "TRIGCAT.spad" 2054022 2054031 2054500 2054505) (-1216 "TRIGCAT.spad" 2053532 2053543 2054012 2054017) (-1215 "TREE.spad" 2052107 2052118 2053139 2053166) (-1214 "TRANFUN.spad" 2051946 2051955 2052097 2052102) (-1213 "TRANFUN.spad" 2051783 2051794 2051936 2051941) (-1212 "TOPSP.spad" 2051457 2051466 2051773 2051778) (-1211 "TOOLSIGN.spad" 2051120 2051131 2051447 2051452) (-1210 "TEXTFILE.spad" 2049681 2049690 2051110 2051115) (-1209 "TEX.spad" 2046827 2046836 2049671 2049676) (-1208 "TEX1.spad" 2046383 2046394 2046817 2046822) (-1207 "TEMUTL.spad" 2045938 2045947 2046373 2046378) (-1206 "TBCMPPK.spad" 2044031 2044054 2045928 2045933) (-1205 "TBAGG.spad" 2043081 2043104 2044011 2044026) (-1204 "TBAGG.spad" 2042139 2042164 2043071 2043076) (-1203 "TANEXP.spad" 2041547 2041558 2042129 2042134) (-1202 "TALGOP.spad" 2041271 2041282 2041537 2041542) (-1201 "TABLE.spad" 2039682 2039705 2039952 2039979) (-1200 "TABLEAU.spad" 2039163 2039174 2039672 2039677) (-1199 "TABLBUMP.spad" 2035966 2035977 2039153 2039158) (-1198 "SYSTEM.spad" 2035194 2035203 2035956 2035961) (-1197 "SYSSOLP.spad" 2032677 2032688 2035184 2035189) (-1196 "SYSPTR.spad" 2032576 2032585 2032667 2032672) (-1195 "SYSNNI.spad" 2031758 2031769 2032566 2032571) (-1194 "SYSINT.spad" 2031162 2031173 2031748 2031753) (-1193 "SYNTAX.spad" 2027368 2027377 2031152 2031157) (-1192 "SYMTAB.spad" 2025436 2025445 2027358 2027363) (-1191 "SYMS.spad" 2021459 2021468 2025426 2025431) (-1190 "SYMPOLY.spad" 2020466 2020477 2020548 2020675) (-1189 "SYMFUNC.spad" 2019967 2019978 2020456 2020461) (-1188 "SYMBOL.spad" 2017470 2017479 2019957 2019962) (-1187 "SWITCH.spad" 2014241 2014250 2017460 2017465) (-1186 "SUTS.spad" 2011146 2011174 2012708 2012805) (-1185 "SUPXS.spad" 2008287 2008315 2009278 2009427) (-1184 "SUP.spad" 2005100 2005111 2005873 2006026) (-1183 "SUPFRACF.spad" 2004205 2004223 2005090 2005095) (-1182 "SUP2.spad" 2003597 2003610 2004195 2004200) (-1181 "SUMRF.spad" 2002571 2002582 2003587 2003592) (-1180 "SUMFS.spad" 2002208 2002225 2002561 2002566) (-1179 "SULS.spad" 1992753 1992781 1993853 1994282) (-1178 "SUCHTAST.spad" 1992522 1992531 1992743 1992748) (-1177 "SUCH.spad" 1992204 1992219 1992512 1992517) (-1176 "SUBSPACE.spad" 1984319 1984334 1992194 1992199) (-1175 "SUBRESP.spad" 1983489 1983503 1984275 1984280) (-1174 "STTF.spad" 1979588 1979604 1983479 1983484) (-1173 "STTFNC.spad" 1976056 1976072 1979578 1979583) (-1172 "STTAYLOR.spad" 1968691 1968702 1975937 1975942) (-1171 "STRTBL.spad" 1967196 1967213 1967345 1967372) (-1170 "STRING.spad" 1966605 1966614 1966619 1966646) (-1169 "STRICAT.spad" 1966393 1966402 1966573 1966600) (-1168 "STREAM.spad" 1963311 1963322 1965918 1965933) (-1167 "STREAM3.spad" 1962884 1962899 1963301 1963306) (-1166 "STREAM2.spad" 1962012 1962025 1962874 1962879) (-1165 "STREAM1.spad" 1961718 1961729 1962002 1962007) (-1164 "STINPROD.spad" 1960654 1960670 1961708 1961713) (-1163 "STEP.spad" 1959855 1959864 1960644 1960649) (-1162 "STEPAST.spad" 1959089 1959098 1959845 1959850) (-1161 "STBL.spad" 1957615 1957643 1957782 1957797) (-1160 "STAGG.spad" 1956690 1956701 1957605 1957610) (-1159 "STAGG.spad" 1955763 1955776 1956680 1956685) (-1158 "STACK.spad" 1955120 1955131 1955370 1955397) (-1157 "SREGSET.spad" 1952824 1952841 1954766 1954793) (-1156 "SRDCMPK.spad" 1951385 1951405 1952814 1952819) (-1155 "SRAGG.spad" 1946528 1946537 1951353 1951380) (-1154 "SRAGG.spad" 1941691 1941702 1946518 1946523) (-1153 "SQMATRIX.spad" 1939307 1939325 1940223 1940310) (-1152 "SPLTREE.spad" 1933859 1933872 1938743 1938770) (-1151 "SPLNODE.spad" 1930447 1930460 1933849 1933854) (-1150 "SPFCAT.spad" 1929256 1929265 1930437 1930442) (-1149 "SPECOUT.spad" 1927808 1927817 1929246 1929251) (-1148 "SPADXPT.spad" 1919403 1919412 1927798 1927803) (-1147 "spad-parser.spad" 1918868 1918877 1919393 1919398) (-1146 "SPADAST.spad" 1918569 1918578 1918858 1918863) (-1145 "SPACEC.spad" 1902768 1902779 1918559 1918564) (-1144 "SPACE3.spad" 1902544 1902555 1902758 1902763) (-1143 "SORTPAK.spad" 1902093 1902106 1902500 1902505) (-1142 "SOLVETRA.spad" 1899856 1899867 1902083 1902088) (-1141 "SOLVESER.spad" 1898384 1898395 1899846 1899851) (-1140 "SOLVERAD.spad" 1894410 1894421 1898374 1898379) (-1139 "SOLVEFOR.spad" 1892872 1892890 1894400 1894405) (-1138 "SNTSCAT.spad" 1892472 1892489 1892840 1892867) (-1137 "SMTS.spad" 1890744 1890770 1892037 1892134) (-1136 "SMP.spad" 1888219 1888239 1888609 1888736) (-1135 "SMITH.spad" 1887064 1887089 1888209 1888214) (-1134 "SMATCAT.spad" 1885174 1885204 1887008 1887059) (-1133 "SMATCAT.spad" 1883216 1883248 1885052 1885057) (-1132 "SKAGG.spad" 1882179 1882190 1883184 1883211) (-1131 "SINT.spad" 1881119 1881128 1882045 1882174) (-1130 "SIMPAN.spad" 1880847 1880856 1881109 1881114) (-1129 "SIG.spad" 1880177 1880186 1880837 1880842) (-1128 "SIGNRF.spad" 1879295 1879306 1880167 1880172) (-1127 "SIGNEF.spad" 1878574 1878591 1879285 1879290) (-1126 "SIGAST.spad" 1877959 1877968 1878564 1878569) (-1125 "SHP.spad" 1875887 1875902 1877915 1877920) (-1124 "SHDP.spad" 1865598 1865625 1866107 1866238) (-1123 "SGROUP.spad" 1865206 1865215 1865588 1865593) (-1122 "SGROUP.spad" 1864812 1864823 1865196 1865201) (-1121 "SGCF.spad" 1857951 1857960 1864802 1864807) (-1120 "SFRTCAT.spad" 1856881 1856898 1857919 1857946) (-1119 "SFRGCD.spad" 1855944 1855964 1856871 1856876) (-1118 "SFQCMPK.spad" 1850581 1850601 1855934 1855939) (-1117 "SFORT.spad" 1850020 1850034 1850571 1850576) (-1116 "SEXOF.spad" 1849863 1849903 1850010 1850015) (-1115 "SEX.spad" 1849755 1849764 1849853 1849858) (-1114 "SEXCAT.spad" 1847536 1847576 1849745 1849750) (-1113 "SET.spad" 1845860 1845871 1846957 1846996) (-1112 "SETMN.spad" 1844310 1844327 1845850 1845855) (-1111 "SETCAT.spad" 1843632 1843641 1844300 1844305) (-1110 "SETCAT.spad" 1842952 1842963 1843622 1843627) (-1109 "SETAGG.spad" 1839501 1839512 1842932 1842947) (-1108 "SETAGG.spad" 1836058 1836071 1839491 1839496) (-1107 "SEQAST.spad" 1835761 1835770 1836048 1836053) (-1106 "SEGXCAT.spad" 1834917 1834930 1835751 1835756) (-1105 "SEG.spad" 1834730 1834741 1834836 1834841) (-1104 "SEGCAT.spad" 1833655 1833666 1834720 1834725) (-1103 "SEGBIND.spad" 1833413 1833424 1833602 1833607) (-1102 "SEGBIND2.spad" 1833111 1833124 1833403 1833408) (-1101 "SEGAST.spad" 1832825 1832834 1833101 1833106) (-1100 "SEG2.spad" 1832260 1832273 1832781 1832786) (-1099 "SDVAR.spad" 1831536 1831547 1832250 1832255) (-1098 "SDPOL.spad" 1828962 1828973 1829253 1829380) (-1097 "SCPKG.spad" 1827051 1827062 1828952 1828957) (-1096 "SCOPE.spad" 1826204 1826213 1827041 1827046) (-1095 "SCACHE.spad" 1824900 1824911 1826194 1826199) (-1094 "SASTCAT.spad" 1824809 1824818 1824890 1824895) (-1093 "SAOS.spad" 1824681 1824690 1824799 1824804) (-1092 "SAERFFC.spad" 1824394 1824414 1824671 1824676) (-1091 "SAE.spad" 1822569 1822585 1823180 1823315) (-1090 "SAEFACT.spad" 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1741755) (-1071 "RNS.spad" 1739743 1739752 1740742 1740835) (-1070 "RNS.spad" 1738732 1738743 1739733 1739738) (-1069 "RNG.spad" 1738467 1738476 1738722 1738727) (-1068 "RNGBIND.spad" 1737627 1737641 1738422 1738427) (-1067 "RMODULE.spad" 1737392 1737403 1737617 1737622) (-1066 "RMCAT2.spad" 1736812 1736869 1737382 1737387) (-1065 "RMATRIX.spad" 1735636 1735655 1735979 1736018) (-1064 "RMATCAT.spad" 1731215 1731246 1735592 1735631) (-1063 "RMATCAT.spad" 1726684 1726717 1731063 1731068) (-1062 "RLINSET.spad" 1726078 1726089 1726674 1726679) (-1061 "RINTERP.spad" 1725966 1725986 1726068 1726073) (-1060 "RING.spad" 1725436 1725445 1725946 1725961) (-1059 "RING.spad" 1724914 1724925 1725426 1725431) (-1058 "RIDIST.spad" 1724306 1724315 1724904 1724909) (-1057 "RGCHAIN.spad" 1722889 1722905 1723791 1723818) (-1056 "RGBCSPC.spad" 1722670 1722682 1722879 1722884) (-1055 "RGBCMDL.spad" 1722200 1722212 1722660 1722665) (-1054 "RF.spad" 1719842 1719853 1722190 1722195) (-1053 "RFFACTOR.spad" 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(-1034 "REALSOLV.spad" 1687958 1687967 1688808 1688813) (-1033 "REAL.spad" 1687830 1687839 1687948 1687953) (-1032 "REAL0Q.spad" 1685128 1685143 1687820 1687825) (-1031 "REAL0.spad" 1681972 1681987 1685118 1685123) (-1030 "RDUCEAST.spad" 1681693 1681702 1681962 1681967) (-1029 "RDIV.spad" 1681348 1681373 1681683 1681688) (-1028 "RDIST.spad" 1680915 1680926 1681338 1681343) (-1027 "RDETRS.spad" 1679779 1679797 1680905 1680910) (-1026 "RDETR.spad" 1677918 1677936 1679769 1679774) (-1025 "RDEEFS.spad" 1677017 1677034 1677908 1677913) (-1024 "RDEEF.spad" 1676027 1676044 1677007 1677012) (-1023 "RCFIELD.spad" 1673213 1673222 1675929 1676022) (-1022 "RCFIELD.spad" 1670485 1670496 1673203 1673208) (-1021 "RCAGG.spad" 1668413 1668424 1670475 1670480) (-1020 "RCAGG.spad" 1666268 1666281 1668332 1668337) (-1019 "RATRET.spad" 1665628 1665639 1666258 1666263) (-1018 "RATFACT.spad" 1665320 1665332 1665618 1665623) (-1017 "RANDSRC.spad" 1664639 1664648 1665310 1665315) (-1016 "RADUTIL.spad" 1664395 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1353188) (-828 "OINTDOM.spad" 1352365 1352373 1352528 1352597) (-827 "OFMONOID.spad" 1350488 1350498 1352321 1352326) (-826 "ODVAR.spad" 1349749 1349759 1350478 1350483) (-825 "ODR.spad" 1349393 1349419 1349561 1349710) (-824 "ODPOL.spad" 1346775 1346785 1347115 1347242) (-823 "ODP.spad" 1336622 1336642 1336995 1337126) (-822 "ODETOOLS.spad" 1335271 1335290 1336612 1336617) (-821 "ODESYS.spad" 1332965 1332982 1335261 1335266) (-820 "ODERTRIC.spad" 1328974 1328991 1332922 1332927) (-819 "ODERED.spad" 1328373 1328397 1328964 1328969) (-818 "ODERAT.spad" 1325988 1326005 1328363 1328368) (-817 "ODEPRRIC.spad" 1323025 1323047 1325978 1325983) (-816 "ODEPROB.spad" 1322282 1322290 1323015 1323020) (-815 "ODEPRIM.spad" 1319616 1319638 1322272 1322277) (-814 "ODEPAL.spad" 1319002 1319026 1319606 1319611) (-813 "ODEPACK.spad" 1305668 1305676 1318992 1318997) (-812 "ODEINT.spad" 1305103 1305119 1305658 1305663) (-811 "ODEIFTBL.spad" 1302498 1302506 1305093 1305098) (-810 "ODEEF.spad" 1297989 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(-640 "LIB.spad" 1001834 1001842 1002280 1002295) (-639 "LGROBP.spad" 999187 999206 1001824 1001829) (-638 "LF.spad" 998142 998158 999177 999182) (-637 "LFCAT.spad" 997201 997209 998132 998137) (-636 "LEXTRIPK.spad" 992704 992719 997191 997196) (-635 "LEXP.spad" 990707 990734 992684 992699) (-634 "LETAST.spad" 990406 990414 990697 990702) (-633 "LEADCDET.spad" 988804 988821 990396 990401) (-632 "LAZM3PK.spad" 987508 987530 988794 988799) (-631 "LAUPOL.spad" 986201 986214 987101 987170) (-630 "LAPLACE.spad" 985784 985800 986191 986196) (-629 "LA.spad" 985224 985238 985706 985745) (-628 "LALG.spad" 985000 985010 985204 985219) (-627 "LALG.spad" 984784 984796 984990 984995) (-626 "KVTFROM.spad" 984519 984529 984774 984779) (-625 "KTVLOGIC.spad" 984031 984039 984509 984514) (-624 "KRCFROM.spad" 983769 983779 984021 984026) (-623 "KOVACIC.spad" 982492 982509 983759 983764) (-622 "KONVERT.spad" 982214 982224 982482 982487) (-621 "KOERCE.spad" 981951 981961 982204 982209) (-620 "KERNEL.spad" 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869148) (-538 "INCRMAPS.spad" 868303 868313 868872 868877) (-537 "INBFILE.spad" 867375 867383 868293 868298) (-536 "INBFF.spad" 863169 863180 867365 867370) (-535 "INBCON.spad" 861459 861467 863159 863164) (-534 "INBCON.spad" 859747 859757 861449 861454) (-533 "INAST.spad" 859408 859416 859737 859742) (-532 "IMPTAST.spad" 859116 859124 859398 859403) (-531 "IMATRIX.spad" 858061 858087 858573 858600) (-530 "IMATQF.spad" 857155 857199 858017 858022) (-529 "IMATLIN.spad" 855760 855784 857111 857116) (-528 "ILIST.spad" 854418 854433 854943 854970) (-527 "IIARRAY2.spad" 853806 853844 854025 854052) (-526 "IFF.spad" 853216 853232 853487 853580) (-525 "IFAST.spad" 852830 852838 853206 853211) (-524 "IFARRAY.spad" 850323 850338 852013 852040) (-523 "IFAMON.spad" 850185 850202 850279 850284) (-522 "IEVALAB.spad" 849590 849602 850175 850180) (-521 "IEVALAB.spad" 848993 849007 849580 849585) (-520 "IDPO.spad" 848791 848803 848983 848988) (-519 "IDPOAMS.spad" 848547 848559 848781 848786) (-518 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"FMTC.spad" 638519 638527 638647 638716) (-394 "FMONOID.spad" 638184 638194 638475 638480) (-393 "FMONCAT.spad" 635337 635347 638174 638179) (-392 "FM.spad" 635032 635044 635271 635298) (-391 "FMFUN.spad" 632062 632070 635022 635027) (-390 "FMC.spad" 631114 631122 632052 632057) (-389 "FMCAT.spad" 628782 628800 631082 631109) (-388 "FM1.spad" 628139 628151 628716 628743) (-387 "FLOATRP.spad" 625874 625888 628129 628134) (-386 "FLOAT.spad" 619188 619196 625740 625869) (-385 "FLOATCP.spad" 616619 616633 619178 619183) (-384 "FLINEXP.spad" 616331 616341 616599 616614) (-383 "FLINEXP.spad" 615997 616009 616267 616272) (-382 "FLASORT.spad" 615323 615335 615987 615992) (-381 "FLALG.spad" 612969 612988 615249 615318) (-380 "FLAGG.spad" 610011 610021 612949 612964) (-379 "FLAGG.spad" 606954 606966 609894 609899) (-378 "FLAGG2.spad" 605679 605695 606944 606949) (-377 "FINRALG.spad" 603740 603753 605635 605674) (-376 "FINRALG.spad" 601727 601742 603624 603629) (-375 "FINITE.spad" 600879 600887 601717 601722) (-374 "FINAALG.spad" 590000 590010 600821 600874) (-373 "FINAALG.spad" 579133 579145 589956 589961) (-372 "FILE.spad" 578716 578726 579123 579128) (-371 "FILECAT.spad" 577242 577259 578706 578711) (-370 "FIELD.spad" 576648 576656 577144 577237) (-369 "FIELD.spad" 576140 576150 576638 576643) (-368 "FGROUP.spad" 574787 574797 576120 576135) (-367 "FGLMICPK.spad" 573574 573589 574777 574782) (-366 "FFX.spad" 572949 572964 573290 573383) (-365 "FFSLPE.spad" 572452 572473 572939 572944) (-364 "FFPOLY.spad" 563714 563725 572442 572447) (-363 "FFPOLY2.spad" 562774 562791 563704 563709) (-362 "FFP.spad" 562171 562191 562490 562583) (-361 "FF.spad" 561619 561635 561852 561945) (-360 "FFNBX.spad" 560131 560151 561335 561428) (-359 "FFNBP.spad" 558644 558661 559847 559940) (-358 "FFNB.spad" 557109 557130 558325 558418) (-357 "FFINTBAS.spad" 554623 554642 557099 557104) (-356 "FFIELDC.spad" 552200 552208 554525 554618) (-355 "FFIELDC.spad" 549863 549873 552190 552195) (-354 "FFHOM.spad" 548611 548628 549853 549858) (-353 "FFF.spad" 546046 546057 548601 548606) (-352 "FFCGX.spad" 544893 544913 545762 545855) (-351 "FFCGP.spad" 543782 543802 544609 544702) (-350 "FFCG.spad" 542574 542595 543463 543556) (-349 "FFCAT.spad" 535747 535769 542413 542569) (-348 "FFCAT.spad" 528999 529023 535667 535672) (-347 "FFCAT2.spad" 528746 528786 528989 528994) (-346 "FEXPR.spad" 520463 520509 528502 528541) (-345 "FEVALAB.spad" 520171 520181 520453 520458) (-344 "FEVALAB.spad" 519664 519676 519948 519953) (-343 "FDIV.spad" 519106 519130 519654 519659) (-342 "FDIVCAT.spad" 517170 517194 519096 519101) (-341 "FDIVCAT.spad" 515232 515258 517160 517165) (-340 "FDIV2.spad" 514888 514928 515222 515227) (-339 "FCTRDATA.spad" 513896 513904 514878 514883) (-338 "FCPAK1.spad" 512463 512471 513886 513891) (-337 "FCOMP.spad" 511842 511852 512453 512458) (-336 "FC.spad" 501849 501857 511832 511837) (-335 "FAXF.spad" 494820 494834 501751 501844) (-334 "FAXF.spad" 487843 487859 494776 494781) (-333 "FARRAY.spad" 485993 486003 487026 487053) (-332 "FAMR.spad" 484129 484141 485891 485988) (-331 "FAMR.spad" 482249 482263 484013 484018) (-330 "FAMONOID.spad" 481917 481927 482203 482208) (-329 "FAMONC.spad" 480213 480225 481907 481912) (-328 "FAGROUP.spad" 479837 479847 480109 480136) (-327 "FACUTIL.spad" 478041 478058 479827 479832) (-326 "FACTFUNC.spad" 477235 477245 478031 478036) (-325 "EXPUPXS.spad" 474068 474091 475367 475516) (-324 "EXPRTUBE.spad" 471356 471364 474058 474063) (-323 "EXPRODE.spad" 468516 468532 471346 471351) (-322 "EXPR.spad" 463791 463801 464505 464912) (-321 "EXPR2UPS.spad" 459913 459926 463781 463786) (-320 "EXPR2.spad" 459618 459630 459903 459908) (-319 "EXPEXPAN.spad" 456558 456583 457190 457283) (-318 "EXIT.spad" 456229 456237 456548 456553) (-317 "EXITAST.spad" 455965 455973 456219 456224) (-316 "EVALCYC.spad" 455425 455439 455955 455960) (-315 "EVALAB.spad" 454997 455007 455415 455420) (-314 "EVALAB.spad" 454567 454579 454987 454992) (-313 "EUCDOM.spad" 452141 452149 454493 454562) (-312 "EUCDOM.spad" 449777 449787 452131 452136) (-311 "ESTOOLS.spad" 441623 441631 449767 449772) (-310 "ESTOOLS2.spad" 441226 441240 441613 441618) (-309 "ESTOOLS1.spad" 440911 440922 441216 441221) (-308 "ES.spad" 433726 433734 440901 440906) (-307 "ES.spad" 426447 426457 433624 433629) (-306 "ESCONT.spad" 423240 423248 426437 426442) (-305 "ESCONT1.spad" 422989 423001 423230 423235) (-304 "ES2.spad" 422494 422510 422979 422984) (-303 "ES1.spad" 422064 422080 422484 422489) (-302 "ERROR.spad" 419391 419399 422054 422059) (-301 "EQTBL.spad" 417863 417885 418072 418099) (-300 "EQ.spad" 412668 412678 415455 415567) (-299 "EQ2.spad" 412386 412398 412658 412663) (-298 "EP.spad" 408712 408722 412376 412381) (-297 "ENV.spad" 407390 407398 408702 408707) (-296 "ENTIRER.spad" 407058 407066 407334 407385) (-295 "EMR.spad" 406346 406387 406984 407053) (-294 "ELTAGG.spad" 404600 404619 406336 406341) (-293 "ELTAGG.spad" 402818 402839 404556 404561) (-292 "ELTAB.spad" 402293 402306 402808 402813) (-291 "ELFUTS.spad" 401680 401699 402283 402288) (-290 "ELEMFUN.spad" 401369 401377 401670 401675) (-289 "ELEMFUN.spad" 401056 401066 401359 401364) (-288 "ELAGG.spad" 399027 399037 401036 401051) (-287 "ELAGG.spad" 396935 396947 398946 398951) (-286 "ELABOR.spad" 396281 396289 396925 396930) (-285 "ELABEXPR.spad" 395213 395221 396271 396276) (-284 "EFUPXS.spad" 391989 392019 395169 395174) (-283 "EFULS.spad" 388825 388848 391945 391950) (-282 "EFSTRUC.spad" 386840 386856 388815 388820) (-281 "EF.spad" 381616 381632 386830 386835) (-280 "EAB.spad" 379892 379900 381606 381611) (-279 "E04UCFA.spad" 379428 379436 379882 379887) (-278 "E04NAFA.spad" 379005 379013 379418 379423) (-277 "E04MBFA.spad" 378585 378593 378995 379000) (-276 "E04JAFA.spad" 378121 378129 378575 378580) (-275 "E04GCFA.spad" 377657 377665 378111 378116) (-274 "E04FDFA.spad" 377193 377201 377647 377652) (-273 "E04DGFA.spad" 376729 376737 377183 377188) (-272 "E04AGNT.spad" 372579 372587 376719 376724) (-271 "DVARCAT.spad" 369268 369278 372569 372574) (-270 "DVARCAT.spad" 365955 365967 369258 369263) (-269 "DSMP.spad" 363422 363436 363727 363854) (-268 "DROPT.spad" 357381 357389 363412 363417) (-267 "DROPT1.spad" 357046 357056 357371 357376) (-266 "DROPT0.spad" 351903 351911 357036 357041) (-265 "DRAWPT.spad" 350076 350084 351893 351898) (-264 "DRAW.spad" 342952 342965 350066 350071) (-263 "DRAWHACK.spad" 342260 342270 342942 342947) (-262 "DRAWCX.spad" 339730 339738 342250 342255) (-261 "DRAWCURV.spad" 339277 339292 339720 339725) (-260 "DRAWCFUN.spad" 328809 328817 339267 339272) (-259 "DQAGG.spad" 326987 326997 328777 328804) (-258 "DPOLCAT.spad" 322336 322352 326855 326982) (-257 "DPOLCAT.spad" 317771 317789 322292 322297) (-256 "DPMO.spad" 309997 310013 310135 310436) (-255 "DPMM.spad" 302236 302254 302361 302662) (-254 "DOMTMPLT.spad" 302007 302015 302226 302231) (-253 "DOMCTOR.spad" 301762 301770 301997 302002) (-252 "DOMAIN.spad" 300849 300857 301752 301757) (-251 "DMP.spad" 298109 298124 298679 298806) (-250 "DLP.spad" 297461 297471 298099 298104) (-249 "DLIST.spad" 296040 296050 296644 296671) (-248 "DLAGG.spad" 294457 294467 296030 296035) (-247 "DIVRING.spad" 293999 294007 294401 294452) (-246 "DIVRING.spad" 293585 293595 293989 293994) (-245 "DISPLAY.spad" 291775 291783 293575 293580) (-244 "DIRPROD.spad" 281355 281371 281995 282126) (-243 "DIRPROD2.spad" 280173 280191 281345 281350) (-242 "DIRPCAT.spad" 279117 279133 280037 280168) (-241 "DIRPCAT.spad" 277790 277808 278712 278717) (-240 "DIOSP.spad" 276615 276623 277780 277785) (-239 "DIOPS.spad" 275611 275621 276595 276610) (-238 "DIOPS.spad" 274581 274593 275567 275572) (-237 "DIFRING.spad" 274187 274195 274561 274576) (-236 "DIFRING.spad" 273801 273811 274177 274182) (-235 "DIFFDOM.spad" 272966 272977 273791 273796) (-234 "DIFFDOM.spad" 272129 272142 272956 272961) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 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"ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
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T) (((-415 (-572))) -2813 (|has| (-1010 |#1|) (-1049 (-415 (-572)))) (|has| |#1| (-1049 (-415 (-572)))))) +(-2813 (|has| |#2| (-174)) (|has| |#2| (-734)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (|has| |#2| (-801)) -(-3783 (|has| |#2| (-801)) (|has| |#2| (-856))) +(-2813 (|has| |#2| (-801)) (|has| |#2| (-856))) (|has| |#1| (-375)) (|has| |#1| (-375)) (|has| |#1| (-375)) @@ -727,7 +725,7 @@ ((((-652 (-930))) . T) (((-870)) . T)) ((((-415 (-572))) . T) (((-870)) . T)) ((((-544)) . T) (((-901 (-572))) . T) (((-386)) . T) (((-227)) . 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T)) -(-3783 (|has| |#2| (-174)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-174)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (|has| |#1| (-564)) (((|#1|) . T)) (((|#1|) . T)) @@ -1146,12 +1143,12 @@ (((|#1| (-415 (-572))) . T)) (((|#3|) . T) (((-620 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) -((((-572)) -3783 (|has| |#2| (-174)) (|has| |#2| (-856)) (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) (|has| |#2| (-1060))) ((|#2|) -3783 (|has| |#2| (-174)) (|has| |#2| (-1111))) (((-415 (-572))) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111)))) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) +((((-572)) -2813 (|has| |#2| (-174)) (|has| |#2| (-856)) (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) (|has| |#2| (-1060))) ((|#2|) -2813 (|has| |#2| (-174)) (|has| |#2| (-1111))) (((-415 (-572))) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111)))) (((|#1|) . T) (((-415 (-572))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-572)) . T) (($) . T) (((-415 (-572))) . T)) @@ -1159,8 +1156,8 @@ ((((-870)) . T)) ((((-870)) . T)) (((|#1| |#1|) . 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T)) (((|#1|) |has| |#1| (-315 |#1|))) @@ -1281,12 +1278,12 @@ (|has| |#1| (-375)) ((((-1188) $) |has| |#1| (-522 (-1188) $)) (($ $) |has| |#1| (-315 $)) ((|#1| |#1|) |has| |#1| (-315 |#1|)) (((-1188) |#1|) |has| |#1| (-522 (-1188) |#1|))) ((((-1188)) |has| |#1| (-909 (-1188)))) -(-3783 (-12 (|has| |#1| (-235 |#1|)) (|has| |#1| (-370))) (|has| |#1| (-356))) +(-2813 (-12 (|has| |#1| (-237)) (|has| |#1| (-370))) (|has| |#1| (-356))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-396) |#1|) . T)) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-356))) (|has| |#1| (-1111)) (((|#2|) . T) (((-870)) . T)) ((((-870)) . T)) @@ -1294,8 +1291,8 @@ ((((-919 |#1|)) . T)) ((((-870)) . T) (((-1193)) . T)) ((((-1193)) . T)) -((((-415 (-572))) |has| |#2| (-38 (-415 (-572)))) ((|#2|) |has| |#2| (-174)) (($) -3783 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918)))) -((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) |has| |#1| (-174)) (($) -3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918)))) +((((-415 (-572))) |has| |#2| (-38 (-415 (-572)))) ((|#2|) |has| |#2| (-174)) (($) -2813 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918)))) +((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) |has| |#1| (-174)) (($) -2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-572)) . T) (($) . T) (((-415 (-572))) . T)) @@ -1304,16 +1301,16 @@ (((|#1|) . T) (((-415 (-572))) . T) (($) . T) (((-572)) . T)) (((|#1| |#1|) . T)) (((#0=(-878 |#1|)) |has| #0# (-315 #0#))) -((((-572)) . 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T)) (|has| |#1| (-1214)) (((#0=(-572) #0#) . T) ((#1=(-415 (-572)) #1#) . T) (($ $) . T)) @@ -1325,8 +1322,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-415 (-572)) #0#) . T)) (|has| |#1| (-370)) ((((-572)) . T) (((-415 (-572))) . T) (($) . T)) -((($ $) . T) ((#0=(-415 (-572)) #0#) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1| |#1|) . T)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((($ $) . T) ((#0=(-415 (-572)) #0#) -2813 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1| |#1|) . T)) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) (((|#1|) . T) (($) . T) (((-415 (-572))) . T)) ((((-870)) . T)) ((((-870)) . T)) @@ -1341,29 +1338,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-856)) (|has| |#1| (-856)) -((($) . T) (((-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) -(-3783 (|has| |#1| (-174)) (|has| |#1| (-564))) +((($) . T) (((-415 (-572))) -2813 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . 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T)) -((((-572) (-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T) ((|#1| |#2|) . T)) +((((-572) (-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T) ((|#1| |#2|) . T)) ((((-415 (-572))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((((-870)) . T)) ((((-919 |#1|)) . T)) (|has| |#1| (-370)) @@ -1371,11 +1368,11 @@ (|has| |#1| (-370)) (|has| |#1| (-15 * (|#1| (-415 (-572)) |#1|))) (|has| |#1| (-856)) -((($) -3783 (|has| |#1| (-313)) (|has| |#1| (-370)) (|has| |#1| (-356)) (|has| |#1| (-564))) (((-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) +((($) -2813 (|has| |#1| (-313)) (|has| |#1| (-370)) (|has| |#1| (-356)) (|has| |#1| (-564))) (((-415 (-572))) -2813 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) (|has| |#1| (-370)) (((|#1|) . T) (($) . T)) (|has| |#1| (-856)) -((($) . T) (((-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) +((($) . 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T)) -(((|#2|) -3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060))) (($) |has| |#2| (-174))) +(((|#2|) -2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060))) (($) |has| |#2| (-174))) (|has| $ (-148)) ((((-415 |#2|)) . T)) ((((-415 (-572))) |has| #0=(-415 |#2|) (-1049 (-415 (-572)))) (((-572)) |has| #0# (-1049 (-572))) ((#0#) . T)) @@ -1516,14 +1513,14 @@ (((|#3|) |has| |#3| (-174))) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) (|has| |#1| (-148)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) (|has| |#1| (-148)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) (|has| |#1| (-148)) (((|#1|) . T)) -(|has| |#2| (-235 |#2|)) +(|has| |#2| (-237)) (((|#2|) . T)) ((((-870)) . T) (((-1193)) . T)) ((((-1193)) . T)) @@ -1534,7 +1531,7 @@ (((|#1| |#1|) . T)) ((((-1188)) |has| |#2| (-909 (-1188)))) ((((-130)) . T)) -(|has| (-415 |#2|) (-235 (-415 |#2|))) +(|has| (-415 |#2|) (-237)) ((((-572) (-112)) . T) (((-1246 (-572)) $) . T)) (|has| |#1| (-564)) (((|#2|) . T)) @@ -1559,7 +1556,7 @@ ((((-1010 |#1|)) . T) ((|#1|) . T)) ((((-870)) . T)) ((((-870)) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((((-415 (-572))) . T) (((-415 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1184 |#1|)) . T)) ((((-572)) . T) (($) . T) (((-415 (-572))) . T)) @@ -1568,8 +1565,8 @@ (((|#1|) . T) (((-572)) . T) (($) . T)) (((|#2|) . T)) ((((-572)) . T) (($) . T) (((-415 (-572))) . T)) -((((-2 (|:| -1640 (-1170)) (|:| -3763 |#1|))) . T)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-2 (|:| -3690 (-1170)) (|:| -1907 |#1|))) . T)) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) ((((-572) |#2|) . T)) (((|#1|) . T) (((-415 (-572))) . T) (((-572)) . T) (($) . T)) ((($) . T) (((-572)) . T) (((-415 (-572))) . T)) @@ -1582,7 +1579,7 @@ (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) ((((-1271 |#1| |#2| |#3|)) |has| |#1| (-370))) -(((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((#0=(-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) #0#) |has| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (-315 (-2 (|:| -1640 |#1|) (|:| -3763 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((#0=(-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) #0#) |has| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (-315 (-2 (|:| -3690 |#1|) (|:| -1907 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1111)) (|has| |#2| (-370)) @@ -1592,16 +1589,16 @@ (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) (((|#1|) |has| |#1| (-174))) -((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) |has| |#1| (-174)) (($) -3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918)))) -((($) -3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) +((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) |has| |#1| (-174)) (($) -2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918)))) +((($) -2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (((|#2|) . T)) (((|#1|) . T)) ((((-1170) (-52)) . T)) (((|#1|) . T)) -((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) . 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T) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (((|#2|) |has| |#2| (-174))) -((($) -3783 (|has| |#2| (-174)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (((-572)) -3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) ((|#2|) -3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060)))) +((($) -2813 (|has| |#2| (-174)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (((-572)) -2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) ((|#2|) -2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060)))) ((((-572) |#3|) . T)) ((((-572) (-145)) . T)) ((((-145)) . T)) @@ -1627,19 +1624,19 @@ (((|#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) (((|#1| |#2|) . T)) ((((-1246 (-572)) $) . T) (((-572) (-145)) . T)) -(((#0=(-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) #0#) |has| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (-315 (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111)))) -((($) -3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) +(((#0=(-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) #0#) |has| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (-315 (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111)))) +((($) -2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (|has| |#1| (-858)) (((|#2| (-779) (-1093)) . T)) (((|#1| |#2|) . T)) -(-3783 (|has| |#1| (-174)) (|has| |#1| (-564))) +(-2813 (|has| |#1| (-174)) (|has| |#1| (-564))) (|has| |#1| (-799)) (((|#1|) |has| |#1| (-174))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3783 (|has| |#1| (-148)) (-12 (|has| |#1| (-370)) (|has| |#2| (-148)))) -(-3783 (|has| |#1| (-146)) (-12 (|has| |#1| (-370)) (|has| |#2| (-146)))) +(-2813 (|has| |#1| (-148)) (-12 (|has| |#1| (-370)) (|has| |#2| (-148)))) +(-2813 (|has| |#1| (-146)) (-12 (|has| |#1| (-370)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1170) |#1|) . T)) @@ -1653,24 +1650,24 @@ (((|#3|) . T)) ((((-1271 |#1| |#2| |#3|)) |has| |#1| (-370))) ((($) . T) (((-572)) . T) (((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) . T)) -((((-415 (-572))) -3783 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (((-1186 |#1| |#2| |#3|)) |has| |#1| (-370)) (((-572)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-415 (-572))) -3783 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (((-572)) . T) (($) . T)) +((((-415 (-572))) -2813 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (((-1186 |#1| |#2| |#3|)) |has| |#1| (-370)) (((-572)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -3783 (|has| |#4| (-174)) (|has| |#4| (-370)))) -(((|#3|) -3783 (|has| |#3| (-174)) (|has| |#3| (-370)))) +(((|#4|) -2813 (|has| |#4| (-174)) (|has| |#4| (-370)))) +(((|#3|) -2813 (|has| |#3| (-174)) (|has| |#3| (-370)))) (|has| |#2| (-370)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -3783 (|has| |#4| (-174)) (|has| |#4| (-370)) (|has| |#4| (-1060))) (($) |has| |#4| (-174))) -(((|#3|) -3783 (|has| |#3| (-174)) (|has| |#3| (-370)) (|has| |#3| (-1060))) (($) |has| |#3| (-174))) +(((|#4|) -2813 (|has| |#4| (-174)) (|has| |#4| (-370)) (|has| |#4| (-1060))) (($) |has| |#4| (-174))) +(((|#3|) -2813 (|has| |#3| (-174)) (|has| |#3| (-370)) (|has| |#3| (-1060))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1060))) ((((-1170) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-315 |#3|)) (|has| |#3| (-1111)))) @@ -1679,8 +1676,8 @@ ((($) . T) (((-572)) . T) (((-415 (-572))) |has| |#2| (-38 (-415 (-572)))) ((|#2|) . T)) ((((-396) (-1170)) . T)) ((($) |has| |#1| (-564)) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) -((((-870)) -3783 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-621 (-870))) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-375)) (|has| |#2| (-734)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060)) (|has| |#2| (-1111))) (((-1279 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1640 (-1170)) (|:| -3763 #0#))) . T)) +((((-870)) -2813 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-621 (-870))) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-375)) (|has| |#2| (-734)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060)) (|has| |#2| (-1111))) (((-1279 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3690 (-1170)) (|:| -1907 #0#))) . T)) (((|#1|) . T)) ((((-870)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111)))) @@ -1689,7 +1686,7 @@ ((((-572)) . T)) (|has| |#2| (-148)) (|has| |#1| (-481)) -(-3783 (|has| |#1| (-481)) (|has| |#1| (-734)) (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060))) +(-2813 (|has| |#1| (-481)) (|has| |#1| (-734)) (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060))) (|has| |#1| (-370)) ((((-870)) . T)) (|has| |#1| (-38 (-415 (-572)))) @@ -1700,8 +1697,8 @@ (|has| |#1| (-856)) ((((-870)) . T)) (((|#2|) . T)) -((((-415 (-572))) -3783 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (($) -3783 (|has| |#1| (-370)) (|has| |#1| (-564))) (((-1271 |#1| |#2| |#3|)) |has| |#1| (-370)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-415 (-572))) -3783 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (($) -3783 (|has| |#1| (-370)) (|has| |#1| (-564)))) +((((-415 (-572))) -2813 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (($) -2813 (|has| |#1| (-370)) (|has| |#1| (-564))) (((-1271 |#1| |#2| |#3|)) |has| |#1| (-370)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-415 (-572))) -2813 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) (($) -2813 (|has| |#1| (-370)) (|has| |#1| (-564)))) ((($) |has| |#1| (-564)) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (((|#2|) . T) (((-572)) . T) (((-827 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1711,7 +1708,7 @@ ((((-870)) . T)) ((((-870)) . T)) (|has| |#1| (-1111)) -(((|#2| (-490 (-3476 |#1|) (-779)) (-872 |#1|)) . T)) +(((|#2| (-490 (-2860 |#1|) (-779)) (-872 |#1|)) . T)) ((((-415 (-572))) . #0=(|has| |#2| (-370))) (($) . #0#)) (((|#1| (-539 (-1188)) (-1188)) . T)) (((|#1|) . T)) @@ -1732,17 +1729,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1640 (-1170)) (|:| -3763 |#1|))) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3690 (-1170)) (|:| -1907 |#1|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))) . T)) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((((-1186 |#1| |#2| |#3|)) |has| |#1| (-370))) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((((-1188) (-52)) . T)) ((((-415 (-572)) |#1|) . T) (($ $) . T)) (((|#1| (-572)) . T)) ((((-919 |#1|)) . 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T) (((-572)) |has| |#1| (-1049 (-572))) (((-415 (-572))) |has| |#1| (-1049 (-415 (-572))))) (|has| |#1| (-858)) (|has| |#1| (-858)) @@ -1760,15 +1757,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-315 |#4|)) (|has| |#4| (-1111)))) (((|#4| |#4|) -12 (|has| |#4| (-315 |#4|)) (|has| |#4| (-1111)))) (((|#1|) |has| |#1| (-174))) -(-3783 (|has| |#1| (-235 |#1|)) (|has| |#1| (-292 |#1| |#1|))) +(-2813 (|has| |#1| (-237)) (|has| |#1| (-292 |#1| |#1|))) (((|#4| |#4|) -12 (|has| |#4| (-315 |#4|)) (|has| |#4| (-1111)))) -(((|#3|) -3783 (|has| |#3| (-174)) (|has| |#3| (-370)))) -((($) -3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) -(-3783 (|has| |#2| (-370)) (|has| |#2| (-460)) (|has| |#2| (-918))) -((($) -3783 (|has| |#1| (-174)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) . 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T)) -(-3783 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) +(-2813 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) (((|#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) ((((-870)) . T)) ((($) . T) (((-572)) . T)) @@ -1942,33 +1939,33 @@ (|has| |#2| (-918)) (|has| |#1| (-370)) (((|#2|) |has| |#2| (-1111))) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((((-572)) . T) (((-415 (-572))) . T) (($) . T)) ((((-544)) . T) (((-415 (-1184 (-572)))) . T) (((-227)) . T) (((-386)) . T)) ((((-386)) . T) (((-227)) . T) (((-870)) . 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T)) ((((-572) (-112)) . T)) @@ -1976,7 +1973,7 @@ (((|#1|) . T)) ((((-572)) . T)) ((((-112)) . T)) -(-3783 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-564))) +(-2813 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-564))) (|has| |#1| (-38 (-415 (-572)))) (((|#1| (-572)) . T)) ((($) . T)) @@ -1999,7 +1996,7 @@ (((|#1| (-779)) . T)) (((|#1|) . T)) ((((-870)) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (|has| |#1| (-1111)) ((((-1170) |#1|) . T)) ((($) . T)) @@ -2019,20 +2016,20 @@ (((|#1|) . T)) ((((-572)) . T)) ((((-870)) . T)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-356))) ((((-870)) . T)) (|has| |#1| (-148)) (((|#3|) . T)) -(-3783 (|has| |#3| (-174)) (|has| |#3| (-856)) (|has| |#3| (-1060))) +(-2813 (|has| |#3| (-174)) (|has| |#3| (-856)) (|has| |#3| (-1060))) ((((-870)) . 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T) (($) . T)) @@ -2240,17 +2237,17 @@ ((((-707)) . T) (((-415 (-572))) . T) (((-572)) . T)) (((|#1| |#1|) |has| |#1| (-174))) (((|#2|) . T)) -((($) . T) (((-572)) . T) (((-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) +((($) . T) (((-572)) . T) (((-415 (-572))) -2813 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . T)) ((((-572) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) (((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) |has| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (-315 (-2 (|:| -1640 |#1|) (|:| -3763 |#2|))))) +(((|#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) (((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) |has| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (-315 (-2 (|:| -3690 |#1|) (|:| -1907 |#2|))))) ((((-386)) . T)) ((((-707)) . T)) ((((-415 (-572))) . #0=(|has| |#2| (-370))) (($) . #0#)) (((|#1|) |has| |#1| (-174))) ((((-415 (-961 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3783 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1060))) @@ -2260,15 +2257,15 @@ ((($) . T)) ((((-1188)) |has| |#2| (-909 (-1188)))) ((((-870)) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((((-415 (-572))) . T) (($) . T)) (|has| |#1| (-481)) (|has| |#1| (-375)) (|has| |#1| (-375)) (|has| |#1| (-375)) (|has| |#1| (-370)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-481)) (|has| |#1| (-564)) (|has| |#1| (-1060)) (|has| |#1| (-1123))) -((($) -3783 (|has| |#1| (-235 |#1|)) (|has| |#1| (-356)))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-481)) (|has| |#1| (-564)) (|has| |#1| (-1060)) (|has| |#1| (-1123))) +((($) -2813 (|has| |#1| (-237)) (|has| |#1| (-356)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-356)) @@ -2289,12 +2286,12 @@ (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-858)) -((((-2 (|:| -1640 (-1170)) (|:| -3763 |#1|))) . T)) +((((-2 (|:| -3690 (-1170)) (|:| -1907 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-572)) . 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T) (((-870)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3783 (|has| |#1| (-296)) (|has| |#1| (-370))) ((#0=(-415 (-572)) #0#) |has| |#1| (-370))) -((((-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -2813 (|has| |#1| (-296)) (|has| |#1| (-370))) ((#0=(-415 (-572)) #0#) |has| |#1| (-370))) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((((-961 |#1|)) . T)) ((($) . T)) ((((-572) |#1|) . T)) ((((-1188)) |has| (-415 |#2|) (-909 (-1188)))) -(((|#1|) . T) (($) -3783 (|has| |#1| (-296)) (|has| |#1| (-370))) (((-415 (-572))) |has| |#1| (-370))) +(((|#1|) . T) (($) -2813 (|has| |#1| (-296)) (|has| |#1| (-370))) (((-415 (-572))) |has| |#1| (-370))) ((((-544)) |has| |#2| (-622 (-544)))) ((((-697 |#2|)) . T) (((-870)) . T)) (((|#1|) . T)) @@ -2406,23 +2402,23 @@ (((|#4|) -12 (|has| |#4| (-315 |#4|)) (|has| |#4| (-1111)))) ((((-878 |#1|)) . 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T)) -(((|#2|) -3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060))) (($) |has| |#2| (-174))) +(((|#2|) -2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-1060))) (($) |has| |#2| (-174))) (((|#3|) -12 (|has| |#3| (-315 |#3|)) (|has| |#3| (-1111)))) ((((-1246 (-572)) $) . T) (((-572) |#1|) . T)) (((|#1|) . T)) @@ -2431,17 +2427,17 @@ ((((-415 (-572))) . T) (($) . T)) ((((-415 (-572))) . T) (($) . T)) ((((-415 (-572))) . T) (($) . T)) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-1233))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-1233))) ((($) . T)) ((((-415 (-572))) |has| #0=(-415 |#2|) (-1049 (-415 (-572)))) (((-572)) |has| #0# (-1049 (-572))) ((#0#) . T)) (((|#2|) . T) (((-572)) |has| |#2| (-647 (-572)))) (((|#1| (-779)) . T)) (|has| |#1| (-858)) (((|#1|) . T) (((-572)) |has| |#1| (-647 (-572)))) -((($) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) (((-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-356))) ((|#1|) . 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T)) +((((-2 (|:| -3690 (-1170)) (|:| -1907 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((((-870)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-572)) . T)) (((|#1| (-415 (-572))) . T)) (((|#1|) . T)) -(-3783 (|has| |#1| (-296)) (|has| |#1| (-370))) +(-2813 (|has| |#1| (-296)) (|has| |#1| (-370))) ((((-145)) . T)) ((((-415 |#2|)) . T) (((-415 (-572))) . T) (($) . T)) (|has| |#1| (-856)) @@ -2753,7 +2749,7 @@ ((((-870)) . T)) ((((-870)) . T)) ((((-189)) . T) (((-870)) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-870)) . T)) ((((-870)) . T)) @@ -2766,9 +2762,9 @@ ((((-870)) . T)) ((((-1170)) . T)) ((((-1188) |#1|) |has| |#1| (-522 (-1188) |#1|)) ((|#1| |#1|) |has| |#1| (-315 |#1|))) -((((-2 (|:| -1640 (-1170)) (|:| -3763 |#1|))) . T)) +((((-2 (|:| -3690 (-1170)) (|:| -1907 |#1|))) . T)) (|has| |#1| (-858)) -((($) -3783 (-12 (|has| (-1186 |#1| |#2| |#3|) (-235 (-1186 |#1| |#2| |#3|))) (|has| |#1| (-370))) (|has| |#1| (-15 * (|#1| (-572) |#1|))))) +((($) -2813 (-12 (|has| (-1186 |#1| |#2| |#3|) (-237)) (|has| |#1| (-370))) (|has| |#1| (-15 * (|#1| (-572) |#1|))))) ((((-870)) . T)) ((((-544)) |has| |#1| (-622 (-544)))) ((($) |has| |#1| (-15 * (|#1| (-415 (-572)) |#1|)))) @@ -2781,16 +2777,16 @@ (((|#2|) . T)) ((((-919 |#1|)) . T) (((-415 (-572))) . T) (($) . T)) ((($) . T) (((-572)) . T) (((-415 (-572))) . T) (((-620 $)) . T)) -(-3783 (|has| |#4| (-174)) (|has| |#4| (-734)) (|has| |#4| (-856)) (|has| |#4| (-1060))) -(-3783 (|has| |#3| (-174)) (|has| |#3| (-734)) (|has| |#3| (-856)) (|has| |#3| (-1060))) +(-2813 (|has| |#4| (-174)) (|has| |#4| (-734)) (|has| |#4| (-856)) (|has| |#4| (-1060))) +(-2813 (|has| |#3| (-174)) (|has| |#3| (-734)) (|has| |#3| (-856)) (|has| |#3| (-1060))) ((((-1188) (-52)) . T)) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3783 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) -(-3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (|has| |#1| (-918)) ((((-919 |#1|)) . T) (((-415 (-572))) . T) (($) . T) (((-572)) . T)) (|has| |#1| (-918)) @@ -2807,12 +2803,12 @@ (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) (|has| |#1| (-828)) (((#0=(-919 |#1|) #0#) . T) (($ $) . T) ((#1=(-415 (-572)) #1#) . T)) ((((-415 |#2|)) . T)) (|has| |#1| (-856)) -((((-1215 |#1|)) . T) (((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-1215 |#1|)) . T) (((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) (((|#1| |#1|) . T) ((#0=(-415 (-572)) #0#) . T) ((#1=(-572) #1#) . T) (($ $) . T)) ((((-919 |#1|)) . T) (($) . T) (((-415 (-572))) . T)) (((|#2|) |has| |#2| (-1060)) (((-572)) -12 (|has| |#2| (-647 (-572))) (|has| |#2| (-1060)))) @@ -2828,35 +2824,34 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) -((((-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))) . T)) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((((-572) |#3|) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1640 (-1188)) (|:| -3763 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3690 (-1188)) (|:| -1907 #0#))) . T)) (|has| |#1| (-356)) ((((-572)) . T)) ((((-870)) . T)) (((|#1|) . T)) (((#0=(-1265 |#1| |#2| |#3| |#4|) $) |has| #0# (-292 #0# #0#))) (|has| |#1| (-370)) -(((|#1|) -3783 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-1060))) (($) -3783 (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060))) (((-572)) -3783 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060)))) +(((|#1|) -2813 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-1060))) (($) -2813 (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060))) (((-572)) -2813 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-909 (-1188))) (|has| |#1| (-1060)))) (((#0=(-1093) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-356))) (((#0=(-415 (-572)) #0#) . T) ((#1=(-707) #1#) . T) (($ $) . T)) ((((-322 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-415 (-572))) |has| |#1| (-370))) ((((-870)) . T)) (|has| |#1| (-1111)) (((|#1|) . T)) -(((|#1|) -3783 (|has| |#2| (-374 |#1|)) (|has| |#2| (-425 |#1|)))) -(((|#1|) -3783 (|has| |#2| (-374 |#1|)) (|has| |#2| (-425 |#1|)))) +(((|#1|) -2813 (|has| |#2| (-374 |#1|)) (|has| |#2| (-425 |#1|)))) +(((|#1|) -2813 (|has| |#2| (-374 |#1|)) (|has| |#2| (-425 |#1|)))) (((|#2|) . T)) ((((-415 (-572))) . T) (((-707)) . T) (($) . T)) ((((-587)) . T)) (((|#3| |#3|) . T)) -(|has| #0=(-117 |#1|) (-235 #0#)) -(|has| |#2| (-235 |#2|)) +(|has| |#2| (-237)) ((((-872 |#1|)) . T)) ((((-1188)) |has| |#1| (-909 (-1188))) ((|#3|) . T)) ((((-652 $)) . T) ((|#1|) . T) ((|#2|) . T) ((|#3|) . T) ((|#4|) . T) ((|#5|) . T)) @@ -2874,10 +2869,10 @@ (|has| |#1| (-1111)) (((|#2|) . T)) (((|#1|) . T)) -((($) |has| |#1| (-235 |#1|))) +((($) |has| |#1| (-237))) ((((-572)) . T)) (((|#2|) . T) (((-415 (-572))) |has| |#1| (-1049 (-415 (-572)))) ((|#1|) . T) (($) . T) (((-572)) . T)) -(-3783 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-174)) (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) (((|#2|) . T) (((-572)) |has| |#2| (-647 (-572)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2915,7 +2910,7 @@ ((($) . T) ((|#1|) . T) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (((|#1|) . T)) (|has| |#2| (-918)) -(|has| |#1| (-235 |#1|)) +(|has| |#1| (-237)) (|has| |#1| (-375)) (|has| |#1| (-375)) (|has| |#1| (-375)) @@ -2925,7 +2920,7 @@ (|has| |#2| (-1033)) ((($) . T)) (|has| |#1| (-918)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2934,10 +2929,10 @@ (|has| |#1| (-370)) ((((-919 |#1|)) . T)) ((($) . T) (((-572)) . T) ((|#1|) . T) (((-415 (-572))) . T)) -((($) -3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) -((($) |has| |#1| (-856)) (((-572)) -3783 (|has| |#1| (-21)) (|has| |#1| (-856)))) +((($) -2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) |has| |#1| (-174)) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) +((($) |has| |#1| (-856)) (((-572)) -2813 (|has| |#1| (-21)) (|has| |#1| (-856)))) ((($ $) . T) ((#0=(-415 (-572)) #0#) . T)) -(-3783 (|has| |#1| (-375)) (|has| |#1| (-858))) +(-2813 (|has| |#1| (-375)) (|has| |#1| (-858))) (((|#1|) . T)) ((((-779)) . T)) ((((-870)) . T)) @@ -2948,17 +2943,17 @@ ((((-572)) . T) (($) . T)) ((((-572)) . T) (($) . T)) ((((-779) |#1|) . T)) -(((|#2| (-244 (-3476 |#1|) (-779))) . T)) +(((|#2| (-244 (-2860 |#1|) (-779))) . T)) (((|#1| (-539 |#3|)) . T)) ((((-415 (-572))) . T)) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((((-1170)) . T) (((-870)) . T)) -(((#0=(-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) #0#) |has| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (-315 (-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))))) +(((#0=(-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) #0#) |has| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (-315 (-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))))) ((((-1170)) . T)) (|has| |#1| (-918)) (|has| |#2| (-370)) (((|#1|) . T) (($) . T) (((-572)) . T)) -(-3783 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) ((((-171 (-386))) . T) (((-227)) . T) (((-386)) . T)) ((((-870)) . T)) (((|#1|) . T)) @@ -2975,11 +2970,11 @@ (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572)))) -(-3783 (|has| |#1| (-313)) (|has| |#1| (-370)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-313)) (|has| |#1| (-370)) (|has| |#1| (-356))) (|has| |#1| (-38 (-415 (-572)))) (-12 (|has| |#1| (-553)) (|has| |#1| (-836))) ((((-870)) . T)) -((((-1188)) -3783 (-12 (|has| |#1| (-15 * (|#1| (-572) |#1|))) (|has| |#1| (-909 (-1188)))) (-12 (|has| |#1| (-370)) (|has| |#2| (-909 (-1188)))))) +((((-1188)) -2813 (-12 (|has| |#1| (-15 * (|#1| (-572) |#1|))) (|has| |#1| (-909 (-1188)))) (-12 (|has| |#1| (-370)) (|has| |#2| (-909 (-1188)))))) (|has| |#1| (-370)) ((((-1188)) -12 (|has| |#1| (-15 * (|#1| (-415 (-572)) |#1|))) (|has| |#1| (-909 (-1188))))) (|has| |#1| (-370)) @@ -2991,19 +2986,21 @@ (((|#2|) |has| |#1| (-370))) (((|#2|) |has| |#1| (-370))) ((((-572)) . T) (($) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) +((($) . T)) (((|#1|) . T)) (((|#2|) . T) (((-1188)) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-1188)))) (((-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-572)))) (((-415 (-572))) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-572))))) (((|#2|) . T)) +((($) . T)) ((((-1188) #0=(-1265 |#1| |#2| |#3| |#4|)) |has| #0# (-522 (-1188) #0#)) ((#0# #0#) |has| #0# (-315 #0#))) ((((-415 (-572))) . T) (($) . T) (((-415 |#1|)) . T) ((|#1|) . T)) ((((-620 $) $) . T) (($ $) . T)) ((((-171 (-227))) . T) (((-171 (-386))) . T) (((-1184 (-707))) . T) (((-901 (-386))) . T)) (((|#3|) . T)) (|has| |#1| (-564)) -(|has| (-415 |#2|) (-235 (-415 |#2|))) +(|has| (-415 |#2|) (-237)) (((|#1| (-415 (-572))) . T)) ((($) . T) (((-415 (-572))) . T) (((-415 |#1|)) . T) ((|#1|) . T)) (((|#3|) . T)) @@ -3020,11 +3017,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) (((|#2|) |has| |#1| (-370))) ((((-386)) -12 (|has| |#1| (-370)) (|has| |#2| (-895 (-386)))) (((-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-895 (-572))))) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-564))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-564))) (|has| |#1| (-370)) (((|#1|) . T)) ((($) . T) (((-572)) . T) ((|#2|) . T)) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-564))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-564))) (((|#3|) . T)) ((((-1170)) . T) (((-514)) . T) (((-227)) . T) (((-572)) . T)) (((|#1|) . T)) @@ -3032,23 +3029,23 @@ (|has| |#1| (-564)) (((|#4| |#4|) -12 (|has| |#4| (-315 |#4|)) (|has| |#4| (-1111)))) ((((-415 |#2|)) . T) (((-415 (-572))) . T) (($) . T) (((-572)) . 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T)) (|has| |#1| (-148)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) (|has| |#1| (-148)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-375))) ((($) . T)) (|has| |#1| (-148)) ((((-589 |#1|)) . T)) @@ -3062,7 +3059,7 @@ ((((-415 (-572))) |has| |#2| (-1049 (-572))) (((-572)) |has| |#2| (-1049 (-572))) (((-1188)) |has| |#2| (-1049 (-1188))) ((|#2|) . T)) (((#0=(-415 |#2|) #0#) . T) ((#1=(-415 (-572)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-3783 (|has| |#1| (-146)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-146)) (|has| |#1| (-356))) (|has| |#1| (-148)) ((((-870)) . T)) ((($) . T)) @@ -3088,7 +3085,7 @@ ((((-919 |#1|)) . T) (((-415 (-572))) . T) (($) . T) (((-572)) . T)) ((((-870)) . T)) ((((-544)) |has| |#1| (-622 (-544)))) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-858)) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-858)) (|has| |#1| (-1111)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3110,7 +3107,7 @@ ((((-572)) . T)) ((((-870)) . T)) ((((-572)) . T)) -(-3783 (|has| |#2| (-801)) (|has| |#2| (-856))) +(-2813 (|has| |#2| (-801)) (|has| |#2| (-856))) ((((-171 (-386))) . T) (((-227)) . T) (((-386)) . T)) ((((-870)) . T)) ((((-870)) . T)) @@ -3122,10 +3119,10 @@ (((|#1|) . T) (($) . T) (((-415 (-572))) . T)) (|has| |#1| (-370)) (|has| |#1| (-370)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) ((((-572) $) . T) (((-652 (-572)) $) . 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T) (($) -2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) . T) (((-415 (-572))) -2813 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-1049 (-415 (-572))))) (((-1188)) . T)) (((#0=(-589 |#1|) #0#) . T) (($ $) . T) ((#1=(-415 (-572)) #1#) . T)) ((($ $) . T) ((#0=(-415 (-572)) #0#) . T)) (((|#1|) |has| |#1| (-174))) @@ -3215,7 +3212,7 @@ (((|#1|) . T)) ((((-870)) . T)) ((((-300 |#3|)) . T)) -(((#0=(-415 (-572)) #0#) |has| |#2| (-38 (-415 (-572)))) ((|#2| |#2|) . T) (($ $) -3783 (|has| |#2| (-174)) (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918)))) +(((#0=(-415 (-572)) #0#) |has| |#2| (-38 (-415 (-572)))) ((|#2| |#2|) . T) (($ $) -2813 (|has| |#2| (-174)) (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-415 (-572))) |has| |#2| (-38 (-415 (-572)))) ((|#2|) . T)) @@ -3223,21 +3220,21 @@ (((|#1|) . T) (((-415 (-572))) . T) (($) . T)) (((|#1|) . T) (((-415 (-572))) . T) (($) . 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T)) (((|#1|) |has| |#1| (-174))) -(-3783 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-801)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (((|#1|) . T)) (((|#1|) . T)) -(-3783 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) +(-2813 (|has| |#2| (-174)) (|has| |#2| (-370)) (|has| |#2| (-856)) (|has| |#2| (-1060))) (((|#1|) . T)) ((((-415 (-572))) . T) (((-572)) . T) (($) . T)) ((((-544)) . T)) ((((-870)) . T)) -((($) -12 (|has| |#3| (-235 |#3|)) (|has| |#3| (-1060)))) +((($) -12 (|has| |#3| (-237)) (|has| |#3| (-1060)))) ((((-572)) . T) (((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-564))) ((((-870)) . T)) ((((-1188)) |has| |#2| (-909 (-1188))) (((-1093)) . T)) @@ -3279,14 +3276,14 @@ ((($ $) . 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T) (($) -3783 (|has| |#1| (-174)) (|has| |#1| (-564)))) +((((-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((|#1|) . T) (($) -2813 (|has| |#1| (-174)) (|has| |#1| (-564)))) (|has| |#1| (-564)) (((|#1|) |has| |#1| (-370))) ((((-572)) . T)) @@ -3302,6 +3299,7 @@ ((((-572) (-779)) . T) ((|#3| (-779)) . T)) (((|#1|) . T)) (((|#1| |#2|) . T)) +((($) . T)) (((|#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) ((((-870)) . T)) ((($) |has| |#1| (-375))) @@ -3309,10 +3307,10 @@ ((($) |has| |#1| (-375))) (|has| |#2| (-828)) (|has| |#2| (-828)) -((((-415 (-572))) -3783 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) ((|#2|) |has| |#1| (-370)) (($) . T) ((|#1|) . T)) +((((-415 (-572))) -2813 (|has| |#1| (-38 (-415 (-572)))) (|has| |#1| (-370))) ((|#2|) |has| |#1| (-370)) (($) . T) ((|#1|) . T)) (((|#1|) . T) (((-572)) |has| |#1| (-1049 (-572))) (((-415 (-572))) |has| |#1| (-1049 (-415 (-572))))) -(((|#1|) . 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T)) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((((-544)) |has| |#2| (-622 (-544))) (((-901 (-386))) |has| |#2| (-622 (-901 (-386)))) (((-901 (-572))) |has| |#2| (-622 (-901 (-572))))) ((((-870)) . T)) ((((-870)) . T)) @@ -3401,7 +3399,7 @@ ((((-652 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-415 (-572)) |#1|)))) ((($) . T) (((-572)) . T) (((-1265 |#1| |#2| |#3| |#4|)) . T) (((-415 (-572))) . 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T) (($) -2813 (|has| |#2| (-174)) (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918)))) +((($) -2813 (|has| |#1| (-174)) (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((|#1|) . T) (((-415 (-572))) |has| |#1| (-38 (-415 (-572))))) (((|#1|) . T) (($) . T) (((-415 (-572))) . T)) (((|#1|) . T) (($) . T) (((-415 (-572))) . T)) (((|#1|) . T) (($) . T) (((-415 (-572))) . T)) @@ -3544,12 +3542,12 @@ (((|#1|) . 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T)) ((((-572)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-572)) . T)) -(-3783 (|has| |#1| (-356)) (|has| |#1| (-375))) +(-2813 (|has| |#1| (-356)) (|has| |#1| (-375))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-415 (-572))) . T) (($) . T) (((-572)) . T)) @@ -3832,7 +3830,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-544)) |has| |#1| (-622 (-544)))) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-858)) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-858)) (|has| |#1| (-1111)))) ((((-572) $) . T) (((-652 (-572)) $) . T)) ((($) . T) (((-415 (-572))) . T)) (|has| |#1| (-918)) @@ -3844,14 +3842,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-572)) . T)) ((((-1193)) . T)) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-564))) -(-3783 (|has| |#1| (-21)) (|has| |#1| (-856))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-564))) +(-2813 (|has| |#1| (-21)) (|has| |#1| (-856))) (((|#2|) . T)) -(-3783 (|has| |#1| (-21)) (|has| |#1| (-856))) +(-2813 (|has| |#1| (-21)) (|has| |#1| (-856))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-870)) -3783 (-12 (|has| |#1| (-621 (-870))) (|has| |#2| (-621 (-870)))) (-12 (|has| |#1| (-1111)) (|has| |#2| (-1111))))) +((((-870)) -2813 (-12 (|has| |#1| (-621 (-870))) (|has| |#2| (-621 (-870)))) (-12 (|has| |#1| (-1111)) (|has| |#2| (-1111))))) ((((-415 |#2|) |#3|) . T)) ((((-415 (-572))) . T) (($) . T)) (|has| |#1| (-38 (-415 (-572)))) @@ -3865,19 +3863,19 @@ (((|#1|) . T) (((-415 (-572))) . T) (((-572)) . T) (($) . T)) (((#0=(-572) #0#) . T)) ((($) . T) (((-415 (-572))) . T)) -(-3783 (|has| |#4| (-174)) (|has| |#4| (-734)) (|has| |#4| (-856)) (|has| |#4| (-1060))) -(-3783 (|has| |#3| (-174)) (|has| |#3| (-734)) (|has| |#3| (-856)) (|has| |#3| (-1060))) +(-2813 (|has| |#4| (-174)) (|has| |#4| (-734)) (|has| |#4| (-856)) (|has| |#4| (-1060))) +(-2813 (|has| |#3| (-174)) (|has| |#3| (-734)) (|has| |#3| (-856)) (|has| |#3| (-1060))) ((((-870)) . T) (((-1193)) . T)) (|has| |#4| (-801)) -(-3783 (|has| |#4| (-801)) (|has| |#4| (-856))) +(-2813 (|has| |#4| (-801)) (|has| |#4| (-856))) (|has| |#4| (-856)) (|has| |#3| (-801)) ((((-1193)) . T)) -(-3783 (|has| |#3| (-801)) (|has| |#3| (-856))) +(-2813 (|has| |#3| (-801)) (|has| |#3| (-856))) (|has| |#3| (-856)) ((((-572)) . T)) (((|#2|) . T)) -((((-1188)) -3783 (-12 (|has| (-1186 |#1| |#2| |#3|) (-909 (-1188))) (|has| |#1| (-370))) (-12 (|has| |#1| (-15 * (|#1| (-572) |#1|))) (|has| |#1| (-909 (-1188)))))) +((((-1188)) -2813 (-12 (|has| (-1186 |#1| |#2| |#3|) (-909 (-1188))) (|has| |#1| (-370))) (-12 (|has| |#1| (-15 * (|#1| (-572) |#1|))) (|has| |#1| (-909 (-1188)))))) ((((-1188)) -12 (|has| |#1| (-15 * (|#1| (-415 (-572)) |#1|))) (|has| |#1| (-909 (-1188))))) ((((-1188)) -12 (|has| |#1| (-15 * (|#1| (-779) |#1|))) (|has| |#1| (-909 (-1188))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3892,11 +3890,11 @@ ((((-1186 |#1| |#2| |#3|)) |has| |#1| (-370))) ((((-1151 |#1| |#2|)) . T)) ((((-1186 |#1| |#2| |#3|)) |has| |#1| (-370))) -(((|#2|) . T) (((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) -((((-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1033)) -(((|#2|) . T) (((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) ((($) . T)) ((((-870)) . T)) ((((-544)) |has| |#2| (-622 (-544))) (((-901 (-572))) |has| |#2| (-622 (-901 (-572)))) (((-901 (-386))) |has| |#2| (-622 (-901 (-386)))) (((-386)) . #0=(|has| |#2| (-1033))) (((-227)) . #0#)) @@ -3914,15 +3912,15 @@ ((((-1186 |#1| |#2| |#3|)) . T)) ((((-1186 |#1| |#2| |#3|)) . T) (((-1179 |#1| |#2| |#3|)) . T)) ((((-870)) . T)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) ((((-572) |#1|) . T)) ((((-1186 |#1| |#2| |#3|)) |has| |#1| (-370))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-370)) -(((|#3|) . T) ((|#2|) . T) (($) -3783 (|has| |#4| (-174)) (|has| |#4| (-856)) (|has| |#4| (-1060))) ((|#4|) -3783 (|has| |#4| (-174)) (|has| |#4| (-370)) (|has| |#4| (-1060)))) -(((|#2|) . T) (($) -3783 (|has| |#3| (-174)) (|has| |#3| (-856)) (|has| |#3| (-1060))) ((|#3|) -3783 (|has| |#3| (-174)) (|has| |#3| (-370)) (|has| |#3| (-1060)))) +(((|#3|) . T) ((|#2|) . T) (($) -2813 (|has| |#4| (-174)) (|has| |#4| (-856)) (|has| |#4| (-1060))) ((|#4|) -2813 (|has| |#4| (-174)) (|has| |#4| (-370)) (|has| |#4| (-1060)))) +(((|#2|) . T) (($) -2813 (|has| |#3| (-174)) (|has| |#3| (-856)) (|has| |#3| (-1060))) ((|#3|) -2813 (|has| |#3| (-174)) (|has| |#3| (-370)) (|has| |#3| (-1060)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -3936,7 +3934,7 @@ ((((-189)) . T) (((-870)) . T)) ((((-870)) . T)) (((|#1|) . T)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) ((((-130)) . T) (((-870)) . T)) ((((-572) |#1|) . T) (((-1246 (-572)) $) . T)) ((((-130)) . T)) @@ -3945,13 +3943,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-370)) (|has| |#2| (-292 |#2| |#2|))) (($ $) . T) (((-572) |#1|) . T)) ((($ $) . T) (((-415 (-572)) |#1|) . T)) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-918))) -(-3783 (|has| |#1| (-858)) (|has| |#1| (-1111))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-460)) (|has| |#1| (-918))) +(-2813 (|has| |#1| (-858)) (|has| |#1| (-1111))) ((((-870)) . T)) ((((-870)) . T)) ((((-870)) . T)) (((|#1| (-539 |#2|)) . T)) -((((-2 (|:| -1640 (-1188)) (|:| -3763 (-52)))) . T)) +((((-2 (|:| -3690 (-1188)) (|:| -1907 (-52)))) . T)) ((((-572) (-130)) . T)) (((|#1| (-572)) . T)) (((|#1| (-415 (-572))) . T)) @@ -3966,8 +3964,8 @@ ((((-1193)) . T)) ((((-870)) . T) (((-1193)) . T)) ((((-870)) . T) (((-1193)) . T)) -(-3783 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) -(-3783 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) +(-2813 (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) +(-2813 (|has| |#1| (-460)) (|has| |#1| (-564)) (|has| |#1| (-918))) ((($) . T)) (((|#2| (-539 (-872 |#1|))) . T)) ((((-1193)) . T)) @@ -3982,13 +3980,13 @@ ((((-1193)) . T)) ((((-870)) . T) (((-1193)) . T)) ((((-1193)) . T)) -((((-870)) -3783 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) +((((-870)) -2813 (|has| |#1| (-621 (-870))) (|has| |#1| (-1111)))) (((|#1|) . T)) (((|#2| (-779)) . T)) (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) ((((-415 |#2|)) . T)) -((((-2 (|:| -1640 |#1|) (|:| -3763 |#2|))) . T)) +((((-2 (|:| -3690 |#1|) (|:| -1907 |#2|))) . T)) (|has| |#1| (-564)) (|has| |#1| (-564)) ((($) . T) ((|#2|) . T)) @@ -3999,14 +3997,14 @@ ((((-572)) . T) (($) . T)) (((|#2| $) |has| |#2| (-292 |#2| |#2|))) (((|#1| (-652 |#1|)) |has| |#1| (-856))) -(-3783 (|has| |#1| (-235 |#1|)) (|has| |#1| (-356))) -(-3783 (|has| |#1| (-370)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-237)) (|has| |#1| (-356))) +(-2813 (|has| |#1| (-370)) (|has| |#1| (-356))) ((((-1275 |#1|)) . T) (((-572)) . T) ((|#2|) . T) (((-415 (-572))) |has| |#2| (-1049 (-415 (-572))))) (|has| |#1| (-1111)) (((|#1|) . T)) -((((-1275 |#1|)) . T) (((-572)) . T) (($) -3783 (|has| |#2| (-370)) (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) (((-1093)) . T) ((|#2|) . T) (((-415 (-572))) -3783 (|has| |#2| (-38 (-415 (-572)))) (|has| |#2| (-1049 (-415 (-572)))))) +((((-1275 |#1|)) . T) (((-572)) . T) (($) -2813 (|has| |#2| (-370)) (|has| |#2| (-460)) (|has| |#2| (-564)) (|has| |#2| (-918))) (((-1093)) . T) ((|#2|) . T) (((-415 (-572))) -2813 (|has| |#2| (-38 (-415 (-572)))) (|has| |#2| (-1049 (-415 (-572)))))) ((((-415 (-572))) . T) (($) . T)) -((((-1010 |#1|)) . T) ((|#1|) . T) (((-572)) -3783 (|has| (-1010 |#1|) (-1049 (-572))) (|has| |#1| (-1049 (-572)))) (((-415 (-572))) -3783 (|has| (-1010 |#1|) (-1049 (-415 (-572)))) (|has| |#1| (-1049 (-415 (-572)))))) +((((-1010 |#1|)) . T) ((|#1|) . T) (((-572)) -2813 (|has| (-1010 |#1|) (-1049 (-572))) (|has| |#1| (-1049 (-572)))) (((-415 (-572))) -2813 (|has| (-1010 |#1|) (-1049 (-415 (-572)))) (|has| |#1| (-1049 (-415 (-572)))))) ((((-919 |#1|)) . T) (((-415 (-572))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) (((|#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111)))) @@ -4023,11 +4021,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1151 |#1| |#2|) #0#) |has| (-1151 |#1| |#2|) (-315 (-1151 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((#0=(-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) #0#) |has| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (-315 (-2 (|:| -1640 |#1|) (|:| -3763 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((#0=(-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) #0#) |has| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (-315 (-2 (|:| -3690 |#1|) (|:| -1907 |#2|))))) (|has| |#1| (-292 |#1| |#1|)) (((#0=(-117 |#1|)) |has| #0# (-315 #0#))) ((($ $) . T)) -(-3783 (|has| |#1| (-858)) (|has| |#1| (-1111))) +(-2813 (|has| |#1| (-858)) (|has| |#1| (-1111))) ((($ $) . T) ((#0=(-872 |#1|) $) . T) ((#0# |#2|) . T)) -((($ $) . T) ((|#2| $) |has| |#1| (-235 |#1|)) ((|#2| |#1|) |has| |#1| (-235 |#1|)) ((|#3| |#1|) . T) ((|#3| $) . 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((-739 . -47) 190063) ((-631 . -38) 190050) ((-362 . -296) T) ((-359 . -296) T) ((-351 . -296) T) ((-269 . -296) 189981) ((-251 . -296) 189912) ((-1047 . -621) 189878) ((-1035 . -102) T) ((-1030 . -621) 189844) ((-634 . -498) 189825) ((-421 . -734) T) ((-118 . -38) 189770) ((-491 . -498) 189751) ((-634 . -621) 189717) ((-421 . -481) T) ((-220 . -498) 189698) ((-491 . -621) 189664) ((-361 . -102) T) ((-220 . -621) 189630) ((-1223 . -1069) T) ((-350 . -654) 189560) ((-719 . -1069) T) ((-1186 . -47) 189537) ((-1185 . -47) 189507) ((-1179 . -47) 189484) ((-129 . -294) 189459) ((-1046 . -152) 189405) ((-919 . -296) T) ((-1137 . -47) 189377) ((-702 . -315) NIL) ((-523 . -621) 189359) ((-518 . -621) 189341) ((-516 . -621) 189323) ((-333 . -1111) 189273) ((-720 . -460) 189204) ((-48 . -102) T) ((-1263 . -292) 189162) ((-1242 . -292) 189062) ((-652 . -674) 189046) ((-652 . -659) 189030) ((-346 . -21) T) ((-346 . -25) T) ((-40 . -356) NIL) ((-176 . -21) T) ((-176 . -25) T) ((-652 . -380) 189014) ((-613 . -498) 188996) ((-610 . -292) 188948) ((-613 . -621) 188915) ((-396 . -102) T) ((-1131 . -144) T) ((-127 . -621) 188847) ((-882 . -1111) T) ((-666 . -419) 188831) ((-722 . -621) 188813) ((-253 . -621) 188780) ((-189 . -621) 188762) ((-163 . -621) 188744) ((-158 . -621) 188726) ((-1294 . -734) T) ((-1113 . -34) T) ((-879 . -803) NIL) ((-879 . -800) NIL) ((-866 . -858) T) ((-739 . -895) NIL) ((-1303 . -132) T) ((-388 . -132) T) ((-901 . -624) 188694) ((-913 . -102) T) ((-739 . -1049) 188570) ((-1186 . -1229) T) ((-539 . -132) T) ((-1185 . -1229) T) ((-1098 . -419) 188554) ((-1011 . -497) 188538) ((-118 . -408) 188515) ((-1179 . -1229) T) ((-790 . -419) 188499) ((-788 . -419) 188483) ((-952 . -34) T) ((-702 . -1163) NIL) ((-256 . -656) 188318) ((-255 . -656) 188140) ((-825 . -929) 188119) ((-462 . -419) 188103) ((-610 . -19) 188087) ((-1157 . -1222) 188056) ((-1179 . -895) NIL) ((-1179 . -893) 188008) ((-610 . -612) 187985) ((-1215 . -621) 187917) ((-1187 . -621) 187899) ((-62 . -403) T) ((-1185 . -1049) 187834) ((-1179 . -1049) 187800) ((-702 . -38) 187750) ((-40 . -654) 187680) ((-482 . -292) 187638) ((-1235 . -621) 187620) ((-739 . -384) 187604) ((-846 . -621) 187586) ((-666 . -1069) T) ((-1263 . -1013) 187552) ((-1242 . -1013) 187518) ((-254 . -1229) T) ((-1099 . -624) 187502) ((-1074 . -1205) 187477) ((-1087 . -624) 187454) ((-880 . -622) 187261) ((-880 . -621) 187243) ((-709 . -235) 187230) ((-1201 . -497) 187167) ((-426 . -1033) 187145) ((-48 . -315) 187132) ((-1074 . -107) 187078) ((-487 . -497) 187015) ((-528 . -1229) T) ((-1179 . -345) 186967) ((-1152 . -497) 186938) ((-1179 . -384) 186890) ((-1098 . -1069) T) ((-445 . -102) T) ((-185 . -1111) T) ((-256 . -34) T) ((-255 . -34) T) ((-790 . -1069) T) ((-788 . -1069) T) ((-739 . -909) 186867) ((-462 . -1069) T) ((-59 . -497) 186851) ((-1045 . -1067) 186825) ((-527 . -497) 186809) ((-524 . -497) 186793) ((-505 . -497) 186777) ((-504 . -497) 186761) ((-249 . -522) 186694) ((-1045 . -111) 186661) ((-1186 . -909) 186574) ((-1185 . -909) 186480) ((-1179 . -909) 186313) ((-1137 . -909) 186297) ((-678 . -1123) T) ((-361 . -1163) T) ((-653 . -93) T) ((-328 . -1067) 186279) ((-256 . -799) 186258) ((-256 . -802) 186209) ((-31 . -498) 186190) ((-256 . -801) 186169) ((-255 . -799) 186148) ((-255 . -802) 186099) ((-255 . -801) 186078) ((-31 . -621) 186044) ((-50 . -1069) T) ((-256 . -734) 185954) ((-255 . -734) 185864) ((-1223 . -1111) T) ((-678 . -23) T) ((-589 . -1069) T) ((-526 . -1069) T) ((-386 . -1067) 185829) ((-328 . -111) 185804) ((-73 . -390) T) ((-73 . -403) T) ((-1035 . -38) 185741) ((-702 . -408) 185723) ((-99 . -102) T) ((-719 . -1111) T) ((-1308 . -1062) 185710) ((-1014 . -146) 185682) ((-1014 . -148) 185654) ((-878 . -654) 185626) ((-386 . -111) 185582) ((-325 . -1233) 185561) ((-482 . -1013) 185527) ((-361 . -38) 185492) ((-40 . -377) 185464) ((-881 . -621) 185336) ((-128 . -126) 185320) ((-122 . -126) 185304) ((-844 . -1067) 185274) ((-841 . -21) 185226) ((-835 . -1067) 185210) ((-841 . -25) 185162) ((-325 . -564) 185113) ((-525 . -624) 185094) ((-572 . -836) T) ((-244 . -1229) T) ((-1045 . -624) 185063) ((-844 . -111) 185028) ((-835 . -111) 185007) ((-1263 . -621) 184989) ((-1242 . -621) 184971) ((-1242 . -622) 184642) ((-1184 . -918) 184621) ((-1136 . -918) 184600) ((-48 . -38) 184565) ((-1301 . -1123) T) ((-544 . -292) 184521) ((-610 . -621) 184433) ((-610 . -622) 184394) ((-1299 . -1123) T) ((-368 . -624) 184378) ((-328 . -624) 184362) ((-244 . -1049) 184189) ((-1184 . -656) 184114) ((-1136 . -656) 184039) ((-862 . -656) 184013) ((-726 . -621) 183995) ((-554 . -375) T) ((-1301 . -23) T) ((-1299 . -23) T) ((-499 . -1111) T) ((-386 . -624) 183945) ((-386 . -626) 183927) ((-1045 . -1060) T) ((-873 . -102) T) ((-1201 . -292) 183906) ((-171 . -375) 183857) ((-1015 . -1229) T) ((-844 . -624) 183811) ((-835 . -624) 183766) ((-44 . -23) T) ((-487 . -292) 183745) ((-594 . -1111) T) ((-1157 . -1120) 183714) ((-1115 . -1114) 183666) ((-398 . -21) T) ((-398 . -25) T) ((-153 . -1123) T) ((-1308 . -102) T) ((-1015 . -893) 183648) ((-1015 . -895) 183630) ((-1223 . -725) 183527) ((-631 . -233) 183511) ((-629 . -21) T) ((-295 . -564) T) ((-629 . -25) T) ((-1209 . -1111) T) ((-719 . -725) 183476) ((-244 . -384) 183445) ((-1015 . -1049) 183405) ((-386 . -1060) T) ((-225 . -1069) T) ((-118 . -233) 183382) ((-59 . -292) 183334) ((-153 . -23) T) ((-524 . -292) 183286) ((-333 . -522) 183219) ((-504 . -292) 183171) ((-386 . -247) T) ((-386 . -237) T) ((-844 . -1060) T) ((-835 . -1060) T) ((-720 . -958) 183140) ((-709 . -858) T) ((-482 . -621) 183122) ((-1265 . -1062) 183027) ((-588 . -654) 182999) ((-572 . -654) 182971) ((-503 . -654) 182921) ((-835 . -237) 182895) ((-135 . -858) T) ((-1265 . -648) 182787) ((-666 . -1111) T) ((-1201 . -612) 182766) ((-558 . -1205) 182745) ((-343 . -1111) T) ((-325 . -370) 182724) ((-415 . -148) 182703) ((-415 . -146) 182682) ((-973 . -1123) 182581) ((-244 . -909) 182513) ((-823 . -1123) 182423) ((-662 . -860) 182407) ((-487 . -612) 182386) ((-558 . -107) 182336) ((-1015 . -384) 182318) ((-1015 . -345) 182300) ((-97 . -1111) T) ((-973 . -23) 182111) ((-485 . -21) T) ((-485 . -25) T) ((-823 . -23) 181981) ((-1188 . -621) 181963) ((-59 . -19) 181947) ((-1188 . -622) 181869) ((-1184 . -734) T) ((-1136 . -734) T) ((-524 . -19) 181853) ((-504 . -19) 181837) ((-59 . -612) 181814) ((-1098 . -1111) T) ((-910 . -102) 181792) ((-862 . -734) T) ((-790 . -1111) T) ((-524 . -612) 181769) ((-504 . -612) 181746) ((-788 . -1111) T) ((-788 . -1076) 181713) ((-469 . -1111) T) ((-462 . -1111) T) ((-594 . -725) 181688) ((-657 . -1111) T) ((-1271 . -47) 181665) ((-1265 . -102) T) ((-1264 . -47) 181635) ((-1243 . -47) 181612) ((-1223 . -174) 181563) ((-1185 . -313) 181542) ((-1179 . -313) 181521) ((-1107 . -624) 181502) ((-1101 . -624) 181483) ((-1091 . -564) 181434) ((-1015 . -909) NIL) ((-1091 . -1233) 181385) ((-678 . -132) T) ((-635 . -1123) T) ((-1084 . -624) 181366) ((-1077 . -624) 181347) ((-1047 . -624) 181328) ((-1030 . -624) 181309) ((-707 . -654) 181259) ((-280 . -1111) T) ((-85 . -449) T) ((-85 . -403) T) ((-722 . -1067) 181229) ((-719 . -174) T) ((-50 . -1111) T) ((-603 . -47) 181206) ((-227 . -656) 181171) ((-589 . -1111) T) ((-526 . -1111) T) ((-495 . -828) T) ((-495 . -929) T) ((-366 . -1233) T) ((-360 . -1233) T) ((-352 . -1233) T) ((-325 . -1123) T) ((-322 . -1062) 181081) ((-319 . -1062) 181010) ((-108 . -1233) T) ((-634 . -624) 180991) ((-366 . -564) T) ((-219 . -929) T) ((-219 . -828) T) ((-322 . -648) 180901) ((-319 . -648) 180830) ((-360 . -564) T) ((-352 . -564) T) ((-491 . -624) 180811) ((-108 . -564) T) ((-666 . -725) 180781) ((-1179 . -1033) NIL) ((-220 . -624) 180762) ((-325 . -23) T) ((-67 . -1229) T) ((-1011 . -621) 180694) ((-702 . -233) 180676) ((-722 . -111) 180641) ((-652 . -34) T) ((-249 . -497) 180625) ((-1308 . -1163) T) ((-1303 . -21) T) ((-1303 . -25) T) ((-1113 . -1109) 180609) ((-173 . -1111) T) ((-1301 . -132) T) ((-1299 . -132) T) ((-1292 . -102) T) ((-1275 . -621) 180575) ((-1271 . -1229) T) ((-961 . -918) 180554) ((-1264 . -1229) T) ((-1264 . -1049) 180489) ((-1243 . -1229) T) ((-523 . -624) 180473) ((-1243 . -895) NIL) ((-1243 . -893) 180425) ((-1243 . -1049) 180391) ((-489 . -918) 180370) ((-1223 . -522) 180337) ((-1201 . -622) NIL) ((-1098 . -725) 180186) ((-1073 . -656) 180173) ((-961 . -656) 180098) ((-605 . -498) 180079) ((-593 . -498) 180060) ((-790 . -725) 179889) ((-605 . -621) 179855) ((-593 . -621) 179821) ((-544 . -621) 179803) ((-544 . -622) 179784) ((-788 . -725) 179633) ((-1088 . -102) T) ((-388 . -25) T) ((-631 . -654) 179605) ((-388 . -21) T) ((-489 . -656) 179530) ((-469 . -725) 179501) ((-462 . -725) 179350) ((-998 . -102) T) ((-1201 . -621) 179332) ((-1153 . -1134) 179277) ((-1057 . -1222) 179206) ((-745 . -102) T) ((-118 . -654) 179136) ((-613 . -624) 179118) ((-910 . -315) 179056) ((-884 . -93) T) ((-539 . -25) T) ((-722 . -624) 179010) ((-689 . -93) T) ((-684 . -93) T) ((-653 . -498) 178991) ((-142 . -102) T) ((-44 . -132) T) ((-672 . -621) 178973) ((-603 . -1229) T) ((-350 . -1069) T) ((-295 . -1123) T) ((-653 . -621) 178926) ((-486 . -93) T) ((-362 . -621) 178908) ((-359 . -621) 178890) ((-351 . -621) 178872) ((-269 . -622) 178620) ((-269 . -621) 178602) ((-251 . -621) 178584) ((-251 . -622) 178445) ((-134 . -93) T) ((-139 . -93) T) ((-138 . -93) T) ((-1152 . -621) 178427) ((-1131 . -648) 178414) ((-1131 . -1062) 178401) ((-827 . -734) T) ((-827 . -865) T) ((-610 . -294) 178378) ((-589 . -725) 178343) ((-487 . -622) NIL) ((-487 . -621) 178325) ((-526 . -725) 178270) ((-322 . -102) T) ((-319 . -102) T) ((-295 . -23) T) ((-153 . -132) T) ((-919 . -621) 178252) ((-919 . -622) 178234) ((-394 . -734) T) ((-880 . -1067) 178186) ((-880 . -111) 178124) ((-722 . -1060) T) ((-720 . -1255) 178108) ((-702 . -356) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-527 . -621) 178040) ((-386 . -803) T) ((-225 . -1111) T) ((-169 . -1229) T) ((-386 . -800) T) ((-227 . -802) T) ((-227 . -799) T) ((-59 . -622) 178001) ((-59 . -621) 177913) ((-227 . -734) T) ((-524 . -622) 177874) ((-524 . -621) 177786) ((-505 . -621) 177718) ((-504 . -622) 177679) ((-504 . -621) 177591) ((-1091 . -370) 177542) ((-40 . -419) 177519) ((-77 . -1229) T) ((-879 . -918) NIL) ((-366 . -335) 177503) ((-366 . -370) T) ((-360 . -335) 177487) ((-360 . -370) T) ((-352 . -335) 177471) ((-352 . -370) T) ((-322 . -290) 177450) ((-108 . -370) T) ((-70 . -1229) T) ((-1243 . -345) 177402) ((-879 . -656) 177347) ((-1243 . -384) 177299) ((-973 . -132) 177154) ((-823 . -132) 177024) ((-967 . -659) 177008) ((-1098 . -174) 176919) ((-967 . -380) 176903) ((-1073 . -802) T) ((-1073 . -799) T) ((-880 . -624) 176801) ((-790 . -174) 176692) ((-788 . -174) 176603) ((-824 . -47) 176565) ((-1073 . -734) T) ((-333 . -497) 176549) ((-961 . -734) T) ((-1292 . -315) 176487) ((-462 . -174) 176398) ((-249 . -292) 176350) ((-1271 . -909) 176263) ((-1264 . -909) 176169) ((-1263 . -1067) 176004) ((-489 . -734) T) ((-1243 . -909) 175837) ((-1242 . -1067) 175645) ((-1223 . -296) 175624) ((-1198 . -1229) T) ((-1195 . -375) T) ((-1194 . -375) T) ((-1157 . -152) 175608) ((-1131 . -102) T) ((-1129 . -1111) T) ((-1091 . -23) T) ((-1091 . -1123) T) ((-1086 . -102) T) ((-1068 . -621) 175575) ((-936 . -964) T) ((-745 . -315) 175513) ((-75 . -1229) T) ((-672 . -389) 175485) ((-171 . -918) 175438) ((-30 . -964) T) ((-112 . -852) T) ((-1 . -621) 175420) ((-1014 . -417) 175392) ((-129 . -659) 175374) ((-50 . -628) 175358) ((-702 . -654) 175293) ((-603 . -909) 175206) ((-446 . -102) T) ((-129 . -380) 175188) ((-142 . -315) NIL) ((-880 . -1060) T) ((-841 . -858) 175167) ((-81 . -1229) T) ((-719 . -296) T) ((-40 . -1069) T) ((-589 . -174) T) ((-526 . -174) T) ((-519 . -621) 175149) ((-171 . -656) 175059) ((-515 . -621) 175041) ((-358 . -148) 175023) ((-358 . -146) T) ((-366 . -1123) T) ((-360 . -1123) T) ((-352 . -1123) T) ((-1015 . -313) T) ((-923 . -313) T) ((-880 . -247) T) ((-108 . -1123) T) ((-880 . -237) 174997) ((-1263 . -111) 174818) ((-1242 . -111) 174607) ((-249 . -1267) 174591) ((-572 . -856) T) ((-366 . -23) T) ((-361 . -356) T) ((-322 . -315) 174578) ((-319 . -315) 174519) ((-360 . -23) T) ((-325 . -132) T) ((-352 . -23) T) ((-1015 . -1033) T) ((-31 . -624) 174500) ((-108 . -23) T) ((-662 . -1062) 174484) ((-249 . -612) 174461) ((-339 . -1111) T) ((-662 . -648) 174431) ((-1265 . -38) 174323) ((-1252 . -918) 174302) ((-112 . -1111) T) ((-824 . -1229) 174276) ((-1046 . -102) T) ((-1252 . -656) 174201) ((-879 . -802) NIL) ((-863 . -656) 174175) ((-879 . -799) NIL) ((-824 . -895) NIL) ((-879 . -734) T) ((-1098 . -522) 174038) ((-790 . -522) 173985) ((-788 . -522) 173937) ((-579 . -656) 173924) ((-824 . -1049) 173752) ((-462 . -522) 173695) ((-396 . -397) T) ((-1263 . -624) 173508) ((-1242 . -624) 173256) ((-60 . -1229) T) ((-629 . -858) 173235) ((-508 . -669) T) ((-1157 . -987) 173204) ((-1035 . -654) 173141) ((-1014 . -460) T) ((-707 . -856) T) ((-518 . -800) T) ((-482 . -1067) 172976) ((-508 . -113) T) ((-350 . -1111) T) ((-319 . -1163) NIL) ((-295 . -132) T) ((-402 . -1111) T) ((-878 . -1069) T) ((-702 . -377) 172943) ((-361 . -654) 172873) ((-225 . -628) 172850) ((-333 . -292) 172802) ((-482 . -111) 172623) ((-1263 . -1060) T) ((-1242 . -1060) T) ((-824 . -384) 172607) ((-171 . -734) T) ((-662 . -102) T) ((-1263 . -247) 172586) ((-1263 . -237) 172538) ((-1242 . -237) 172438) ((-1242 . -247) 172417) ((-1014 . -410) NIL) ((-678 . -647) 172365) ((-322 . -38) 172275) ((-319 . -38) 172204) ((-69 . -621) 172186) ((-325 . -501) 172152) ((-48 . -654) 172102) ((-1201 . -294) 172081) ((-1237 . -858) T) ((-1124 . -1123) 171991) ((-83 . -1229) T) ((-61 . -621) 171973) ((-487 . -294) 171952) ((-1294 . -1049) 171929) ((-1176 . -1111) T) ((-1124 . -23) 171799) ((-824 . -909) 171735) ((-1252 . -734) T) ((-1113 . -1229) T) ((-482 . -624) 171561) ((-1098 . -296) 171492) ((-975 . -1111) T) ((-902 . -102) T) ((-790 . -296) 171403) ((-333 . -19) 171387) ((-59 . -294) 171364) ((-788 . -296) 171295) ((-863 . -734) T) ((-118 . -856) NIL) ((-524 . -294) 171272) ((-333 . -612) 171249) ((-504 . -294) 171226) ((-462 . -296) 171157) ((-1046 . -315) 171008) ((-884 . -498) 170989) ((-884 . -621) 170955) ((-689 . -498) 170936) ((-579 . -734) T) ((-684 . -498) 170917) ((-689 . -621) 170867) ((-684 . -621) 170833) ((-670 . -621) 170815) ((-486 . -498) 170796) ((-486 . -621) 170762) ((-249 . -622) 170723) ((-249 . -498) 170700) ((-139 . -498) 170681) ((-138 . -498) 170662) ((-134 . -498) 170643) ((-249 . -621) 170535) ((-215 . -102) T) ((-139 . -621) 170501) ((-138 . -621) 170467) ((-134 . -621) 170433) ((-1158 . -34) T) ((-952 . -1229) T) ((-350 . -725) 170378) ((-678 . -25) T) ((-678 . -21) T) ((-1188 . -624) 170359) ((-482 . -1060) T) ((-643 . -425) 170324) ((-615 . -425) 170289) ((-1131 . -1163) T) ((-720 . -1062) 170112) ((-589 . -296) T) ((-526 . -296) T) ((-1264 . -313) 170091) ((-482 . -237) 170043) ((-482 . -247) 170022) ((-1243 . -313) 170001) ((-720 . -648) 169830) ((-1243 . -1033) NIL) ((-1091 . -132) T) ((-880 . -803) 169809) ((-145 . -102) T) ((-40 . -1111) T) ((-880 . -800) 169788) ((-652 . -1021) 169772) ((-588 . -1069) T) ((-572 . -1069) T) ((-503 . -1069) T) ((-415 . -460) T) ((-366 . -132) T) ((-322 . -408) 169756) ((-319 . -408) 169717) ((-360 . -132) T) ((-352 . -132) T) ((-1193 . -1111) T) ((-1131 . -38) 169704) ((-1105 . -621) 169671) ((-108 . -132) T) ((-963 . -1111) T) ((-930 . -1111) T) ((-779 . -1111) T) ((-680 . -1111) T) ((-709 . -148) T) ((-117 . -148) T) ((-1301 . -21) T) ((-1301 . -25) T) ((-1299 . -21) T) ((-1299 . -25) T) ((-672 . -1067) 169655) ((-539 . -858) T) ((-508 . -858) T) ((-362 . -1067) 169607) ((-359 . -1067) 169559) ((-351 . -1067) 169511) ((-256 . -1229) T) ((-255 . -1229) T) ((-269 . -1067) 169354) ((-251 . -1067) 169197) ((-672 . -111) 169176) ((-555 . -852) T) ((-362 . -111) 169114) ((-359 . -111) 169052) ((-351 . -111) 168990) ((-269 . -111) 168819) ((-251 . -111) 168648) ((-825 . -1233) 168627) ((-631 . -419) 168611) ((-44 . -21) T) ((-44 . -25) T) ((-823 . -647) 168517) ((-825 . -564) 168496) ((-256 . -1049) 168323) ((-255 . -1049) 168150) ((-127 . -120) 168134) ((-919 . -1067) 168099) ((-720 . -102) T) ((-707 . -1069) T) ((-605 . -624) 168080) ((-593 . -624) 168061) ((-544 . -626) 167964) ((-350 . -174) T) ((-88 . -621) 167946) ((-153 . -21) T) ((-153 . -25) T) ((-919 . -111) 167902) ((-40 . -725) 167847) ((-878 . -1111) T) ((-672 . -624) 167824) ((-653 . -624) 167805) ((-362 . -624) 167742) ((-359 . -624) 167679) ((-555 . -1111) T) ((-351 . -624) 167616) ((-333 . -622) 167577) ((-333 . -621) 167489) ((-269 . -624) 167242) ((-251 . -624) 167027) ((-1242 . -800) 166980) ((-1242 . -803) 166933) ((-256 . -384) 166902) ((-255 . -384) 166871) ((-662 . -38) 166841) ((-616 . -34) T) ((-490 . -1123) 166751) ((-483 . -34) T) ((-1124 . -132) 166621) ((-973 . -25) 166432) ((-919 . -624) 166382) ((-882 . -621) 166364) ((-973 . -21) 166319) ((-823 . -21) 166229) ((-823 . -25) 166080) ((-1235 . -375) T) ((-631 . -1069) T) ((-1190 . -564) 166059) ((-1184 . -47) 166036) ((-362 . -1060) T) ((-359 . -1060) T) ((-490 . -23) 165906) ((-351 . -1060) T) ((-269 . -1060) T) ((-251 . -1060) T) ((-1136 . -47) 165878) ((-118 . -1069) T) ((-1045 . -656) 165852) ((-967 . -34) T) ((-362 . -237) 165831) ((-362 . -247) T) ((-359 . -237) 165810) ((-359 . -247) T) ((-351 . -237) 165789) ((-351 . -247) T) ((-269 . -332) 165761) ((-251 . -332) 165718) ((-269 . -237) 165692) ((-1168 . -152) 165676) ((-256 . -909) 165608) ((-255 . -909) 165540) ((-1093 . -858) T) ((-422 . -1123) T) ((-1065 . -23) T) ((-919 . -1060) T) ((-328 . -656) 165522) ((-1035 . -856) T) ((-678 . -235) 165490) ((-1223 . -1013) 165456) ((-1185 . -929) 165435) ((-1179 . -929) 165414) ((-1179 . -828) NIL) ((-1010 . -1062) 165310) ((-976 . -1229) T) ((-919 . -247) T) ((-825 . -370) 165289) ((-392 . -23) T) ((-128 . -1111) 165267) ((-122 . -1111) 165245) ((-919 . -237) T) ((-129 . -34) T) ((-386 . -656) 165210) ((-1010 . -648) 165158) ((-878 . -725) 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164170) ((-1136 . -384) 164154) ((-1035 . -419) 164116) ((-142 . -231) 164098) ((-386 . -802) T) ((-386 . -799) T) ((-878 . -174) T) ((-386 . -734) T) ((-719 . -621) 164080) ((-720 . -38) 163909) ((-1279 . -1277) 163893) ((-358 . -410) T) ((-1279 . -1111) 163843) ((-1202 . -1111) T) ((-588 . -725) 163830) ((-572 . -725) 163817) ((-503 . -725) 163782) ((-1265 . -654) 163672) ((-322 . -637) 163651) ((-844 . -734) T) ((-835 . -734) T) ((-652 . -1229) T) ((-1091 . -647) 163599) ((-1184 . -909) 163542) ((-1136 . -909) 163526) ((-823 . -235) 163467) ((-670 . -1067) 163451) ((-108 . -647) 163433) ((-490 . -132) 163303) ((-1190 . -1123) T) ((-961 . -47) 163272) ((-631 . -1111) T) ((-670 . -111) 163251) ((-499 . -621) 163217) ((-333 . -294) 163194) ((-489 . -47) 163151) ((-1190 . -23) T) ((-118 . -1111) T) ((-103 . -102) 163129) ((-1291 . -1123) T) ((-556 . -858) T) ((-227 . -1229) T) ((-1065 . -132) T) ((-1035 . -1069) T) ((-827 . -1049) 163113) ((-1291 . -23) T) ((-1014 . -732) 163085) 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T) ((-1065 . -21) T) ((-719 . -1060) T) ((-392 . -21) T) ((-392 . -25) T) ((-702 . -522) NIL) ((-1035 . -174) T) ((-719 . -247) T) ((-1073 . -553) T) ((-720 . -654) 155828) ((-514 . -102) T) ((-510 . -102) T) ((-361 . -174) T) ((-350 . -621) 155810) ((-415 . -1062) 155762) ((-402 . -621) 155744) ((-1131 . -856) T) ((-482 . -734) T) ((-901 . -1049) 155712) ((-415 . -648) 155664) ((-108 . -858) T) ((-666 . -1067) 155648) ((-495 . -132) T) ((-1265 . -1069) T) ((-219 . -132) T) ((-1168 . -102) 155626) ((-99 . -1111) T) ((-249 . -674) 155610) ((-249 . -659) 155594) ((-666 . -111) 155573) ((-594 . -624) 155557) ((-322 . -419) 155541) ((-249 . -380) 155525) ((-1171 . -239) 155472) ((-1010 . -233) 155456) ((-74 . -1229) T) ((-48 . -174) T) ((-709 . -395) T) ((-709 . -144) T) ((-1302 . -102) T) ((-1209 . -624) 155438) ((-1098 . -1067) 155281) ((-1087 . -1229) T) ((-269 . -918) 155260) ((-251 . -918) 155239) ((-790 . -1067) 155062) ((-788 . -1067) 154905) ((-616 . -1229) T) ((-1176 . -621) 154887) ((-1098 . -111) 154716) ((-1057 . -102) T) ((-483 . -1229) T) ((-469 . -1067) 154687) ((-462 . -1067) 154530) ((-672 . -656) 154514) ((-879 . -313) T) ((-790 . -111) 154323) ((-788 . -111) 154152) ((-362 . -656) 154104) ((-359 . -656) 154056) ((-351 . -656) 154008) ((-269 . -656) 153933) ((-251 . -656) 153858) ((-1170 . -858) T) ((-1099 . -1049) 153842) ((-469 . -111) 153803) ((-462 . -111) 153632) ((-1087 . -1049) 153609) ((-1011 . -34) T) ((-975 . -621) 153591) ((-967 . -1229) T) ((-127 . -1021) 153575) ((-972 . -1123) T) ((-879 . -1033) NIL) ((-743 . -1123) T) ((-723 . -1123) T) ((-666 . -624) 153493) ((-1279 . -497) 153477) ((-1153 . -38) 153437) ((-972 . -23) T) ((-919 . -656) 153402) ((-873 . -1111) T) ((-851 . -102) T) ((-825 . -21) T) ((-643 . -1062) 153386) ((-615 . -1062) 153370) ((-825 . -25) T) ((-743 . -23) T) ((-723 . -23) T) ((-643 . -648) 153354) ((-110 . -669) T) ((-615 . -648) 153338) ((-589 . -1067) 153303) ((-526 . -1067) 153248) ((-229 . -57) 153206) ((-461 . -23) T) ((-415 . -102) T) ((-268 . -102) T) ((-110 . -113) T) ((-702 . -296) T) ((-874 . -38) 153176) ((-589 . -111) 153132) ((-526 . -111) 153061) ((-1098 . -624) 152797) ((-426 . -1123) T) ((-322 . -1069) 152687) ((-319 . -1069) T) ((-129 . -1229) T) ((-790 . -624) 152435) ((-788 . -624) 152201) ((-666 . -1060) T) ((-1308 . -1111) T) ((-462 . -624) 151986) ((-171 . -313) 151917) ((-426 . -23) T) ((-40 . -621) 151899) ((-40 . -622) 151883) ((-108 . -1003) 151865) ((-117 . -877) 151849) ((-657 . -624) 151833) ((-48 . -522) 151799) ((-1215 . -1021) 151783) ((-1193 . -621) 151750) ((-1201 . -34) T) ((-963 . -621) 151716) ((-930 . -621) 151698) ((-1124 . -858) 151649) ((-779 . -621) 151631) ((-680 . -621) 151613) ((-1168 . -315) 151551) ((-487 . -34) T) ((-1103 . -1229) T) ((-485 . -460) T) ((-1152 . -34) T) ((-1098 . -1060) T) ((-50 . -624) 151520) ((-790 . -1060) T) ((-788 . -1060) T) ((-655 . -239) 151504) ((-640 . -239) 151450) ((-589 . -624) 151400) ((-526 . -624) 151330) ((-490 . -235) 151271) ((-1252 . -313) 151250) ((-1098 . -332) 151211) ((-462 . -1060) T) ((-1190 . -21) T) ((-1098 . -237) 151185) ((-790 . -332) 151162) ((-790 . -237) T) ((-788 . -332) 151134) ((-739 . -1233) 151113) ((-333 . -659) 151097) ((-1190 . -25) T) ((-59 . -34) T) ((-527 . -34) T) ((-524 . -34) T) ((-462 . -332) 151076) ((-333 . -380) 151060) ((-505 . -34) T) ((-504 . -34) T) ((-1014 . -1163) NIL) ((-739 . -564) 150991) ((-643 . -102) T) ((-615 . -102) T) ((-362 . -734) T) ((-359 . -734) T) ((-351 . -734) T) ((-269 . -734) T) ((-251 . -734) T) ((-386 . -1229) T) ((-1057 . -315) 150899) ((-1291 . -21) T) ((-910 . -1111) 150877) ((-50 . -1060) T) ((-1291 . -25) T) ((-1186 . -564) 150856) ((-1185 . -1233) 150835) ((-1185 . -564) 150786) ((-1179 . -1233) 150765) ((-1179 . -564) 150716) ((-589 . -1060) T) ((-526 . -1060) T) ((-1035 . -296) T) ((-368 . -1049) 150700) ((-328 . -1049) 150684) ((-1014 . -38) 150629) ((-386 . -895) 150611) ((-1010 . -654) 150534) ((-844 . -1229) T) ((-835 . -1229) 150508) ((-807 . -1123) T) ((-919 . -734) T) ((-589 . -247) T) ((-589 . -237) T) ((-526 . -237) T) ((-526 . -247) T) ((-1137 . -564) 150487) ((-361 . -296) T) ((-655 . -703) 150471) ((-386 . -1049) 150431) ((-300 . -1062) 150352) ((-1131 . -1069) T) ((-103 . -126) 150336) ((-300 . -648) 150278) ((-807 . -23) T) ((-1301 . -1296) 150254) ((-1279 . -292) 150206) ((-415 . -315) 150171) ((-1299 . -1296) 150150) ((-1265 . -1111) T) ((-878 . -621) 150132) ((-844 . -1049) 150101) ((-205 . -795) T) ((-204 . -795) T) ((-203 . -795) T) ((-202 . -795) T) ((-201 . -795) T) ((-200 . -795) T) ((-199 . -795) T) ((-198 . -795) T) ((-197 . -795) T) ((-196 . -795) T) ((-555 . -621) 150083) ((-503 . -1013) T) ((-279 . -847) T) ((-278 . -847) T) ((-277 . -847) T) ((-276 . -847) T) ((-48 . -296) T) ((-275 . -847) T) ((-274 . -847) T) ((-273 . -847) T) ((-195 . -795) T) ((-620 . -858) T) ((-662 . -419) 150067) ((-225 . -624) 150029) ((-110 . -858) T) ((-661 . -21) T) ((-661 . -25) T) ((-1302 . -38) 149999) ((-118 . -292) 149950) ((-1279 . -19) 149934) ((-1279 . -612) 149911) ((-1292 . -1111) T) ((-358 . -1062) 149856) ((-1088 . -1111) T) ((-998 . -1111) T) ((-972 . -132) T) ((-825 . -235) 149843) ((-745 . -1111) T) ((-358 . -648) 149788) ((-743 . -132) T) ((-723 . -132) T) ((-519 . -801) T) ((-519 . -802) T) ((-461 . -132) T) ((-415 . -1163) 149766) ((-225 . -1060) T) ((-300 . -102) 149548) ((-142 . -1111) T) ((-707 . -1013) T) ((-1116 . -292) 149504) ((-91 . -1229) T) ((-128 . -621) 149436) ((-122 . -621) 149368) ((-1308 . -174) T) ((-1185 . -370) 149347) ((-1179 . -370) 149326) ((-322 . -1111) T) ((-426 . -132) T) ((-319 . -1111) T) ((-415 . -38) 149278) ((-1144 . -102) T) ((-1265 . -725) 149170) ((-662 . -1069) T) ((-1146 . -1274) T) ((-325 . -146) 149149) ((-325 . -148) 149128) ((-140 . -1111) T) ((-137 . -1111) T) ((-115 . -1111) T) ((-866 . -102) T) ((-588 . -621) 149110) ((-572 . -622) 149009) ((-572 . -621) 148991) ((-503 . -621) 148973) ((-503 . -622) 148918) ((-493 . -23) T) ((-490 . -858) 148869) ((-495 . -647) 148851) ((-974 . -621) 148833) ((-219 . -647) 148815) ((-227 . -412) T) ((-670 . -656) 148799) ((-55 . -621) 148781) ((-1184 . -929) 148760) ((-739 . -1123) T) ((-358 . -102) T) ((-1228 . -1094) T) ((-1131 . -852) T) ((-826 . -858) T) ((-739 . -23) T) ((-350 . -1067) 148705) ((-1170 . -1169) T) ((-1158 . -107) 148689) ((-1186 . -1123) T) ((-1185 . -1123) T) ((-523 . -1049) 148673) ((-1179 . -1123) T) ((-1137 . -1123) T) ((-350 . -111) 148602) ((-1015 . -1233) T) ((-127 . -1229) T) ((-923 . -1233) T) ((-702 . -292) NIL) ((-722 . -1229) T) ((-1280 . -621) 148584) ((-1186 . -23) T) ((-1185 . -23) T) ((-1179 . -23) T) ((-1015 . -564) T) ((-1153 . -233) 148568) ((-923 . -564) T) ((-1137 . -23) T) ((-252 . -621) 148550) ((-1086 . -1111) T) ((-807 . -132) T) ((-718 . -621) 148532) ((-322 . -725) 148442) ((-319 . -725) 148371) ((-707 . -621) 148353) ((-707 . -622) 148298) ((-415 . -408) 148282) ((-446 . -1111) T) ((-495 . -25) T) ((-495 . -21) T) 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-132) T) ((-629 . -856) 122513) ((-1157 . -621) 122475) ((-1157 . -622) 122436) ((-1035 . -799) T) ((-1035 . -802) T) ((-1035 . -734) T) ((-720 . -1067) 122259) ((-492 . -315) 122197) ((-461 . -425) 122167) ((-358 . -174) T) ((-256 . -235) 122108) ((-255 . -235) 122049) ((-295 . -38) 122036) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-276 . -102) T) ((-275 . -102) T) ((-274 . -102) T) ((-350 . -1049) 122013) ((-273 . -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) ((-361 . -734) T) ((-720 . -111) 121822) ((-678 . -233) 121806) ((-589 . -313) T) ((-526 . -313) T) ((-300 . -522) 121755) ((-108 . -315) NIL) ((-72 . -403) T) ((-1124 . -102) 121545) ((-841 . -419) 121529) ((-1131 . -803) T) ((-1131 . -800) T) ((-709 . -1111) T) ((-586 . -621) 121511) ((-386 . -370) T) ((-171 . -501) 121489) ((-224 . -621) 121421) ((-135 . -1111) T) ((-117 . -1111) T) ((-975 . -1229) T) ((-48 . -734) T) ((-1057 . -497) 121386) ((-142 . -433) 121368) ((-142 . -375) T) ((-1038 . -102) T) ((-520 . -517) 121347) ((-720 . -624) 121103) ((-484 . -102) T) ((-471 . -102) T) ((-1045 . -1123) T) ((-1236 . -621) 121085) ((-1193 . -1049) 121021) ((-1186 . -35) 120987) ((-1186 . -95) 120953) ((-1186 . -1217) 120919) ((-1186 . -1214) 120885) ((-1185 . -1214) 120851) ((-1185 . -1217) 120817) ((-1170 . -315) NIL) ((-89 . -404) T) ((-89 . -403) T) ((-1091 . -1163) 120796) ((-40 . -1229) 120756) ((-1185 . -95) 120722) ((-1045 . -23) T) ((-1185 . -35) 120688) ((-579 . -501) T) ((-1179 . -1214) 120654) ((-1179 . -1217) 120620) ((-1179 . -95) 120586) ((-1179 . -35) 120552) ((-368 . -1123) T) ((-366 . -1163) 120531) ((-360 . -1163) 120510) ((-352 . -1163) 120489) ((-1115 . -292) 120445) ((-1137 . -35) 120411) ((-1137 . -95) 120377) 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. -102) T) ((-110 . -102) T) ((-490 . -648) 119133) ((-40 . -384) 119110) ((-96 . -102) T) ((-661 . -860) 119094) ((-1184 . -235) 119081) ((-1146 . -1094) T) ((-1073 . -21) T) ((-1073 . -25) T) ((-1065 . -1062) 119065) ((-823 . -233) 119034) ((-961 . -25) T) ((-961 . -21) T) ((-1065 . -648) 118976) ((-629 . -1069) T) ((-1131 . -375) T) ((-1038 . -315) 118914) ((-678 . -654) 118873) ((-489 . -25) T) ((-489 . -21) T) ((-392 . -1062) 118857) ((-898 . -621) 118839) ((-894 . -621) 118821) ((-531 . -522) 118754) ((-256 . -858) 118705) ((-255 . -858) 118656) ((-392 . -648) 118626) ((-879 . -647) 118603) ((-484 . -315) 118541) ((-471 . -315) 118479) ((-358 . -296) T) ((-1168 . -1267) 118463) ((-1153 . -621) 118425) ((-1153 . -622) 118386) ((-1151 . -102) T) ((-1010 . -1067) 118282) ((-40 . -909) 118234) ((-1168 . -612) 118211) ((-1308 . -656) 118198) ((-874 . -498) 118175) ((-1074 . -152) 118121) ((-880 . -1233) T) ((-1010 . -111) 118003) ((-346 . -725) 117987) ((-874 . -621) 117949) ((-176 . 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113275) ((-394 . -858) 113254) ((-1271 . -1217) 113220) ((-1271 . -1214) 113186) ((-1264 . -1214) 113152) ((-523 . -132) T) ((-1264 . -1217) 113118) ((-1243 . -1214) 113084) ((-1243 . -1217) 113050) ((-1271 . -35) 113016) ((-1271 . -95) 112982) ((-1264 . -95) 112948) ((-643 . -621) 112917) ((-615 . -621) 112886) ((-227 . -858) T) ((-1264 . -35) 112852) ((-1263 . -1123) T) ((-1243 . -95) 112818) ((-1131 . -656) 112805) ((-1243 . -35) 112771) ((-1242 . -1123) T) ((-601 . -152) 112753) ((-1091 . -356) 112732) ((-176 . -296) T) ((-118 . -384) 112709) ((-118 . -345) 112686) ((-171 . -235) 112626) ((-878 . -313) T) ((-319 . -802) NIL) ((-319 . -799) NIL) ((-322 . -734) 112475) ((-319 . -734) T) ((-482 . -370) 112454) ((-366 . -356) 112433) ((-360 . -356) 112412) ((-352 . -356) 112391) ((-322 . -481) 112370) ((-1263 . -23) T) ((-1242 . -23) T) ((-726 . -1123) T) ((-722 . -132) T) ((-661 . -102) T) ((-485 . -725) 112335) ((-45 . -288) 112285) ((-105 . -1111) T) ((-68 . -621) 112267) ((-981 . 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. -656) 95162) ((-484 . -1111) T) ((-471 . -1111) T) ((-594 . -23) T) ((-579 . -35) T) ((-579 . -95) T) ((-435 . -102) T) ((-1074 . -231) 95108) ((-1186 . -38) 95005) ((-874 . -734) T) ((-702 . -929) T) ((-519 . -25) T) ((-515 . -21) T) ((-515 . -25) T) ((-1185 . -38) 94846) ((-346 . -1060) T) ((-1179 . -38) 94642) ((-1091 . -174) T) ((-176 . -1060) T) ((-1137 . -38) 94539) ((-720 . -47) 94516) ((-366 . -174) T) ((-360 . -174) T) ((-527 . -57) 94490) ((-505 . -57) 94440) ((-358 . -1298) 94417) ((-227 . -460) T) ((-325 . -296) 94368) ((-352 . -174) T) ((-176 . -247) T) ((-1242 . -858) 94267) ((-108 . -174) T) ((-880 . -1003) 94251) ((-666 . -1123) T) ((-589 . -370) T) ((-589 . -335) 94238) ((-526 . -335) 94215) ((-526 . -370) T) ((-322 . -313) 94194) ((-319 . -313) T) ((-610 . -858) 94173) ((-1124 . -725) 94115) ((-528 . -288) 94099) ((-666 . -23) T) ((-426 . -233) 94083) ((-319 . -1033) NIL) ((-343 . -23) T) ((-103 . -1021) 94067) ((-45 . -36) 94046) ((-620 . -1111) T) ((-358 . -375) 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90068) ((-1264 . -290) 90034) ((-1091 . -296) 89985) ((-495 . -856) T) ((-225 . -1123) T) ((-1243 . -290) 89951) ((-1223 . -501) 89917) ((-1015 . -38) 89867) ((-219 . -856) T) ((-426 . -654) 89826) ((-923 . -38) 89778) ((-851 . -802) 89757) ((-851 . -799) 89736) ((-851 . -734) 89715) ((-366 . -296) T) ((-360 . -296) T) ((-352 . -296) T) ((-171 . -460) 89646) ((-435 . -38) 89630) ((-108 . -296) T) ((-225 . -23) T) ((-415 . -802) 89609) ((-415 . -799) 89588) ((-415 . -734) T) ((-508 . -294) 89563) ((-485 . -1067) 89528) ((-666 . -132) T) ((-629 . -624) 89497) ((-1124 . -522) 89430) ((-343 . -132) T) ((-171 . -410) 89409) ((-490 . -725) 89351) ((-823 . -292) 89328) ((-485 . -111) 89284) ((-661 . -1069) T) ((-824 . -1062) 89127) ((-1290 . -1094) T) ((-1252 . -460) 89058) ((-824 . -648) 88907) ((-1289 . -1094) T) ((-1098 . -132) T) ((-1065 . -725) 88849) ((-790 . -132) T) ((-788 . -132) T) ((-579 . -460) T) ((-1038 . -522) 88782) ((-629 . -1060) T) ((-600 . -1111) T) ((-541 . -175) T) 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. -146) 83371) ((-1242 . -148) 83296) ((-1294 . -1300) 83275) ((-484 . -497) 83259) ((-471 . -497) 83243) ((-531 . -34) T) ((-661 . -725) 83213) ((-112 . -978) T) ((-670 . -858) 83192) ((-1190 . -174) 83143) ((-372 . -102) T) ((-244 . -242) 83122) ((-256 . -102) T) ((-255 . -102) T) ((-1252 . -958) 83091) ((-249 . -858) 83070) ((-824 . -38) 82919) ((-45 . -522) 82711) ((-1170 . -292) 82661) ((-216 . -1111) T) ((-1161 . -1111) T) ((-1161 . -618) 82640) ((-594 . -25) T) ((-594 . -21) T) ((-1113 . -315) 82578) ((-972 . -419) 82562) ((-707 . -1233) T) ((-640 . -292) 82515) ((-1098 . -647) 82463) ((-790 . -647) 82411) ((-788 . -647) 82359) ((-350 . -132) T) ((-295 . -621) 82341) ((-914 . -1111) T) ((-707 . -564) T) ((-130 . -624) 82323) ((-878 . -1123) T) ((-462 . -647) 82271) ((-914 . -912) 82255) ((-386 . -460) T) ((-495 . -1111) T) ((-952 . -315) 82193) ((-709 . -656) 82180) ((-557 . -852) T) ((-219 . -1111) T) ((-322 . -929) 82159) ((-319 . -929) T) ((-319 . -828) NIL) ((-398 . -728) T) 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. -564) T) ((-469 . -21) T) ((-462 . -25) T) ((-462 . -21) T) ((-1263 . -95) 80810) ((-1162 . -93) T) ((-1153 . -1049) 80706) ((-825 . -296) 80685) ((-1246 . -102) 80663) ((-831 . -1111) T) ((-975 . -978) T) ((-678 . -111) 80642) ((-625 . -1229) T) ((-301 . -522) 80434) ((-1243 . -233) 80386) ((-1242 . -1214) 80352) ((-1242 . -1217) 80318) ((-256 . -315) 80256) ((-255 . -315) 80194) ((-1237 . -375) T) ((-1171 . -622) NIL) ((-1171 . -621) 80176) ((-1234 . -852) T) ((-1153 . -384) 80160) ((-1131 . -828) T) ((-96 . -93) T) ((-1131 . -929) T) ((-1124 . -612) 80137) ((-1091 . -622) 80121) ((-1015 . -654) 80071) ((-923 . -654) 80008) ((-823 . -294) 79985) ((-492 . -621) 79917) ((-616 . -152) 79864) ((-495 . -725) 79814) ((-426 . -1069) T) ((-490 . -497) 79798) ((-435 . -654) 79757) ((-333 . -858) 79736) ((-346 . -656) 79710) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -725) 79660) ((-171 . -732) 79631) ((-176 . -656) 79563) ((-589 . -21) T) ((-589 . -25) T) ((-526 . -25) T) ((-526 . -21) T) 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-23) T) ((-702 . -564) T) ((-227 . -1062) 77747) ((-655 . -621) 77679) ((-655 . -622) 77640) ((-640 . -622) NIL) ((-640 . -621) 77622) ((-495 . -174) T) ((-227 . -648) 77587) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-482 . -1217) 77553) ((-482 . -1214) 77519) ((-279 . -621) 77501) ((-278 . -621) 77483) ((-277 . -621) 77465) ((-276 . -621) 77447) ((-275 . -621) 77429) ((-508 . -659) 77411) ((-274 . -621) 77393) ((-346 . -734) T) ((-273 . -621) 77375) ((-110 . -19) 77357) ((-176 . -734) T) ((-508 . -380) 77339) ((-214 . -621) 77321) ((-528 . -1160) 77305) ((-508 . -124) T) ((-110 . -612) 77280) ((-213 . -621) 77262) ((-482 . -35) 77228) ((-482 . -95) 77194) ((-211 . -621) 77176) ((-210 . -621) 77158) ((-209 . -621) 77140) ((-208 . -621) 77122) ((-205 . -621) 77104) ((-204 . -621) 77086) ((-203 . -621) 77068) ((-202 . -621) 77050) ((-201 . -621) 77032) ((-200 . -621) 77014) ((-199 . -621) 76996) ((-544 . -1114) 76948) ((-198 . -621) 76930) ((-197 . -621) 76912) ((-45 . -497) 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. -1111) T) ((-483 . -497) 13657) ((-415 . -647) 13605) ((-661 . -1049) 13501) ((-967 . -497) 13485) ((-362 . -1069) T) ((-359 . -1069) T) ((-351 . -1069) T) ((-269 . -1069) T) ((-251 . -1069) T) ((-879 . -622) NIL) ((-879 . -621) 13467) ((-1290 . -498) 13448) ((-1289 . -498) 13429) ((-1302 . -21) T) ((-1290 . -621) 13395) ((-1289 . -621) 13361) ((-579 . -1013) T) ((-739 . -734) T) ((-1302 . -25) T) ((-256 . -1060) 13291) ((-255 . -1060) 13221) ((-72 . -1229) T) ((-256 . -237) 13168) ((-255 . -237) 13115) ((-1153 . -235) 13083) ((-40 . -102) T) ((-919 . -1069) T) ((-1193 . -102) T) ((-129 . -497) 13065) ((-1186 . -734) T) ((-1185 . -734) T) ((-1179 . -734) T) ((-1179 . -799) NIL) ((-1179 . -802) NIL) ((-963 . -102) T) ((-930 . -102) T) ((-878 . -1062) 13052) ((-1137 . -734) T) ((-779 . -102) T) ((-680 . -102) T) ((-878 . -648) 13039) ((-554 . -621) 13021) ((-482 . -1111) T) ((-346 . -1123) T) ((-176 . -1123) T) ((-325 . -929) 13000) ((-1263 . -725) 12841) ((-880 . -174) T) ((-1242 . 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. -612) 9119) ((-483 . -612) 9098) ((-343 . -342) 9067) ((-605 . -1111) T) ((-593 . -1111) T) ((-544 . -1111) T) ((-485 . -564) T) ((-1184 . -1060) T) ((-1136 . -1060) T) ((-862 . -1060) T) ((-244 . -799) 9046) ((-244 . -802) 8997) ((-244 . -801) 8976) ((-1184 . -332) 8953) ((-244 . -734) 8863) ((-967 . -19) 8847) ((-495 . -384) 8829) ((-495 . -345) 8811) ((-1136 . -332) 8783) ((-361 . -1286) 8760) ((-219 . -384) 8742) ((-219 . -345) 8724) ((-967 . -612) 8701) ((-1184 . -237) T) ((-1275 . -1111) T) ((-672 . -1111) T) ((-653 . -1111) T) ((-1201 . -1111) T) ((-1098 . -258) 8638) ((-594 . -654) 8598) ((-362 . -1111) T) ((-359 . -1111) T) ((-351 . -1111) T) ((-269 . -1111) T) ((-251 . -1111) T) ((-84 . -1229) T) ((-128 . -102) 8576) ((-122 . -102) 8554) ((-1242 . -522) 8414) ((-1201 . -618) 8393) ((-1152 . -1111) T) ((-1126 . -624) 8374) ((-1091 . -929) 8325) ((-487 . -1111) T) ((-1015 . -802) T) ((-1015 . -799) T) ((-487 . -618) 8304) ((-256 . -803) 8255) ((-256 . -800) 8206) ((-255 . 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. -622) 177379) ((-59 . -621) 177291) ((-227 . -734) T) ((-524 . -622) 177252) ((-524 . -621) 177164) ((-505 . -621) 177096) ((-504 . -622) 177057) ((-504 . -621) 176969) ((-1091 . -370) 176920) ((-40 . -419) 176897) ((-77 . -1229) T) ((-879 . -918) NIL) ((-366 . -335) 176881) ((-366 . -370) T) ((-360 . -335) 176865) ((-360 . -370) T) ((-352 . -335) 176849) ((-352 . -370) T) ((-322 . -290) 176828) ((-108 . -370) T) ((-70 . -1229) T) ((-1243 . -345) 176780) ((-879 . -656) 176725) ((-1243 . -384) 176677) ((-973 . -132) 176532) ((-823 . -132) 176402) ((-967 . -659) 176386) ((-1098 . -174) 176297) ((-967 . -380) 176281) ((-1073 . -802) T) ((-1073 . -799) T) ((-880 . -624) 176179) ((-790 . -174) 176070) ((-788 . -174) 175981) ((-824 . -47) 175943) ((-1073 . -734) T) ((-333 . -497) 175927) ((-961 . -734) T) ((-1292 . -315) 175865) ((-462 . -174) 175776) ((-249 . -292) 175728) ((-1271 . -909) 175641) ((-1264 . -909) 175547) ((-1263 . -1067) 175382) ((-489 . -734) T) ((-1243 . -909) 175215) 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174201) ((-1242 . -111) 173990) ((-249 . -1267) 173974) ((-572 . -856) T) ((-366 . -23) T) ((-361 . -356) T) ((-322 . -315) 173961) ((-319 . -315) 173902) ((-360 . -23) T) ((-325 . -132) T) ((-352 . -23) T) ((-1015 . -1033) T) ((-31 . -624) 173883) ((-108 . -23) T) ((-662 . -1062) 173867) ((-249 . -612) 173844) ((-339 . -1111) T) ((-662 . -648) 173814) ((-1265 . -38) 173706) ((-1252 . -918) 173685) ((-112 . -1111) T) ((-824 . -1229) 173664) ((-1046 . -102) T) ((-1252 . -656) 173589) ((-879 . -802) NIL) ((-863 . -656) 173563) ((-879 . -799) NIL) ((-824 . -895) NIL) ((-879 . -734) T) ((-1098 . -522) 173436) ((-790 . -522) 173383) ((-788 . -522) 173335) ((-579 . -656) 173322) ((-824 . -1049) 173150) ((-462 . -522) 173093) ((-396 . -397) T) ((-1263 . -624) 172906) ((-1242 . -624) 172654) ((-60 . -1229) T) ((-629 . -858) 172633) ((-508 . -669) T) ((-1157 . -987) 172602) ((-1035 . -654) 172539) ((-1014 . -460) T) ((-707 . -856) T) ((-518 . -800) T) ((-482 . -1067) 172374) ((-508 . -113) T) 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NIL) ((-1091 . -132) T) ((-880 . -803) 169212) ((-145 . -102) T) ((-40 . -1111) T) ((-880 . -800) 169191) ((-652 . -1021) 169175) ((-588 . -1069) T) ((-572 . -1069) T) ((-503 . -1069) T) ((-415 . -460) T) ((-366 . -132) T) ((-322 . -408) 169159) ((-319 . -408) 169120) ((-360 . -132) T) ((-352 . -132) T) ((-1193 . -1111) T) ((-1131 . -38) 169107) ((-1105 . -621) 169074) ((-108 . -132) T) ((-963 . -1111) T) ((-930 . -1111) T) ((-779 . -1111) T) ((-680 . -1111) T) ((-709 . -148) T) ((-117 . -148) T) ((-1301 . -21) T) ((-1301 . -25) T) ((-1299 . -21) T) ((-1299 . -25) T) ((-672 . -1067) 169058) ((-539 . -858) T) ((-508 . -858) T) ((-362 . -1067) 169010) ((-359 . -1067) 168962) ((-351 . -1067) 168914) ((-256 . -1229) T) ((-255 . -1229) T) ((-269 . -1067) 168757) ((-251 . -1067) 168600) ((-672 . -111) 168579) ((-555 . -852) T) ((-362 . -111) 168517) ((-359 . -111) 168455) ((-351 . -111) 168393) ((-269 . -111) 168222) ((-251 . -111) 168051) ((-825 . -1233) 168030) ((-631 . -419) 168014) ((-44 . -21) T) ((-44 . -25) T) ((-823 . -647) 167920) ((-825 . -564) 167899) ((-256 . -1049) 167726) ((-255 . -1049) 167553) ((-127 . -120) 167537) ((-919 . -1067) 167502) ((-720 . -102) T) ((-707 . -1069) T) ((-605 . -624) 167483) ((-593 . -624) 167464) ((-544 . -626) 167367) ((-350 . -174) T) ((-88 . -621) 167349) ((-153 . -21) T) ((-153 . -25) T) ((-919 . -111) 167305) ((-40 . -725) 167250) ((-878 . -1111) T) ((-672 . -624) 167227) ((-653 . -624) 167208) ((-362 . -624) 167145) ((-359 . -624) 167082) ((-555 . -1111) T) ((-351 . -624) 167019) ((-333 . -622) 166980) ((-333 . -621) 166892) ((-269 . -624) 166645) ((-251 . -624) 166430) ((-1242 . -800) 166383) ((-1242 . -803) 166336) ((-256 . -384) 166305) ((-255 . -384) 166274) ((-662 . -38) 166244) ((-616 . -34) T) ((-490 . -1123) 166154) ((-483 . -34) T) ((-1124 . -132) 166024) ((-973 . -25) 165835) ((-919 . -624) 165785) ((-882 . -621) 165767) ((-973 . -21) 165722) ((-823 . -21) 165632) ((-823 . -25) 165483) ((-1235 . -375) T) ((-631 . -1069) T) ((-1190 . -564) 165462) ((-1184 . -47) 165439) ((-362 . -1060) T) ((-359 . -1060) T) ((-490 . -23) 165309) ((-351 . -1060) T) ((-269 . -1060) T) ((-251 . -1060) T) ((-1136 . -47) 165281) ((-118 . -1069) T) ((-1045 . -656) 165255) ((-967 . -34) T) ((-362 . -237) 165234) ((-362 . -247) T) ((-359 . -237) 165213) ((-359 . -247) T) ((-351 . -237) 165192) ((-351 . -247) T) ((-269 . -332) 165164) ((-251 . -332) 165121) ((-269 . -237) 165100) ((-1168 . -152) 165084) ((-256 . -909) 165016) ((-255 . -909) 164948) ((-1093 . -858) T) ((-422 . -1123) T) ((-1065 . -23) T) ((-919 . -1060) T) ((-328 . -656) 164930) ((-1035 . -856) T) ((-678 . -235) 164903) ((-1223 . -1013) 164869) ((-1185 . -929) 164848) ((-1179 . -929) 164827) ((-1179 . -828) NIL) ((-1010 . -1062) 164723) ((-976 . -1229) T) ((-919 . -247) T) ((-825 . -370) 164702) ((-392 . -23) T) ((-128 . -1111) 164680) ((-122 . -1111) 164658) ((-919 . -237) T) ((-129 . -34) T) ((-386 . -656) 164623) ((-1010 . -648) 164571) ((-878 . -725) 164558) ((-1308 . -654) 164530) ((-1057 . -152) 164495) ((-1004 . -1229) T) ((-40 . -174) T) ((-702 . -419) 164477) ((-720 . -315) 164464) ((-844 . -656) 164424) ((-835 . -656) 164398) ((-325 . -25) T) ((-325 . -21) T) ((-666 . -292) 164377) ((-588 . -1111) T) ((-572 . -1111) T) ((-503 . -1111) T) ((-249 . -294) 164354) ((-1184 . -1229) T) ((-319 . -233) 164315) ((-1184 . -895) NIL) ((-55 . -1111) T) ((-1136 . -895) 164174) ((-130 . -858) T) ((-1184 . -1049) 164054) ((-1136 . -1049) 163937) ((-185 . -621) 163919) ((-862 . -1049) 163815) ((-790 . -292) 163742) ((-825 . -1123) T) ((-1045 . -734) T) ((-610 . -659) 163726) ((-1057 . -987) 163655) ((-1010 . -102) T) ((-825 . -23) T) ((-720 . -1163) 163633) ((-702 . -1069) T) ((-610 . -380) 163617) ((-358 . -460) T) ((-350 . -296) T) ((-1280 . -1111) T) ((-252 . -1111) T) ((-407 . -102) T) ((-295 . -21) T) ((-295 . -25) T) ((-368 . -734) T) ((-718 . -1111) T) ((-707 . -1111) T) ((-368 . -481) T) ((-1223 . -621) 163599) ((-1184 . -384) 163583) ((-1136 . -384) 163567) ((-1035 . -419) 163529) ((-142 . -231) 163511) ((-386 . -802) T) ((-386 . -799) T) ((-878 . -174) T) ((-386 . -734) T) ((-719 . -621) 163493) ((-720 . -38) 163322) ((-1279 . -1277) 163306) ((-358 . -410) T) ((-1279 . -1111) 163256) ((-1202 . -1111) T) ((-588 . -725) 163243) ((-572 . -725) 163230) ((-503 . -725) 163195) ((-1265 . -654) 163085) ((-322 . -637) 163064) ((-844 . -734) T) ((-835 . -734) T) ((-652 . -1229) T) ((-1091 . -647) 163012) ((-1184 . -909) 162955) ((-1136 . -909) 162939) ((-823 . -235) 162885) ((-670 . -1067) 162869) ((-108 . -647) 162851) ((-490 . -132) 162721) ((-1190 . -1123) T) ((-961 . -47) 162690) ((-631 . -1111) T) ((-670 . -111) 162669) ((-499 . -621) 162635) ((-333 . -294) 162612) ((-489 . -47) 162569) ((-1190 . -23) T) ((-118 . -1111) T) ((-103 . -102) 162547) ((-1291 . -1123) T) ((-556 . -858) T) ((-227 . -1229) T) ((-1065 . -132) T) ((-1035 . -1069) T) ((-827 . -1049) 162531) ((-1291 . -23) T) ((-1014 . -732) 162503) 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-744) 161621) ((-343 . -621) 161603) ((-68 . -390) T) ((-68 . -403) T) ((-1113 . -107) 161587) ((-1073 . -895) 161569) ((-961 . -895) 161494) ((-661 . -1123) T) ((-631 . -725) 161481) ((-489 . -895) NIL) ((-1157 . -102) T) ((-1105 . -626) 161465) ((-1073 . -1049) 161447) ((-97 . -621) 161429) ((-485 . -148) T) ((-961 . -1049) 161309) ((-118 . -725) 161254) ((-661 . -23) T) ((-489 . -1049) 161130) ((-1098 . -622) NIL) ((-1098 . -621) 161112) ((-790 . -622) NIL) ((-790 . -621) 161073) ((-788 . -622) 160707) ((-788 . -621) 160621) ((-1124 . -647) 160527) ((-469 . -621) 160509) ((-462 . -621) 160491) ((-462 . -622) 160352) ((-1046 . -231) 160298) ((-880 . -918) 160277) ((-127 . -34) T) ((-825 . -132) T) ((-657 . -621) 160259) ((-586 . -102) T) ((-362 . -1298) 160243) ((-359 . -1298) 160227) ((-351 . -1298) 160211) ((-128 . -522) 160144) ((-122 . -522) 160077) ((-519 . -800) T) ((-519 . -803) T) ((-518 . -802) T) ((-103 . -315) 160015) ((-224 . -102) 159993) ((-707 . -174) T) ((-702 . -1111) T) ((-880 . -656) 159945) ((-65 . -391) T) ((-280 . -621) 159927) ((-65 . -403) T) ((-961 . -384) 159911) ((-878 . -296) T) ((-50 . -621) 159893) ((-1010 . -38) 159841) ((-1131 . -654) 159813) ((-589 . -621) 159795) ((-489 . -384) 159779) ((-589 . -622) 159761) ((-526 . -621) 159743) ((-919 . -1298) 159730) ((-879 . -1229) T) ((-709 . -460) T) ((-503 . -522) 159696) ((-495 . -370) T) ((-362 . -375) 159675) ((-359 . -375) 159654) ((-351 . -375) 159633) ((-722 . -734) T) ((-219 . -370) T) ((-117 . -460) T) ((-1302 . -1293) 159617) ((-879 . -893) 159594) ((-879 . -895) NIL) ((-973 . -858) 159493) ((-823 . -858) 159444) ((-1236 . -102) T) ((-662 . -664) 159428) ((-1215 . -34) T) ((-173 . -621) 159410) ((-1124 . -21) 159320) ((-1124 . -25) 159171) ((-879 . -1049) 159148) ((-961 . -909) 159129) ((-1252 . -47) 159106) ((-919 . -375) T) ((-59 . -659) 159090) ((-524 . -659) 159074) ((-489 . -909) 159051) ((-71 . -449) T) ((-71 . -403) T) ((-504 . -659) 159035) ((-59 . -380) 159019) 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T) ((-1065 . -21) T) ((-719 . -1060) T) ((-392 . -21) T) ((-392 . -25) T) ((-702 . -522) NIL) ((-1035 . -174) T) ((-719 . -247) T) ((-1073 . -553) T) ((-720 . -654) 155243) ((-514 . -102) T) ((-510 . -102) T) ((-361 . -174) T) ((-350 . -621) 155225) ((-415 . -1062) 155177) ((-402 . -621) 155159) ((-1131 . -856) T) ((-482 . -734) T) ((-901 . -1049) 155127) ((-415 . -648) 155079) ((-108 . -858) T) ((-666 . -1067) 155063) ((-495 . -132) T) ((-1265 . -1069) T) ((-219 . -132) T) ((-1168 . -102) 155041) ((-99 . -1111) T) ((-249 . -674) 155025) ((-249 . -659) 155009) ((-666 . -111) 154988) ((-594 . -624) 154972) ((-322 . -419) 154956) ((-249 . -380) 154940) ((-1171 . -239) 154887) ((-1010 . -233) 154871) ((-74 . -1229) T) ((-48 . -174) T) ((-709 . -395) T) ((-709 . -144) T) ((-1302 . -102) T) ((-1209 . -624) 154853) ((-1098 . -1067) 154696) ((-1087 . -1229) T) ((-269 . -918) 154675) ((-251 . -918) 154654) ((-790 . -1067) 154477) ((-788 . -1067) 154320) ((-616 . -1229) T) ((-1176 . -621) 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. -23) T) ((-415 . -102) T) ((-268 . -102) T) ((-110 . -113) T) ((-702 . -296) T) ((-874 . -38) 152591) ((-589 . -111) 152547) ((-526 . -111) 152476) ((-1098 . -624) 152212) ((-426 . -1123) T) ((-322 . -1069) 152102) ((-319 . -1069) T) ((-129 . -1229) T) ((-790 . -624) 151850) ((-788 . -624) 151616) ((-666 . -1060) T) ((-1308 . -1111) T) ((-462 . -624) 151401) ((-171 . -313) 151332) ((-426 . -23) T) ((-40 . -621) 151314) ((-40 . -622) 151298) ((-108 . -1003) 151280) ((-117 . -877) 151264) ((-657 . -624) 151248) ((-48 . -522) 151214) ((-1215 . -1021) 151198) ((-1193 . -621) 151165) ((-1201 . -34) T) ((-963 . -621) 151131) ((-930 . -621) 151113) ((-1124 . -858) 151064) ((-779 . -621) 151046) ((-680 . -621) 151028) ((-1168 . -315) 150966) ((-487 . -34) T) ((-1103 . -1229) T) ((-485 . -460) T) ((-1152 . -34) T) ((-1098 . -1060) T) ((-50 . -624) 150935) ((-790 . -1060) T) ((-788 . -1060) T) ((-655 . -239) 150919) ((-640 . -239) 150865) ((-589 . -624) 150815) ((-526 . -624) 150745) ((-490 . 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. -132) T) ((-666 . -656) 141198) ((-249 . -1021) 141182) ((-880 . -313) T) ((-1303 . -1293) 141166) ((-779 . -800) T) ((-779 . -803) T) ((-709 . -38) 141153) ((-572 . -237) T) ((-503 . -247) T) ((-503 . -237) T) ((-1161 . -239) 141103) ((-1098 . -918) 141082) ((-117 . -38) 141069) ((-211 . -808) T) ((-210 . -808) T) ((-209 . -808) T) ((-208 . -808) T) ((-880 . -1033) 141047) ((-1292 . -497) 141031) ((-790 . -918) 141010) ((-788 . -918) 140989) ((-362 . -1229) 140968) ((-359 . -1229) 140947) ((-351 . -1229) 140926) ((-1201 . -1229) T) ((-269 . -1229) 140905) ((-462 . -918) 140884) ((-745 . -497) 140868) ((-1098 . -656) 140793) ((-707 . -624) 140728) ((-790 . -656) 140653) ((-631 . -1067) 140640) ((-487 . -1229) T) ((-350 . -375) T) ((-142 . -497) 140622) ((-788 . -656) 140547) ((-1152 . -1229) T) ((-557 . -858) T) ((-469 . -656) 140518) ((-269 . -895) 140377) ((-251 . -895) NIL) ((-118 . -1067) 140322) ((-462 . -656) 140247) ((-672 . -1049) 140224) ((-631 . -111) 140209) ((-398 . 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-648) 137089) ((-702 . -624) 137024) ((-1294 . -23) T) ((-1281 . -102) T) ((-177 . -621) 137006) ((-1153 . -1069) T) ((-555 . -375) T) ((-678 . -752) 136990) ((-1190 . -146) 136969) ((-1190 . -148) 136948) ((-1157 . -1111) T) ((-1157 . -1082) 136917) ((-69 . -1229) T) ((-1035 . -1067) 136854) ((-358 . -654) 136784) ((-874 . -1069) T) ((-244 . -647) 136690) ((-702 . -1060) T) ((-361 . -1067) 136635) ((-61 . -1229) T) ((-1035 . -111) 136551) ((-910 . -621) 136462) ((-702 . -247) T) ((-702 . -237) NIL) ((-851 . -856) 136441) ((-707 . -803) T) ((-707 . -800) T) ((-1014 . -419) 136418) ((-361 . -111) 136347) ((-386 . -929) T) ((-415 . -856) 136326) ((-720 . -296) 136237) ((-225 . -734) T) ((-1271 . -501) 136203) ((-1264 . -501) 136169) ((-1243 . -501) 136135) ((-586 . -1111) T) ((-322 . -1013) 136114) ((-224 . -1111) 136092) ((-1236 . -852) T) ((-325 . -984) 136054) ((-105 . -102) T) ((-48 . -1067) 136019) ((-1303 . -102) T) ((-388 . -102) T) ((-48 . -111) 135975) ((-1015 . -647) 135957) 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. -622) 134661) ((-745 . -621) 134643) ((-1179 . -235) 134524) ((-807 . -858) 134503) ((-1171 . -152) 134450) ((-1010 . -522) 134362) ((-361 . -237) T) ((-361 . -247) T) ((-396 . -624) 134343) ((-1015 . -25) T) ((-142 . -621) 134325) ((-142 . -622) 134284) ((-919 . -313) T) ((-1015 . -21) T) ((-982 . -25) T) ((-923 . -21) T) ((-923 . -25) T) ((-435 . -21) T) ((-435 . -25) T) ((-851 . -419) 134268) ((-48 . -1060) T) ((-1301 . -1293) 134252) ((-1299 . -1293) 134236) ((-1046 . -612) 134211) ((-322 . -622) 134072) ((-322 . -621) 134054) ((-319 . -622) NIL) ((-319 . -621) 134036) ((-48 . -247) T) ((-48 . -237) T) ((-662 . -292) 133997) ((-558 . -239) 133947) ((-140 . -621) 133914) ((-137 . -621) 133896) ((-115 . -621) 133878) ((-485 . -38) 133843) ((-1303 . -1300) 133822) ((-1294 . -132) T) ((-1302 . -1069) T) ((-1093 . -102) T) ((-88 . -1229) T) ((-508 . -315) NIL) ((-1011 . -107) 133806) ((-898 . -1111) T) ((-894 . -1111) T) ((-1279 . -659) 133790) ((-1279 . -380) 133774) ((-333 . -1229) T) ((-601 . -858) T) ((-1153 . -1111) T) ((-1153 . -1064) 133714) ((-103 . -522) 133647) ((-936 . -621) 133629) ((-350 . -734) T) ((-30 . -621) 133611) ((-874 . -1111) T) ((-851 . -1069) 133590) ((-40 . -656) 133535) ((-227 . -1233) T) ((-415 . -1069) T) ((-1170 . -152) 133517) ((-1010 . -296) 133468) ((-625 . -1111) T) ((-227 . -564) T) ((-325 . -1260) 133452) ((-325 . -1257) 133422) ((-709 . -654) 133394) ((-1201 . -1205) 133373) ((-1086 . -621) 133355) ((-1201 . -107) 133305) ((-655 . -152) 133289) ((-640 . -152) 133235) ((-117 . -654) 133207) ((-487 . -1205) 133186) ((-495 . -148) T) ((-495 . -146) NIL) ((-1131 . -622) 133101) ((-446 . -621) 133083) ((-219 . -148) T) ((-219 . -146) NIL) ((-1131 . -621) 133065) ((-130 . -102) T) ((-52 . -102) T) ((-1243 . -647) 133017) ((-487 . -107) 132967) ((-1004 . -23) T) ((-1303 . -38) 132937) ((-1184 . -1123) T) ((-1136 . -1123) T) ((-1073 . -1233) T) ((-244 . -235) 132883) ((-317 . -102) T) ((-862 . -1123) T) ((-961 . -1233) 132862) ((-489 . -1233) 132841) ((-1073 . -564) T) ((-961 . -564) 132772) ((-1184 . -23) T) ((-1162 . -1094) T) ((-1136 . -23) T) ((-862 . -23) T) ((-489 . -564) 132703) ((-1153 . -725) 132635) ((-678 . -1062) 132619) ((-1157 . -522) 132552) ((-678 . -648) 132536) ((-1046 . -622) NIL) ((-1046 . -621) 132518) ((-96 . -1094) T) ((-874 . -725) 132488) ((-1308 . -1067) 132475) ((-1223 . -47) 132444) ((-256 . -132) T) ((-255 . -132) T) ((-1115 . -1111) T) ((-1014 . -1111) T) ((-62 . -621) 132426) ((-1179 . -858) NIL) ((-1035 . -800) T) ((-1035 . -803) T) ((-1308 . -111) 132411) ((-1271 . -25) T) ((-1271 . -21) T) ((-1264 . -21) T) ((-878 . -656) 132398) ((-1264 . -25) T) ((-1243 . -21) T) ((-1243 . -25) T) ((-1038 . -152) 132382) ((-1015 . -235) 132369) ((-880 . -828) 132348) ((-880 . -929) T) ((-720 . -292) 132275) ((-604 . -21) T) ((-346 . -654) 132234) ((-604 . -25) T) ((-603 . -21) T) ((-176 . -654) 132151) ((-40 . -734) T) ((-224 . -522) 132084) ((-603 . -25) T) ((-484 . -152) 132068) ((-471 . -152) 132052) ((-930 . -802) T) ((-930 . -734) T) ((-779 . -801) T) ((-779 . -802) T) ((-514 . -1111) T) ((-510 . -1111) T) ((-779 . -734) T) ((-227 . -370) T) ((-1301 . -1062) 132036) ((-1299 . -1062) 132020) ((-1301 . -648) 131990) ((-1168 . -1111) 131968) ((-879 . -1233) T) ((-1299 . -648) 131938) ((-662 . -621) 131920) ((-879 . -564) T) ((-702 . -375) NIL) ((-44 . -1062) 131904) ((-1308 . -624) 131886) ((-1302 . -1111) T) ((-678 . -102) T) ((-366 . -1286) 131870) ((-360 . -1286) 131854) ((-44 . -648) 131838) ((-352 . -1286) 131822) ((-556 . -102) T) ((-528 . -858) 131801) ((-1057 . -1111) T) ((-825 . -460) 131780) ((-153 . -1062) 131764) ((-1057 . -1082) 131693) ((-1038 . -987) 131662) ((-827 . -1123) T) ((-1014 . -725) 131607) ((-153 . -648) 131591) ((-394 . -1123) T) ((-484 . -987) 131560) ((-471 . -987) 131529) ((-110 . -152) 131511) ((-73 . -621) 131493) ((-902 . -621) 131475) ((-1091 . -732) 131454) ((-1308 . -1060) T) ((-824 . -647) 131402) ((-300 . -1069) 131344) ((-171 . -1233) 131249) ((-227 . -1123) T) ((-330 . -23) T) ((-1179 . -1003) 131201) ((-851 . -1111) T) ((-1265 . -1067) 131106) ((-1137 . -748) 131085) ((-1263 . -929) 131064) ((-1242 . -929) 131043) ((-878 . -734) T) ((-171 . -564) 130954) ((-588 . -656) 130941) ((-572 . -656) 130928) ((-415 . -1111) T) ((-268 . -1111) T) ((-215 . -621) 130910) ((-503 . -656) 130875) ((-227 . -23) T) ((-1242 . -828) 130828) ((-1301 . -102) T) ((-361 . -1298) 130805) ((-1299 . -102) T) ((-1265 . -111) 130697) ((-823 . -1062) 130594) ((-823 . -648) 130536) ((-145 . -621) 130518) ((-1004 . -132) T) ((-44 . -102) T) ((-244 . -858) 130469) ((-1252 . -1233) 130448) ((-103 . -497) 130432) ((-1302 . -725) 130402) ((-1098 . -47) 130363) ((-1073 . -1123) T) ((-961 . -1123) T) ((-128 . -34) T) ((-122 . -34) T) ((-790 . -47) 130340) ((-788 . -47) 130312) ((-1252 . -564) 130223) ((-361 . -375) T) ((-489 . -1123) T) ((-1184 . -132) T) ((-1136 . -132) T) ((-462 . -47) 130202) ((-879 . -370) T) ((-862 . -132) T) ((-153 . -102) T) 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-1049) 128238) ((-1098 . -1229) 128217) ((-1046 . -294) 128192) ((-588 . -734) T) ((-572 . -802) T) ((-171 . -370) 128143) ((-572 . -799) T) ((-572 . -734) T) ((-503 . -734) T) ((-790 . -1229) T) ((-1157 . -497) 128127) ((-1098 . -895) NIL) ((-879 . -1123) T) ((-118 . -918) NIL) ((-1301 . -1300) 128103) ((-1299 . -1300) 128082) ((-790 . -895) NIL) ((-788 . -895) 127941) ((-1294 . -25) T) ((-1294 . -21) T) ((-1226 . -102) 127919) ((-1117 . -403) T) ((-631 . -656) 127906) ((-462 . -895) NIL) ((-683 . -102) 127884) ((-1098 . -1049) 127711) ((-879 . -23) T) ((-790 . -1049) 127570) ((-788 . -1049) 127427) ((-118 . -656) 127372) ((-462 . -1049) 127248) ((-322 . -624) 126812) ((-319 . -624) 126695) ((-398 . -654) 126664) ((-657 . -1049) 126648) ((-589 . -1229) T) ((-635 . -102) T) ((-526 . -1229) T) ((-224 . -497) 126632) ((-1279 . -34) T) ((-629 . -654) 126591) ((-295 . -1062) 126578) ((-137 . -624) 126562) ((-295 . -648) 126549) ((-643 . -725) 126533) ((-615 . -725) 126517) ((-678 . -38) 126477) ((-325 . -102) T) ((-85 . -621) 126459) ((-50 . -1049) 126443) ((-1131 . -1067) 126430) ((-1098 . -384) 126414) ((-790 . -384) 126398) ((-707 . -734) T) ((-707 . -802) T) ((-707 . -799) T) ((-589 . -1049) 126385) ((-526 . -1049) 126362) ((-60 . -57) 126324) ((-330 . -132) T) ((-322 . -1060) 126214) ((-319 . -1060) T) ((-171 . -1123) T) ((-788 . -384) 126198) ((-45 . -152) 126148) ((-1015 . -1003) 126130) ((-462 . -384) 126114) ((-415 . -174) T) ((-322 . -247) 126093) ((-319 . -247) T) ((-319 . -237) NIL) ((-300 . -1111) 125875) ((-227 . -132) T) ((-1131 . -111) 125860) ((-171 . -23) T) ((-807 . -148) 125839) ((-807 . -146) 125818) ((-256 . -647) 125724) ((-255 . -647) 125630) ((-325 . -290) 125596) ((-1168 . -522) 125529) ((-485 . -654) 125479) ((-1144 . -1111) T) ((-227 . -1071) T) ((-823 . -315) 125417) ((-1098 . -909) 125352) ((-790 . -909) 125295) ((-788 . -909) 125279) ((-1301 . -38) 125249) ((-1299 . -38) 125219) ((-1252 . -1123) T) ((-863 . -1123) T) ((-462 . -909) 125196) ((-866 . -1111) T) ((-1252 . -23) T) ((-1131 . -624) 125168) ((-1073 . -132) T) ((-579 . -1123) T) ((-863 . -23) T) ((-631 . -734) T) ((-362 . -929) T) ((-359 . -929) T) ((-295 . -102) T) ((-351 . -929) T) ((-981 . -1094) T) ((-961 . -132) T) ((-824 . -235) 125141) ((-118 . -802) NIL) ((-118 . -799) NIL) ((-118 . -734) T) ((-702 . -918) NIL) ((-1057 . -522) 125042) ((-489 . -132) T) ((-579 . -23) T) ((-683 . -315) 124980) ((-643 . -769) T) ((-615 . -769) T) ((-1243 . -858) NIL) ((-1091 . -1062) 124890) ((-1014 . -296) T) ((-702 . -656) 124840) ((-256 . -21) T) ((-358 . -1111) T) ((-256 . -25) T) ((-255 . -21) T) ((-255 . -25) T) ((-153 . -38) 124824) ((-2 . -102) T) ((-919 . -929) T) ((-1091 . -648) 124692) ((-490 . -1286) 124662) ((-1131 . -1060) T) ((-719 . -313) T) ((-366 . -1062) 124614) ((-360 . -1062) 124566) ((-352 . -1062) 124518) ((-366 . -648) 124470) ((-225 . -1049) 124447) ((-360 . -648) 124399) ((-108 . -1062) 124349) ((-352 . -648) 124301) ((-300 . -725) 124243) 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((-1243 . -1003) 123219) ((-346 . -1069) T) ((-112 . -1229) T) ((-176 . -1069) T) ((-103 . -621) 123151) ((-1186 . -146) 123130) ((-1186 . -148) 123109) ((-386 . -564) T) ((-1185 . -148) 123088) ((-1185 . -146) 123067) ((-1179 . -146) 122974) ((-415 . -296) T) ((-1179 . -148) 122881) ((-1137 . -148) 122860) ((-1137 . -146) 122839) ((-325 . -38) 122680) ((-171 . -132) T) ((-319 . -803) NIL) ((-319 . -800) NIL) ((-662 . -1060) T) ((-48 . -656) 122645) ((-1124 . -1062) 122542) ((-902 . -624) 122519) ((-1124 . -648) 122461) ((-1178 . -102) T) ((-1005 . -102) T) ((-1004 . -21) T) ((-128 . -1021) 122445) ((-122 . -1021) 122429) ((-1004 . -25) T) ((-910 . -120) 122413) ((-1170 . -102) T) ((-1252 . -132) T) ((-1184 . -25) T) ((-350 . -1229) T) ((-1184 . -21) T) ((-863 . -132) T) ((-1136 . -25) T) ((-1136 . -21) T) ((-862 . -25) T) ((-862 . -21) T) ((-790 . -313) 122392) ((-1171 . -315) 122187) ((-1168 . -497) 122171) ((-655 . -102) 122149) ((-640 . -102) T) ((-1161 . -152) 122099) ((-579 . -132) T) ((-629 . -856) 122078) ((-1157 . -621) 122040) ((-1157 . -622) 122001) ((-1035 . -799) T) ((-1035 . -802) T) ((-1035 . -734) T) ((-720 . -1067) 121824) ((-492 . -315) 121762) ((-461 . -425) 121732) ((-358 . -174) T) ((-256 . -235) 121678) ((-255 . -235) 121624) ((-295 . -38) 121611) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-276 . -102) T) ((-275 . -102) T) ((-274 . -102) T) ((-350 . -1049) 121588) ((-273 . -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) ((-361 . -734) T) ((-720 . -111) 121397) ((-678 . -233) 121381) ((-589 . -313) T) ((-526 . -313) T) ((-300 . -522) 121330) ((-108 . -315) NIL) ((-72 . -403) T) ((-1124 . -102) 121120) ((-841 . -419) 121104) ((-1131 . -803) T) ((-1131 . -800) T) ((-709 . -1111) T) ((-586 . -621) 121086) ((-386 . -370) T) ((-171 . -501) 121064) ((-224 . -621) 120996) ((-135 . -1111) T) ((-117 . -1111) T) ((-975 . -1229) T) ((-48 . -734) T) ((-1057 . -497) 120961) ((-142 . -433) 120943) ((-142 . -375) T) ((-1038 . -102) T) ((-520 . -517) 120922) ((-720 . -624) 120678) ((-484 . -102) T) ((-471 . -102) T) ((-1045 . -1123) T) ((-1236 . -621) 120660) ((-1193 . -1049) 120596) ((-1186 . -35) 120562) ((-1186 . -95) 120528) ((-1186 . -1217) 120494) ((-1186 . -1214) 120460) ((-1185 . -1214) 120426) ((-1185 . -1217) 120392) ((-1170 . -315) NIL) ((-89 . -404) T) ((-89 . -403) T) ((-1091 . -1163) 120371) ((-40 . -1229) 120343) ((-1185 . -95) 120309) ((-1045 . -23) T) ((-1185 . -35) 120275) ((-579 . -501) T) ((-1179 . -1214) 120241) ((-1179 . -1217) 120207) ((-1179 . -95) 120173) ((-1179 . -35) 120139) ((-368 . -1123) T) ((-366 . -1163) 120118) ((-360 . -1163) 120097) ((-352 . -1163) 120076) ((-1115 . -292) 120032) ((-1137 . -35) 119998) ((-1137 . -95) 119964) 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. -102) T) ((-110 . -102) T) ((-490 . -648) 118720) ((-40 . -384) 118697) ((-96 . -102) T) ((-661 . -860) 118681) ((-1184 . -235) 118668) ((-1146 . -1094) T) ((-1073 . -21) T) ((-1073 . -25) T) ((-1065 . -1062) 118652) ((-823 . -233) 118621) ((-961 . -25) T) ((-961 . -21) T) ((-1065 . -648) 118563) ((-629 . -1069) T) ((-1131 . -375) T) ((-1038 . -315) 118501) ((-678 . -654) 118460) ((-489 . -25) T) ((-489 . -21) T) ((-392 . -1062) 118444) ((-898 . -621) 118426) ((-894 . -621) 118408) ((-531 . -522) 118341) ((-256 . -858) 118292) ((-255 . -858) 118243) ((-392 . -648) 118213) ((-879 . -647) 118190) ((-484 . -315) 118128) ((-471 . -315) 118066) ((-358 . -296) T) ((-1168 . -1267) 118050) ((-1153 . -621) 118012) ((-1153 . -622) 117973) ((-1151 . -102) T) ((-1010 . -1067) 117869) ((-40 . -909) 117821) ((-1168 . -612) 117798) ((-1308 . -656) 117785) ((-874 . -498) 117762) ((-1074 . -152) 117708) ((-880 . -1233) T) ((-1010 . -111) 117590) ((-346 . -725) 117574) ((-874 . -621) 117536) ((-176 . 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. -1214) 96110) ((-211 . -1111) T) ((-210 . -1111) T) ((-117 . -1060) T) ((-209 . -1111) T) ((-208 . -1111) T) ((-205 . -1111) T) ((-204 . -1111) T) ((-203 . -1111) T) ((-202 . -1111) T) ((-201 . -1111) T) ((-200 . -1111) T) ((-199 . -1111) T) ((-198 . -1111) T) ((-197 . -1111) T) ((-196 . -1111) T) ((-195 . -1111) T) ((-244 . -102) 95900) ((-171 . -35) 95878) ((-171 . -95) 95856) ((-662 . -1049) 95752) ((-490 . -1069) 95682) ((-1124 . -1111) 95472) ((-1153 . -34) T) ((-678 . -497) 95456) ((-73 . -1229) T) ((-105 . -621) 95438) ((-1303 . -621) 95420) ((-388 . -621) 95402) ((-346 . -624) 95354) ((-176 . -624) 95271) ((-1228 . -498) 95252) ((-739 . -38) 95101) ((-579 . -1217) T) ((-579 . -1214) T) ((-539 . -621) 95083) ((-528 . -315) 95021) ((-508 . -621) 95003) ((-508 . -622) 94985) ((-1228 . -621) 94951) ((-1179 . -1163) NIL) ((-1038 . -1082) 94920) ((-1038 . -1111) T) ((-1015 . -102) T) ((-982 . -102) T) ((-923 . -102) T) ((-902 . -1049) 94897) ((-1153 . -734) T) ((-1014 . -656) 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. -102) T) ((-503 . -27) T) ((-244 . -315) 93664) ((-1098 . -1123) T) ((-1302 . -656) 93638) ((-790 . -1123) T) ((-788 . -1123) T) ((-1190 . -419) 93622) ((-462 . -1123) T) ((-1073 . -460) T) ((-1162 . -1111) T) ((-961 . -460) 93573) ((-1126 . -1094) T) ((-110 . -1111) T) ((-1098 . -23) T) ((-1171 . -522) 93356) ((-825 . -1069) T) ((-790 . -23) T) ((-788 . -23) T) ((-489 . -460) 93307) ((-469 . -23) T) ((-388 . -389) 93286) ((-362 . -235) 93259) ((-359 . -235) 93232) ((-351 . -235) 93205) ((-462 . -23) T) ((-269 . -235) 93178) ((-96 . -1111) T) ((-720 . -1229) T) ((-678 . -292) 93155) ((-492 . -522) 93088) ((-1271 . -1062) 92971) ((-1271 . -648) 92868) ((-1264 . -648) 92709) ((-1264 . -1062) 92544) ((-1243 . -648) 92340) ((-295 . -296) T) ((-1243 . -1062) 92130) ((-1093 . -621) 92112) ((-1093 . -622) 92093) ((-415 . -918) 92072) ((-1223 . -132) T) ((-50 . -1123) T) ((-1179 . -408) 92024) ((-1035 . -929) T) ((-1014 . -734) T) ((-851 . -656) 91997) ((-720 . -895) NIL) ((-604 . -1062) 91957) ((-589 . -1123) T) ((-526 . -1123) T) ((-603 . -1062) 91840) ((-1168 . -34) T) ((-1015 . -315) NIL) ((-823 . -497) 91824) ((-604 . -648) 91797) ((-361 . -929) T) ((-603 . -648) 91694) ((-919 . -235) 91681) ((-415 . -656) 91633) ((-50 . -23) T) ((-719 . -132) T) ((-720 . -1049) 91513) ((-589 . -23) T) ((-108 . -522) NIL) ((-526 . -23) T) ((-171 . -417) 91484) ((-1151 . -1111) T) ((-1294 . -1293) 91468) ((-709 . -803) T) ((-709 . -800) T) ((-1131 . -313) T) ((-386 . -148) T) ((-286 . -621) 91450) ((-285 . -621) 91432) ((-1242 . -1003) 91402) ((-48 . -929) T) ((-683 . -497) 91386) ((-256 . -1286) 91356) ((-255 . -1286) 91326) ((-1188 . -858) T) ((-1124 . -174) 91305) ((-1131 . -1033) T) ((-1057 . -34) T) ((-844 . -148) 91284) ((-844 . -146) 91263) ((-745 . -107) 91247) ((-620 . -133) T) ((-490 . -1111) 91037) ((-1190 . -1069) T) ((-879 . -460) T) ((-85 . -1229) T) ((-244 . -38) 91007) ((-142 . -107) 90989) ((-720 . -384) 90973) ((-841 . -624) 90841) ((-1302 . -734) T) ((-1291 . 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. -290) 89719) ((-1091 . -296) 89670) ((-495 . -856) T) ((-225 . -1123) T) ((-1243 . -290) 89636) ((-1223 . -501) 89602) ((-1015 . -38) 89552) ((-219 . -856) T) ((-426 . -654) 89511) ((-923 . -38) 89463) ((-851 . -802) 89442) ((-851 . -799) 89421) ((-851 . -734) 89400) ((-366 . -296) T) ((-360 . -296) T) ((-352 . -296) T) ((-171 . -460) 89331) ((-435 . -38) 89315) ((-108 . -296) T) ((-225 . -23) T) ((-415 . -802) 89294) ((-415 . -799) 89273) ((-415 . -734) T) ((-508 . -294) 89248) ((-485 . -1067) 89213) ((-666 . -132) T) ((-629 . -624) 89182) ((-1124 . -522) 89115) ((-343 . -132) T) ((-171 . -410) 89094) ((-490 . -725) 89036) ((-823 . -292) 89013) ((-485 . -111) 88969) ((-661 . -1069) T) ((-824 . -1062) 88812) ((-1290 . -1094) T) ((-1252 . -460) 88743) ((-824 . -648) 88592) ((-1289 . -1094) T) ((-1098 . -132) T) ((-1065 . -725) 88534) ((-790 . -132) T) ((-788 . -132) T) ((-579 . -460) T) ((-1038 . -522) 88467) ((-629 . -1060) T) ((-600 . -1111) T) ((-541 . -175) T) ((-469 . -132) T) 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85923) ((-841 . -803) 85902) ((-841 . -800) 85881) ((-1228 . -624) 85862) ((-604 . -38) 85835) ((-603 . -38) 85732) ((-878 . -564) T) ((-225 . -132) T) ((-325 . -1013) 85698) ((-79 . -621) 85680) ((-720 . -313) 85659) ((-300 . -734) 85561) ((-832 . -102) T) ((-872 . -852) T) ((-300 . -481) 85540) ((-1294 . -102) T) ((-40 . -370) T) ((-880 . -148) 85519) ((-493 . -654) 85501) ((-880 . -146) 85480) ((-1170 . -497) 85462) ((-1303 . -1060) T) ((-490 . -522) 85395) ((-1157 . -1229) T) ((-973 . -621) 85377) ((-655 . -497) 85361) ((-640 . -497) 85292) ((-823 . -621) 85023) ((-48 . -27) T) ((-1190 . -725) 84920) ((-661 . -1111) T) ((-869 . -868) T) ((-444 . -371) 84894) ((-739 . -654) 84804) ((-1113 . -102) T) ((-981 . -1111) T) ((-872 . -1111) T) ((-824 . -315) 84791) ((-541 . -535) T) ((-541 . -584) T) ((-1299 . -389) 84763) ((-1065 . -522) 84696) ((-1171 . -292) 84672) ((-244 . -233) 84641) ((-256 . -1062) 84538) ((-255 . -1062) 84435) ((-1291 . -725) 84405) ((-1178 . -93) T) ((-1005 . -93) 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. -564) T) ((-227 . -1062) 77454) ((-655 . -621) 77386) ((-655 . -622) 77347) ((-640 . -622) NIL) ((-640 . -621) 77329) ((-495 . -174) T) ((-227 . -648) 77294) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-482 . -1217) 77260) ((-482 . -1214) 77226) ((-279 . -621) 77208) ((-278 . -621) 77190) ((-277 . -621) 77172) ((-276 . -621) 77154) ((-275 . -621) 77136) ((-508 . -659) 77118) ((-274 . -621) 77100) ((-346 . -734) T) ((-273 . -621) 77082) ((-110 . -19) 77064) ((-176 . -734) T) ((-508 . -380) 77046) ((-214 . -621) 77028) ((-528 . -1160) 77012) ((-508 . -124) T) ((-110 . -612) 76987) ((-213 . -621) 76969) ((-482 . -35) 76935) ((-482 . -95) 76901) ((-211 . -621) 76883) ((-210 . -621) 76865) ((-209 . -621) 76847) ((-208 . -621) 76829) ((-205 . -621) 76811) ((-204 . -621) 76793) ((-203 . -621) 76775) ((-202 . -621) 76757) ((-201 . -621) 76739) ((-200 . -621) 76721) ((-199 . -621) 76703) ((-544 . -1114) 76655) ((-198 . -621) 76637) ((-197 . -621) 76619) ((-45 . -497) 76556) ((-196 . 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-1062) 69914) ((-490 . -621) 69645) ((-244 . -419) 69614) ((-961 . -315) 69601) ((-579 . -648) 69588) ((-65 . -1229) T) ((-1074 . -522) 69432) ((-679 . -1111) T) ((-631 . -132) T) ((-489 . -315) 69419) ((-614 . -1111) T) ((-554 . -102) T) ((-118 . -132) T) ((-295 . -1060) T) ((-182 . -1111) T) ((-162 . -1111) T) ((-157 . -1111) T) ((-155 . -1111) T) ((-461 . -769) T) ((-31 . -1094) T) ((-972 . -174) 69370) ((-981 . -93) T) ((-1091 . -1067) 69280) ((-629 . -802) 69259) ((-601 . -1111) T) ((-629 . -799) 69238) ((-629 . -734) T) ((-301 . -292) 69217) ((-300 . -1229) T) ((-1065 . -621) 69179) ((-1065 . -622) 69140) ((-1035 . -1123) T) ((-171 . -102) T) ((-280 . -858) T) ((-1177 . -1111) T) ((-826 . -621) 69122) ((-1124 . -294) 69099) ((-1113 . -231) 69083) ((-1014 . -313) T) ((-807 . -725) 69067) ((-366 . -1067) 69019) ((-361 . -1123) T) ((-360 . -1067) 68971) ((-422 . -621) 68953) ((-392 . -621) 68935) ((-352 . -1067) 68887) ((-229 . -621) 68819) ((-1091 . -111) 68715) ((-1035 . -23) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 7d8d20f6..dbaa9aad 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3485464568) +(30 . 3485478044) (4457 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -484,661 +484,661 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |bfKeys| |stoseInvertibleSetsqfreg| |mapSolve| - |aromberg| |iitanh| |over| |elementary| |clearTable!| |poisson| - |minimize| |inputBinaryFile| |presuper| |lhs| |option?| |iExquo| - |uncouplingMatrices| |intChoose| |irreducible?| - |stoseIntegralLastSubResultant| |meshPar2Var| |setPoly| |lcm| - |patternMatch| |rhs| |createNormalElement| |setlast!| |chvar| |isList| - |hcrf| |bfEntry| |curveColorPalette| |leftRankPolynomial| - |removeCoshSq| |closeComponent| |generate| |ideal| |squareMatrix| - |f02aff| |diagonalProduct| |zeroDimPrime?| |primextendedint| |s18acf| - |tanIfCan| |numberOfCycles| |SFunction| |append| |currentEnv| - |rootBound| |dmpToHdmp| |HermiteIntegrate| |insert!| |negative?| - |pattern| |flagFactor| |cAcos| |OMlistSymbols| |clearDenominator| - |gcd| |count| |incrementBy| |ellipticCylindrical| |tan2trig| - |nextPrimitivePoly| |bivariate?| |mainCoefficients| |real?| - |padicFraction| |OMmakeConn| |simpsono| |changeMeasure| |false| |lp| - |category| |expand| |combineFeatureCompatibility| |critM| |upperBound| - |sin2csc| |rischNormalize| |ptree| |sech2cosh| |moreAlgebraic?| - |symFunc| |coerceP| |gethi| |flatten| |binarySearchTree| |filterWhile| - |numericalIntegration| |cyclicGroup| |hexDigit?| |domain| - |isConnected?| 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|chiSquare| |f02akf| |lowerBound| |optAttributes| - |var2StepsDefault| |partialQuotients| |kmax| |subst| |supersub| - |subTriSet?| |subspace| |extractBottom!| |squareFreePrim| |monomials| - |acscIfCan| |edf2efi| |rule| |nextSublist| |rarrow| |KrullNumber| - |taylorQuoByVar| |internalZeroSetSplit| |makeRecord| |mapExponents| - |d01gaf| |secIfCan| |parent| LODO2FUN |complexLimit| |minPoly| - |mapBivariate| |zeroOf| |ddFact| |outerProduct| |f02abf| |minColIndex| - |clip| |stoseSquareFreePart| |monomialIntegrate| |mindegTerm| - |fortranDouble| |surface| |exprHasLogarithmicWeights| |myDegree| - |alternating| |disjunction| |declare!| |unary?| |wholeRadix| |lookup| - |OMgetInteger| |clearTheFTable| |axesColorDefault| |OMputAtp| - |diophantineSystem| |rank| |belong?| |inGroundField?| |setPosition| - |style| |rename| |midpoint| |tValues| |low| |sincos| |resultantReduit| - |derivative| |every?| |elaborateFile| |df2fi| |rk4a| |leadingIndex| - |initials| |status| |pseudoRemainder| |objects| |cdr| |rules| - |useSingleFactorBound?| |primes| |partialNumerators| |limitedint| - |padicallyExpand| |bigEndian| |recolor| |realRoots| |LyndonBasis| - |base| |numFunEvals3D| |sin?| |pushdown| |ipow| - |tryFunctionalDecomposition?| |iiacosh| |coefficients| - |fillPascalTriangle| |ridHack1| |lambert| |step| |spherical| |makeSUP| - |dmp2rfi| |difference| |makeVariable| |f02agf| |irCtor| |c05pbf| - |checkForZero| |identitySquareMatrix| |meatAxe| |close!| |someBasis| - |palgint0| |quotientByP| |remainder| |scanOneDimSubspaces| - |genericRightTrace| |rightGcd| |getMatch| |segment| |pushup| |cyclic?| - |resultantnaif| |optional?| |insertTop!| |writable?| |vconcat| |lists| - |rubiksGroup| |limitPlus| |dioSolve| |cAcsc| - |tableForDiscreteLogarithm| |toseSquareFreePart| |space| |composites| - |d01anf| |iiasec| |discriminant| |OMsupportsCD?| |list?| |s18adf| - |rotate!| |qroot| |maxrow| |createNormalPrimitivePoly| |top!| - |reopen!| |iisqrt2| |rightDiscriminant| |divergence| - |showTheSymbolTable| |constantRight| |factorFraction| |Hausdorff| - |crushedSet| |deref| |lowerCase?| |psolve| |maximumExponent| - |branchPointAtInfinity?| |basisOfNucleus| |scale| |yCoord| |qPot| - |plenaryPower| |parseString| |bracket| |e04gcf| |key| |listBranches| - |lfextlimint| |Si| |returnTypeOf| |d01amf| |s17acf| - |integralMatrixAtInfinity| |listRepresentation| |outlineRender| - |leadingExponent| |jordanAdmissible?| |printingInfo?| |value| - |removeRoughlyRedundantFactorsInPol| |generalSqFr| |extend| - |exprToGenUPS| |euclideanGroebner| |tablePow| |filename| |fTable| - |addMatch| |seed| |previous| |stopMusserTrials| |binaryTournament| - |inverseIntegralMatrix| |sqfrFactor| |ScanFloatIgnoreSpacesIfCan| - |integer?| |leastAffineMultiple| |pdf2df| |cycleRagits| |rotatez| - |basisOfCenter| |mkAnswer| |stiffnessAndStabilityFactor| |makeEq| - |bipolar| |parse| |viewport3D| |scaleRoots| |before?| |outputAsScript| - |ListOfTerms| |coerceListOfPairs| |associatedEquations| - |leftScalarTimes!| |datalist| |showFortranOutputStack| |setUnion| - |exQuo| |zeroSetSplit| |stop| |resetNew| |beauzamyBound| |coerceS| - |trivialIdeal?| |cscIfCan| |mr| |arguments| |imagi| |inconsistent?| - |outputGeneral| |numberOfMonomials| |fixedPoint| |OMputEndObject| - |initiallyReduce| |isobaric?| |continuedFraction| |iiatanh| - |bezoutDiscriminant| |lfinfieldint| RF2UTS |inf| |fixPredicate| - |moduleSum| |factorPolynomial| |ParCond| |normalForm| |element?| - |groebner| |precision| |result| |setErrorBound| |setRealSteps| |iipow| - |FormatArabic| |nthRoot| |pointColorDefault| |getlo| |equiv| - |selectPDERoutines| |removeDuplicates!| |localReal?| |quotedOperators| - |hclf| |normDeriv2| |f04jgf| |iiGamma| |normalizedDivide| |quadratic?| - |algDsolve| |makeResult| |makeViewport2D| |tower| |computeCycleEntry| - |factorSquareFree| |horizConcat| |subResultantChain| |euclideanSize| - |rombergo| |blankSeparate| |cosh2sech| |just| |palgRDE0| |s18aff| - |tanNa| |generalTwoFactor| |makeTerm| |dot| |readUInt8!| |karatsuba| - |elRow1!| |taylor| |comment| |leftRegularRepresentation| |modularGcd| - |perfectNthPower?| |leftFactor| |btwFact| |reverseLex| |explogs2trigs| - |iflist2Result| |concat!| |interpret| |internalSubPolSet?| |laurent| - |createPrimitivePoly| |shade| |selectPolynomials| |infRittWu?| - |e02bdf| |rst| |e01baf| |build| |puiseux| |unrankImproperPartitions1| - |oddlambert| |fixedDivisor| |rootOf| |evaluate| |matrix| |index| - |floor| |s17adf| |internalDecompose| |getCurve| |evenInfiniteProduct| - |medialSet| |flexible?| |degreeSubResultant| - |rewriteIdealWithRemainder| |createLowComplexityNormalBasis| - |csch2sinh| |open?| |leftMult| |charClass| |inv| |dfRange| |lambda| - |antisymmetricTensors| |graphStates| |gradient| |s17akf| |writeBytes!| - |ground?| |hermite| |d02gbf| |recip| |factorGroebnerBasis| |s19adf| - |edf2df| |mkcomm| |pair| |OMreadFile| |solveLinearPolynomialEquation| - |randnum| |ground| |ref| |localUnquote| |antiCommutator| - |fortranCompilerName| |totalLex| |acoshIfCan| |atoms| |llprop| - |polygamma| |cyclicEntries| |leadingMonomial| |finiteBasis| - |nullSpace| |OMgetVariable| |nextPrime| |nonLinearPart| - |leadingSupport| |s18aef| |sum| |baseRDE| |box| |validExponential| - |reverse| |leadingCoefficient| |tanintegrate| |algebraicOf| |any| - |c06fqf| |directory| |cAtan| |internal?| |triangularSystems| - |rightFactorIfCan| |primitiveMonomials| |shrinkable| |closedCurve| - |fortranLogical| |purelyAlgebraic?| |stiffnessAndStabilityOfODEIF| - |retract| |modifyPointData| |tanQ| |trueEqual| |bernoulliB| |reductum| - |firstSubsetGray| |cSin| |contractSolve| |more?| |leftOne| |elem?| - |asinhIfCan| |particularSolution| |lfextendedint| |nlde| |lexico| - |contains?| |bothWays| |singular?| |maxRowIndex| |cAsinh| F2FG - |tubePlot| |lastSubResultantElseSplit| |getButtonValue| - |numberOfOperations| |atanhIfCan| |connect| |categoryFrame| - |insertionSort!| |drawComplexVectorField| |integral| |f04arf| - |mainCharacterization| |SturmHabichtMultiple| |argscript| |applyRules| - |addPoint| |f02bbf| |acotIfCan| |jordanAlgebra?| |asinIfCan| - |constantToUnaryFunction| |relerror| |geometric| |fractionPart| - |sizePascalTriangle| |nthFactor| |newTypeLists| |shiftLeft| - |jacobiIdentity?| |iiatan| |makeFR| |s20acf| |getMeasure| |pr2dmp| - |set| |e01bef| |OMgetString| |iiasin| |iterationVar| - |reducedDiscriminant| |reducedSystem| |decomposeFunc| |replace| - |printStats!| |expenseOfEvaluation| |inRadical?| |numberOfChildren| - |coth2trigh| |showAll?| |lSpaceBasis| |singRicDE| |rightExactQuotient| - |scalarTypeOf| |numberOfComputedEntries| |lowerPolynomial| |coHeight| - |mergeFactors| |mindeg| |useSingleFactorBound| |c05nbf| |f01rcf| - |constant?| |normalizedAssociate| |removeSquaresIfCan| |lieAlgebra?| - |OMgetEndAtp| |overlabel| |stoseInvertible?sqfreg| |contract| |cycle| - |accuracyIF| |pquo| |basisOfCommutingElements| |packageCall| - |resultantEuclidean| |radix| |redPol| |putColorInfo| |s17agf| - |critBonD| |sylvesterSequence| |cfirst| |squareFreeLexTriangular| - |coordinates| |primintegrate| |FormatRoman| |lllp| |d01alf| - |signature| |OMputEndError| |symmetricProduct| |anfactor| |getGraph| - |basisOfLeftNucloid| |row| |choosemon| |quadratic| |bezoutMatrix| - |f02ajf| |pile| |alphabetic| |nonSingularModel| |typeForm| - |setIntersection| |tubePoints| |multiplyExponents| |search| |expr| - |createMultiplicationMatrix| |LyndonWordsList1| |littleEndian| - |pushNewContour| |atrapezoidal| |stronglyReduced?| |firstDenom| - |algebraicVariables| |oneDimensionalArray| |currentSubProgram| - |tanSum| |taylorIfCan| |setLength!| |newLine| - |semiDiscriminantEuclidean| |BasicMethod| |binomial| |outputForm| - |outputList| |splitLinear| |measure2Result| |s18dcf| |listOfLists| - |copyInto!| |acothIfCan| |mainValue| |symmetricSquare| - |recoverAfterFail| |tube| |writeInt8!| |cyclicSubmodule| |show| - |digits| |taylorRep| |shellSort| |shallowExpand| |binaryFunction| - |infieldIntegrate| |isPlus| |split| |length| |rootProduct| - |infiniteProduct| |variable| |divisorCascade| |att2Result| |imagj| - |monic?| |critpOrder| |mkPrim| |linearDependence| |signatureAst| - |scripts| |OMencodingUnknown| |invertibleSet| |trace| |fortranReal| - |iterators| |degreePartition| |mergeDifference| |eigenvalues| - |solveLinearPolynomialEquationByRecursion| |isAtom| |indices| |s19acf| - |weights| |c06gbf| |linear?| |denominator| |iisin| |hessian| |coerceL| - |changeThreshhold| |systemCommand| |lighting| |lazyIrreducibleFactors| - |char| |iiacoth| |OMreceive| |nullity| |checkPrecision| - |purelyAlgebraicLeadingMonomial?| |point?| |printInfo!| |figureUnits| - |stopTable!| |prinpolINFO| |maxColIndex| |invertibleElseSplit?| - |cothIfCan| |hexDigit| |integralDerivationMatrix| |fglmIfCan| - |evenlambert| |pow| |trigs| |iCompose| |eulerE| |squareFreeFactors| - |s19aaf| |sparsityIF| |overbar| |functionIsOscillatory| |lifting| - |rootPoly| |OMcloseConn| |definingEquations| |lyndon?| |normal| |sign| - |simplifyLog| |algSplitSimple| |powers| |elColumn2!| |quasiRegular?| - |cond| |rowEchelonLocal| |deriv| |permutations| |removeZeroes| |shape| - |concat| |makeUnit| |select!| |nextPartition| |increasePrecision| - |lazyPrem| |extension| |commonDenominator| |rightRankPolynomial| - |lflimitedint| |iicosh| |generic?| |outputBinaryFile| |complement| - |duplicates?| |fi2df| |deleteRoutine!| |integerBound| - |normalizeAtInfinity| |csch| |OMputSymbol| |decompose| |s17dlf| - |basisOfMiddleNucleus| |makeMulti| |normalise| |unaryFunction| - |refine| |float| |leaf?| |environment| |asinh| |OMsupportsSymbol?| - |eigenvectors| |testModulus| |triangular?| |univariatePolynomial| - |overlap| |extractPoint| |tableau| |LiePolyIfCan| |lepol| - |fullDisplay| |acosh| |integralAtInfinity?| |monicModulo| |stirling1| - |reduceLODE| |solveLinear| |odd?| |principalIdeal| |primeFactor| - |conjug| |toScale| |arg1| |curryLeft| |atanh| |child?| |updatD| - |readBytes!| |monomRDEsys| |nsqfree| |completeEval| |hyperelliptic| - |op| |invmultisect| |pToDmp| |readLine!| |byteBuffer| |arg2| |rowEch| - |acoth| |removeIrreducibleRedundantFactors| |principal?| |totalDegree| - |isAbsolutelyIrreducible?| |rationalPoint?| |solid?| |physicalLength!| - |palgextint0| |polyred| |pushdterm| |asech| |truncate| - |printStatement| |f04maf| |OMgetAtp| |kroneckerDelta| |numer| - |ratpart| |multinomial| |bitLength| |powern| |readLineIfCan!| - |eisensteinIrreducible?| |paren| |coshIfCan| |exactQuotient!| - |conditions| |sequences| |variables| |front| |eulerPhi| |denom| - |removeRedundantFactors| |se2rfi| |zeroSetSplitIntoTriangularSystems| - |extractTop!| |irForm| |dAndcExp| |f02fjf| |multiple| |match| - |complexForm| |options| |smith| |mapdiv| |matrixDimensions| - |regularRepresentation| |f04asf| |quasiAlgebraicSet| |aspFilename| - |firstNumer| |applyQuote| |hasSolution?| |frst| - |expenseOfEvaluationIF| |unitNormal| |subresultantSequence| |pi| - |semiResultantEuclideannaif| |tree| |changeBase| |monomial?| |cCosh| - |isAnd| |leastPower| |d01gbf| |exp1| |wordsForStrongGenerators| - |besselY| |infinity| |repSq| |OMgetType| |e02dcf| |union| - |complexSolve| |nullary| |copy!| |string| |setOrder| |palgRDE| - |prepareDecompose| |tubePointsDefault| |transpose| |s21bbf| - |defineProperty| |getGoodPrime| |primitivePart| |f01qdf| |ruleset| - |stoseInvertibleSetreg| |linearPart| |internalIntegrate| - |create3Space| |shallowCopy| |d01bbf| |indiceSubResultantEuclidean| - |factorByRecursion| |setVariableOrder| |leftExactQuotient| |dark| - |f04faf| |viewPosDefault| |blue| |kernel| |genericRightDiscriminant| - |heap| |stopTableInvSet!| |high| |headReduced?| |digamma| |typeLists| - |rootRadius| |quadraticNorm| |setClosed| |list| |complexNumeric| - |findBinding| |setColumn!| |symbolIfCan| |factorial| |aCubic| - |dimensionOfIrreducibleRepresentation| |e01daf| |suchThat| |remove!| - |restorePrecision| |rroot| |trailingCoefficient| |draw| |formula| - |rotatex| |numberOfVariables| |nativeModuleExtension| |palglimint| - |partition| |dualSignature| |iicot| |seriesToOutputForm| - |rightRemainder| |linearDependenceOverZ| - |noncommutativeJordanAlgebra?| |extractIndex| |intermediateResultsIF| - |diagonal?| |SturmHabichtSequence| |collectQuasiMonic| |curry| - |integers| |powmod| |s14aaf| |setDifference| |regime| |airyAi| - |rdHack1| |csc2sin| |setAttributeButtonStep| |makeSeries| |expint| - |solve| |f02aef| |compound?| |matrixGcd| |cup| |basisOfRightNucloid| - |f04atf| |writeByte!| |prod| |showTheFTable| |orbits| |leftRemainder| - |hostPlatform| |innerEigenvectors| |makeObject| |nrows| |palgLODE0| - |iiexp| |lowerCase| |rewriteIdealWithQuasiMonicGenerators| - |quasiMonic?| |freeOf?| |cSinh| |screenResolution| |read!| |center| - |measure| |ncols| |coef| |minimumExponent| |OMconnInDevice| - |pseudoDivide| |in?| |leftExtendedGcd| |stack| |neglist| |cosIfCan| - |goodnessOfFit| |simplifyExp| |resetAttributeButtons| |label| - |goodPoint| |augment| |iifact| |representationType| |ratDsolve| - |realZeros| |hasTopPredicate?| |wordInGenerators| |identity| - |thetaCoord| |name| |mapDown!| |s01eaf| |constantOpIfCan| - |initializeGroupForWordProblem| |basisOfLeftAnnihilator| - |genericRightNorm| |cartesian| |maxPoints| |primitivePart!| - |OMputBVar| |digit?| |body| |cCsc| ** |factorials| |explicitEntries?| - |modularFactor| |e02aef| |leftNorm| |monicLeftDivide| |newReduc| - |bumprow| |increase| |quote| |relationsIdeal| |lex| - |linearlyDependent?| |hasoln| |componentUpperBound| |hconcat| - |normalizeIfCan| |f04mbf| |laplacian| |bivariateSLPEBR| |constDsolve| - |evaluateInverse| |s17aff| |setMaxPoints| |diagonal| |f02axf| - |tensorProduct| |stopTableGcd!| |fractRagits| |subSet| |sec2cos| - |squareFreePart| |minRowIndex| |stoseInvertible?reg| |range| - |bandedJacobian| |f04axf| |e04jaf| |cycleEntry| |printCode| |weighted| - |updatF| |addiag| |point| |binary| |stoseInternalLastSubResultant| - |direction| |simpleBounds?| |cPower| |iilog| |generalPosition| - |totalfract| |resize| |fractionFreeGauss!| |setMaxPoints3D| |option| - |e01sbf| |fractRadix| |innerint| |probablyZeroDim?| - |irreducibleFactor| |positiveRemainder| SEGMENT |c02aff| |numFunEvals| - |frobenius| |Vectorise| |attributeData| |withPredicates| - |oddInfiniteProduct| |rationalFunction| |port| |e04dgf| - |extendedResultant| |countable?| |mat| |series| - |createMultiplicationTable| |connectTo| |repeating| |trigs2explogs| - |nthExponent| |laplace| |triangulate| |stripCommentsAndBlanks| - |setLabelValue| |pointLists| |red| |bumptab| |OMsend| - |toseInvertible?| |t| |useEisensteinCriterion?| |queue| |rischDEsys| - |epilogue| |linSolve| |rk4| |patternMatchTimes| |OMreadStr| - |extendedEuclidean| |lyndon| |exprHasWeightCosWXorSinWX| |cCsch| - |cAsec| |normalized?| |numberOfIrreduciblePoly| |backOldPos| - |newSubProgram| |inverse| |ramifiedAtInfinity?| |hermiteH| - |identityMatrix| |ScanFloatIgnoreSpaces| |forLoop| |generic| |sup| - |setvalue!| |OMunhandledSymbol| |min| |factorset| |hasPredicate?| - |meshFun2Var| |content| |arbitrary| |matrixConcat3D| - |derivationCoordinates| |isTimes| |subPolSet?| |partitions| |nor| - |OMUnknownCD?| |mdeg| |OMputInteger| |boundOfCauchy| - |antiCommutative?| |monicRightFactorIfCan| |finiteBound| - |roughUnitIdeal?| |unknown| |OMputAttr| |whatInfinity| |apply| - |chiSquare1| |removeSuperfluousQuasiComponents| |indicialEquation| - |ParCondList| |hypergeometric0F1| |rootNormalize| |substitute| - |mathieu24| |npcoef| |symmetricGroup| |first| |yCoordinates| - |signAround| |linearPolynomials| |unrankImproperPartitions0| - |invertible?| |constantKernel| |OMencodingXML| |setRow!| - |removeSuperfluousCases| |head| |rest| |complexEigenvalues| - |viewSizeDefault| |polar| |conical| |binaryTree| |resetBadValues| - |Frobenius| |viewPhiDefault| |aQuadratic| |case| |imag| |rename!| - |color| |viewWriteAvailable| |flexibleArray| |s19abf| - |viewDeltaYDefault| |realSolve| |OMsetEncoding| - |rewriteIdealWithHeadRemainder| |maxint| |Zero| |minimalPolynomial| - |anticoord| |comp| |rightRecip| |keys| |expt| |OMputEndAttr| |true| - |log2| |void| |hash| |ip4Address| |SturmHabicht| |zCoord| - |exponential| |One| |top| |computeBasis| |complexNumericIfCan| - |inverseColeman| |sPol| |randomR| |cyclotomic| |RittWuCompare| - |splitNodeOf!| |imagk| |nthRootIfCan| |continue| |cubic| - |firstUncouplingMatrix| |copies| |d01fcf| |doubleResultant| - |setMinPoints| |size?| |host| |plusInfinity| |sort| |palgLODE| - |inputOutputBinaryFile| |cCoth| |tab1| |initTable!| |reduced?| - |setProperty| |OMputObject| |quotient| |minusInfinity| |makeprod| - |critT| |aQuartic| |multiEuclideanTree| |genus| |headAst| |nthExpon| - |viewZoomDefault| |semiResultantEuclidean2| |cot2tan| |critMonD1| - |leftFactorIfCan| |readUInt32!| |radicalSolve| |coefChoose| |id| - |basisOfRightNucleus| |points| |iiperm| |changeWeightLevel| - |definingInequation| |viewport2D| |zeroDimensional?| |mainExpression| - |gcdPolynomial| |isOr| |subCase?| |elt| |lo| |unitVector| |OMgetBind| - |lastSubResultant| |listYoungTableaus| |removeCosSq| |random| |part?| - |graphCurves| |divide| |besselJ| |logGamma| |eq?| |stFunc1| |next| - |numberOfNormalPoly| |transform| |normInvertible?| |fprindINFO| - |noValueMode| |nilFactor| |fibonacci| |lyndonIfCan| |extendedint| - |mkIntegral| |polyPart| |ratDenom| |cyclicParents| |mulmod| |setTex!| - |setref| |endOfFile?| |e02agf| |e04ycf| |weakBiRank| |multiset| - |leftTraceMatrix| |overset?| |rootSimp| |getIdentifier| - |replaceKthElement| |stoseInvertibleSet| |LowTriBddDenomInv| - |linkToFortran| |iisinh| |leftDiscriminant| |symbol?| |trim| - |complexIntegrate| |algebraic?| |logpart| |arity| |extendIfCan| |kind| - |halfExtendedSubResultantGcd2| |cCos| |nil?| |OMwrite| |solveRetract| - |clipParametric| |node?| |functorData| |s17dgf| - |extendedSubResultantGcd| |insert| |physicalLength| |logical?| - |singleFactorBound| |ldf2vmf| |mapMatrixIfCan| |exteriorDifferential| - |messagePrint| |rightTraceMatrix| |semiResultantReduitEuclidean| - |clipWithRanges| |numberOfHues| |leader| |ranges| |hdmpToP| |swap!| - |makingStats?| |rotatey| |entries| |OMgetEndAttr| |e01bff| |s14baf| - |getProperty| |iiacsc| |position!| |selectfirst| |superscript| |Nul| - |cos2sec| |primintfldpoly| |slash| |bytes| |interpretString| - |cRationalPower| |invmod| |hitherPlane| |checkRur| GF2FG |zerosOf| - |groebgen| |iiabs| |LagrangeInterpolation| |roughBasicSet| |lquo| - |logIfCan| |viewThetaDefault| |HenselLift| |OMconnectTCP| |s14abf| - |airyBi| |e02daf| |directSum| |create| |nextColeman| |printTypes| - |conjugate| |c02agf| |dflist| |palgintegrate| |nthCoef| |vertConcat| - |graphs| |genericPosition| |symbolTableOf| |drawComplex| |hspace| - |meshPar1Var| |reciprocalPolynomial| |has?| |adaptive3D?| - |createPrimitiveElement| |wholePart| |conditionsForIdempotents| - |dmpToP| |plot| |mainPrimitivePart| |symbolTable| - |internalSubQuasiComponent?| |f07aef| |listOfMonoms| |dominantTerm| - |clipPointsDefault| |quadraticForm| |droot| |findConstructor| - |expintegrate| |bat1| |diagonals| |sample| |linearAssociatedLog| - |lexTriangular| |exprex| |acschIfCan| |iiacos| |f2df| - |radicalEigenvalues| |pushFortranOutputStack| |entry?| |setClipValue| - |weierstrass| |safeCeiling| |rotate| |d03edf| |buildSyntax| - |popFortranOutputStack| |optpair| |completeEchelonBasis| |d01asf| - |OMgetEndBVar| |GospersMethod| |width| |subHeight| |e02ajf| - |purelyTranscendental?| |generateIrredPoly| |max| |super| - |setButtonValue| |pureLex| |even?| |outputAsFortran| - |tubeRadiusDefault| |d02bhf| |setScreenResolution| |predicates| - |square?| |thenBranch| |opeval| Y |sizeMultiplication| |conjunction| - |perfectNthRoot| |addBadValue| |moebius| |factors| |computeInt| - |outputAsTex| |iteratedInitials| |var1StepsDefault| |f04qaf| - |enumerate| |wronskianMatrix| |coercePreimagesImages| |asimpson| - |UnVectorise| |curveColor| |e01bhf| |integerIfCan| |f02awf| - |complementaryBasis| |polyRicDE| |separateDegrees| |e01sef| - |sizeLess?| |ran| |charthRoot| |symmetricTensors| - |shanksDiscLogAlgorithm| |lineColorDefault| |exprToUPS| - |positiveSolve| |increment| |delay| |exprHasAlgebraicWeight| - |clearCache| |bringDown| |genericRightTraceForm| |pack!| |table| - |lift| |exptMod| |simpson| |setleaves!| |writeUInt8!| - |genericLeftTraceForm| |karatsubaOnce| |SturmHabichtCoefficients| - |putProperty| |leftZero| |insertMatch| |new| |reduce| |string?| - |solveLinearlyOverQ| |obj| |euler| |semiIndiceSubResultantEuclidean| - |chebyshevT| |userOrdered?| |limitedIntegrate| |optional| |badValues| - |nand| |constantCoefficientRicDE| |rootKerSimp| |basicSet| - |outputMeasure| |integralBasisAtInfinity| |outputFloating| |quickSort| - |cache| |binomThmExpt| |generalizedContinuumHypothesisAssumed?| - |rightTrace| |li| |repeating?| |strongGenerators| |makeViewport3D| - |coord| |quatern| |duplicates| |complexEigenvectors| |f02wef| - |makeCrit| |virtualDegree| |property| |explimitedint| |e02bbf| - |closed| |pole?| |zeroDim?| |complete| |selectSumOfSquaresRoutines| - |d02bbf| |edf2ef| |d01akf| |rangePascalTriangle| |adaptive?| |factor| - |removeRoughlyRedundantFactorsInPols| |showScalarValues| |leftTrace| - |removeRedundantFactorsInPols| |lazyIntegrate| |polygon?| - |reducedQPowers| |showArrayValues| |normalElement| |gderiv| |getCode| - |getMultiplicationTable| |transcendentalDecompose| |qelt| |inR?| - |iitan| |parametersOf| |pmComplexintegrate| |setfirst!| |cAcot| - |resetVariableOrder| |qsetelt| |approxSqrt| |setTopPredicate| - |plotPolar| |constantIfCan| |vector| |credPol| |countRealRoots| - |getConstant| |cyclicCopy| |reindex| |varselect| |leftAlternative?| - |inverseLaplace| |monicRightDivide| |createThreeSpace| |xRange| - |differentiate| |besselI| |realElementary| |voidMode| |OMgetSymbol| - |pop!| |getPickedPoints| |predicate| |createIrreduciblePoly| |diag| - |monomRDE| |yRange| |screenResolution3D| |setPrologue!| |minPol| - |splitSquarefree| |e02adf| |BumInSepFFE| |alphanumeric?| |deepestTail| - |zRange| |currentScope| |setStatus!| |balancedBinaryTree| |coordinate| - |setPredicates| |size| |e02baf| |alternatingGroup| |monomial| |left| - |coth2tanh| |cross| |dom| |test| |sncndn| |map!| |cAcosh| - |countRealRootsMultiple| |characteristicSerie| |byte| |nextNormalPoly| - |dequeue| |lazyResidueClass| |iisech| |factorList| |right| - |determinant| |multivariate| |lazyPquo| |qsetelt!| - |radicalEigenvectors| |sh| |latex| |setEmpty!| |splitDenominator| - |systemSizeIF| |biRank| |cAsech| |integralLastSubResultant| |lprop| - |retractIfCan| EQ |bounds| |stoseInvertible?| |divideExponents| - |lazyPseudoRemainder| |pointColor| |mapGen| |elRow2!| |interReduce| - |linear| |close| |ffactor| |central?| |const| |OMread| |lazy?| - |divideIfCan!| |cSec| |OMopenFile| |sechIfCan| |sqrt| - |fortranCharacter| |totolex| |isImplies| |autoReduced?| |separant| - |getZechTable| |getStream| |linGenPos| |polynomial| |redmat| |leaves| - |display| |real| |mainForm| |title| |setnext!| |split!| |ravel| - |solve1| |linearMatrix| |removeDuplicates| |prefix| |mpsode| - |prolateSpheroidal| |radPoly| |s15adf| |acsch| |reshape| - |chainSubResultants| |OMputFloat| |toroidal| |f02aaf| |iibinom| - |bsolve| |parameters| |integral?| |dn| |rationalIfCan| |leftUnit| - |decreasePrecision| |critMTonD1| |listConjugateBases| |reflect| |int| - |cycleLength| |localIntegralBasis| |e| |gcdPrimitive| |push| |s17ahf| - |assign| |node| |viewpoint| |iidsum| |corrPoly| |changeNameToObjf| - |irreducibleRepresentation| |quasiRegular| |headRemainder| - |directProduct| |character?| |completeHensel| |reorder| |legendreP| - |readUInt16!| |input| |recur| |map| |nextIrreduciblePoly| |modulus| - |extractIfCan| |kernels| |write!| |code| |resultantEuclideannaif| - |s15aef| |enqueue!| |library| |baseRDEsys| |externalList| |OMbindTCP| - |permutationRepresentation| |nonQsign| |exists?| - |setLegalFortranSourceExtensions| |update| |eq| |operator| |phiCoord| - |mesh| |leftPower| |fortran| |ode2| |makeop| |showSummary| |gcdprim| - |froot| |irVar| |e01saf| |operators| |denomLODE| |iter| |degree| - |createZechTable| |innerSolve| 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|infinite| |arbitraryExponent| + |Record| |Union| |bitCoef| |parents| |complexLimit| |clearDenominator| + |algSplitSimple| |closed?| |OMwrite| |patternVariable| |systemCommand| + |inv| |ravel| |match?| |createLowComplexityNormalBasis| |hasoln| + |roughEqualIdeals?| |rightQuotient| |ellipticCylindrical| |minPoly| + |autoCoerce| |external?| |powers| |solveRetract| |twoFactor| |ground?| + |reshape| |csch2sinh| |createLowComplexityTable| |componentUpperBound| + |rightCharacteristicPolynomial| |mapBivariate| |elColumn2!| + |ricDsolve| |clipParametric| |getExplanations| |ground| |open?| + |hconcat| |norm| |infinityNorm| |zeroOf| |topPredicate| + |quasiRegular?| |s21baf| |node?| |leadingMonomial| |normal| |leftMult| + |complex?| |normalizeIfCan| |ord| |ddFact| |iroot| |rowEchelonLocal| + |functorData| |padecf| |leadingCoefficient| |charClass| |leftUnits| + |f04mbf| |getOperands| |f02abf| |gcdcofactprim| |deriv| + |rootOfIrreduciblePoly| |s17dgf| |primitiveMonomials| |close| + |dfRange| |powerSum| |laplacian| |birth| F |minColIndex| + |permutations| |mainMonomials| |iomode| |extendedSubResultantGcd| + |reductum| |update| |antisymmetricTensors| |bivariateSLPEBR| + |transcendenceDegree| |composite| |clip| |removeZeroes| |resultant| + |leftRank| |physicalLength| |display| |graphStates| |graphImage| + |constDsolve| |component| |stoseSquareFreePart| |enterInCache| |shape| + |logical?| |limit| |gradient| |numberOfFactors| |evaluateInverse| + |unravel| |monomialIntegrate| |makeSketch| |makeUnit| |heapSort| + |singleFactorBound| |tanh2coth| |s17akf| |twist| |s17aff| + |generalInfiniteProduct| |mindegTerm| |select!| + |nextNormalPrimitivePoly| |ldf2vmf| |submod| |writeBytes!| + |setMaxPoints| |semiLastSubResultantEuclidean| |s17def| + |fortranDouble| |primlimitedint| |nextPartition| |mapMatrixIfCan| + |OMgetFloat| |position| |hermite| |expr| |diagonal| |radicalRoots| + |selectMultiDimensionalRoutines| |surface| |increasePrecision| + |dihedralGroup| |exteriorDifferential| |satisfy?| |input| ** |d02gbf| + |f02axf| |generalLambert| |decrease| |exprHasLogarithmicWeights| + |operation| |mapExpon| |lazyPrem| |reverse!| |messagePrint| |library| + |recip| |variationOfParameters| |tensorProduct| |singularitiesOf| + |bfKeys| |myDegree| |extension| |Ci| |rightTraceMatrix| |sequence| + |factorGroebnerBasis| |scopes| |stopTableGcd!| |associatorDependence| + |alternating| |expandLog| |commonDenominator| + |stoseInvertibleSetsqfreg| |omError| |semiResultantReduitEuclidean| + |s19adf| |fractRagits| |size| |cyclicEqual?| |variable| |pade| + |basisOfCentroid| |disjunction| |trace2PowMod| |rightRankPolynomial| + |clipWithRanges| |mapSolve| |edf2df| |sumOfDivisors| |iterators| + |subSet| |rootSplit| |unary?| |numberOfHues| |nthFlag| |lflimitedint| + |intcompBasis| |aromberg| |set| |mkcomm| |useNagFunctions| |sec2cos| + |morphism| |iicosh| |wholeRadix| |iitanh| |numericalOptimization| + |ranges| |cAsin| |OMreadFile| |deepCopy| |squareFreePart| |idealiser| + |previous| 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|package| |option?| + |normalizeAtInfinity| |linears| |s14baf| |write| |quoted?| |inc| + |OMputEndObject| |printCode| |minIndex| |exp| |leadingTerm| + |getProperty| |save| |OMputSymbol| |collectUnder| |iExquo| |green| + |initiallyReduce| |show| |innerSolve1| |weighted| |idealiserMatrix| + |basisOfLeftNucleus| |uncouplingMatrices| |decompose| |iiacsc| + |eigenMatrix| |isobaric?| |updatF| |cAcos| |bandedHessian| |groebner?| + |makeCos| |position!| |intChoose| |continuedFraction| |trace| + |insertRoot!| |OMlistSymbols| |addiag| |PollardSmallFactor| |totolex| + |outputForm| |irreducible?| |selectfirst| |Lazard| |iiatanh| |binary| + |cAtanh| |subResultantsChain| |splitLinear| |isImplies| |denomRicDE| + |superscript| |varList| |stoseIntegralLastSubResultant| + |bezoutDiscriminant| |stoseInternalLastSubResultant| |qqq| + |graphState| |measure2Result| |autoReduced?| |Nul| |meshPar2Var| + |OMgetEndApp| |lfinfieldint| |mapCoef| |separant| |s18dcf| |setPoly| + |rational?| |cos2sec| RF2UTS |convergents| |integers| |open| |nodeOf?| + |getZechTable| |listOfLists| |primintfldpoly| + |semiSubResultantGcdEuclidean1| |patternMatch| |inf| |powmod| + |lastSubResultantEuclidean| |transcendent?| |copyInto!| |getStream| + |createNormalElement| |slash| |allRootsOf| |fixPredicate| |tubeRadius| + |s14aaf| |usingTable?| |obj| |retractIfCan| |linGenPos| |acothIfCan| + |setlast!| |double| |moduleSum| |gbasis| |setDifference| |iisec| + |cache| |constant| |redmat| |mainValue| |multiEuclideanTree| + |lfintegrate| |chvar| |factorPolynomial| |regime| |cosSinInfo| + |operations| |callForm?| |symmetricSquare| |mainForm| |genus| + |indiceSubResultant| |isList| |ParCond| |OMputEndBind| |airyAi| + |leftCharacteristicPolynomial| |setnext!| |recoverAfterFail| |headAst| + |member?| |hcrf| |log10| |normalForm| |cschIfCan| |rdHack1| |tube| + |split!| |cTanh| |nthExpon| |bfEntry| |gcdcofact| |element?| |csc2sin| + |bitand| |infinity| |rquo| |solve1| |writeInt8!| |swapColumns!| + |viewZoomDefault| |curveColorPalette| |setAttributeButtonStep| + |groebner| |hex| |bitior| |deepestInitial| |linearMatrix| + |cyclicSubmodule| |squareTop| |semiResultantEuclidean2| + |leftRankPolynomial| |setErrorBound| |cAcoth| |makeSeries| |keys| + |edf2fi| |removeDuplicates| |digits| |pdct| |cot2tan| |removeCoshSq| + |setRealSteps| |hMonic| |expint| |kernel| |shuffle| |critMonD1| |map| + |taylorRep| |mpsode| |isQuotient| |characteristicSet| |rspace| + |closeComponent| |iipow| |setStatus| |solve| |factorsOfDegree| |list| + |mapUp!| |prolateSpheroidal| |shellSort| |ideal| |addmod| + |leftFactorIfCan| |print| |lhs| |FormatArabic| |rationalPoints| + |f02aef| |draw| |nextSubsetGray| |radPoly| |pointColorPalette| + |shallowExpand| |readUInt32!| |resolve| |csubst| |rhs| |squareMatrix| + |nthRoot| |OMputError| |compound?| |alphanumeric| |binaryFunction| + |s15adf| |alternative?| |radicalSolve| |topFortranOutputStack| + |f02aff| |pointColorDefault| |matrixGcd| |imagI| |prinb| |currentEnv| + |infieldIntegrate| 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|f04mcf| + |normDeriv2| |leftRemainder| |isPower| |addMatchRestricted| |entry| + |rationalIfCan| |monic?| |viewWriteDefault| |mainExpression| + |wholeRagits| |f04jgf| |presub| |hostPlatform| |f01bsf| |leftUnit| + |critpOrder| |gcdPolynomial| |sinIfCan| |yellow| |iiGamma| + |innerEigenvectors| |internalLastSubResultant| |s17dhf| + |decreasePrecision| |mkPrim| |isOr| |headReduce| |s18acf| |children| + |normalizedDivide| |readable?| |palgLODE0| |members| |critMTonD1| + |linearDependence| |dihedral| |subCase?| |cLog| |tanIfCan| + |quadratic?| |iiexp| |routines| |selectsecond| |bivariate?| + |listConjugateBases| |signatureAst| |repeatUntilLoop| |unitVector| + |ramified?| |incr| |algDsolve| |notelem| |lowerCase| |intPatternMatch| + |mainCoefficients| |reflect| |OMencodingUnknown| |OMgetBind| + |antisymmetric?| |colorDef| |constructor| |hi| |makeResult| + |readByte!| |rewriteIdealWithQuasiMonicGenerators| + |tryFunctionalDecomposition| |tail| |invertibleSet| |cycleLength| + |lastSubResultant| |drawStyle| |laguerreL| |makeViewport2D| |rightLcm| + |quasiMonic?| |completeHermite| |option| |fortranReal| + |localIntegralBasis| |tracePowMod| |listYoungTableaus| |showSummary| + |getVariableOrder| |computeCycleEntry| |freeOf?| |extendedIntegrate| + |deleteProperty!| |iicos| |degreePartition| |gcdPrimitive| |harmonic| + |removeCosSq| |rules| |units| |factorSquareFree| |cSinh| + |possiblyInfinite?| |groebnerIdeal| |top| |push| |mergeDifference| + |part?| |quasiComponent| |showAttributes| |f07fdf| |horizConcat| + |screenResolution| |complexElementary| |iiacsch| |continue| + |eigenvalues| |s17ahf| |ScanArabic| |graphCurves| |pToHdmp| + |subResultantChain| |read!| |setelt!| |basis| |assign| + |solveLinearPolynomialEquationByRecursion| |rightDivide| |divide| + |parametric?| |euclideanSize| |measure| |name| |hasHi| |unknown| + |irreducibleFactors| |isAtom| |viewpoint| |createRandomElement| + |besselJ| |moebiusMu| |comment| |minimumExponent| |rombergo| |body| + |tan2cot| |pseudoQuotient| |iidsum| |indices| |logGamma| |e02bef| + |code| |infix| |blankSeparate| |OMconnInDevice| |eyeDistance| + |besselK| |corrPoly| |s19acf| |eq?| |prime?| |nthr| |cosh2sech| + |sinhcosh| |pseudoDivide| |incrementKthElement| |null| |weights| + |changeNameToObjf| |stFunc1| |squareFree| |mvar| |just| |in?| + |cyclePartition| |mesh?| |delta| |not| EQ |irreducibleRepresentation| + |c06gbf| |numberOfNormalPoly| + |rewriteSetByReducingWithParticularGenerators| |integralMatrix| + |palgRDE0| |leftExtendedGcd| |Gamma| |fracPart| |and| |linear?| + |quasiRegular| |jokerMode| |transform| |torsion?| |s18aff| |generate| + |neglist| |useEisensteinCriterion| |tanh2trigh| |or| |headRemainder| + |denominator| |normInvertible?| |check| |traceMatrix| |tanNa| + |polCase| |cosIfCan| |d01aqf| |iisin| |xor| |character?| |fprindINFO| + |sqfree| |assert| |zoom| |putProperties| |incrementBy| + |generalTwoFactor| |goodnessOfFit| |port| |ODESolve| |pattern| |case| + |completeHensel| |hessian| |noValueMode| |trunc| |child| |makeTerm| + |expand| |d02ejf| |simplifyExp| |argumentListOf| |Zero| |reorder| + |coerceL| |nilFactor| |subQuasiComponent?| |monomialIntPoly| + |resetAttributeButtons| |filterWhile| |dot| |bernoulli| |t| + |expressIdealMember| |One| |legendreP| |changeThreshhold| + |rightMinimalPolynomial| |fibonacci| |crest| |readUInt8!| + |filterUntil| |goodPoint| |stirling2| |f01rdf| |lambda| |readUInt16!| + |numberOfCycles| |lighting| |lyndonIfCan| |OMgetBVar| |search| + |realEigenvectors| |select| |karatsuba| |rationalApproximation| + |augment| |selectOrPolynomials| |message| |SFunction| |recur| + |lazyIrreducibleFactors| |reduceBasisAtInfinity| |extendedint| + |getOrder| |elRow1!| |iifact| |drawToScale| |genericLeftNorm| + |iiacoth| |nextIrreduciblePoly| |mkIntegral| |rightMult| + |nextPrimitiveNormalPoly| |leftRegularRepresentation| + |sylvesterMatrix| |representationType| |extractClosed| |nrows| + |OMreceive| |modulus| |polyPart| |expandTrigProducts| |e04mbf| + |ratDsolve| |doubleComplex?| |ncols| |elt| |nullity| |extractIfCan| + |ratDenom| |uniform| |Si| |distFact| |retract| |realZeros| + |selectODEIVPRoutines| |write!| |purelyAlgebraicLeadingMonomial?| + |subresultantVector| |cyclicParents| |dilog| |zero| |returnTypeOf| + |lifting1| |hasTopPredicate?| |traverse| |resultantEuclideannaif| + |point?| |mulmod| |endSubProgram| |d01amf| |cons| |sin| |makeRecord| + |var2Steps| |wordInGenerators| |adjoint| |maxrank| |setTex!| |nothing| + |s17acf| |And| |cos| |identity| |c06ekf| |factor1| |OMgetEndAtp| + |screenResolution3D| |setref| |ceiling| |integralMatrixAtInfinity| + |Or| |tan| |powerAssociative?| |thetaCoord| |rectangularMatrix| + |overlabel| |setPrologue!| |rootPower| |endOfFile?| |Not| + |listRepresentation| |cot| |mapDown!| |pointData| |computePowers| + |minPol| |stoseInvertible?sqfreg| |algintegrate| |e02agf| |condition| + |sec| |outlineRender| |terms| |changeMeasure| |contract| + |splitSquarefree| |e04ycf| |conditionP| |leadingExponent| |csc| + |setCondition!| |defineProperty| |internalAugment| + |combineFeatureCompatibility| |e02adf| |cycle| |weakBiRank| + |commutativeEquality| |jordanAdmissible?| |interpret| |source| |asin| + |getGoodPrime| |sturmVariationsOf| |readInt32!| |accuracyIF| + |BumInSepFFE| |permutation| |multiset| |dec| |acos| |printingInfo?| + |mix| |primitivePart| |readInt16!| |alphanumeric?| |pquo| |f01qdf| + |removeRoughlyRedundantFactorsInPol| |atan| |plusInfinity| + |mainSquareFreePart| |coerceImages| |basisOfCommutingElements| + |deepestTail| |conical| |nextLatticePermutation| |maxIndex| |acot| + |generalSqFr| |minusInfinity| |stoseInvertibleSetreg| |swap| + |binaryTree| |packageCall| |currentScope| |char| |rightPower| |asec| + |extend| |linearPart| |column| |rightExtendedGcd| |resultantEuclidean| + |setStatus!| |reducedContinuedFraction| |resetBadValues| + |exprToGenUPS| |acsc| |target| |internalIntegrate| |laurentIfCan| + |balancedBinaryTree| |radix| |elaboration| |Frobenius| + |euclideanGroebner| |sinh| |cardinality| |create3Space| |polyRicDE| + |resultantReduitEuclidean| |redPol| |coordinate| |e04naf| + |viewPhiDefault| |tablePow| |cosh| |shallowCopy| |lagrange| + |separateDegrees| |solveid| |putColorInfo| |setPredicates| + |aQuadratic| UP2UTS |type| |fTable| |tanh| |leftMinimalPolynomial| + |d01bbf| |zeroMatrix| |e01sef| |outputList| |e02baf| |s17agf| + |permanent| |rename!| |addMatch| |coth| |bit?| + |indiceSubResultantEuclidean| |sizeLess?| |laguerre| |nary?| + |critBonD| |color| |alternatingGroup| |float| |qelt| |exactQuotient| + |ran| |seed| |sech| |factorByRecursion| |univariatePolynomialsGcds| + |PDESolve| |second| |qsetelt| |sylvesterSequence| |coth2tanh| + |addPointLast| |viewWriteAvailable| |compactFraction| |ignore?| + |stopMusserTrials| |csch| |removeConstantTerm| |setVariableOrder| + |charthRoot| |third| |flexibleArray| |cross| |cfirst| |octon| |xRange| + |linearAssociatedExp| |binaryTournament| |asinh| |elseBranch| + |leftExactQuotient| |symmetricTensors| |preprocess| |sncndn| |lintgcd| + |compile| |squareFreeLexTriangular| |s19abf| |yRange| |diagonalMatrix| + |void| |inverseIntegralMatrix| |acosh| |cylindrical| |dark| + |shanksDiscLogAlgorithm| |outputSpacing| |cAcosh| |algebraicDecompose| + |coordinates| |viewDeltaYDefault| |zRange| |bivariatePolynomials| |sn| + |sqfrFactor| |atanh| |commutative?| |f04faf| |c06ecf| + |lineColorDefault| |map!| |primintegrate| |countRealRootsMultiple| + |primaryDecomp| |realSolve| |OMReadError?| + |ScanFloatIgnoreSpacesIfCan| |acoth| |enterPointData| |viewPosDefault| + |exprToUPS| |atom?| |qsetelt!| |FormatRoman| |characteristicSerie| + |OMsetEncoding| |youngDiagram| |htrigs| |integer?| |asech| |Aleph| + |blue| |mappingAst| |positiveSolve| |nextNormalPoly| |lllp| |c06frf| + |rewriteIdealWithHeadRemainder| |e02zaf| |leastAffineMultiple| + |genericRightDiscriminant| |saturate| |increment| |sinhIfCan| + |dequeue| |ldf2lst| |d01alf| |maxint| GE |squareFreePolynomial| + |pdf2df| |multiple| |genericLeftDiscriminant| |heap| |positive?| + |delay| |minimalPolynomial| |OMputEndError| |lazyResidueClass| + |approxNthRoot| GT |dimension| |applyQuote| |cycleRagits| |d01ajf| + |stopTableInvSet!| |exprHasAlgebraicWeight| |elements| |iisech| + |anticoord| |symmetricProduct| LE |coefficient| |setprevious!| + |rotatez| |rightAlternative?| |high| |bringDown| |OMgetEndObject| + |predicate| |anfactor| |factorList| |rightRecip| |diff| LT |acsch| + |specialTrigs| |basisOfCenter| |genericRightTraceForm| |imagE| + |headReduced?| |numericalIntegration| |OMgetEndError| |determinant| + |getGraph| |expt| |mapmult| |rangeIsFinite| |mkAnswer| |ruleset| + |subset?| |digamma| |normal?| |pack!| |basisOfLeftNucloid| |lazyPquo| + |LyndonWordsList| |OMputEndAttr| |subst| |createPrimitiveNormalPoly| + |stiffnessAndStabilityFactor| |exptMod| |d03faf| |typeLists| + |prefixRagits| |cyclicGroup| |radicalEigenvectors| |row| |log2| + |e02bcf| |errorInfo| |hexDigit?| |makeEq| |rootRadius| + |primPartElseUnitCanonical!| |numberOfDivisors| |simpson| |choosemon| + |sh| |setleft!| |ip4Address| |directory| |lazyPremWithDefault| + |setleaves!| |bipolar| |suchThat| |quadraticNorm| |showClipRegion| + |primeFrobenius| |tree| |index| |latex| |quadratic| |makeSin| + |SturmHabicht| |loopPoints| |viewport3D| |fullPartialFraction| + |setClosed| |c06fpf| |writeUInt8!| |bezoutMatrix| |setEmpty!| + |realEigenvalues| |zCoord| |initial| |leftLcm| |scaleRoots| + |findBinding| |sinh2csch| |genericLeftTraceForm| |s17aef| |f02ajf| + |splitDenominator| |constantOperator| |exponential| + |cyclotomicFactorization| |setColumn!| |before?| |rCoord| |shiftRight| + |negative?| |karatsubaOnce| |pair| |systemSizeIF| |pile| + |differentialVariables| |computeBasis| |iicsch| |objects| |flagFactor| + |rightTrim| |symbolIfCan| |outputAsScript| |bright| |maxdeg| + |SturmHabichtCoefficients| |components| |parameters| |biRank| + |alphabetic| |complexNumericIfCan| |showTheRoutinesTable| |base| + |commaSeparate| |leftTrim| |ListOfTerms| |inrootof| |factorial| + |putProperty| |cotIfCan| |arg1| |nonSingularModel| |cAsech| + |numerators| |inverseColeman| |completeSmith| |coerceListOfPairs| + |light| |aCubic| |eval| |leftZero| |minus!| |arg2| |setIntersection| + |integralLastSubResultant| |sPol| |lazyEvaluate| + |monicCompleteDecompose| |associatedEquations| |elliptic| + |dimensionOfIrreducibleRepresentation| |halfExtendedResultant2| + |insertMatch| |tubePoints| |lprop| |randomR| |stFunc2| + |setScreenResolution3D| |leftScalarTimes!| |e01daf| |fortranTypeOf| + |rightNorm| |string?| |conditions| |bounds| |multiplyExponents| + |cyclotomic| |rowEchelon| |rightOne| |error| |showFortranOutputStack| + |primitive?| |remove!| |reducedForm| |solveLinearlyOverQ| + |isConnected?| |match| |createMultiplicationMatrix| |stoseInvertible?| + |generalizedContinuumHypothesisAssumed| |RittWuCompare| |isExpt| + |algint| |setUnion| |restorePrecision| |equation| |janko2| |euler| + |cyclotomicDecomposition| |LyndonWordsList1| |divideExponents| + |exponent| |splitNodeOf!| |iiacot| |exQuo| |rroot| + |extractSplittingLeaf| |semiIndiceSubResultantEuclidean| + |degreeSubResultantEuclidean| |littleEndian| |variable?| + |lazyPseudoRemainder| |function| |imagk| |universe| |optimize| + |zeroSetSplit| |trailingCoefficient| |vspace| |var1Steps| |chebyshevT| + |pointColor| |pushNewContour| |numberOfPrimitivePoly| |nthRootIfCan| + |shiftRoots| |resetNew| |rotatex| |fixedPointExquo| |exponential1| + |userOrdered?| |mapGen| |atrapezoidal| |certainlySubVariety?| |cubic| + |parabolicCylindrical| BY |beauzamyBound| |digit| |numberOfVariables| + |limitedIntegrate| |viewDefaults| |elRow2!| |stronglyReduced?| + |invertIfCan| |firstUncouplingMatrix| |clipBoolean| |coerceS| + |primitiveElement| |nativeModuleExtension| |badValues| |distance| + |firstDenom| |interReduce| |copies| |leftRecip| |orthonormalBasis| + |trivialIdeal?| |parabolic| |palglimint| |nand| |polynomialZeros| + |ffactor| |algebraicVariables| |denominators| |d01fcf| |multMonom| + |cscIfCan| |iprint| |partition| |constantCoefficientRicDE| |Is| + |oneDimensionalArray| |central?| |sort| |doubleResultant| |B1solve| + |noKaratsuba| |imagi| |dualSignature| |showTheIFTable| |rootKerSimp| + |d02cjf| |const| |currentSubProgram| |polarCoordinates| |setMinPoints| + |power| |rem| |inconsistent?| |iicot| |simplify| |LyndonCoordinates| + |basicSet| |size?| |OMread| |tanSum| |properties| |Beta| + |homogeneous?| |outputGeneral| |quo| |seriesToOutputForm| + |numericIfCan| |outputMeasure| |f02bjf| |id| |critB| NOT |lazy?| + |taylorIfCan| |host| |translate| |cAcsch| |numberOfMonomials| + |OMclose| |rightRemainder| |integralBasisAtInfinity| |OMgetEndBind| + |lo| |setLength!| OR |divideIfCan!| |random| |palgLODE| |expIfCan| + |randomLC| |fixedPoint| |div| |zag| |linearDependenceOverZ| + |antiAssociative?| |outputFloating| |newLine| |lcm| AND + |inputOutputBinaryFile| |cSec| |numberOfImproperPartitions| + |monicDecomposeIfCan| |perfectSquare?| |cyclic| |exquo| + |noncommutativeJordanAlgebra?| |delete| |quickSort| |curve?| + |qinterval| |OMopenFile| |semiDiscriminantEuclidean| |cCoth| + |listLoops| |reduceByQuasiMonic| |quotientByP| ~= |c06fuf| + |extractIndex| |binomThmExpt| |block| |lift| |getMultiplicationMatrix| + |BasicMethod| |append| |sechIfCan| |tRange| |tab1| |s17ajf| + |remainder| |#| |intermediateResultsIF| |clearFortranOutputStack| + |generalizedContinuumHypothesisAssumed?| |prologue| |reduce| |divisor| + |fortranCharacter| |binomial| |gcd| |bubbleSort!| |initTable!| |rur| + |scanOneDimSubspaces| ~ |standardBasisOfCyclicSubmodule| |diagonal?| + |rightTrace| |schema| |symmetricDifference| |false| |reduced?| + |triangSolve| |iicsc| |genericRightTrace| |testDim| + |SturmHabichtSequence| |repeating?| |cycleTail| + |drawComplexVectorField| |property| |setProperty| |colorFunction| + |startTableInvSet!| |outputArgs| |rightGcd| |elaborate| + |collectQuasiMonic| |apply| |strongGenerators| |bat| |explimitedint| + |integral| |discreteLog| |OMputObject| |prime| |radicalEigenvector| + |/\\| |getMatch| |curry| |argumentList!| |matrix| |first| |adaptive| + |makeViewport3D| |e02bbf| |f04arf| |groebSolve| |quotient| + |viewDeltaXDefault| |imaginary| |pushup| |\\/| |rest| |coord| + |moduloP| |closed| |mainCharacterization| |lp| |divisors| + |indicialEquations| |makeprod| |trapezoidalo| |cyclic?| + |kroneckerDelta| |lazyVariations| |quatern| |prem| |pole?| + |SturmHabichtMultiple| |coerce| * |critT| |mainVariable?| + |selectFiniteRoutines| |rootDirectory| |resultantnaif| |ratpart| + |rational| |duplicates| |setEpilogue!| |zeroDim?| |argscript| + |construct| |radicalOfLeftTraceForm| |ef2edf| |aQuartic| |slex| + |optional?| |multinomial| |hostByteOrder| |complexExpand| + |complexEigenvectors| |numer| |applyRules| |complete| |cap| + |generator| |roughSubIdeal?| |insertTop!| |bitLength| + |leadingCoefficientRicDE| |f02wef| |OMencodingBinary| |denom| + |backOldPos| |selectSumOfSquaresRoutines| |addPoint| = |unexpand| + |exprToXXP| |round| |writable?| |powern| |subscript| + |generalizedEigenvectors| |makeCrit| |d02bbf| |f02bbf| + |relativeApprox| |newSubProgram| |call| |shufflein| |vconcat| + |graeffe| |readLineIfCan!| |virtualDegree| |idealSimplify| |pi| |byte| + |distribute| |edf2ef| |acotIfCan| < |inverse| |minrank| |separate| + |rubiksGroup| |eisensteinIrreducible?| |curve| |ramifiedAtInfinity?| + |width| |jordanAlgebra?| |d01akf| > |quasiMonicPolynomials| + |rightRegularRepresentation| |genericLeftMinimalPolynomial| + |limitPlus| |mapUnivariateIfCan| |paren| |unit| |sample| + |rangePascalTriangle| |asinIfCan| <= |OMgetError| |hermiteH| + |nextItem| |setProperties| |dioSolve| |setFormula!| |coshIfCan| + |linearAssociatedLog| |expandPower| |constantToUnaryFunction| + |makeGraphImage| |identityMatrix| |adaptive?| >= |abs| |quoByVar| + |postfix| |cAcsc| |s13acf| |exactQuotient!| |extract!| |lexTriangular| + |relerror| |rightScalarTimes!| |removeRoughlyRedundantFactorsInPols| + |f01ref| |ScanFloatIgnoreSpaces| |ode| |tableForDiscreteLogarithm| + |symmetricRemainder| |sequences| |module| |exprex| |forLoop| + |showScalarValues| |geometric| |cCot| |d02gaf| |domainTemplate| + |OMParseError?| |toseSquareFreePart| |front| |findCycle| + |compiledFunction| |acschIfCan| |leftTrace| |generic| |fractionPart| + |tab| + |doubleFloatFormat| |numberOfComponents| |getOperator| |space| + |value| |iiacos| |clearCache| |eulerPhi| |selectAndPolynomials| + |numeric| |currentCategoryFrame| |bottom!| |int| |sizePascalTriangle| + |removeRedundantFactorsInPols| - |sup| |summation| |setAdaptive3D| + |f2df| |composites| |sort!| |removeRedundantFactors| |radical| + |magnitude| FG2F |optional| |nthFactor| |lazyIntegrate| / |setvalue!| + |primextintfrac| |numerator| |d01anf| |se2rfi| |isNot| |one?| + |radicalEigenvalues| |polygon?| |newTypeLists| |log| + |characteristicPolynomial| |OMunhandledSymbol| + |semiSubResultantGcdEuclidean2| |sub| |iiasec| |infieldint| + |zeroSetSplitIntoTriangularSystems| |entry?| |f07adf| |reducedQPowers| + |shiftLeft| |factorset| |divideIfCan| |weight| |nextsubResultant2| + |discriminant| |extractTop!| |univariateSolve| |modTree| + |setClipValue| |signature| |jacobiIdentity?| |showArrayValues| + |setelt| |hasPredicate?| |coleman| |OMencodingSGML| |retractable?| + |OMsupportsCD?| |cycleElt| |irForm| |normalDenom| |weierstrass| + |iiatan| |normalElement| |meshFun2Var| |tanAn| |rightFactorCandidate| + |lazyGintegrate| |declare!| |list?| |dAndcExp| |normal01| + |safeCeiling| |polyRDE| |makeFR| |gderiv| |copy| |d01apf| |content| + |compBound| |showRegion| |s18adf| |iisqrt3| |f02fjf| |OMputBind| + |rotate| |getCode| |s20acf| |arbitrary| |mightHaveRoots| + |functionIsFracPolynomial?| |atanIfCan| |rotate!| |OMputApp| + |complexForm| |d03edf| |redpps| |datalist| |getMultiplicationTable| + |getMeasure| |matrixConcat3D| |calcRanges| |knownInfBasis| |setOfMinN| + |qroot| |multiple?| |smith| |goto| |buildSyntax| |critM| |pr2dmp| + |transcendentalDecompose| |internalIntegrate0| |derivationCoordinates| + |upperCase?| |fortranComplex| |maxrow| |factorsOfCyclicGroupSize| + |mapdiv| |f01qcf| |optpair| |options| |upperBound| |e01bef| |inR?| + |fortranDoubleComplex| |isTimes| |palglimint0| |complexNormalize| + |createNormalPrimitivePoly| |df2mf| |matrixDimensions| |setright!| + |completeEchelonBasis| |iitan| |OMgetString| |subPolSet?| + |explicitlyFinite?| |brillhartTrials| |mainMonomial| |top!| + |regularRepresentation| |isOpen?| |d01asf| |hdmpToDmp| |iiasin| + |parametersOf| |lieAdmissible?| |partitions| |showIntensityFunctions| + |empty?| |segment| |sumOfSquares| |reopen!| |f04asf| |maxPoints3D| + |OMgetEndBVar| |output| |string| |pmComplexintegrate| |iterationVar| + |nor| |updateStatus!| |rowEchLocal| |untab| |iisqrt2| + |quasiAlgebraicSet| |initiallyReduced?| |simplifyPower| + |GospersMethod| |reducedDiscriminant| |setfirst!| |OMUnknownCD?| + |algebraicCoefficients?| |startPolynomial| |explicitlyEmpty?| + |rightDiscriminant| |balancedFactorisation| |aspFilename| |subHeight| + |mainVariable| |sin2csc| |cAcot| |reducedSystem| |mdeg| |henselFact| + |sortConstraints| |semiDegreeSubResultantEuclidean| |iiasech| + |divergence| |firstNumer| |LazardQuotient2| |rischNormalize| |e02ajf| + |cond| |HermiteIntegrate| |decomposeFunc| |resetVariableOrder| + |normalize| |OMputInteger| |unknownEndian| |symmetricPower| + |showTheSymbolTable| |rightUnits| |hasSolution?| |eigenvector| + |purelyTranscendental?| |insert!| |approxSqrt| |replace| + |fortranLiteral| |boundOfCauchy| |iiasinh| |infinite?| |constantRight| + |frst| |e02dff| |expintfldpoly| |generateIrredPoly| |setTopPredicate| + |printStats!| |antiCommutative?| |integralBasis| |rk4f| + |unprotectedRemoveRedundantFactors| |factorFraction| + |expenseOfEvaluationIF| |c06gcf| |failed?| |max| |expenseOfEvaluation| + |plotPolar| |prepareSubResAlgo| |monicRightFactorIfCan| + |brillhartIrreducible?| |euclideanNormalForm| |Hausdorff| |df2ef| + |unitNormal| |setButtonValue| |scan| |inRadical?| |tan2trig| + |constantIfCan| |remove| |finiteBound| |appendPoint| |d03eef| |root?| + |crushedSet| |times!| |subresultantSequence| |rootsOf| |pureLex| + |nextPrimitivePoly| |credPol| |numberOfChildren| |associator| + |roughUnitIdeal?| |noLinearFactor?| |isEquiv| |deref| |f01brf| + |semiResultantEuclideannaif| |wreath| |even?| |countRealRoots| + |coth2trigh| |center| |last| |romberg| |OMputAttr| |radicalSimplify| + |lowerCase?| |univcase| |changeBase| |toseInvertibleSet| + |tubeRadiusDefault| |assoc| |getConstant| |showAll?| |whatInfinity| + |perspective| |rightRank| |psolve| |startTableGcd!| |monomial?| + |integralRepresents| |d02bhf| |formula| |lSpaceBasis| |cyclicCopy| + |fortranInteger| |chiSquare1| |escape| |maximumExponent| |cCosh| + |solveLinearPolynomialEquationByFractions| |outputFixed| + |setScreenResolution| |reindex| |s13adf| |singRicDE| |symFunc| + |removeSuperfluousQuasiComponents| |selectIntegrationRoutines| + |branchPointAtInfinity?| |isAnd| |reseed| |primlimintfrac| + |predicates| |coerceP| |varselect| |rightExactQuotient| + |integralCoordinates| |indicialEquation| |binding| |basisOfNucleus| + |leastPower| |pointSizeDefault| |square?| |extractProperty| + |leftAlternative?| |scalarTypeOf| |genericLeftTrace| |ParCondList| + |getProperties| |scale| |qfactor| |d01gbf| |thenBranch| |drawCurves| + |inverseLaplace| |numberOfComputedEntries| |hypergeometric0F1| + |kovacic| |plus!| |yCoord| |exp1| |ode1| |exportedOperators| |opeval| + |lowerPolynomial| |monicRightDivide| |rootNormalize| |f2st| |df2st| + |qPot| |c05adf| |wordsForStrongGenerators| |sizeMultiplication| + |prindINFO| |createThreeSpace| |coHeight| |exponentialOrder| + |substitute| |musserTrials| |plenaryPower| |sdf2lst| |besselY| + |conjunction| |possiblyNewVariety?| |mergeFactors| |besselI| + |genericRightMinimalPolynomial| |mathieu24| |double?| |parseString| + |repSq| |support| |perfectNthRoot| |scripted?| |realElementary| + |mindeg| |e02def| |npcoef| |OMopenString| |bracket| |bindings| + |OMgetType| |addBadValue| |qualifier| |useSingleFactorBound| + |voidMode| |symmetricGroup| |minset| |scalarMatrix| |e04gcf| |e02dcf| + |back| |palginfieldint| |moebius| |functionIsContinuousAtEndPoints| + |c05nbf| |OMgetSymbol| |gethi| |yCoordinates| |jacobian| + |listBranches| |complexSolve| |processTemplate| |factors| + |factorSquareFreeByRecursion| |binarySearchTree| |f01rcf| |pop!| + |signAround| |chebyshevU| |pleskenSplit| |lfextlimint| |nullary| + |d02raf| |computeInt| |setImagSteps| |leviCivitaSymbol| + |getPickedPoints| |constant?| |linearPolynomials| |leaves| |null?| + |copy!| |f02adf| |symmetric?| |outputAsTex| |createIrreduciblePoly| + |normalizedAssociate| |splitConstant| |unrankImproperPartitions0| + |semicolonSeparate| |axesColorDefault| |nil| |s20adf| |setOrder| + |vedf2vef| |iteratedInitials| |macroExpand| |diag| + |removeSquaresIfCan| |halfExtendedResultant1| |invertible?| |less?| + |OMputAtp| |palgRDE| |sts2stst| |collect| |var1StepsDefault| + |lieAlgebra?| |monomRDE| |constantKernel| |minordet| |rdregime| + |diophantineSystem| |prepareDecompose| |polygon| |safeFloor| |f04qaf| + |cExp| |OMencodingXML| |curryRight| |belong?| |approximate| + |paraboloidal| |tubePointsDefault| |minPoints| |enumerate| |totalLex| + |setRow!| |trapezoidal| |superHeight| |sum| |inGroundField?| |complex| + |transpose| |unmakeSUP| |wronskianMatrix| |infLex?| |acoshIfCan| + |mainContent| |removeSuperfluousCases| |extensionDegree| |setPosition| + |exponents| |s21bbf| |lazyPseudoQuotient| |coercePreimagesImages| + |atoms| |generators| |head| |bezoutResultant| |style| |asimpson| + |order| |llprop| |rank| |complexEigenvalues| |cot2trig| |lfunc| + |s17dcf| |rename| |s17dlf| |point| |any?| |UnVectorise| |cn| + |polygamma| |iFTable| |viewSizeDefault| |Ei| |debug| |failed| + |midpoint| |basisOfMiddleNucleus| |bumptab1| |curveColor| |real?| + |fmecg| |cyclicEntries| |polar| |pushucoef| |f02xef| D |tValues| + |makeMulti| |listexp| |normalDeriv| |e01bhf| |padicFraction| + |finiteBasis| |doubleRank| |normalise| |low| |largest| |series| + |complexRoots| |integerIfCan| |nullSpace| |dual| |direction| + |intensity| |sincos| |unaryFunction| |e02ddf| |f02awf| |contours| + |OMgetVariable| |simpleBounds?| |tanhIfCan| |reduction| + |resultantReduit| |refine| |selectOptimizationRoutines| + |complementaryBasis| |float?| |nextPrime| |cPower| |middle| + |inHallBasis?| |derivative| |solid| |leaf?| |super| |nonLinearPart| + |lists| |iilog| |linearAssociatedOrder| |supDimElseRittWu?| + |environment| |every?| |chineseRemainder| |min| |bytes| + |unitsColorDefault| |leadingSupport| |generalPosition| |cTan| + |approximants| |elaborateFile| |charpol| |OMsupportsSymbol?| + |printInfo| |interpretString| |karatsubaDivide| |s18aef| |totalfract| + |linearlyDependentOverZ?| |e02gaf| |df2fi| |eigenvectors| |ptFunc| + |cRationalPower| |mirror| |baseRDE| |unparse| |resize| |testModulus| + |checkPrecision| |rk4a| |invmod| |rewriteSetWithReduction| + |substring?| |semiResultantEuclidean1| |validExponential| |key| + |fractionFreeGauss!| |ReduceOrder| |subNodeOf?| |leadingIndex| + |groebnerFactorize| |triangular?| |arrayStack| |hitherPlane| + |tanintegrate| |pascalTriangle| |setMaxPoints3D| |removeZero| |leader| + |checkRur| |initials| |leftQuotient| |univariatePolynomial| |suffix?| + |toseLastSubResultant| |filename| |algebraicOf| |cSech| |e01sbf| + |capacity| |status| |doublyTransitive?| |overlap| GF2FG + |OMUnknownSymbol?| |symbolTable| |loadNativeModule| |c06fqf| + |fractRadix| |subResultantGcd| |e01bgf| |zerosOf| |pseudoRemainder| + |socf2socdf| |extractPoint| |prefix?| |algebraicSort| |cAtan| |parse| + |innerint| |OMputEndApp| |wordInStrongGenerators| |gensym| |fortran| + |abelianGroup| |cdr| |tableau| |multisect| |groebgen| |plus| + |pushFortranOutputStack| |internal?| |inspect| |probablyZeroDim?| + |equality| |useSingleFactorBound?| |OMgetApp| |LiePolyIfCan| + |generalizedEigenvector| |iiabs| |popFortranOutputStack| + |triangularSystems| |dictionary| |irreducibleFactor| |irDef| |primes| + |lepol| |univariate?| |represents| |LagrangeInterpolation| + |outputAsFortran| |rightFactorIfCan| |lookupFunction| + |positiveRemainder| |e04ucf| |partialNumerators| |bipolarCylindrical| + |fullDisplay| |s21bcf| |roughBasicSet| |table| |shrinkable| |c02aff| + |OMserve| |oddintegers| |raisePolynomial| |integralAtInfinity?| + |limitedint| |precision| |dimensionsOf| |times| |lquo| |new| + |closedCurve| |numFunEvals| |cycleSplit!| |fill!| |s21bdf| + |padicallyExpand| |logIfCan| |monicModulo| |leastMonomial| |infix?| + |ptree| |fortranLogical| |multiEuclidean| |frobenius| |modifyPoint| + |bigEndian| |stirling1| |flatten| |sayLength| |UP2ifCan| |mask| + |viewThetaDefault| |purelyAlgebraic?| |Vectorise| |conjugates| + |mathieu23| |recolor| |init| |categoryMode| |reduceLODE| |HenselLift| + |e01sff| |stiffnessAndStabilityOfODEIF| |attributeData| |implies| + |skewSFunction| |realRoots| |eof?| |solveLinear| |d02kef| + |OMconnectTCP| |monom| |modifyPointData| |pastel| |withPredicates| + |unvectorise| |comparison| |LyndonBasis| |s14abf| |odd?| |is?| |rule| + |tanQ| |mainDefiningPolynomial| |oddInfiniteProduct| |deepExpand| + |numFunEvals3D| |principalIdeal| |supRittWu?| |ksec| |airyBi| + |trueEqual| |imagK| |rationalFunction| |subtractIfCan| |common| |sin?| + |primeFactor| |makeYoungTableau| |c06gsf| |e02daf| |bernoulliB| + |e04dgf| |putGraph| |distdfact| |script| |pushdown| |conjug| + |setrest!| |directSum| |stronglyReduce| |firstSubsetGray| |rightUnit| + |extendedResultant| |interpolate| |ipow| |title| |toScale| + |zeroVector| |create| |controlPanel| |cSin| |countable?| |OMlistCDs| + |minGbasis| |tryFunctionalDecomposition?| |zeroSquareMatrix| + |curryLeft| |c06gqf| |nextColeman| |left| |vector| |contractSolve| + |mat| |doubleDisc| |expPot| |tex| |iiacosh| |outerProduct| + |companionBlocks| |child?| |alphabetic?| |printTypes| |right| + |differentiate| |more?| |createMultiplicationTable| |f01maf| + |readIfCan!| |e| |rootBound| |coefficients| |whileLoop| |updatD| + |acosIfCan| |conjugate| |leftOne| |connectTo| |createGenericMatrix| + |decimal| |fillPascalTriangle| |dmpToHdmp| |readBytes!| |integrate| + |bombieriNorm| |c02agf| |elem?| |iicoth| |repeating| |typeList| + |ridHack1| |monomRDEsys| |monicDivide| |dflist| |car| |asinhIfCan| + |trigs2explogs| |power!| |stosePrepareSubResAlgo| |lambert| + |absolutelyIrreducible?| |nsqfree| |palgintegrate| |root| + |particularSolution| |totalDifferential| |nthExponent| |palgint| + |spherical| |completeEval| |internalInfRittWu?| |nthCoef| |debug3D| + |lfextendedint| |box| |jacobi| |laplace| |clipSurface| |shift| + |makeSUP| |interactiveEnv| |hyperelliptic| |identification| + |vertConcat| |any| |nlde| |hash| |getRef| |triangulate| + |RemainderList| |dmp2rfi| |laurentRep| |invmultisect| |fintegrate| + |graphs| |count| |lexico| |getBadValues| |stripCommentsAndBlanks| + |next| |closedCurve?| |difference| |pToDmp| |univariatePolynomials| + |genericPosition| |imagJ| |contains?| |setLabelValue| |xCoord| + |OMputString| |makeVariable| |nullary?| |readLine!| + |basisOfRightAnnihilator| |symbolTableOf| |bothWays| |ratPoly| + |pointLists| |returns| |byteBuffer| |f02agf| + |indicialEquationAtInfinity| |OMmakeConn| |oblateSpheroidal| + |drawComplex| |symbol| |singular?| |red| |compose| |c06ebf| + |setFieldInfo| |irCtor| |rowEch| |simpsono| |hspace| |zero?| + |expression| |maxRowIndex| |highCommonTerms| |bumptab| |finite?| + |c05pbf| |torsionIfCan| |removeIrreducibleRedundantFactors| |redPo| + |meshPar1Var| |integer| |cAsinh| |OMsend| |legendre| + |halfExtendedSubResultantGcd1| |checkForZero| |principal?| |linear| + |multiplyCoefficients| |reciprocalPolynomial| |asechIfCan| F2FG + |toseInvertible?| |stFuncN| |mainKernel| |identitySquareMatrix| + |number?| |totalDegree| |has?| |sturmSequence| |tubePlot| + |useEisensteinCriterion?| UTS2UP |mapUnivariate| |meatAxe| |nodes| + |isAbsolutelyIrreducible?| |polynomial| |fortranCarriageReturn| + |adaptive3D?| |lastSubResultantElseSplit| |swapRows!| |queue| |badNum| + |close!| |rationalPoint?| |makeFloatFunction| |createPrimitiveElement| + |lazyPseudoDivide| |getButtonValue| |separateFactors| |rischDEsys| + |OMgetObject| |solid?| |someBasis| |erf| |result| + |numberOfFractionalTerms| |associatedSystem| |wholePart| + |numberOfOperations| |epilogue| |rationalPower| |li| + |removeRoughlyRedundantFactorsInContents| |palgint0| |physicalLength!| + |pair?| |conditionsForIdempotents| |nthFractionalTerm| |atanhIfCan| + |safetyMargin| |linSolve| |mappingMode| |stack| |tower| |palgextint0| + |fortranLinkerArgs| |dmpToP| |asecIfCan| |connect| |expextendedint| + |rk4| |fortranLiteralLine| |e02akf| |polyred| |printHeader| + |computeCycleLength| |plot| |categoryFrame| |mathieu12| + |patternMatchTimes| |lexGroebner| |clearTheIFTable| |bag| |pushdterm| + |ocf2ocdf| |mainPrimitivePart| |insertionSort!| |pdf2ef| |OMreadStr| + |clearTheSymbolTable| |empty| |c06eaf| |eq| |truncate| |OMputVariable| + |internalSubQuasiComponent?| |extendedEuclidean| |sumSquares| + |solveInField| |unitCanonical| |principalAncestors| |printStatement| + |iter| |f07aef| |ScanRoman| |dim| |modularGcd| |length| |lyndon| + |constantLeft| |hue| |orbit| |bitTruth| |f04maf| |changeVar| + |listOfMonoms| |complexNumeric| |perfectNthPower?| |step| |scripts| + |exprHasWeightCosWXorSinWX| |OMputEndBVar| |minimumDegree| + |collectUpper| |OMgetAtp| |setAdaptive| |startTable!| |dominantTerm| + |leftFactor| |concat| |cCsch| |uniform01| |quartic| + |nextsousResultant2| |test| |kernels| |clipPointsDefault| |errorKind| + |btwFact| |generalizedInverse| |cAsec| |addPoint2| |upDateBranches| + |s15aef| |printInfo!| |operator| |quadraticForm| |LazardQuotient| + |reverseLex| |elliptic?| |normalized?| |interval| |pmintegrate| + |figureUnits| |enqueue!| |droot| |move| |explogs2trigs| + |numberOfIrreduciblePoly| |associates?| |subMatrix| |chiSquare| + |baseRDEsys| |stopTable!| |findConstructor| |f01mcf| |univariate| + |iflist2Result| |unitNormalize| |f02akf| |prinpolINFO| |externalList| + |expintegrate| |roughBase?| |concat!| |prinshINFO| |s01eaf| + |mathieu11| |lowerBound| |OMbindTCP| |maxColIndex| |xn| |bat1| + |internalSubPolSet?| |constantOpIfCan| |mathieu22| |removeSinhSq| + |prefix| |optAttributes| |permutationRepresentation| + |invertibleElseSplit?| |factor| |totalGroebner| |diagonals| + |createPrimitivePoly| |associative?| |initializeGroupForWordProblem| + |pushuconst| |var2StepsDefault| |cothIfCan| |nonQsign| |sqrt| |shade| + |basisOfLeftAnnihilator| |perfectSqrt| |whitePoint| |partialQuotients| + |hexDigit| |exists?| |partialDenominators| |leftTraceMatrix| |real| + |selectPolynomials| |genericRightNorm| |palgextint| |insertBottom!| + |kmax| |integralDerivationMatrix| |setLegalFortranSourceExtensions| + |argument| |overset?| |imag| |cartesian| |infRittWu?| |declare| + |partialFraction| |stop| |startStats!| |supersub| |fglmIfCan| + |phiCoord| |rootSimp| |removeRedundantFactorsInContents| + |directProduct| |e02bdf| |consnewpol| |maxPoints| |subTriSet?| |mr| + |mesh| |evenlambert| |getIdentifier| |product| |rst| + |factorSFBRlcUnit| |primitivePart!| |cycles| |pow| |subspace| + |leftPower| SEGMENT |compdegd| |replaceKthElement| |brace| |kind| + |e01baf| |createNormalPoly| |OMputBVar| |e04fdf| |extractBottom!| + |categories| |trigs| |ode2| |stoseInvertibleSet| |writeLine!| + |destruct| |digit?| |build| |sumOfKthPowerDivisors| |op| |roman| + |iCompose| |mantissa| |squareFreePrim| |makeop| |depth| |pointPlot| + |LowTriBddDenomInv| |unrankImproperPartitions1| |cCsc| |fixedPoints| + |singularAtInfinity?| |typeForm| |monomials| |gcdprim| |eulerE| + |linkToFortran| |bits| |oddlambert| |factorials| |modularGcdPrimitive| + |problemPoints| |acscIfCan| |level| |froot| |squareFreeFactors| + |iisinh| |merge!| |fixedDivisor| |explicitEntries?| |vectorise| + |lowerCase!| |edf2efi| |irVar| |s19aaf| |leftDiscriminant| |isOp| + |monomial| |rootOf| |modularFactor| |setMinPoints3D| |complexZeros| + |nextSublist| |sparsityIF| |e01saf| |index?| |symbol?| |multivariate| + |evaluate| |LiePoly| |e02aef| |iidprod| |rarrow| |operators| |overbar| + |gramschmidt| |trim| |variables| |leftNorm| |floor| + |subResultantGcdEuclidean| |union| |leadingBasisTerm| |KrullNumber| + |functionIsOscillatory| |denomLODE| |sorted?| |complexIntegrate| + |s17adf| |subscriptedVariables| |monicLeftDivide| |setsubMatrix!| + |taylorQuoByVar| |lifting| |degree| |leftDivide| |algebraic?| + |internalDecompose| |newReduc| |definingPolynomial| |po| + |internalZeroSetSplit| |rootPoly| |createZechTable| |logpart| + |OMgetAttr| |getCurve| |numberOfComposites| |bumprow| |subNode?| + |mapExponents| |innerSolve| |OMcloseConn| |arity| |Lazard2| + |evenInfiniteProduct| |increase| |characteristic| |unit?| |d01gaf| + |discriminantEuclidean| |definingEquations| |extendIfCan| |dimensions| + |taylor| |comp| |medialSet| |quote| |push!| |factorOfDegree| + |secIfCan| |lyndon?| |An| |wrregime| |halfExtendedSubResultantGcd2| + |laurent| |flexible?| |relationsIdeal| |region| |upperCase| |parent| + |prevPrime| |sign| |delete!| |cCos| |reverse| |puiseux| + |degreeSubResultant| |youngGroup| |lex| |upperCase!| LODO2FUN + |factorSquareFreePolynomial| |simplifyLog| |permutationGroup| |nil?| + |rewriteIdealWithRemainder| |inverseIntegralMatrixAtInfinity| + |linearlyDependent?| |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 1b9968af..073956f5 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5387 +1,5387 @@ -(3230304 . 3485464589) -((-3819 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3311 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-415 (-572))) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-38 |#1|) . T) ((-38 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-35) |has| |#1| (-1214)) ((-95) |has| |#1| (-1214)) ((-102) . T) ((-111 #0# #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2813 (|has| |#1| (-356)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-624 #0#) -2813 (|has| |#1| (-1049 (-415 (-572)))) (|has| |#1| (-356)) (|has| |#1| (-370))) ((-624 (-572)) . T) ((-624 |#1|) . T) ((-624 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-621 (-870)) . T) ((-174) . T) ((-622 (-171 (-227))) |has| |#1| (-1033)) ((-622 (-171 (-386))) |has| |#1| (-1033)) ((-622 (-544)) |has| |#1| (-622 (-544))) ((-622 (-901 (-386))) |has| |#1| (-622 (-901 (-386)))) ((-622 (-901 (-572))) |has| |#1| (-622 (-901 (-572)))) ((-622 #1=(-1184 |#1|)) . T) ((-235 $) -2813 (|has| |#1| (-356)) (|has| |#1| (-237))) ((-233 |#1|) . T) ((-237) -2813 (|has| |#1| (-356)) (|has| |#1| (-237))) ((-247) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-290) |has| |#1| (-1214)) ((-292 |#1| $) |has| |#1| (-292 |#1| |#1|)) ((-296) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-313) -2813 (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-315 |#1|) |has| |#1| (-315 |#1|)) ((-370) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-410) |has| |#1| (-356)) ((-375) -2813 (|has| |#1| (-375)) (|has| |#1| (-356))) ((-356) |has| |#1| (-356)) ((-377 |#1| #1#) . T) ((-417 |#1| #1#) . T) ((-345 |#1|) . T) ((-384 |#1|) . T) ((-408 |#1|) . T) ((-419 |#1|) . T) ((-460) -2813 (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-501) |has| |#1| (-1214)) ((-522 (-1188) |#1|) |has| |#1| (-522 (-1188) |#1|)) ((-522 |#1| |#1|) |has| |#1| (-315 |#1|)) ((-564) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-654 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-654 (-572)) . T) ((-654 |#1|) . T) ((-654 $) . T) ((-656 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-656 |#1|) . T) ((-656 $) . T) ((-648 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-648 |#1|) . T) ((-648 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-647 (-572)) |has| |#1| (-647 (-572))) ((-647 |#1|) . T) ((-725 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-725 |#1|) . T) ((-725 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-732 |#1| #1#) . T) ((-734) . T) ((-909 (-1188)) |has| |#1| (-909 (-1188))) ((-895 (-386)) |has| |#1| (-895 (-386))) ((-895 (-572)) |has| |#1| (-895 (-572))) ((-893 |#1|) . T) ((-918) -12 (|has| |#1| (-313)) (|has| |#1| (-918))) ((-929) -2813 (|has| |#1| (-356)) (|has| |#1| (-370)) (|has| |#1| (-313))) ((-1013) -12 (|has| |#1| (-1013)) (|has| |#1| (-1214))) ((-1049 (-415 (-572))) |has| |#1| (-1049 (-415 (-572)))) ((-1049 (-572)) |has| |#1| (-1049 (-572))) ((-1049 |#1|) . T) ((-1062 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-1062 |#1|) . T) ((-1062 $) . T) ((-1067 #0#) -2813 (|has| |#1| (-356)) (|has| |#1| (-370))) ((-1067 |#1|) . T) ((-1067 $) . T) ((-1060) . T) ((-1069) . T) ((-1123) . T) ((-1111) . T) ((-1163) |has| |#1| (-356)) ((-1214) |has| |#1| (-1214)) ((-1217) |has| |#1| (-1214)) ((-1229) . 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(|has| |#2| (-801)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -3783 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3783 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-624 #0=(-415 (-572))) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111))) ((-624 (-572)) -3783 (|has| |#2| (-1060)) (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-624 |#2|) -3783 (|has| |#2| (-1111)) (|has| |#2| (-174))) ((-621 (-870)) -3783 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-621 (-870))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-621 (-1279 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-235 $) -12 (|has| |#2| (-235 |#2|)) (|has| |#2| (-1060))) ((-233 |#2|) |has| |#2| (-1060)) ((-237) -12 (|has| |#2| (-235 |#2|)) (|has| |#2| (-1060))) ((-292 #1=(-572) |#2|) . T) ((-294 #1# |#2|) . T) ((-315 |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((-375) |has| |#2| (-375)) ((-384 |#2|) |has| |#2| (-1060)) ((-419 |#2|) |has| |#2| (-1111)) ((-497 |#2|) . T) ((-612 #1# |#2|) . T) ((-522 |#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((-654 (-572)) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-654 |#2|) -3783 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-654 $) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-656 |#2|) -3783 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-656 $) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-648 |#2|) -3783 (|has| |#2| (-370)) (|has| |#2| (-174))) ((-647 (-572)) -12 (|has| |#2| (-647 (-572))) (|has| |#2| (-1060))) ((-647 |#2|) |has| |#2| (-1060)) ((-725 |#2|) -3783 (|has| |#2| (-370)) (|has| |#2| (-174))) ((-734) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-734)) (|has| |#2| (-174))) ((-799) |has| |#2| (-856)) ((-800) -3783 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-801) |has| |#2| (-801)) ((-802) -3783 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-803) -3783 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-856) |has| |#2| (-856)) ((-858) -3783 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-909 (-1188)) -12 (|has| |#2| (-909 (-1188))) (|has| |#2| (-1060))) ((-1049 #0#) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111))) ((-1049 (-572)) -12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) ((-1049 |#2|) |has| |#2| (-1111)) ((-1062 |#2|) -3783 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-1062 $) |has| |#2| (-174)) ((-1067 |#2|) -3783 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-1067 $) |has| |#2| (-174)) ((-1060) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-1069) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-1123) -3783 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-734)) (|has| |#2| (-174))) ((-1111) -3783 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1229) . T) ((-1286 |#2|) |has| |#2| (-370))) -((-3971 (((-244 |#1| |#3|) (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|) 21)) (-2925 ((|#3| (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|) 23)) (-3161 (((-244 |#1| |#3|) (-1 |#3| |#2|) (-244 |#1| |#2|)) 18))) -(((-243 |#1| |#2| |#3|) (-10 -7 (-15 -3971 ((-244 |#1| |#3|) (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -2925 (|#3| (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -3161 ((-244 |#1| |#3|) (-1 |#3| |#2|) (-244 |#1| |#2|)))) (-779) (-1229) (-1229)) (T -243)) -((-3161 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-244 *5 *6)) (-14 *5 (-779)) (-4 *6 (-1229)) (-4 *7 (-1229)) (-5 *2 (-244 *5 *7)) (-5 *1 (-243 *5 *6 *7)))) (-2925 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-244 *5 *6)) (-14 *5 (-779)) (-4 *6 (-1229)) (-4 *2 (-1229)) (-5 *1 (-243 *5 *6 *2)))) (-3971 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-244 *6 *7)) (-14 *6 (-779)) (-4 *7 (-1229)) (-4 *5 (-1229)) (-5 *2 (-244 *6 *5)) (-5 *1 (-243 *6 *7 *5))))) -(-10 -7 (-15 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(($ $ (-652 (-1188))) NIL (-12 (|has| |#2| (-909 (-1188))) (|has| |#2| (-1060)))) (($ $ (-1188) (-779)) NIL (-12 (|has| |#2| (-909 (-1188))) (|has| |#2| (-1060)))) (($ $ (-652 (-1188)) (-652 (-779))) NIL (-12 (|has| |#2| (-909 (-1188))) (|has| |#2| (-1060)))) (($ $ (-1 |#2| |#2|) (-779)) NIL (|has| |#2| (-1060))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1060)))) (-3976 (((-112) $ $) NIL (-3783 (|has| |#2| (-801)) (|has| |#2| (-856))))) (-3954 (((-112) $ $) NIL (-3783 (|has| |#2| (-801)) (|has| |#2| (-856))))) (-3921 (((-112) $ $) 27 (|has| |#2| (-1111)))) (-3965 (((-112) $ $) NIL (-3783 (|has| |#2| (-801)) (|has| |#2| (-856))))) (-3943 (((-112) $ $) 66 (-3783 (|has| |#2| (-801)) (|has| |#2| (-856))))) (-4029 (($ $ |#2|) NIL (|has| |#2| (-370)))) (-4018 (($ $ $) NIL (|has| |#2| (-1060))) (($ $) NIL (|has| |#2| (-1060)))) (-4005 (($ $ $) 34 (|has| |#2| (-25)))) (** (($ $ (-779)) NIL (|has| |#2| (-734))) (($ $ (-930)) NIL (|has| |#2| (-734)))) (* (($ (-572) $) NIL (|has| |#2| (-1060))) (($ $ $) 46 (|has| |#2| (-734))) (($ $ |#2|) 44 (|has| |#2| (-734))) (($ |#2| $) 45 (|has| |#2| (-734))) (($ (-779) $) NIL (|has| |#2| (-132))) (($ (-930) $) NIL (|has| |#2| (-25)))) (-3476 (((-779) $) NIL (|has| $ (-6 -4454))))) +((-4259 (*1 *1 *2) (-12 (-5 *2 (-1279 *4)) (-4 *4 (-1229)) (-4 *1 (-242 *3 *4)))) (-1950 (*1 *1 *2) (-12 (-5 *2 (-930)) (-4 *1 (-242 *3 *4)) (-4 *4 (-1060)) (-4 *4 (-1229)))) (-2139 (*1 *2 *1 *1) (-12 (-4 *1 (-242 *3 *2)) (-4 *2 (-1229)) (-4 *2 (-1060)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-242 *3 *2)) (-4 *2 (-1229)) (-4 *2 (-734)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-242 *3 *2)) (-4 *2 (-1229)) (-4 *2 (-734))))) +(-13 (-612 (-572) |t#2|) (-621 (-1279 |t#2|)) (-10 -8 (-6 -4454) (-15 -4259 ($ (-1279 |t#2|))) (IF (|has| |t#2| (-1111)) (-6 (-419 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1060)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-233 |t#2|)) (-6 (-384 |t#2|)) (-15 -1950 ($ (-930))) (-15 -2139 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-734)) (PROGN (-6 (-734)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-375)) (-6 (-375)) |%noBranch|) (IF (|has| |t#2| (-174)) (PROGN (-6 (-38 |t#2|)) (-6 (-174))) |%noBranch|) (IF (|has| |t#2| (-6 -4451)) (-6 -4451) |%noBranch|) (IF (|has| |t#2| (-856)) (-6 (-856)) |%noBranch|) (IF (|has| |t#2| (-801)) (-6 (-801)) |%noBranch|) (IF (|has| |t#2| (-370)) (-6 (-1286 |t#2|)) |%noBranch|))) +(((-21) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-23) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2813 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2813 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-624 #0=(-415 (-572))) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111))) ((-624 (-572)) -2813 (|has| |#2| (-1060)) (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-624 |#2|) -2813 (|has| |#2| (-1111)) (|has| |#2| (-174))) ((-621 (-870)) -2813 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-621 (-870))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-621 (-1279 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-235 $) -12 (|has| |#2| (-237)) (|has| |#2| (-1060))) ((-233 |#2|) |has| |#2| (-1060)) ((-237) -12 (|has| |#2| (-237)) (|has| |#2| (-1060))) ((-292 #1=(-572) |#2|) . T) ((-294 #1# |#2|) . T) ((-315 |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((-375) |has| |#2| (-375)) ((-384 |#2|) |has| |#2| (-1060)) ((-419 |#2|) |has| |#2| (-1111)) ((-497 |#2|) . T) ((-612 #1# |#2|) . T) ((-522 |#2| |#2|) -12 (|has| |#2| (-315 |#2|)) (|has| |#2| (-1111))) ((-654 (-572)) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-654 |#2|) -2813 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-654 $) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-656 |#2|) -2813 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-656 $) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-648 |#2|) -2813 (|has| |#2| (-370)) (|has| |#2| (-174))) ((-647 (-572)) -12 (|has| |#2| (-647 (-572))) (|has| |#2| (-1060))) ((-647 |#2|) |has| |#2| (-1060)) ((-725 |#2|) -2813 (|has| |#2| (-370)) (|has| |#2| (-174))) ((-734) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-734)) (|has| |#2| (-174))) ((-799) |has| |#2| (-856)) ((-800) -2813 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-801) |has| |#2| (-801)) ((-802) -2813 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-803) -2813 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-856) |has| |#2| (-856)) ((-858) -2813 (|has| |#2| (-856)) (|has| |#2| (-801))) ((-909 (-1188)) -12 (|has| |#2| (-909 (-1188))) (|has| |#2| (-1060))) ((-1049 #0#) -12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111))) ((-1049 (-572)) -12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111))) ((-1049 |#2|) |has| |#2| (-1111)) ((-1062 |#2|) -2813 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-1062 $) |has| |#2| (-174)) ((-1067 |#2|) -2813 (|has| |#2| (-1060)) (|has| |#2| (-370)) (|has| |#2| (-174))) ((-1067 $) |has| |#2| (-174)) ((-1060) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-1069) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-174))) ((-1123) -2813 (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-734)) (|has| |#2| (-174))) ((-1111) -2813 (|has| |#2| (-1111)) (|has| |#2| (-1060)) (|has| |#2| (-856)) (|has| |#2| (-801)) (|has| |#2| (-734)) (|has| |#2| (-375)) (|has| |#2| (-370)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1229) . T) ((-1286 |#2|) |has| |#2| (-370))) +((-3328 (((-244 |#1| |#3|) (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|) 21)) (-2865 ((|#3| (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|) 23)) (-1776 (((-244 |#1| |#3|) (-1 |#3| |#2|) (-244 |#1| |#2|)) 18))) +(((-243 |#1| |#2| |#3|) (-10 -7 (-15 -3328 ((-244 |#1| |#3|) (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -2865 (|#3| (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -1776 ((-244 |#1| |#3|) (-1 |#3| |#2|) (-244 |#1| |#2|)))) (-779) (-1229) (-1229)) (T -243)) +((-1776 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-244 *5 *6)) (-14 *5 (-779)) (-4 *6 (-1229)) (-4 *7 (-1229)) (-5 *2 (-244 *5 *7)) (-5 *1 (-243 *5 *6 *7)))) (-2865 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-244 *5 *6)) (-14 *5 (-779)) (-4 *6 (-1229)) (-4 *2 (-1229)) (-5 *1 (-243 *5 *6 *2)))) (-3328 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-244 *6 *7)) (-14 *6 (-779)) (-4 *7 (-1229)) (-4 *5 (-1229)) (-5 *2 (-244 *6 *5)) (-5 *1 (-243 *6 *7 *5))))) +(-10 -7 (-15 -3328 ((-244 |#1| |#3|) (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -2865 (|#3| (-1 |#3| |#2| |#3|) (-244 |#1| |#2|) |#3|)) (-15 -1776 ((-244 |#1| |#3|) (-1 |#3| |#2|) (-244 |#1| |#2|)))) +((-2846 (((-112) $ $) NIL (|has| |#2| (-1111)))) (-4013 (((-112) $) NIL (|has| |#2| (-132)))) (-1950 (($ (-930)) 62 (|has| |#2| (-1060)))) (-1536 (((-1284) $ (-572) (-572)) NIL (|has| $ (-6 -4455)))) (-3092 (($ $ $) 68 (|has| |#2| (-801)))) (-3852 (((-3 $ "failed") $ $) 53 (|has| |#2| (-132)))) (-2786 (((-112) $ (-779)) NIL)) (-1485 (((-779)) NIL (|has| |#2| (-375)))) (-4418 (((-572) $) NIL (|has| |#2| (-856)))) (-3140 ((|#2| $ (-572) |#2|) NIL (|has| $ (-6 -4455)))) (-3022 (($) NIL T CONST)) (-1695 (((-3 (-572) "failed") $) NIL (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111)))) (((-3 (-415 (-572)) "failed") $) NIL (-12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111)))) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1111)))) (-2203 (((-572) $) NIL (-12 (|has| |#2| (-1049 (-572))) (|has| |#2| (-1111)))) (((-415 (-572)) $) NIL (-12 (|has| |#2| (-1049 (-415 (-572)))) (|has| |#2| (-1111)))) ((|#2| $) 28 (|has| |#2| (-1111)))) (-3271 (((-697 (-572)) (-697 $)) NIL (-12 (|has| |#2| (-647 (-572))) (|has| |#2| (-1060)))) (((-2 (|:| -3891 (-697 (-572))) (|:| |vec| (-1279 (-572)))) (-697 $) (-1279 $)) NIL (-12 (|has| |#2| (-647 (-572))) (|has| |#2| (-1060)))) (((-2 (|:| -3891 (-697 |#2|)) (|:| |vec| (-1279 |#2|))) (-697 $) (-1279 $)) NIL (|has| |#2| (-1060))) (((-697 |#2|) (-697 $)) NIL (|has| |#2| (-1060)))) (-1463 (((-3 $ "failed") $) 58 (|has| |#2| (-734)))) (-2815 (($) NIL (|has| |#2| (-375)))) (-2453 ((|#2| $ (-572) |#2|) NIL (|has| $ (-6 -4455)))) (-2380 ((|#2| $ (-572)) 56)) (-2485 (((-112) $) NIL (|has| |#2| (-856)))) (-1862 (((-652 |#2|) $) 14 (|has| $ (-6 -4454)))) (-3112 (((-112) $) NIL (|has| |#2| (-734)))) (-2602 (((-112) $) NIL (|has| |#2| (-856)))) (-3903 (((-112) $ (-779)) NIL)) (-1607 (((-572) $) 19 (|has| (-572) (-858)))) (-3657 (($ $ $) NIL (-2813 (|has| |#2| 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-415 (-572)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-624 #0#) -3783 (|has| |#1| (-1049 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 |#1|) . T) ((-624 |#2|) . T) ((-624 |#3|) . T) ((-624 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-621 (-870)) . 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T) ((-656 #0#) |has| |#1| (-38 (-415 (-572)))) ((-656 |#1|) . T) ((-656 $) . T) ((-648 #0#) |has| |#1| (-38 (-415 (-572)))) ((-648 |#1|) |has| |#1| (-174)) ((-648 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-647 (-572)) |has| |#1| (-647 (-572))) ((-647 |#1|) . T) ((-725 #0#) |has| |#1| (-38 (-415 (-572)))) ((-725 |#1|) |has| |#1| (-174)) ((-725 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-734) . T) ((-909 (-1188)) |has| |#1| (-909 (-1188))) ((-909 |#3|) . T) ((-895 (-386)) -12 (|has| |#1| (-895 (-386))) (|has| |#3| (-895 (-386)))) ((-895 (-572)) -12 (|has| |#1| (-895 (-572))) (|has| |#3| (-895 (-572)))) ((-958 |#1| |#4| |#3|) . T) ((-918) |has| |#1| (-918)) ((-1049 (-415 (-572))) |has| |#1| (-1049 (-415 (-572)))) ((-1049 (-572)) |has| |#1| (-1049 (-572))) ((-1049 |#1|) . T) ((-1049 |#2|) . T) ((-1049 |#3|) . T) ((-1062 #0#) |has| |#1| (-38 (-415 (-572)))) ((-1062 |#1|) . T) ((-1062 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-174))) ((-1067 #0#) |has| |#1| (-38 (-415 (-572)))) ((-1067 |#1|) . T) ((-1067 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-174))) ((-1060) . T) ((-1069) . T) ((-1123) . T) ((-1111) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-415 (-572)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-624 #0#) -2813 (|has| |#1| (-1049 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 |#1|) . T) ((-624 |#2|) . T) ((-624 |#3|) . T) ((-624 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-621 (-870)) . T) ((-174) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-174))) ((-622 (-544)) -12 (|has| |#1| (-622 (-544))) (|has| |#3| (-622 (-544)))) ((-622 (-901 (-386))) -12 (|has| |#1| (-622 (-901 (-386)))) (|has| |#3| (-622 (-901 (-386))))) ((-622 (-901 (-572))) -12 (|has| |#1| (-622 (-901 (-572)))) (|has| |#3| (-622 (-901 (-572))))) ((-235 $) |has| |#1| (-237)) ((-233 |#1|) . T) ((-237) |has| |#1| (-237)) ((-296) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-315 $) . T) ((-332 |#1| |#4|) . T) ((-384 |#1|) . T) ((-419 |#1|) . T) ((-460) -2813 (|has| |#1| (-918)) (|has| |#1| (-460))) ((-522 |#2| |#1|) |has| |#1| (-237)) ((-522 |#2| $) |has| |#1| (-237)) ((-522 |#3| |#1|) . T) ((-522 |#3| $) . T) ((-522 $ $) . T) ((-564) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-654 #0#) |has| |#1| (-38 (-415 (-572)))) ((-654 (-572)) . T) ((-654 |#1|) . T) ((-654 $) . T) ((-656 #0#) |has| |#1| (-38 (-415 (-572)))) ((-656 |#1|) . T) ((-656 $) . T) ((-648 #0#) |has| |#1| (-38 (-415 (-572)))) ((-648 |#1|) |has| |#1| (-174)) ((-648 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-647 (-572)) |has| |#1| (-647 (-572))) ((-647 |#1|) . T) ((-725 #0#) |has| |#1| (-38 (-415 (-572)))) ((-725 |#1|) |has| |#1| (-174)) ((-725 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460))) ((-734) . T) ((-909 (-1188)) |has| |#1| (-909 (-1188))) ((-909 |#3|) . T) ((-895 (-386)) -12 (|has| |#1| (-895 (-386))) (|has| |#3| (-895 (-386)))) ((-895 (-572)) -12 (|has| |#1| (-895 (-572))) (|has| |#3| (-895 (-572)))) ((-958 |#1| |#4| |#3|) . T) ((-918) |has| |#1| (-918)) ((-1049 (-415 (-572))) |has| |#1| (-1049 (-415 (-572)))) ((-1049 (-572)) |has| |#1| (-1049 (-572))) ((-1049 |#1|) . T) ((-1049 |#2|) . T) ((-1049 |#3|) . T) ((-1062 #0#) |has| |#1| (-38 (-415 (-572)))) ((-1062 |#1|) . 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T) ((-308) . T) ((-370) |has| |#1| (-564)) ((-384 |#1|) |has| |#1| (-1060)) ((-408 |#1|) . T) ((-419 |#1|) . T) ((-460) |has| |#1| (-564)) ((-481) |has| |#1| (-481)) ((-522 (-620 $) $) . T) ((-522 $ $) . 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T) ((-23) . T) ((-47 |#1| #0=(-572)) . T) ((-25) . T) ((-38 #1=(-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-370)) ((-38 $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-35) |has| |#1| (-38 (-415 (-572)))) ((-95) |has| |#1| (-38 (-415 (-572)))) ((-102) . T) ((-111 #1# #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-370)) ((-111 $ $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-132) . T) ((-146) -3783 (-12 (|has| |#1| (-370)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -3783 (-12 (|has| |#1| (-370)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-624 #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 #2=(-1188)) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-1188)))) ((-624 |#1|) |has| |#1| (-174)) ((-624 |#2|) . 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T) ((-648 #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-648 |#1|) |has| |#1| (-174)) ((-648 |#2|) |has| |#1| (-370)) ((-648 $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-647 (-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-647 (-572)))) ((-647 |#2|) |has| |#1| (-370)) ((-725 #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-725 |#1|) |has| |#1| (-174)) ((-725 |#2|) |has| |#1| (-370)) ((-725 $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-734) . 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T) ((-23) . T) ((-47 |#1| #0=(-572)) . T) ((-25) . T) ((-38 #1=(-415 (-572))) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-370)) ((-38 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-35) |has| |#1| (-38 (-415 (-572)))) ((-95) |has| |#1| (-38 (-415 (-572)))) ((-102) . T) ((-111 #1# #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-370)) ((-111 $ $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-624 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 #2=(-1188)) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-1188)))) ((-624 |#1|) |has| |#1| (-174)) ((-624 |#2|) . T) ((-624 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-621 (-870)) . T) ((-174) -2813 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-622 (-227)) -12 (|has| |#1| (-370)) (|has| |#2| (-1033))) ((-622 (-386)) -12 (|has| |#1| (-370)) (|has| |#2| (-1033))) ((-622 (-544)) -12 (|has| |#1| (-370)) (|has| |#2| (-622 (-544)))) ((-622 (-901 (-386))) -12 (|has| |#1| (-370)) (|has| |#2| (-622 (-901 (-386))))) ((-622 (-901 (-572))) -12 (|has| |#1| (-370)) (|has| |#2| (-622 (-901 (-572))))) ((-235 $) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-237))) (|has| |#1| (-15 * (|#1| (-572) |#1|)))) ((-233 |#2|) |has| |#1| (-370)) ((-237) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-237))) (|has| |#1| (-15 * (|#1| (-572) |#1|)))) ((-247) |has| |#1| (-370)) ((-290) |has| |#1| (-38 (-415 (-572)))) ((-292 #0# |#1|) . T) ((-292 |#2| $) -12 (|has| |#1| (-370)) (|has| |#2| (-292 |#2| |#2|))) ((-292 $ $) |has| (-572) (-1123)) ((-296) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-313) |has| |#1| (-370)) ((-315 |#2|) -12 (|has| |#1| (-370)) (|has| |#2| (-315 |#2|))) ((-370) |has| |#1| (-370)) ((-345 |#2|) |has| |#1| (-370)) ((-384 |#2|) |has| |#1| (-370)) ((-408 |#2|) |has| |#1| (-370)) ((-460) |has| |#1| (-370)) ((-501) |has| |#1| (-38 (-415 (-572)))) ((-522 (-1188) |#2|) -12 (|has| |#1| (-370)) (|has| |#2| (-522 (-1188) |#2|))) ((-522 |#2| |#2|) -12 (|has| |#1| (-370)) (|has| |#2| (-315 |#2|))) ((-564) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-654 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-654 (-572)) . T) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-370)) ((-654 $) . T) ((-656 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-656 |#1|) . T) ((-656 |#2|) |has| |#1| (-370)) ((-656 $) . T) ((-648 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-648 |#1|) |has| |#1| (-174)) ((-648 |#2|) |has| |#1| (-370)) ((-648 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-647 (-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-647 (-572)))) ((-647 |#2|) |has| |#1| (-370)) ((-725 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-725 |#1|) |has| |#1| (-174)) ((-725 |#2|) |has| |#1| (-370)) ((-725 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-734) . T) ((-799) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-800) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-802) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-803) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-828) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-856) -12 (|has| |#1| (-370)) (|has| |#2| (-828))) ((-858) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-858))) (-12 (|has| |#1| (-370)) (|has| |#2| (-828)))) ((-909 (-1188)) -2813 (-12 (|has| |#1| (-370)) (|has| |#2| (-909 (-1188)))) (-12 (|has| |#1| (-15 * (|#1| (-572) |#1|))) (|has| |#1| (-909 (-1188))))) ((-895 (-386)) -12 (|has| |#1| (-370)) (|has| |#2| (-895 (-386)))) ((-895 (-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-895 (-572)))) ((-893 |#2|) |has| |#1| (-370)) ((-918) -12 (|has| |#1| (-370)) (|has| |#2| (-918))) ((-984 |#1| #0# (-1093)) . T) ((-929) |has| |#1| (-370)) ((-1003 |#2|) |has| |#1| (-370)) ((-1013) |has| |#1| (-38 (-415 (-572)))) ((-1033) -12 (|has| |#1| (-370)) (|has| |#2| (-1033))) ((-1049 (-415 (-572))) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-572)))) ((-1049 (-572)) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-572)))) ((-1049 #2#) -12 (|has| |#1| (-370)) (|has| |#2| (-1049 (-1188)))) ((-1049 |#2|) . T) ((-1062 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-1062 |#1|) . T) ((-1062 |#2|) |has| |#1| (-370)) ((-1062 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-1067 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-1067 |#1|) . T) ((-1067 |#2|) |has| |#1| (-370)) ((-1067 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-1060) . T) ((-1069) . T) ((-1123) . T) ((-1111) . T) ((-1163) -12 (|has| |#1| (-370)) (|has| |#2| (-1163))) ((-1214) |has| |#1| (-38 (-415 (-572)))) ((-1217) |has| |#1| (-38 (-415 (-572)))) ((-1229) . T) ((-1233) |has| |#1| (-370)) ((-1239 |#1|) . T) ((-1257 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-779)) . T) ((-25) . T) ((-38 #1=(-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-415 (-572)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-624 #1#) -3783 (|has| |#1| (-1049 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 #2=(-1093)) . T) ((-624 |#1|) . T) ((-624 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-621 (-870)) . T) ((-174) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-622 (-544)) -12 (|has| (-1093) (-622 (-544))) (|has| |#1| (-622 (-544)))) ((-622 (-901 (-386))) -12 (|has| (-1093) (-622 (-901 (-386)))) (|has| |#1| (-622 (-901 (-386))))) ((-622 (-901 (-572))) -12 (|has| (-1093) (-622 (-901 (-572)))) (|has| |#1| (-622 (-901 (-572))))) ((-235 $) . T) ((-233 |#1|) . T) ((-237) . T) ((-292 (-415 $) (-415 $)) |has| |#1| (-564)) ((-292 |#1| |#1|) . T) ((-292 $ $) . T) ((-296) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-313) |has| |#1| (-370)) ((-315 $) . T) ((-332 |#1| #0#) . T) ((-384 |#1|) . T) ((-419 |#1|) . T) ((-460) -3783 (|has| |#1| (-918)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-522 #2# |#1|) . T) ((-522 #2# $) . T) ((-522 $ $) . T) ((-564) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-654 #1#) |has| |#1| (-38 (-415 (-572)))) ((-654 (-572)) . T) ((-654 |#1|) . T) ((-654 $) . T) ((-656 #1#) |has| |#1| (-38 (-415 (-572)))) ((-656 |#1|) . T) ((-656 $) . T) ((-648 #1#) |has| |#1| (-38 (-415 (-572)))) ((-648 |#1|) |has| |#1| (-174)) ((-648 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-647 (-572)) |has| |#1| (-647 (-572))) ((-647 |#1|) . T) ((-725 #1#) |has| |#1| (-38 (-415 (-572)))) ((-725 |#1|) |has| |#1| (-174)) ((-725 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-734) . T) ((-909 #2#) . T) ((-909 (-1188)) |has| |#1| (-909 (-1188))) ((-895 (-386)) -12 (|has| (-1093) (-895 (-386))) (|has| |#1| (-895 (-386)))) ((-895 (-572)) -12 (|has| (-1093) (-895 (-572))) (|has| |#1| (-895 (-572)))) ((-958 |#1| #0# #2#) . T) ((-918) |has| |#1| (-918)) ((-929) |has| |#1| (-370)) ((-1049 (-415 (-572))) |has| |#1| (-1049 (-415 (-572)))) ((-1049 (-572)) |has| |#1| (-1049 (-572))) ((-1049 #2#) . T) ((-1049 |#1|) . T) ((-1062 #1#) |has| |#1| (-38 (-415 (-572)))) ((-1062 |#1|) . T) ((-1062 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-1067 #1#) |has| |#1| (-38 (-415 (-572)))) ((-1067 |#1|) . T) ((-1067 $) -3783 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-1060) . T) ((-1069) . T) ((-1123) . T) ((-1111) . T) ((-1163) |has| |#1| (-1163)) ((-1229) . T) ((-1233) |has| |#1| (-918))) -((-2221 (((-652 (-1093)) $) 34)) (-1874 (($ $) 31)) (-3040 (($ |#2| |#3|) NIL) (($ $ (-1093) |#3|) 28) (($ $ (-652 (-1093)) (-652 |#3|)) 27)) (-1840 (($ $) 14)) (-1853 ((|#2| $) 12)) (-3196 ((|#3| $) 10))) -(((-1256 |#1| |#2| |#3|) (-10 -8 (-15 -2221 ((-652 (-1093)) |#1|)) (-15 -3040 (|#1| |#1| (-652 (-1093)) (-652 |#3|))) (-15 -3040 (|#1| |#1| (-1093) |#3|)) (-15 -1874 (|#1| |#1|)) (-15 -3040 (|#1| |#2| |#3|)) (-15 -3196 (|#3| |#1|)) (-15 -1840 (|#1| |#1|)) (-15 -1853 (|#2| |#1|))) (-1257 |#2| |#3|) (-1060) (-800)) (T -1256)) -NIL -(-10 -8 (-15 -2221 ((-652 (-1093)) |#1|)) (-15 -3040 (|#1| |#1| (-652 (-1093)) (-652 |#3|))) (-15 -3040 (|#1| |#1| (-1093) |#3|)) (-15 -1874 (|#1| |#1|)) (-15 -3040 (|#1| |#2| |#3|)) (-15 -3196 (|#3| |#1|)) (-15 -1840 (|#1| |#1|)) (-15 -1853 (|#2| |#1|))) -((-3464 (((-112) $ $) 7)) (-3911 (((-112) $) 17)) (-2221 (((-652 (-1093)) $) 86)) (-2043 (((-1188) $) 117)) (-2248 (((-2 (|:| -3940 $) (|:| -4441 $) (|:| |associate| $)) 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T) ((-23) . T) ((-47 |#1| #0=(-779)) . T) ((-25) . T) ((-38 #1=(-415 (-572))) |has| |#1| (-38 (-415 (-572)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-415 (-572)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-624 #1#) -2813 (|has| |#1| (-1049 (-415 (-572)))) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 #2=(-1093)) . T) ((-624 |#1|) . T) ((-624 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-621 (-870)) . T) ((-174) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-622 (-544)) -12 (|has| (-1093) (-622 (-544))) (|has| |#1| (-622 (-544)))) ((-622 (-901 (-386))) -12 (|has| (-1093) (-622 (-901 (-386)))) (|has| |#1| (-622 (-901 (-386))))) ((-622 (-901 (-572))) -12 (|has| (-1093) (-622 (-901 (-572)))) (|has| |#1| (-622 (-901 (-572))))) ((-235 $) . T) ((-233 |#1|) . T) ((-237) . T) ((-292 (-415 $) (-415 $)) |has| |#1| (-564)) ((-292 |#1| |#1|) . T) ((-292 $ $) . T) ((-296) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-313) |has| |#1| (-370)) ((-315 $) . T) ((-332 |#1| #0#) . T) ((-384 |#1|) . T) ((-419 |#1|) . T) ((-460) -2813 (|has| |#1| (-918)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-522 #2# |#1|) . T) ((-522 #2# $) . T) ((-522 $ $) . T) ((-564) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-654 #1#) |has| |#1| (-38 (-415 (-572)))) ((-654 (-572)) . T) ((-654 |#1|) . T) ((-654 $) . T) ((-656 #1#) |has| |#1| (-38 (-415 (-572)))) ((-656 |#1|) . T) ((-656 $) . T) ((-648 #1#) |has| |#1| (-38 (-415 (-572)))) ((-648 |#1|) |has| |#1| (-174)) ((-648 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-647 (-572)) |has| |#1| (-647 (-572))) ((-647 |#1|) . T) ((-725 #1#) |has| |#1| (-38 (-415 (-572)))) ((-725 |#1|) |has| |#1| (-174)) ((-725 $) -2813 (|has| |#1| (-918)) (|has| |#1| (-564)) (|has| |#1| (-460)) (|has| |#1| (-370))) ((-734) . T) ((-909 #2#) . T) ((-909 (-1188)) |has| |#1| (-909 (-1188))) ((-895 (-386)) -12 (|has| (-1093) (-895 (-386))) (|has| |#1| (-895 (-386)))) ((-895 (-572)) -12 (|has| (-1093) (-895 (-572))) (|has| |#1| (-895 (-572)))) ((-958 |#1| #0# #2#) . 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T) ((-23) . T) ((-47 |#1| #0=(-415 (-572))) . T) ((-25) . T) ((-38 #1=(-415 (-572))) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-35) |has| |#1| (-38 (-415 (-572)))) ((-95) |has| |#1| (-38 (-415 (-572)))) ((-102) . T) ((-111 #1# #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-624 #1#) -3783 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-624 (-572)) . T) ((-624 |#1|) |has| |#1| (-174)) ((-624 |#2|) . T) ((-624 $) -3783 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-621 (-870)) . 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T) ((-102) |has| |#1| (-1111)) ((-621 (-870)) -2813 (|has| |#1| (-1111)) (|has| |#1| (-621 (-870)))) ((-315 |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-497 |#1|) . T) ((-522 |#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-1021 |#1|) . T) ((-1111) |has| |#1| (-1111)) ((-1229) . 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3019648 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1246 3017709 3018446 3018723 "UNISEG" 3019000 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1245 3016924 3017051 3017256 "UNISEG2" 3017552 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1244 3015984 3016164 3016390 "UNIFACT" 3016740 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1243 2999916 3015161 3015412 "ULS" 3015791 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1242 2987914 2999820 2999892 "ULSCONS" 2999897 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1241 2969808 2981795 2981857 "ULSCCAT" 2982495 NIL ULSCCAT (NIL T T) -9 NIL 2982784 NIL) (-1240 2968858 2969103 2969491 "ULSCCAT-" 2969496 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1239 2958145 2964627 2964670 "ULSCAT" 2965533 NIL ULSCAT (NIL T) -9 NIL 2966264 NIL) (-1238 2957575 2957654 2957833 "ULS2" 2958060 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1237 2956694 2957204 2957311 "UINT8" 2957422 T UINT8 (NIL) -8 NIL NIL 2957507) (-1236 2955812 2956322 2956429 "UINT64" 2956540 T UINT64 (NIL) -8 NIL NIL 2956625) (-1235 2954930 2955440 2955547 "UINT32" 2955658 T UINT32 (NIL) -8 NIL NIL 2955743) (-1234 2954048 2954558 2954665 "UINT16" 2954776 T UINT16 (NIL) -8 NIL NIL 2954861) (-1233 2952351 2953308 2953338 "UFD" 2953550 T UFD (NIL) -9 NIL 2953664 NIL) (-1232 2952145 2952191 2952286 "UFD-" 2952291 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1231 2951227 2951410 2951626 "UDVO" 2951951 T UDVO (NIL) -7 NIL NIL NIL) (-1230 2949043 2949452 2949923 "UDPO" 2950791 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1229 2948976 2948981 2949011 "TYPE" 2949016 T TYPE (NIL) -9 NIL NIL NIL) (-1228 2948736 2948931 2948962 "TYPEAST" 2948967 T TYPEAST (NIL) -8 NIL NIL NIL) (-1227 2947707 2947909 2948149 "TWOFACT" 2948530 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1226 2946730 2947116 2947351 "TUPLE" 2947507 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1225 2944421 2944940 2945479 "TUBETOOL" 2946213 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1224 2943270 2943475 2943716 "TUBE" 2944214 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1223 2937999 2942242 2942525 "TS" 2943022 NIL TS (NIL T) -8 NIL NIL NIL) (-1222 2926639 2930758 2930855 "TSETCAT" 2936124 NIL TSETCAT (NIL T T T T) -9 NIL 2937655 NIL) (-1221 2921371 2922971 2924862 "TSETCAT-" 2924867 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1220 2916010 2916857 2917786 "TRMANIP" 2920507 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1219 2915451 2915514 2915677 "TRIMAT" 2915942 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1218 2913317 2913554 2913911 "TRIGMNIP" 2915200 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1217 2912837 2912950 2912980 "TRIGCAT" 2913193 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1216 2912506 2912585 2912726 "TRIGCAT-" 2912731 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1215 2909351 2911364 2911645 "TREE" 2912260 NIL TREE (NIL T) -8 NIL NIL NIL) (-1214 2908625 2909153 2909183 "TRANFUN" 2909218 T TRANFUN (NIL) -9 NIL 2909284 NIL) (-1213 2907904 2908095 2908375 "TRANFUN-" 2908380 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1212 2907708 2907740 2907801 "TOPSP" 2907865 T TOPSP (NIL) -7 NIL NIL NIL) (-1211 2907056 2907171 2907325 "TOOLSIGN" 2907589 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1210 2905690 2906233 2906472 "TEXTFILE" 2906839 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1209 2903602 2904143 2904572 "TEX" 2905283 T TEX (NIL) -8 NIL NIL NIL) (-1208 2903383 2903414 2903486 "TEX1" 2903565 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1207 2903031 2903094 2903184 "TEMUTL" 2903315 T TEMUTL (NIL) -7 NIL NIL NIL) (-1206 2901185 2901465 2901790 "TBCMPPK" 2902754 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1205 2892962 2899345 2899401 "TBAGG" 2899801 NIL TBAGG (NIL T T) -9 NIL 2900012 NIL) (-1204 2888032 2889520 2891274 "TBAGG-" 2891279 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1203 2887416 2887523 2887668 "TANEXP" 2887921 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1202 2886927 2887191 2887281 "TALGOP" 2887361 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1201 2880317 2886784 2886877 "TABLE" 2886882 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1200 2879729 2879828 2879966 "TABLEAU" 2880214 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1199 2874337 2875557 2876805 "TABLBUMP" 2878515 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1198 2873559 2873706 2873887 "SYSTEM" 2874178 T SYSTEM (NIL) -8 NIL NIL NIL) (-1197 2870018 2870717 2871500 "SYSSOLP" 2872810 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1196 2869816 2869973 2870004 "SYSPTR" 2870009 T SYSPTR (NIL) -8 NIL NIL NIL) (-1195 2868852 2869357 2869476 "SYSNNI" 2869662 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869747) (-1194 2868151 2868610 2868689 "SYSINT" 2868749 NIL SYSINT (NIL NIL) -8 NIL NIL 2868794) (-1193 2864483 2865429 2866139 "SYNTAX" 2867463 T SYNTAX (NIL) -8 NIL NIL NIL) (-1192 2861641 2862243 2862875 "SYMTAB" 2863873 T SYMTAB (NIL) -8 NIL NIL NIL) (-1191 2856890 2857792 2858775 "SYMS" 2860680 T SYMS (NIL) -8 NIL NIL NIL) (-1190 2854125 2856348 2856578 "SYMPOLY" 2856695 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1189 2853642 2853717 2853840 "SYMFUNC" 2854037 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1188 2849662 2850954 2851767 "SYMBOL" 2852851 T SYMBOL (NIL) -8 NIL NIL NIL) (-1187 2843201 2844890 2846610 "SWITCH" 2847964 T SWITCH (NIL) -8 NIL NIL NIL) (-1186 2836435 2842022 2842325 "SUTS" 2842956 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2828501 2835682 2835955 "SUPXS" 2836220 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2820260 2828119 2828245 "SUP" 2828410 NIL SUP (NIL T) -8 NIL NIL NIL) (-1183 2819419 2819546 2819763 "SUPFRACF" 2820128 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1182 2819040 2819099 2819212 "SUP2" 2819354 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1181 2817488 2817762 2818118 "SUMRF" 2818739 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1180 2816823 2816889 2817081 "SUMFS" 2817409 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1179 2800790 2816000 2816251 "SULS" 2816630 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1178 2800392 2800612 2800682 "SUCHTAST" 2800742 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1177 2799687 2799917 2800057 "SUCH" 2800300 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1176 2793554 2794593 2795552 "SUBSPACE" 2798775 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1175 2792984 2793074 2793238 "SUBRESP" 2793442 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1174 2786352 2787649 2788960 "STTF" 2791720 NIL STTF (NIL T) -7 NIL NIL NIL) (-1173 2780525 2781645 2782792 "STTFNC" 2785252 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1172 2771838 2773707 2775501 "STTAYLOR" 2778766 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1171 2764968 2771702 2771785 "STRTBL" 2771790 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1170 2760332 2764923 2764954 "STRING" 2764959 T STRING (NIL) -8 NIL NIL NIL) (-1169 2755161 2759675 2759705 "STRICAT" 2759764 T STRICAT (NIL) -9 NIL 2759826 NIL) (-1168 2747914 2752780 2753391 "STREAM" 2754585 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1167 2747424 2747501 2747645 "STREAM3" 2747831 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1166 2746406 2746589 2746824 "STREAM2" 2747237 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1165 2746094 2746146 2746239 "STREAM1" 2746348 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1164 2745110 2745291 2745522 "STINPROD" 2745910 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1163 2744662 2744872 2744902 "STEP" 2744982 T STEP (NIL) -9 NIL 2745060 NIL) (-1162 2743849 2744151 2744299 "STEPAST" 2744536 T STEPAST (NIL) -8 NIL NIL NIL) (-1161 2737281 2743748 2743825 "STBL" 2743830 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1160 2732376 2736472 2736515 "STAGG" 2736668 NIL STAGG (NIL T) -9 NIL 2736757 NIL) (-1159 2730078 2730680 2731552 "STAGG-" 2731557 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1158 2728225 2729848 2729940 "STACK" 2730021 NIL STACK (NIL T) -8 NIL NIL NIL) (-1157 2720920 2726366 2726822 "SREGSET" 2727855 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1156 2713345 2714714 2716227 "SRDCMPK" 2719526 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1155 2706230 2710755 2710785 "SRAGG" 2712088 T SRAGG (NIL) -9 NIL 2712696 NIL) (-1154 2705247 2705502 2705881 "SRAGG-" 2705886 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1153 2699707 2704194 2704615 "SQMATRIX" 2704873 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1152 2693392 2696425 2697152 "SPLTREE" 2699052 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1151 2689355 2690048 2690694 "SPLNODE" 2692818 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1150 2688402 2688635 2688665 "SPFCAT" 2689109 T SPFCAT (NIL) -9 NIL NIL NIL) (-1149 2687139 2687349 2687613 "SPECOUT" 2688160 T SPECOUT (NIL) -7 NIL NIL NIL) (-1148 2678249 2680121 2680151 "SPADXPT" 2684827 T SPADXPT (NIL) -9 NIL 2686991 NIL) (-1147 2678010 2678050 2678119 "SPADPRSR" 2678202 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1146 2676059 2677965 2677996 "SPADAST" 2678001 T SPADAST (NIL) -8 NIL NIL NIL) (-1145 2668004 2669777 2669820 "SPACEC" 2674193 NIL SPACEC (NIL T) -9 NIL 2676009 NIL) (-1144 2666134 2667936 2667985 "SPACE3" 2667990 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1143 2664886 2665057 2665348 "SORTPAK" 2665939 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1142 2662978 2663281 2663693 "SOLVETRA" 2664550 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1141 2662028 2662250 2662511 "SOLVESER" 2662751 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1140 2657332 2658220 2659215 "SOLVERAD" 2661080 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1139 2653147 2653756 2654485 "SOLVEFOR" 2656699 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1138 2647417 2652496 2652593 "SNTSCAT" 2652598 NIL SNTSCAT (NIL T T T T) -9 NIL 2652668 NIL) (-1137 2641523 2645740 2646131 "SMTS" 2647107 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1136 2636208 2641411 2641488 "SMP" 2641493 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1135 2634367 2634668 2635066 "SMITH" 2635905 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1134 2627040 2631237 2631340 "SMATCAT" 2632691 NIL SMATCAT (NIL NIL T T T) -9 NIL 2633241 NIL) (-1133 2623980 2624803 2625981 "SMATCAT-" 2625986 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1132 2621646 2623216 2623259 "SKAGG" 2623520 NIL SKAGG (NIL T) -9 NIL 2623655 NIL) (-1131 2617972 2621119 2621303 "SINT" 2621455 T SINT (NIL) -8 NIL NIL 2621617) (-1130 2617744 2617782 2617848 "SIMPAN" 2617928 T SIMPAN (NIL) -7 NIL NIL NIL) (-1129 2617023 2617279 2617419 "SIG" 2617626 T SIG (NIL) -8 NIL NIL NIL) (-1128 2615861 2616082 2616357 "SIGNRF" 2616782 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1127 2614694 2614845 2615129 "SIGNEF" 2615690 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1126 2614000 2614277 2614401 "SIGAST" 2614592 T SIGAST (NIL) -8 NIL NIL NIL) (-1125 2611690 2612144 2612650 "SHP" 2613541 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1124 2605542 2611591 2611667 "SHDP" 2611672 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1123 2605115 2605307 2605337 "SGROUP" 2605430 T SGROUP (NIL) -9 NIL 2605492 NIL) (-1122 2604973 2604999 2605072 "SGROUP-" 2605077 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1121 2601764 2602462 2603185 "SGCF" 2604272 T SGCF (NIL) -7 NIL NIL NIL) (-1120 2596132 2601211 2601308 "SFRTCAT" 2601313 NIL SFRTCAT (NIL T T T T) -9 NIL 2601352 NIL) (-1119 2589553 2590571 2591707 "SFRGCD" 2595115 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1118 2582679 2583752 2584938 "SFQCMPK" 2588486 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1117 2582299 2582388 2582499 "SFORT" 2582620 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1116 2581417 2582139 2582260 "SEXOF" 2582265 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1115 2580524 2581298 2581366 "SEX" 2581371 T SEX (NIL) -8 NIL NIL NIL) (-1114 2576305 2577020 2577115 "SEXCAT" 2579737 NIL SEXCAT (NIL T T T T T) -9 NIL 2580297 NIL) (-1113 2573458 2576239 2576287 "SET" 2576292 NIL SET (NIL T) -8 NIL NIL NIL) (-1112 2571682 2572171 2572476 "SETMN" 2573199 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1111 2571178 2571330 2571360 "SETCAT" 2571536 T SETCAT (NIL) -9 NIL 2571646 NIL) (-1110 2570870 2570948 2571078 "SETCAT-" 2571083 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1109 2567231 2569331 2569374 "SETAGG" 2570244 NIL SETAGG (NIL T) -9 NIL 2570584 NIL) (-1108 2566689 2566805 2567042 "SETAGG-" 2567047 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1107 2566132 2566385 2566486 "SEQAST" 2566610 T SEQAST (NIL) -8 NIL NIL NIL) (-1106 2565331 2565625 2565686 "SEGXCAT" 2565972 NIL SEGXCAT (NIL T T) -9 NIL 2566092 NIL) (-1105 2564337 2564997 2565179 "SEG" 2565184 NIL SEG (NIL T) -8 NIL NIL NIL) (-1104 2563316 2563530 2563573 "SEGCAT" 2564095 NIL SEGCAT (NIL T) -9 NIL 2564316 NIL) (-1103 2562248 2562679 2562887 "SEGBIND" 2563143 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1102 2561869 2561928 2562041 "SEGBIND2" 2562183 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1101 2561442 2561670 2561747 "SEGAST" 2561814 T SEGAST (NIL) -8 NIL NIL NIL) (-1100 2560661 2560787 2560991 "SEG2" 2561286 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1099 2560071 2560596 2560643 "SDVAR" 2560648 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1098 2552598 2559841 2559971 "SDPOL" 2559976 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1097 2551191 2551457 2551776 "SCPKG" 2552313 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1096 2550355 2550527 2550719 "SCOPE" 2551021 T SCOPE (NIL) -8 NIL NIL NIL) (-1095 2549575 2549709 2549888 "SCACHE" 2550210 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1094 2549221 2549407 2549437 "SASTCAT" 2549442 T SASTCAT (NIL) -9 NIL 2549455 NIL) (-1093 2548708 2549056 2549132 "SAOS" 2549167 T SAOS (NIL) -8 NIL NIL NIL) (-1092 2548273 2548308 2548481 "SAERFFC" 2548667 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1091 2542212 2548170 2548250 "SAE" 2548255 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1090 2541805 2541840 2541999 "SAEFACT" 2542171 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1089 2540126 2540440 2540841 "RURPK" 2541471 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1088 2538763 2539069 2539374 "RULESET" 2539960 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1087 2535986 2536516 2536974 "RULE" 2538444 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1086 2535598 2535780 2535863 "RULECOLD" 2535938 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1085 2535388 2535416 2535487 "RTVALUE" 2535549 T RTVALUE (NIL) -8 NIL NIL NIL) (-1084 2534859 2535105 2535199 "RSTRCAST" 2535316 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1083 2529707 2530502 2531422 "RSETGCD" 2534058 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1082 2518937 2524016 2524113 "RSETCAT" 2528232 NIL RSETCAT (NIL T T T T) -9 NIL 2529329 NIL) (-1081 2516864 2517403 2518227 "RSETCAT-" 2518232 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1080 2509250 2510626 2512146 "RSDCMPK" 2515463 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1079 2507229 2507696 2507770 "RRCC" 2508856 NIL RRCC (NIL T T) -9 NIL 2509200 NIL) (-1078 2506580 2506754 2507033 "RRCC-" 2507038 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1077 2506023 2506276 2506377 "RPTAST" 2506501 T RPTAST (NIL) -8 NIL NIL NIL) (-1076 2479869 2489228 2489295 "RPOLCAT" 2499961 NIL RPOLCAT (NIL T T T) -9 NIL 2503121 NIL) (-1075 2471367 2473707 2476829 "RPOLCAT-" 2476834 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1074 2462298 2469578 2470060 "ROUTINE" 2470907 T ROUTINE (NIL) -8 NIL NIL NIL) (-1073 2459096 2461924 2462064 "ROMAN" 2462180 T ROMAN (NIL) -8 NIL NIL NIL) (-1072 2457340 2457956 2458216 "ROIRC" 2458901 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1071 2453572 2455856 2455886 "RNS" 2456190 T RNS (NIL) -9 NIL 2456464 NIL) (-1070 2452081 2452464 2452998 "RNS-" 2453073 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1069 2451484 2451892 2451922 "RNG" 2451927 T RNG (NIL) -9 NIL 2451948 NIL) (-1068 2450487 2450849 2451051 "RNGBIND" 2451335 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1067 2449886 2450274 2450317 "RMODULE" 2450322 NIL RMODULE (NIL T) -9 NIL 2450349 NIL) (-1066 2448722 2448816 2449152 "RMCAT2" 2449787 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1065 2445572 2448068 2448365 "RMATRIX" 2448484 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1064 2438399 2440659 2440774 "RMATCAT" 2444133 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2445115 NIL) (-1063 2437774 2437921 2438228 "RMATCAT-" 2438233 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1062 2437175 2437396 2437439 "RLINSET" 2437633 NIL RLINSET (NIL T) -9 NIL 2437724 NIL) (-1061 2436742 2436817 2436945 "RINTERP" 2437094 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1060 2435800 2436354 2436384 "RING" 2436440 T RING (NIL) -9 NIL 2436532 NIL) (-1059 2435592 2435636 2435733 "RING-" 2435738 NIL RING- (NIL T) -8 NIL NIL NIL) (-1058 2434433 2434670 2434928 "RIDIST" 2435356 T RIDIST (NIL) -7 NIL NIL NIL) (-1057 2425722 2433901 2434107 "RGCHAIN" 2434281 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1056 2425072 2425478 2425519 "RGBCSPC" 2425577 NIL RGBCSPC (NIL T) -9 NIL 2425629 NIL) (-1055 2424230 2424611 2424652 "RGBCMDL" 2424884 NIL RGBCMDL (NIL T) -9 NIL 2424998 NIL) (-1054 2421224 2421838 2422508 "RF" 2423594 NIL RF (NIL T) -7 NIL NIL NIL) (-1053 2420870 2420933 2421036 "RFFACTOR" 2421155 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1052 2420595 2420630 2420727 "RFFACT" 2420829 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1051 2418712 2419076 2419458 "RFDIST" 2420235 T RFDIST (NIL) -7 NIL NIL NIL) (-1050 2418165 2418257 2418420 "RETSOL" 2418614 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1049 2417801 2417881 2417924 "RETRACT" 2418057 NIL RETRACT (NIL T) -9 NIL 2418144 NIL) (-1048 2417650 2417675 2417762 "RETRACT-" 2417767 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1047 2417252 2417472 2417542 "RETAST" 2417602 T RETAST (NIL) -8 NIL NIL NIL) (-1046 2409990 2416905 2417032 "RESULT" 2417147 T RESULT (NIL) -8 NIL NIL NIL) (-1045 2408581 2409259 2409458 "RESRING" 2409893 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1044 2408217 2408266 2408364 "RESLATC" 2408518 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1043 2407922 2407957 2408064 "REPSQ" 2408176 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1042 2405344 2405924 2406526 "REP" 2407342 T REP (NIL) -7 NIL NIL NIL) (-1041 2405041 2405076 2405187 "REPDB" 2405303 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1040 2398941 2400330 2401553 "REP2" 2403853 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1039 2395318 2395999 2396807 "REP1" 2398168 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1038 2388014 2393459 2393915 "REGSET" 2394948 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1037 2386779 2387162 2387412 "REF" 2387799 NIL REF (NIL T) -8 NIL NIL NIL) (-1036 2386156 2386259 2386426 "REDORDER" 2386663 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1035 2382124 2385369 2385596 "RECLOS" 2385984 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1034 2381176 2381357 2381572 "REALSOLV" 2381931 T REALSOLV (NIL) -7 NIL NIL NIL) (-1033 2381022 2381063 2381093 "REAL" 2381098 T REAL (NIL) -9 NIL 2381133 NIL) (-1032 2377505 2378307 2379191 "REAL0Q" 2380187 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1031 2373106 2374094 2375155 "REAL0" 2376486 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1030 2372577 2372823 2372917 "RDUCEAST" 2373034 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1029 2371982 2372054 2372261 "RDIV" 2372499 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1028 2371050 2371224 2371437 "RDIST" 2371804 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1027 2369647 2369934 2370306 "RDETRS" 2370758 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1026 2367459 2367913 2368451 "RDETR" 2369189 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1025 2366084 2366362 2366759 "RDEEFS" 2367175 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1024 2364593 2364899 2365324 "RDEEF" 2365772 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1023 2358654 2361574 2361604 "RCFIELD" 2362899 T RCFIELD (NIL) -9 NIL 2363630 NIL) (-1022 2356718 2357222 2357918 "RCFIELD-" 2357993 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1021 2352987 2354819 2354862 "RCAGG" 2355946 NIL RCAGG (NIL T) -9 NIL 2356411 NIL) (-1020 2352615 2352709 2352872 "RCAGG-" 2352877 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1019 2351950 2352062 2352227 "RATRET" 2352499 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1018 2351503 2351570 2351691 "RATFACT" 2351878 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1017 2350811 2350931 2351083 "RANDSRC" 2351373 T RANDSRC (NIL) -7 NIL NIL NIL) (-1016 2350545 2350589 2350662 "RADUTIL" 2350760 T RADUTIL (NIL) -7 NIL NIL NIL) (-1015 2343659 2349376 2349687 "RADIX" 2350268 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1014 2335278 2343501 2343631 "RADFF" 2343636 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1013 2334925 2335000 2335030 "RADCAT" 2335190 T RADCAT (NIL) -9 NIL NIL NIL) (-1012 2334707 2334755 2334855 "RADCAT-" 2334860 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1011 2332805 2334477 2334569 "QUEUE" 2334650 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1010 2329342 2332738 2332786 "QUAT" 2332791 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1009 2328973 2329016 2329147 "QUATCT2" 2329293 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2322311 2325657 2325699 "QUATCAT" 2326490 NIL QUATCAT (NIL T) -9 NIL 2327256 NIL) (-1007 2318450 2319487 2320877 "QUATCAT-" 2320973 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1006 2315915 2317526 2317569 "QUAGG" 2317950 NIL QUAGG (NIL T) -9 NIL 2318125 NIL) (-1005 2315517 2315737 2315807 "QQUTAST" 2315867 T QQUTAST (NIL) -8 NIL NIL NIL) (-1004 2314530 2315030 2315195 "QFORM" 2315398 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1003 2305484 2310723 2310765 "QFCAT" 2311433 NIL QFCAT (NIL T) -9 NIL 2312434 NIL) (-1002 2301051 2302252 2303846 "QFCAT-" 2303942 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2300682 2300725 2300856 "QFCAT2" 2301002 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1000 2300137 2300247 2300379 "QEQUAT" 2300572 T QEQUAT (NIL) -8 NIL NIL NIL) (-999 2293283 2294356 2295540 "QCMPACK" 2299070 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-998 2290832 2291280 2291708 "QALGSET" 2292938 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-997 2290077 2290251 2290483 "QALGSET2" 2290652 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-996 2288767 2288991 2289308 "PWFFINTB" 2289850 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-995 2286949 2287117 2287471 "PUSHVAR" 2288581 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-994 2282867 2283921 2283962 "PTRANFN" 2285846 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-993 2281269 2281560 2281882 "PTPACK" 2282578 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-992 2280901 2280958 2281067 "PTFUNC2" 2281206 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-991 2275346 2279743 2279784 "PTCAT" 2280080 NIL PTCAT (NIL T) -9 NIL 2280233 NIL) (-990 2275004 2275039 2275163 "PSQFR" 2275305 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-989 2273599 2273897 2274231 "PSEUDLIN" 2274702 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-988 2260362 2262733 2265057 "PSETPK" 2271359 NIL PSETPK (NIL T T T T) -7 NIL NIL 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NIL 2046656 NIL) (-892 2044497 2044892 2045315 "PARTPERM" 2045912 T PARTPERM (NIL) -7 NIL NIL NIL) (-891 2044118 2044181 2044283 "PARSURF" 2044428 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-890 2043750 2043807 2043916 "PARSU2" 2044055 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-889 2043514 2043554 2043621 "PARSER" 2043703 T PARSER (NIL) -7 NIL NIL NIL) (-888 2043135 2043198 2043300 "PARSCURV" 2043445 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-887 2042767 2042824 2042933 "PARSC2" 2043072 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-886 2042406 2042464 2042561 "PARPCURV" 2042703 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-885 2042038 2042095 2042204 "PARPC2" 2042343 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-884 2041099 2041411 2041593 "PARAMAST" 2041876 T PARAMAST (NIL) -8 NIL NIL NIL) (-883 2040619 2040705 2040824 "PAN2EXPR" 2041000 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-882 2039396 2039740 2039968 "PALETTE" 2040411 T PALETTE (NIL) -8 NIL NIL NIL) (-881 2037789 2038401 2038761 "PAIR" 2039082 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-880 2031657 2037046 2037241 "PADICRC" 2037643 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-879 2024884 2031001 2031186 "PADICRAT" 2031504 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-878 2023199 2024821 2024866 "PADIC" 2024871 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-877 2020309 2021873 2021913 "PADICCT" 2022494 NIL PADICCT (NIL NIL) -9 NIL 2022776 NIL) (-876 2019266 2019466 2019734 "PADEPAC" 2020096 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-875 2018478 2018611 2018817 "PADE" 2019128 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-874 2016865 2017686 2017966 "OWP" 2018282 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-873 2016358 2016571 2016668 "OVERSET" 2016788 T OVERSET (NIL) -8 NIL NIL NIL) (-872 2015404 2015963 2016135 "OVAR" 2016226 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-871 2014668 2014789 2014950 "OUT" 2015263 T OUT (NIL) -7 NIL NIL NIL) (-870 2003540 2005777 2007977 "OUTFORM" 2012488 T OUTFORM (NIL) -8 NIL NIL NIL) (-869 2002876 2003137 2003264 "OUTBFILE" 2003433 T OUTBFILE (NIL) -8 NIL NIL NIL) (-868 2002183 2002348 2002376 "OUTBCON" 2002694 T OUTBCON (NIL) -9 NIL 2002860 NIL) (-867 2001784 2001896 2002053 "OUTBCON-" 2002058 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-866 2001164 2001513 2001602 "OSI" 2001715 T OSI (NIL) -8 NIL NIL NIL) (-865 2000694 2001032 2001060 "OSGROUP" 2001065 T OSGROUP (NIL) -9 NIL 2001087 NIL) (-864 1999439 1999666 1999951 "ORTHPOL" 2000441 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-863 1996990 1999274 1999395 "OREUP" 1999400 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-862 1994393 1996681 1996808 "ORESUP" 1996932 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-861 1991921 1992421 1992982 "OREPCTO" 1993882 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-860 1985607 1987808 1987849 "OREPCAT" 1990197 NIL OREPCAT (NIL T) -9 NIL 1991301 NIL) (-859 1982754 1983536 1984594 "OREPCAT-" 1984599 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-858 1981905 1982203 1982231 "ORDSET" 1982540 T ORDSET (NIL) -9 NIL 1982704 NIL) (-857 1981336 1981484 1981708 "ORDSET-" 1981713 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-856 1979901 1980692 1980720 "ORDRING" 1980922 T ORDRING (NIL) -9 NIL 1981047 NIL) (-855 1979546 1979640 1979784 "ORDRING-" 1979789 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-854 1978926 1979389 1979417 "ORDMON" 1979422 T ORDMON (NIL) -9 NIL 1979443 NIL) (-853 1978088 1978235 1978430 "ORDFUNS" 1978775 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-852 1977426 1977845 1977873 "ORDFIN" 1977938 T ORDFIN (NIL) -9 NIL 1978012 NIL) (-851 1973985 1976012 1976421 "ORDCOMP" 1977050 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-850 1973251 1973378 1973564 "ORDCOMP2" 1973845 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-849 1969832 1970742 1971556 "OPTPROB" 1972457 T OPTPROB (NIL) -8 NIL NIL NIL) (-848 1966634 1967273 1967977 "OPTPACK" 1969148 T OPTPACK (NIL) -7 NIL NIL NIL) (-847 1964321 1965087 1965115 "OPTCAT" 1965934 T OPTCAT (NIL) -9 NIL 1966584 NIL) (-846 1963705 1963998 1964103 "OPSIG" 1964236 T OPSIG (NIL) -8 NIL NIL NIL) (-845 1963473 1963512 1963578 "OPQUERY" 1963659 T OPQUERY (NIL) -7 NIL NIL NIL) (-844 1960604 1961784 1962288 "OP" 1963002 NIL OP (NIL T) -8 NIL NIL NIL) (-843 1959978 1960204 1960245 "OPERCAT" 1960457 NIL OPERCAT (NIL T) -9 NIL 1960554 NIL) (-842 1959733 1959789 1959906 "OPERCAT-" 1959911 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-841 1956546 1958530 1958899 "ONECOMP" 1959397 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-840 1955851 1955966 1956140 "ONECOMP2" 1956418 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1955270 1955376 1955506 "OMSERVER" 1955741 T OMSERVER (NIL) -7 NIL NIL NIL) (-838 1952132 1954710 1954750 "OMSAGG" 1954811 NIL OMSAGG (NIL T) -9 NIL 1954875 NIL) (-837 1950755 1951018 1951300 "OMPKG" 1951870 T OMPKG (NIL) -7 NIL NIL NIL) (-836 1950185 1950288 1950316 "OM" 1950615 T OM (NIL) -9 NIL NIL NIL) (-835 1948702 1949724 1949898 "OMLO" 1950061 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-834 1947662 1947809 1948029 "OMEXPR" 1948528 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-833 1946953 1947208 1947344 "OMERR" 1947546 T OMERR (NIL) -8 NIL NIL NIL) (-832 1946104 1946374 1946534 "OMERRK" 1946813 T OMERRK (NIL) -8 NIL NIL NIL) (-831 1945555 1945781 1945889 "OMENC" 1946016 T OMENC (NIL) -8 NIL NIL NIL) (-830 1939450 1940635 1941806 "OMDEV" 1944404 T OMDEV (NIL) -8 NIL NIL NIL) (-829 1938519 1938690 1938884 "OMCONN" 1939276 T OMCONN (NIL) -8 NIL NIL NIL) (-828 1937040 1938016 1938044 "OINTDOM" 1938049 T OINTDOM (NIL) -9 NIL 1938070 NIL) (-827 1934378 1935728 1936065 "OFMONOID" 1936735 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-826 1933789 1934315 1934360 "ODVAR" 1934365 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-825 1931212 1933534 1933689 "ODR" 1933694 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-824 1923793 1930988 1931114 "ODPOL" 1931119 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-823 1917615 1923665 1923770 "ODP" 1923775 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-822 1916381 1916596 1916871 "ODETOOLS" 1917389 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-821 1913348 1914006 1914722 "ODESYS" 1915714 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-820 1908230 1909138 1910163 "ODERTRIC" 1912423 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-819 1907656 1907738 1907932 "ODERED" 1908142 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-818 1904544 1905092 1905769 "ODERAT" 1907079 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-817 1901503 1901968 1902565 "ODEPRRIC" 1904073 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-816 1899446 1900042 1900528 "ODEPROB" 1901037 T ODEPROB (NIL) -8 NIL NIL NIL) (-815 1895966 1896451 1897098 "ODEPRIM" 1898925 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-814 1895215 1895317 1895577 "ODEPAL" 1895858 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-813 1891377 1892168 1893032 "ODEPACK" 1894371 T ODEPACK (NIL) -7 NIL NIL NIL) (-812 1890438 1890545 1890767 "ODEINT" 1891266 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-811 1884539 1885964 1887411 "ODEIFTBL" 1889011 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-810 1879937 1880723 1881675 "ODEEF" 1883698 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-809 1879286 1879375 1879598 "ODECONST" 1879842 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-808 1877411 1878072 1878100 "ODECAT" 1878705 T ODECAT (NIL) -9 NIL 1879236 NIL) (-807 1874266 1877116 1877238 "OCT" 1877321 NIL OCT (NIL T) -8 NIL NIL NIL) (-806 1873904 1873947 1874074 "OCTCT2" 1874217 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-805 1868515 1870950 1870990 "OC" 1872087 NIL OC (NIL T) -9 NIL 1872945 NIL) (-804 1865742 1866490 1867480 "OC-" 1867574 NIL OC- (NIL T T) -8 NIL NIL NIL) (-803 1865094 1865562 1865590 "OCAMON" 1865595 T OCAMON (NIL) -9 NIL 1865616 NIL) (-802 1864625 1864966 1864994 "OASGP" 1864999 T OASGP (NIL) -9 NIL 1865019 NIL) (-801 1863886 1864375 1864403 "OAMONS" 1864443 T OAMONS (NIL) -9 NIL 1864486 NIL) (-800 1863300 1863733 1863761 "OAMON" 1863766 T OAMON (NIL) -9 NIL 1863786 NIL) (-799 1862558 1863076 1863104 "OAGROUP" 1863109 T OAGROUP (NIL) -9 NIL 1863129 NIL) (-798 1862248 1862298 1862386 "NUMTUBE" 1862502 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-797 1855821 1857339 1858875 "NUMQUAD" 1860732 T NUMQUAD (NIL) -7 NIL NIL NIL) (-796 1851577 1852565 1853590 "NUMODE" 1854816 T NUMODE (NIL) -7 NIL NIL NIL) (-795 1848932 1849812 1849840 "NUMINT" 1850763 T NUMINT (NIL) -9 NIL 1851527 NIL) (-794 1847880 1848077 1848295 "NUMFMT" 1848734 T NUMFMT (NIL) -7 NIL NIL NIL) (-793 1834239 1837184 1839716 "NUMERIC" 1845387 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-792 1828609 1833688 1833783 "NTSCAT" 1833788 NIL NTSCAT (NIL T T T T) -9 NIL 1833827 NIL) (-791 1827803 1827968 1828161 "NTPOLFN" 1828448 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-790 1815880 1824628 1825440 "NSUP" 1827024 NIL NSUP (NIL T) -8 NIL NIL NIL) (-789 1815512 1815569 1815678 "NSUP2" 1815817 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-788 1805738 1815286 1815419 "NSMP" 1815424 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-787 1804170 1804471 1804828 "NREP" 1805426 NIL NREP (NIL T) -7 NIL NIL NIL) (-786 1802761 1803013 1803371 "NPCOEF" 1803913 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-785 1801827 1801942 1802158 "NORMRETR" 1802642 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-784 1799868 1800158 1800567 "NORMPK" 1801535 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-783 1799553 1799581 1799705 "NORMMA" 1799834 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-782 1799353 1799510 1799539 "NONE" 1799544 T NONE (NIL) -8 NIL NIL NIL) (-781 1799142 1799171 1799240 "NONE1" 1799317 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-780 1798639 1798701 1798880 "NODE1" 1799074 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-779 1796920 1797771 1798026 "NNI" 1798373 T NNI (NIL) -8 NIL NIL 1798608) (-778 1795340 1795653 1796017 "NLINSOL" 1796588 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-777 1791581 1792576 1793475 "NIPROB" 1794461 T NIPROB (NIL) -8 NIL NIL NIL) (-776 1790338 1790572 1790874 "NFINTBAS" 1791343 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-775 1789512 1789988 1790029 "NETCLT" 1790201 NIL NETCLT (NIL T) -9 NIL 1790283 NIL) (-774 1788220 1788451 1788732 "NCODIV" 1789280 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-773 1787982 1788019 1788094 "NCNTFRAC" 1788177 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-772 1786162 1786526 1786946 "NCEP" 1787607 NIL NCEP (NIL T) -7 NIL NIL NIL) (-771 1785013 1785786 1785814 "NASRING" 1785924 T NASRING (NIL) -9 NIL 1786004 NIL) (-770 1784808 1784852 1784946 "NASRING-" 1784951 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-769 1783915 1784440 1784468 "NARNG" 1784585 T NARNG (NIL) -9 NIL 1784676 NIL) (-768 1783607 1783674 1783808 "NARNG-" 1783813 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-767 1782486 1782693 1782928 "NAGSP" 1783392 T NAGSP (NIL) -7 NIL NIL NIL) (-766 1773758 1775442 1777115 "NAGS" 1780833 T NAGS (NIL) -7 NIL NIL NIL) (-765 1772306 1772614 1772945 "NAGF07" 1773447 T NAGF07 (NIL) -7 NIL NIL NIL) (-764 1766844 1768135 1769442 "NAGF04" 1771019 T NAGF04 (NIL) -7 NIL NIL NIL) (-763 1759812 1761426 1763059 "NAGF02" 1765231 T NAGF02 (NIL) -7 NIL NIL NIL) (-762 1755036 1756136 1757253 "NAGF01" 1758715 T NAGF01 (NIL) -7 NIL NIL NIL) (-761 1748664 1750230 1751815 "NAGE04" 1753471 T NAGE04 (NIL) -7 NIL NIL NIL) (-760 1739833 1741954 1744084 "NAGE02" 1746554 T NAGE02 (NIL) -7 NIL NIL NIL) (-759 1735786 1736733 1737697 "NAGE01" 1738889 T NAGE01 (NIL) -7 NIL NIL NIL) (-758 1733581 1734115 1734673 "NAGD03" 1735248 T NAGD03 (NIL) -7 NIL NIL NIL) (-757 1725331 1727259 1729213 "NAGD02" 1731647 T NAGD02 (NIL) -7 NIL NIL NIL) (-756 1719142 1720567 1722007 "NAGD01" 1723911 T NAGD01 (NIL) -7 NIL NIL NIL) (-755 1715351 1716173 1717010 "NAGC06" 1718325 T NAGC06 (NIL) -7 NIL NIL NIL) (-754 1713816 1714148 1714504 "NAGC05" 1715015 T NAGC05 (NIL) -7 NIL NIL NIL) (-753 1713192 1713311 1713455 "NAGC02" 1713692 T NAGC02 (NIL) -7 NIL NIL NIL) (-752 1712151 1712734 1712774 "NAALG" 1712853 NIL NAALG (NIL T) -9 NIL 1712914 NIL) (-751 1711986 1712015 1712105 "NAALG-" 1712110 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-750 1705936 1707044 1708231 "MULTSQFR" 1710882 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-749 1705255 1705330 1705514 "MULTFACT" 1705848 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-748 1697979 1701892 1701945 "MTSCAT" 1703015 NIL MTSCAT (NIL T T) -9 NIL 1703530 NIL) (-747 1697691 1697745 1697837 "MTHING" 1697919 NIL MTHING (NIL T) -7 NIL NIL NIL) (-746 1697483 1697516 1697576 "MSYSCMD" 1697651 T MSYSCMD (NIL) -7 NIL NIL NIL) (-745 1693565 1696238 1696558 "MSET" 1697196 NIL MSET (NIL T) -8 NIL NIL NIL) (-744 1690634 1693126 1693167 "MSETAGG" 1693172 NIL MSETAGG (NIL T) -9 NIL 1693206 NIL) (-743 1686476 1688013 1688758 "MRING" 1689934 NIL MRING (NIL T T) -8 NIL NIL NIL) (-742 1686042 1686109 1686240 "MRF2" 1686403 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-741 1685660 1685695 1685839 "MRATFAC" 1686001 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-740 1683272 1683567 1683998 "MPRFF" 1685365 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-739 1677569 1683126 1683223 "MPOLY" 1683228 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-738 1677059 1677094 1677302 "MPCPF" 1677528 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-737 1676573 1676616 1676800 "MPC3" 1677010 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-736 1675768 1675849 1676070 "MPC2" 1676488 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-735 1674069 1674406 1674796 "MONOTOOL" 1675428 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-734 1673294 1673611 1673639 "MONOID" 1673858 T MONOID (NIL) -9 NIL 1674005 NIL) (-733 1672840 1672959 1673140 "MONOID-" 1673145 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-732 1663134 1669086 1669145 "MONOGEN" 1669819 NIL MONOGEN (NIL T T) -9 NIL 1670275 NIL) (-731 1660352 1661087 1662087 "MONOGEN-" 1662206 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-730 1659185 1659631 1659659 "MONADWU" 1660051 T MONADWU (NIL) -9 NIL 1660289 NIL) (-729 1658557 1658716 1658964 "MONADWU-" 1658969 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-728 1657916 1658160 1658188 "MONAD" 1658395 T MONAD (NIL) -9 NIL 1658507 NIL) (-727 1657601 1657679 1657811 "MONAD-" 1657816 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-726 1655890 1656514 1656793 "MOEBIUS" 1657354 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-725 1655168 1655572 1655612 "MODULE" 1655617 NIL MODULE (NIL T) -9 NIL 1655656 NIL) (-724 1654736 1654832 1655022 "MODULE-" 1655027 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-723 1652416 1653100 1653427 "MODRING" 1654560 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1649360 1650521 1651042 "MODOP" 1651945 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-721 1647948 1648427 1648704 "MODMONOM" 1649223 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-720 1637992 1646239 1646653 "MODMON" 1647585 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-719 1635148 1636836 1637112 "MODFIELD" 1637867 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-718 1634125 1634429 1634619 "MMLFORM" 1634978 T MMLFORM (NIL) -8 NIL NIL NIL) (-717 1633651 1633694 1633873 "MMAP" 1634076 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-716 1631730 1632497 1632538 "MLO" 1632961 NIL MLO (NIL T) -9 NIL 1633203 NIL) (-715 1629096 1629612 1630214 "MLIFT" 1631211 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-714 1628487 1628571 1628725 "MKUCFUNC" 1629007 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-713 1628086 1628156 1628279 "MKRECORD" 1628410 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-712 1627133 1627295 1627523 "MKFUNC" 1627897 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-711 1626521 1626625 1626781 "MKFLCFN" 1627016 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-710 1625798 1625900 1626085 "MKBCFUNC" 1626414 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-709 1622505 1625352 1625488 "MINT" 1625682 T MINT (NIL) -8 NIL NIL NIL) (-708 1621317 1621560 1621837 "MHROWRED" 1622260 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-707 1616697 1619852 1620257 "MFLOAT" 1620932 T MFLOAT (NIL) -8 NIL NIL NIL) (-706 1616054 1616130 1616301 "MFINFACT" 1616609 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-705 1612369 1613217 1614101 "MESH" 1615190 T MESH (NIL) -7 NIL NIL NIL) (-704 1610759 1611071 1611424 "MDDFACT" 1612056 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-703 1607554 1609918 1609959 "MDAGG" 1610214 NIL MDAGG (NIL T) -9 NIL 1610357 NIL) (-702 1597294 1606847 1607054 "MCMPLX" 1607367 T MCMPLX (NIL) -8 NIL NIL NIL) (-701 1596431 1596577 1596778 "MCDEN" 1597143 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-700 1594321 1594591 1594971 "MCALCFN" 1596161 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-699 1593246 1593486 1593719 "MAYBE" 1594127 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-698 1590858 1591381 1591943 "MATSTOR" 1592717 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-697 1586815 1590230 1590478 "MATRIX" 1590643 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-696 1582581 1583288 1584024 "MATLIN" 1586172 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-695 1572687 1575873 1575950 "MATCAT" 1580830 NIL MATCAT (NIL T T T) -9 NIL 1582247 NIL) (-694 1569043 1570064 1571420 "MATCAT-" 1571425 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-693 1567637 1567790 1568123 "MATCAT2" 1568878 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-692 1565749 1566073 1566457 "MAPPKG3" 1567312 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-691 1564730 1564903 1565125 "MAPPKG2" 1565573 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-690 1563229 1563513 1563840 "MAPPKG1" 1564436 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-689 1562308 1562635 1562812 "MAPPAST" 1563072 T MAPPAST (NIL) -8 NIL NIL NIL) (-688 1561919 1561977 1562100 "MAPHACK3" 1562244 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-687 1561511 1561572 1561686 "MAPHACK2" 1561851 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-686 1560949 1561052 1561194 "MAPHACK1" 1561402 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-685 1559028 1559649 1559953 "MAGMA" 1560677 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-684 1558507 1558752 1558843 "MACROAST" 1558957 T MACROAST (NIL) -8 NIL NIL NIL) (-683 1554925 1556746 1557207 "M3D" 1558079 NIL M3D (NIL T) -8 NIL NIL NIL) (-682 1549000 1553264 1553305 "LZSTAGG" 1554087 NIL LZSTAGG (NIL T) -9 NIL 1554382 NIL) (-681 1544958 1546131 1547588 "LZSTAGG-" 1547593 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-680 1542045 1542849 1543336 "LWORD" 1544503 NIL LWORD (NIL T) -8 NIL NIL NIL) (-679 1541621 1541849 1541924 "LSTAST" 1541990 T LSTAST (NIL) -8 NIL NIL NIL) (-678 1534787 1541392 1541526 "LSQM" 1541531 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-677 1534011 1534150 1534378 "LSPP" 1534642 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-676 1531823 1532124 1532580 "LSMP" 1533700 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-675 1528602 1529276 1530006 "LSMP1" 1531125 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-674 1522448 1527739 1527780 "LSAGG" 1527842 NIL LSAGG (NIL T) -9 NIL 1527920 NIL) (-673 1519143 1520067 1521280 "LSAGG-" 1521285 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-672 1516742 1518287 1518536 "LPOLY" 1518938 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-671 1516324 1516409 1516532 "LPEFRAC" 1516651 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-670 1514645 1515418 1515671 "LO" 1516156 NIL LO (NIL T T T) -8 NIL NIL NIL) (-669 1514297 1514409 1514437 "LOGIC" 1514548 T LOGIC (NIL) -9 NIL 1514629 NIL) (-668 1514159 1514182 1514253 "LOGIC-" 1514258 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-667 1513352 1513492 1513685 "LODOOPS" 1514015 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-666 1510775 1513268 1513334 "LODO" 1513339 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-665 1509313 1509548 1509901 "LODOF" 1510522 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-664 1505517 1507948 1507989 "LODOCAT" 1508427 NIL LODOCAT (NIL T) -9 NIL 1508638 NIL) (-663 1505250 1505308 1505435 "LODOCAT-" 1505440 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-662 1502570 1505091 1505209 "LODO2" 1505214 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-661 1500005 1502507 1502552 "LODO1" 1502557 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-660 1498886 1499051 1499356 "LODEEF" 1499828 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-659 1494189 1497080 1497121 "LNAGG" 1497983 NIL LNAGG (NIL T) -9 NIL 1498418 NIL) (-658 1493336 1493550 1493892 "LNAGG-" 1493897 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-657 1489472 1490261 1490900 "LMOPS" 1492751 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-656 1488875 1489263 1489304 "LMODULE" 1489309 NIL LMODULE (NIL T) -9 NIL 1489335 NIL) (-655 1486073 1488520 1488643 "LMDICT" 1488785 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-654 1485479 1485700 1485741 "LLINSET" 1485932 NIL LLINSET (NIL T) -9 NIL 1486023 NIL) (-653 1485178 1485387 1485447 "LITERAL" 1485452 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-652 1478341 1484112 1484416 "LIST" 1484907 NIL LIST (NIL T) -8 NIL NIL NIL) (-651 1477866 1477940 1478079 "LIST3" 1478261 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-650 1476873 1477051 1477279 "LIST2" 1477684 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-649 1475007 1475319 1475718 "LIST2MAP" 1476520 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-648 1474603 1474840 1474881 "LINSET" 1474886 NIL LINSET (NIL T) -9 NIL 1474920 NIL) (-647 1473264 1473934 1473975 "LINEXP" 1474230 NIL LINEXP (NIL T) -9 NIL 1474379 NIL) (-646 1471911 1472171 1472468 "LINDEP" 1473016 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-645 1468678 1469397 1470174 "LIMITRF" 1471166 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-644 1466981 1467277 1467686 "LIMITPS" 1468373 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-643 1461409 1466492 1466720 "LIE" 1466802 NIL LIE (NIL T T) -8 NIL NIL NIL) (-642 1460357 1460826 1460866 "LIECAT" 1461006 NIL LIECAT (NIL T) -9 NIL 1461157 NIL) (-641 1460198 1460225 1460313 "LIECAT-" 1460318 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-640 1452785 1459738 1459894 "LIB" 1460062 T LIB (NIL) -8 NIL NIL NIL) (-639 1448420 1449303 1450238 "LGROBP" 1451902 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-638 1446418 1446692 1447042 "LF" 1448141 NIL LF (NIL T T) -7 NIL NIL NIL) (-637 1445258 1445950 1445978 "LFCAT" 1446185 T LFCAT (NIL) -9 NIL 1446324 NIL) (-636 1442160 1442790 1443478 "LEXTRIPK" 1444622 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-635 1438904 1439730 1440233 "LEXP" 1441740 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-634 1438380 1438625 1438717 "LETAST" 1438832 T LETAST (NIL) -8 NIL NIL NIL) (-633 1436778 1437091 1437492 "LEADCDET" 1438062 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-632 1435968 1436042 1436271 "LAZM3PK" 1436699 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-631 1430885 1434045 1434583 "LAUPOL" 1435480 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-630 1430464 1430508 1430669 "LAPLACE" 1430835 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-629 1428403 1429565 1429816 "LA" 1430297 NIL LA (NIL T T T) -8 NIL NIL NIL) (-628 1427397 1427981 1428022 "LALG" 1428084 NIL LALG (NIL T) -9 NIL 1428143 NIL) (-627 1427111 1427170 1427306 "LALG-" 1427311 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-626 1426946 1426970 1427011 "KVTFROM" 1427073 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-625 1425869 1426313 1426498 "KTVLOGIC" 1426781 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-624 1425704 1425728 1425769 "KRCFROM" 1425831 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-623 1424608 1424795 1425094 "KOVACIC" 1425504 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-622 1424443 1424467 1424508 "KONVERT" 1424570 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-621 1424278 1424302 1424343 "KOERCE" 1424405 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-620 1422109 1422871 1423248 "KERNEL" 1423934 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-619 1421605 1421686 1421818 "KERNEL2" 1422023 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-618 1415375 1420144 1420198 "KDAGG" 1420575 NIL KDAGG (NIL T T) -9 NIL 1420781 NIL) (-617 1414904 1415028 1415233 "KDAGG-" 1415238 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1408052 1414565 1414720 "KAFILE" 1414782 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-615 1402480 1407563 1407791 "JORDAN" 1407873 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-614 1401859 1402129 1402250 "JOINAST" 1402379 T JOINAST (NIL) -8 NIL NIL NIL) (-613 1401705 1401764 1401819 "JAVACODE" 1401824 T JAVACODE (NIL) -8 NIL NIL NIL) (-612 1397957 1399910 1399964 "IXAGG" 1400893 NIL IXAGG (NIL T T) -9 NIL 1401352 NIL) (-611 1396876 1397182 1397601 "IXAGG-" 1397606 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-610 1392406 1396798 1396857 "IVECTOR" 1396862 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-609 1391172 1391409 1391675 "ITUPLE" 1392173 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-608 1389674 1389851 1390146 "ITRIGMNP" 1390994 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-607 1388419 1388623 1388906 "ITFUN3" 1389450 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-606 1388051 1388108 1388217 "ITFUN2" 1388356 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-605 1387210 1387531 1387705 "ITFORM" 1387897 T ITFORM (NIL) -8 NIL NIL NIL) (-604 1385171 1386230 1386508 "ITAYLOR" 1386965 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-603 1374116 1379308 1380471 "ISUPS" 1384041 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-602 1373220 1373360 1373596 "ISUMP" 1373963 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-601 1368595 1373165 1373206 "ISTRING" 1373211 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-600 1368071 1368316 1368408 "ISAST" 1368523 T ISAST (NIL) -8 NIL NIL NIL) (-599 1367280 1367362 1367578 "IRURPK" 1367985 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-598 1366216 1366417 1366657 "IRSN" 1367060 T IRSN (NIL) -7 NIL NIL NIL) (-597 1364287 1364642 1365071 "IRRF2F" 1365854 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-596 1364034 1364072 1364148 "IRREDFFX" 1364243 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-595 1362649 1362908 1363207 "IROOT" 1363767 NIL IROOT (NIL T) -7 NIL NIL NIL) (-594 1359253 1360333 1361025 "IR" 1361989 NIL IR (NIL T) -8 NIL NIL NIL) (-593 1358458 1358746 1358897 "IRFORM" 1359122 T IRFORM (NIL) -8 NIL NIL NIL) (-592 1356071 1356566 1357132 "IR2" 1357936 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-591 1355171 1355284 1355498 "IR2F" 1355954 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-590 1354962 1354996 1355056 "IPRNTPK" 1355131 T IPRNTPK (NIL) -7 NIL NIL NIL) (-589 1351543 1354851 1354920 "IPF" 1354925 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-588 1349870 1351468 1351525 "IPADIC" 1351530 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-587 1349182 1349430 1349560 "IP4ADDR" 1349760 T IP4ADDR (NIL) -8 NIL NIL NIL) (-586 1348556 1348811 1348943 "IOMODE" 1349070 T IOMODE (NIL) -8 NIL NIL NIL) (-585 1347629 1348153 1348280 "IOBFILE" 1348449 T IOBFILE (NIL) -8 NIL NIL NIL) (-584 1347117 1347533 1347561 "IOBCON" 1347566 T IOBCON (NIL) -9 NIL 1347587 NIL) (-583 1346628 1346686 1346869 "INVLAPLA" 1347053 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-582 1336276 1338630 1341016 "INTTR" 1344292 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-581 1332611 1333353 1334218 "INTTOOLS" 1335461 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-580 1332197 1332288 1332405 "INTSLPE" 1332514 T INTSLPE (NIL) -7 NIL NIL NIL) (-579 1330150 1332120 1332179 "INTRVL" 1332184 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-578 1327752 1328264 1328839 "INTRF" 1329635 NIL INTRF (NIL T) -7 NIL NIL NIL) (-577 1327163 1327260 1327402 "INTRET" 1327650 NIL INTRET (NIL T) -7 NIL NIL NIL) (-576 1325160 1325549 1326019 "INTRAT" 1326771 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-575 1322423 1323006 1323625 "INTPM" 1324645 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-574 1319168 1319767 1320505 "INTPAF" 1321809 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-573 1314347 1315309 1316360 "INTPACK" 1318137 T INTPACK (NIL) -7 NIL NIL NIL) (-572 1311295 1314144 1314253 "INT" 1314258 T INT (NIL) -8 NIL NIL NIL) (-571 1310547 1310699 1310907 "INTHERTR" 1311137 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-570 1309986 1310066 1310254 "INTHERAL" 1310461 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-569 1307832 1308275 1308732 "INTHEORY" 1309549 T INTHEORY (NIL) -7 NIL NIL NIL) (-568 1299238 1300859 1302631 "INTG0" 1306184 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-567 1279811 1284601 1289411 "INTFTBL" 1294448 T INTFTBL (NIL) -8 NIL NIL NIL) (-566 1279060 1279198 1279371 "INTFACT" 1279670 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-565 1276487 1276933 1277490 "INTEF" 1278614 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-564 1274854 1275593 1275621 "INTDOM" 1275922 T INTDOM (NIL) -9 NIL 1276129 NIL) (-563 1274223 1274397 1274639 "INTDOM-" 1274644 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-562 1270611 1272539 1272593 "INTCAT" 1273392 NIL INTCAT (NIL T) -9 NIL 1273713 NIL) (-561 1270083 1270186 1270314 "INTBIT" 1270503 T INTBIT (NIL) -7 NIL NIL NIL) (-560 1268782 1268936 1269243 "INTALG" 1269928 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-559 1268265 1268355 1268512 "INTAF" 1268686 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-558 1261608 1268075 1268215 "INTABL" 1268220 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-557 1260941 1261407 1261472 "INT8" 1261506 T INT8 (NIL) -8 NIL NIL 1261551) (-556 1260273 1260739 1260804 "INT64" 1260838 T INT64 (NIL) -8 NIL NIL 1260883) (-555 1259605 1260071 1260136 "INT32" 1260170 T INT32 (NIL) -8 NIL NIL 1260215) (-554 1258937 1259403 1259468 "INT16" 1259502 T INT16 (NIL) -8 NIL NIL 1259547) (-553 1253817 1256531 1256559 "INS" 1257493 T INS (NIL) -9 NIL 1258158 NIL) (-552 1251057 1251828 1252802 "INS-" 1252875 NIL INS- (NIL T) -8 NIL NIL NIL) (-551 1249832 1250059 1250357 "INPSIGN" 1250810 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-550 1248950 1249067 1249264 "INPRODPF" 1249712 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-549 1247844 1247961 1248198 "INPRODFF" 1248830 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-548 1246844 1246996 1247256 "INNMFACT" 1247680 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-547 1246041 1246138 1246326 "INMODGCD" 1246743 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-546 1244549 1244794 1245118 "INFSP" 1245786 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-545 1243733 1243850 1244033 "INFPROD0" 1244429 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-544 1240588 1241798 1242313 "INFORM" 1243226 T INFORM (NIL) -8 NIL NIL NIL) (-543 1240198 1240258 1240356 "INFORM1" 1240523 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-542 1239721 1239810 1239924 "INFINITY" 1240104 T INFINITY (NIL) -7 NIL NIL NIL) (-541 1238897 1239441 1239542 "INETCLTS" 1239640 T INETCLTS (NIL) -8 NIL NIL NIL) (-540 1237513 1237763 1238084 "INEP" 1238645 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-539 1236762 1237410 1237475 "INDE" 1237480 NIL INDE (NIL T) -8 NIL NIL NIL) (-538 1236326 1236394 1236511 "INCRMAPS" 1236689 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-537 1235144 1235595 1235801 "INBFILE" 1236140 T INBFILE (NIL) -8 NIL NIL NIL) (-536 1230443 1231380 1232324 "INBFF" 1234232 NIL INBFF (NIL T) -7 NIL NIL NIL) (-535 1229351 1229620 1229648 "INBCON" 1230161 T INBCON (NIL) -9 NIL 1230427 NIL) (-534 1228603 1228826 1229102 "INBCON-" 1229107 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-533 1228082 1228327 1228418 "INAST" 1228532 T INAST (NIL) -8 NIL NIL NIL) (-532 1227509 1227761 1227867 "IMPTAST" 1227996 T IMPTAST (NIL) -8 NIL NIL NIL) (-531 1223955 1227353 1227457 "IMATRIX" 1227462 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-530 1222663 1222786 1223102 "IMATQF" 1223811 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-529 1220883 1221110 1221447 "IMATLIN" 1222419 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-528 1215461 1220807 1220865 "ILIST" 1220870 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-527 1213366 1215321 1215434 "IIARRAY2" 1215439 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-526 1208764 1213277 1213341 "IFF" 1213346 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-525 1208111 1208381 1208497 "IFAST" 1208668 T IFAST (NIL) -8 NIL NIL NIL) (-524 1203106 1207403 1207591 "IFARRAY" 1207968 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-523 1202286 1203010 1203083 "IFAMON" 1203088 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-522 1201870 1201935 1201989 "IEVALAB" 1202196 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-521 1201545 1201613 1201773 "IEVALAB-" 1201778 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-520 1201176 1201459 1201522 "IDPO" 1201527 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-519 1200426 1201065 1201140 "IDPOAMS" 1201145 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-518 1199733 1200315 1200390 "IDPOAM" 1200395 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-517 1198792 1199068 1199121 "IDPC" 1199534 NIL IDPC (NIL T T) -9 NIL 1199683 NIL) (-516 1198261 1198684 1198757 "IDPAM" 1198762 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-515 1197637 1198153 1198226 "IDPAG" 1198231 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-514 1197282 1197473 1197548 "IDENT" 1197582 T IDENT (NIL) -8 NIL NIL NIL) (-513 1193537 1194385 1195280 "IDECOMP" 1196439 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-512 1186374 1187460 1188507 "IDEAL" 1192573 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-511 1185534 1185646 1185846 "ICDEN" 1186258 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-510 1184605 1185014 1185161 "ICARD" 1185407 T ICARD (NIL) -8 NIL NIL NIL) (-509 1182665 1182978 1183383 "IBPTOOLS" 1184282 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-508 1178272 1182285 1182398 "IBITS" 1182584 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-507 1174995 1175571 1176266 "IBATOOL" 1177689 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-506 1172774 1173236 1173769 "IBACHIN" 1174530 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-505 1170603 1172620 1172723 "IARRAY2" 1172728 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-504 1166709 1170529 1170586 "IARRAY1" 1170591 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-503 1160818 1165121 1165602 "IAN" 1166248 T IAN (NIL) -8 NIL NIL NIL) (-502 1160329 1160386 1160559 "IALGFACT" 1160755 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-501 1159857 1159970 1159998 "HYPCAT" 1160205 T HYPCAT (NIL) -9 NIL NIL NIL) (-500 1159395 1159512 1159698 "HYPCAT-" 1159703 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-499 1158990 1159190 1159273 "HOSTNAME" 1159332 T HOSTNAME (NIL) -8 NIL NIL NIL) (-498 1158835 1158872 1158913 "HOMOTOP" 1158918 NIL HOMOTOP (NIL T) -9 NIL 1158951 NIL) (-497 1155467 1156845 1156886 "HOAGG" 1157867 NIL HOAGG (NIL T) -9 NIL 1158546 NIL) (-496 1154061 1154460 1154986 "HOAGG-" 1154991 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-495 1148063 1153654 1153804 "HEXADEC" 1153931 T HEXADEC (NIL) -8 NIL NIL NIL) (-494 1146811 1147033 1147296 "HEUGCD" 1147840 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-493 1145887 1146648 1146778 "HELLFDIV" 1146783 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-492 1144066 1145664 1145752 "HEAP" 1145831 NIL HEAP (NIL T) -8 NIL NIL NIL) (-491 1143329 1143618 1143752 "HEADAST" 1143952 T HEADAST (NIL) -8 NIL NIL NIL) (-490 1137195 1143244 1143306 "HDP" 1143311 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-489 1131183 1136830 1136982 "HDMP" 1137096 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-488 1130507 1130647 1130811 "HB" 1131039 T HB (NIL) -7 NIL NIL NIL) (-487 1123893 1130353 1130457 "HASHTBL" 1130462 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-486 1123369 1123614 1123706 "HASAST" 1123821 T HASAST (NIL) -8 NIL NIL NIL) (-485 1121147 1122991 1123173 "HACKPI" 1123207 T HACKPI (NIL) -8 NIL NIL NIL) (-484 1116815 1121000 1121113 "GTSET" 1121118 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-483 1110230 1116693 1116791 "GSTBL" 1116796 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-482 1102508 1109261 1109526 "GSERIES" 1110021 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-481 1101649 1102066 1102094 "GROUP" 1102297 T GROUP (NIL) -9 NIL 1102431 NIL) (-480 1101015 1101174 1101425 "GROUP-" 1101430 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-479 1099382 1099703 1100090 "GROEBSOL" 1100692 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-478 1098296 1098584 1098635 "GRMOD" 1099164 NIL GRMOD (NIL T T) -9 NIL 1099332 NIL) (-477 1098064 1098100 1098228 "GRMOD-" 1098233 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-476 1093354 1094418 1095418 "GRIMAGE" 1097084 T GRIMAGE (NIL) -8 NIL NIL NIL) (-475 1091820 1092081 1092405 "GRDEF" 1093050 T GRDEF (NIL) -7 NIL NIL NIL) (-474 1091264 1091380 1091521 "GRAY" 1091699 T GRAY (NIL) -7 NIL NIL NIL) (-473 1090451 1090857 1090908 "GRALG" 1091061 NIL GRALG (NIL T T) -9 NIL 1091154 NIL) (-472 1090112 1090185 1090348 "GRALG-" 1090353 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-471 1086889 1089697 1089875 "GPOLSET" 1090019 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-470 1086243 1086300 1086558 "GOSPER" 1086826 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-469 1081975 1082681 1083207 "GMODPOL" 1085942 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-468 1080980 1081164 1081402 "GHENSEL" 1081787 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-467 1075136 1075979 1076999 "GENUPS" 1080064 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-466 1074833 1074884 1074973 "GENUFACT" 1075079 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-465 1074245 1074322 1074487 "GENPGCD" 1074751 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-464 1073719 1073754 1073967 "GENMFACT" 1074204 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-463 1072285 1072542 1072849 "GENEEZ" 1073462 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-462 1066433 1071896 1072058 "GDMP" 1072208 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-461 1055776 1060204 1061310 "GCNAALG" 1065416 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-460 1054103 1054965 1054993 "GCDDOM" 1055248 T GCDDOM (NIL) -9 NIL 1055405 NIL) (-459 1053573 1053700 1053915 "GCDDOM-" 1053920 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-458 1052245 1052430 1052734 "GB" 1053352 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-457 1040861 1043191 1045583 "GBINTERN" 1049936 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-456 1038698 1038990 1039411 "GBF" 1040536 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-455 1037479 1037644 1037911 "GBEUCLID" 1038514 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-454 1036828 1036953 1037102 "GAUSSFAC" 1037350 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-453 1035195 1035497 1035811 "GALUTIL" 1036547 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-452 1033503 1033777 1034101 "GALPOLYU" 1034922 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-451 1030868 1031158 1031565 "GALFACTU" 1033200 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-450 1022674 1024173 1025781 "GALFACT" 1029300 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-449 1020062 1020720 1020748 "FVFUN" 1021904 T FVFUN (NIL) -9 NIL 1022624 NIL) (-448 1019328 1019510 1019538 "FVC" 1019829 T FVC (NIL) -9 NIL 1020012 NIL) (-447 1018971 1019153 1019221 "FUNDESC" 1019280 T FUNDESC (NIL) -8 NIL NIL NIL) (-446 1018586 1018768 1018849 "FUNCTION" 1018923 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-445 1016330 1016908 1017374 "FT" 1018140 T FT (NIL) -8 NIL NIL NIL) (-444 1015121 1015631 1015834 "FTEM" 1016147 T FTEM (NIL) -8 NIL NIL NIL) (-443 1013412 1013701 1014098 "FSUPFACT" 1014812 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-442 1011809 1012098 1012430 "FST" 1013100 T FST (NIL) -8 NIL NIL NIL) (-441 1011008 1011114 1011302 "FSRED" 1011691 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-440 1009707 1009963 1010310 "FSPRMELT" 1010723 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-439 1007013 1007451 1007937 "FSPECF" 1009270 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-438 988651 996982 997023 "FS" 1000907 NIL FS (NIL T) -9 NIL 1003196 NIL) (-437 977294 980287 984344 "FS-" 984644 NIL FS- (NIL T T) -8 NIL NIL NIL) (-436 976822 976876 977046 "FSINT" 977235 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-435 975114 975815 976118 "FSERIES" 976601 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-434 974156 974272 974496 "FSCINT" 974994 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-433 970364 973100 973141 "FSAGG" 973511 NIL FSAGG (NIL T) -9 NIL 973770 NIL) (-432 968126 968727 969523 "FSAGG-" 969618 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-431 967168 967311 967538 "FSAGG2" 967979 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-430 964850 965130 965677 "FS2UPS" 966886 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-429 964484 964527 964656 "FS2" 964801 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-428 963362 963533 963835 "FS2EXPXP" 964309 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 962788 962903 963055 "FRUTIL" 963242 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-426 954201 958283 959641 "FR" 961462 NIL FR (NIL T) -8 NIL NIL NIL) (-425 949215 951890 951930 "FRNAALG" 953250 NIL FRNAALG (NIL T) -9 NIL 953848 NIL) (-424 944888 945964 947239 "FRNAALG-" 947989 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-423 944526 944569 944696 "FRNAAF2" 944839 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-422 942901 943375 943671 "FRMOD" 944338 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-421 940644 941276 941594 "FRIDEAL" 942692 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-420 939835 939922 940213 "FRIDEAL2" 940551 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-419 938968 939382 939423 "FRETRCT" 939428 NIL FRETRCT (NIL T) -9 NIL 939604 NIL) (-418 938080 938311 938662 "FRETRCT-" 938667 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-417 935168 936378 936437 "FRAMALG" 937319 NIL FRAMALG (NIL T T) -9 NIL 937611 NIL) (-416 933302 933757 934387 "FRAMALG-" 934610 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-415 927221 932775 933052 "FRAC" 933057 NIL FRAC (NIL T) -8 NIL NIL NIL) (-414 926857 926914 927021 "FRAC2" 927158 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-413 926493 926550 926657 "FR2" 926794 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-412 921006 923899 923927 "FPS" 925046 T FPS (NIL) -9 NIL 925603 NIL) (-411 920455 920564 920728 "FPS-" 920874 NIL FPS- (NIL T) -8 NIL NIL NIL) (-410 917757 919426 919454 "FPC" 919679 T FPC (NIL) -9 NIL 919821 NIL) (-409 917550 917590 917687 "FPC-" 917692 NIL FPC- (NIL T) -8 NIL NIL NIL) (-408 916340 917038 917079 "FPATMAB" 917084 NIL FPATMAB (NIL T) -9 NIL 917236 NIL) (-407 914013 914516 914942 "FPARFRAC" 915977 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-406 909407 909905 910587 "FORTRAN" 913445 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-405 907123 907623 908162 "FORT" 908888 T FORT (NIL) -7 NIL NIL NIL) (-404 904799 905361 905389 "FORTFN" 906449 T FORTFN (NIL) -9 NIL 907073 NIL) (-403 904563 904613 904641 "FORTCAT" 904700 T FORTCAT (NIL) -9 NIL 904762 NIL) (-402 902669 903179 903569 "FORMULA" 904193 T FORMULA (NIL) -8 NIL NIL NIL) (-401 902457 902487 902556 "FORMULA1" 902633 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-400 901980 902032 902205 "FORDER" 902399 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-399 901076 901240 901433 "FOP" 901807 T FOP (NIL) -7 NIL NIL NIL) (-398 899657 900356 900530 "FNLA" 900958 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-397 898386 898801 898829 "FNCAT" 899289 T FNCAT (NIL) -9 NIL 899549 NIL) (-396 897925 898345 898373 "FNAME" 898378 T FNAME (NIL) -8 NIL NIL NIL) (-395 896488 897451 897479 "FMTC" 897484 T FMTC (NIL) -9 NIL 897520 NIL) (-394 895234 896424 896470 "FMONOID" 896475 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-393 892062 893230 893271 "FMONCAT" 894488 NIL FMONCAT (NIL T) -9 NIL 895093 NIL) (-392 891254 891804 891953 "FM" 891958 NIL FM (NIL T T) -8 NIL NIL NIL) (-391 888678 889324 889352 "FMFUN" 890496 T FMFUN (NIL) -9 NIL 891204 NIL) (-390 887947 888128 888156 "FMC" 888446 T FMC (NIL) -9 NIL 888628 NIL) (-389 885026 885886 885940 "FMCAT" 887135 NIL FMCAT (NIL T T) -9 NIL 887630 NIL) (-388 883892 884792 884892 "FM1" 884971 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-387 881666 882082 882576 "FLOATRP" 883443 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-386 875244 879395 880016 "FLOAT" 881065 T FLOAT (NIL) -8 NIL NIL NIL) (-385 872682 873182 873760 "FLOATCP" 874711 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-384 871422 872260 872301 "FLINEXP" 872306 NIL FLINEXP (NIL T) -9 NIL 872399 NIL) (-383 870576 870811 871139 "FLINEXP-" 871144 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-382 869652 869796 870020 "FLASORT" 870428 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-381 866768 867636 867688 "FLALG" 868915 NIL FLALG (NIL T T) -9 NIL 869382 NIL) (-380 860472 864224 864265 "FLAGG" 865527 NIL FLAGG (NIL T) -9 NIL 866179 NIL) (-379 859198 859537 860027 "FLAGG-" 860032 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-378 858240 858383 858610 "FLAGG2" 859051 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-377 855091 856099 856158 "FINRALG" 857286 NIL FINRALG (NIL T T) -9 NIL 857794 NIL) (-376 854251 854480 854819 "FINRALG-" 854824 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-375 853631 853870 853898 "FINITE" 854094 T FINITE (NIL) -9 NIL 854201 NIL) (-374 845988 848175 848215 "FINAALG" 851882 NIL FINAALG (NIL T) -9 NIL 853335 NIL) (-373 841320 842370 843514 "FINAALG-" 844893 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-372 840688 841075 841178 "FILE" 841250 NIL FILE (NIL T) -8 NIL NIL NIL) (-371 839346 839684 839738 "FILECAT" 840422 NIL FILECAT (NIL T T) -9 NIL 840638 NIL) (-370 837062 838590 838618 "FIELD" 838658 T FIELD (NIL) -9 NIL 838738 NIL) (-369 835682 836067 836578 "FIELD-" 836583 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-368 833532 834317 834664 "FGROUP" 835368 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-367 832622 832786 833006 "FGLMICPK" 833364 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-366 828454 832547 832604 "FFX" 832609 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-365 828055 828116 828251 "FFSLPE" 828387 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-364 824045 824827 825623 "FFPOLY" 827291 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-363 823549 823585 823794 "FFPOLY2" 824003 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-362 819395 823468 823531 "FFP" 823536 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-361 814793 819306 819370 "FF" 819375 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-360 809919 814136 814326 "FFNBX" 814647 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-359 804847 809054 809312 "FFNBP" 809773 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-358 799480 804131 804342 "FFNB" 804680 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-357 798312 798510 798825 "FFINTBAS" 799277 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-356 794351 796572 796600 "FFIELDC" 797220 T FFIELDC (NIL) -9 NIL 797596 NIL) (-355 793013 793384 793881 "FFIELDC-" 793886 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-354 792582 792628 792752 "FFHOM" 792955 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-353 790277 790764 791281 "FFF" 792097 NIL FFF (NIL T) -7 NIL NIL NIL) (-352 785895 790019 790120 "FFCGX" 790220 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-351 781517 785627 785734 "FFCGP" 785838 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-350 776700 781244 781352 "FFCG" 781453 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-349 757852 766934 767020 "FFCAT" 772185 NIL FFCAT (NIL T T T) -9 NIL 773636 NIL) (-348 753049 754097 755411 "FFCAT-" 756641 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-347 752460 752503 752738 "FFCAT2" 753000 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 741783 745432 746652 "FEXPR" 751312 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-345 740745 741180 741221 "FEVALAB" 741305 NIL FEVALAB (NIL T) -9 NIL 741566 NIL) (-344 739904 740114 740452 "FEVALAB-" 740457 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-343 738470 739287 739490 "FDIV" 739803 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-342 735490 736231 736346 "FDIVCAT" 737914 NIL FDIVCAT (NIL T T T T) -9 NIL 738351 NIL) (-341 735252 735279 735449 "FDIVCAT-" 735454 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-340 734472 734559 734836 "FDIV2" 735159 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 733446 733767 733969 "FCTRDATA" 734290 T FCTRDATA (NIL) -8 NIL NIL NIL) (-338 732132 732391 732680 "FCPAK1" 733177 T FCPAK1 (NIL) -7 NIL NIL NIL) (-337 731231 731632 731773 "FCOMP" 732023 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-336 714936 718381 721919 "FC" 727713 T FC (NIL) -8 NIL NIL NIL) (-335 707242 711270 711310 "FAXF" 713112 NIL FAXF (NIL T) -9 NIL 713804 NIL) (-334 704519 705176 706001 "FAXF-" 706466 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-333 699571 703895 704071 "FARRAY" 704376 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-332 694465 696532 696585 "FAMR" 697608 NIL FAMR (NIL T T) -9 NIL 698068 NIL) (-331 693355 693657 694092 "FAMR-" 694097 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-330 692524 693277 693330 "FAMONOID" 693335 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-329 690310 691020 691073 "FAMONC" 692014 NIL FAMONC (NIL T T) -9 NIL 692400 NIL) (-328 688974 690064 690201 "FAGROUP" 690206 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-327 686769 687088 687491 "FACUTIL" 688655 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-326 685868 686053 686275 "FACTFUNC" 686579 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-325 678290 685171 685370 "EXPUPXS" 685724 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-324 675773 676313 676899 "EXPRTUBE" 677724 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-323 672044 672636 673366 "EXPRODE" 675112 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-322 657529 670693 671122 "EXPR" 671648 NIL EXPR (NIL T) -8 NIL NIL NIL) (-321 652083 652670 653476 "EXPR2UPS" 656827 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-320 651715 651772 651881 "EXPR2" 652020 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-319 643103 650866 651157 "EXPEXPAN" 651551 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-318 642903 643060 643089 "EXIT" 643094 T EXIT (NIL) -8 NIL NIL NIL) (-317 642383 642627 642718 "EXITAST" 642832 T EXITAST (NIL) -8 NIL NIL NIL) (-316 642010 642072 642185 "EVALCYC" 642315 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-315 641551 641669 641710 "EVALAB" 641880 NIL EVALAB (NIL T) -9 NIL 641984 NIL) (-314 641032 641154 641375 "EVALAB-" 641380 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-313 638400 639702 639730 "EUCDOM" 640285 T EUCDOM (NIL) -9 NIL 640635 NIL) (-312 636805 637247 637837 "EUCDOM-" 637842 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-311 624344 627103 629853 "ESTOOLS" 634075 T ESTOOLS (NIL) -7 NIL NIL NIL) (-310 623976 624033 624142 "ESTOOLS2" 624281 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-309 623727 623769 623849 "ESTOOLS1" 623928 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-308 617764 619372 619400 "ES" 622168 T ES (NIL) -9 NIL 623578 NIL) (-307 612711 613998 615815 "ES-" 615979 NIL ES- (NIL T) -8 NIL NIL NIL) (-306 609085 609846 610626 "ESCONT" 611951 T ESCONT (NIL) -7 NIL NIL NIL) (-305 608830 608862 608944 "ESCONT1" 609047 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 608505 608555 608655 "ES2" 608774 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-303 608135 608193 608302 "ES1" 608441 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-302 607351 607480 607656 "ERROR" 607979 T ERROR (NIL) -7 NIL NIL NIL) (-301 600743 607210 607301 "EQTBL" 607306 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-300 593246 596057 597506 "EQ" 599327 NIL -3073 (NIL T) -8 NIL NIL NIL) (-299 592878 592935 593044 "EQ2" 593183 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-298 588169 589216 590309 "EP" 591817 NIL EP (NIL T) -7 NIL NIL NIL) (-297 586769 587060 587366 "ENV" 587883 T ENV (NIL) -8 NIL NIL NIL) (-296 585863 586417 586445 "ENTIRER" 586450 T ENTIRER (NIL) -9 NIL 586496 NIL) (-295 582557 584045 584406 "EMR" 585671 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-294 581687 581872 581926 "ELTAGG" 582306 NIL ELTAGG (NIL T T) -9 NIL 582517 NIL) (-293 581406 581468 581609 "ELTAGG-" 581614 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-292 581170 581199 581253 "ELTAB" 581337 NIL ELTAB (NIL T T) -9 NIL 581389 NIL) (-291 580296 580442 580641 "ELFUTS" 581021 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-290 580038 580094 580122 "ELEMFUN" 580227 T ELEMFUN (NIL) -9 NIL NIL NIL) (-289 579908 579929 579997 "ELEMFUN-" 580002 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-288 574722 577978 578019 "ELAGG" 578959 NIL ELAGG (NIL T) -9 NIL 579422 NIL) (-287 573007 573441 574104 "ELAGG-" 574109 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-286 572319 572456 572612 "ELABOR" 572871 T ELABOR (NIL) -8 NIL NIL NIL) (-285 570980 571259 571553 "ELABEXPR" 572045 T ELABEXPR (NIL) -8 NIL NIL NIL) (-284 563844 565647 566474 "EFUPXS" 570256 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-283 557294 559095 559905 "EFULS" 563120 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-282 554779 555137 555609 "EFSTRUC" 556926 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-281 544570 546136 547684 "EF" 553294 NIL EF (NIL T T) -7 NIL NIL NIL) (-280 543644 544055 544204 "EAB" 544441 T EAB (NIL) -8 NIL NIL NIL) (-279 542826 543603 543631 "E04UCFA" 543636 T E04UCFA (NIL) -8 NIL NIL NIL) (-278 542008 542785 542813 "E04NAFA" 542818 T E04NAFA (NIL) -8 NIL NIL NIL) (-277 541190 541967 541995 "E04MBFA" 542000 T E04MBFA (NIL) -8 NIL NIL NIL) (-276 540372 541149 541177 "E04JAFA" 541182 T E04JAFA (NIL) -8 NIL NIL NIL) (-275 539556 540331 540359 "E04GCFA" 540364 T E04GCFA (NIL) -8 NIL NIL NIL) (-274 538740 539515 539543 "E04FDFA" 539548 T E04FDFA (NIL) -8 NIL NIL NIL) (-273 537922 538699 538727 "E04DGFA" 538732 T E04DGFA (NIL) -8 NIL NIL NIL) (-272 532095 533447 534811 "E04AGNT" 536578 T E04AGNT (NIL) -7 NIL NIL NIL) (-271 530775 531281 531321 "DVARCAT" 531796 NIL DVARCAT (NIL T) -9 NIL 531995 NIL) (-270 529979 530191 530505 "DVARCAT-" 530510 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-269 523116 529778 529907 "DSMP" 529912 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-268 517897 519061 520129 "DROPT" 522068 T DROPT (NIL) -8 NIL NIL NIL) (-267 517562 517621 517719 "DROPT1" 517832 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-266 512677 513803 514940 "DROPT0" 516445 T DROPT0 (NIL) -7 NIL NIL NIL) (-265 511022 511347 511733 "DRAWPT" 512311 T DRAWPT (NIL) -7 NIL NIL NIL) (-264 505609 506532 507611 "DRAW" 509996 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 505242 505295 505413 "DRAWHACK" 505550 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-262 503973 504242 504533 "DRAWCX" 504971 T DRAWCX (NIL) -7 NIL NIL NIL) (-261 503488 503557 503708 "DRAWCURV" 503899 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-260 493956 495918 498033 "DRAWCFUN" 501393 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-259 490720 492649 492690 "DQAGG" 493319 NIL DQAGG (NIL T) -9 NIL 493593 NIL) (-258 478708 485222 485305 "DPOLCAT" 487160 NIL DPOLCAT (NIL T T T T) -9 NIL 487711 NIL) (-257 473545 474893 476851 "DPOLCAT-" 476856 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-256 466667 473406 473504 "DPMO" 473509 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-255 459692 466447 466614 "DPMM" 466619 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-254 459262 459476 459565 "DOMTMPLT" 459623 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-253 458695 459064 459144 "DOMCTOR" 459202 T DOMCTOR (NIL) -8 NIL NIL NIL) (-252 457907 458175 458326 "DOMAIN" 458564 T DOMAIN (NIL) -8 NIL NIL NIL) (-251 451895 457542 457694 "DMP" 457808 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-250 451495 451551 451695 "DLP" 451833 NIL DLP (NIL T) -7 NIL NIL NIL) (-249 445317 450822 451012 "DLIST" 451337 NIL DLIST (NIL T) -8 NIL NIL NIL) (-248 442114 444170 444211 "DLAGG" 444761 NIL DLAGG (NIL T) -9 NIL 444991 NIL) (-247 440790 441454 441482 "DIVRING" 441574 T DIVRING (NIL) -9 NIL 441657 NIL) (-246 440027 440217 440517 "DIVRING-" 440522 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-245 438129 438486 438892 "DISPLAY" 439641 T DISPLAY (NIL) -7 NIL NIL NIL) (-244 432015 438043 438106 "DIRPROD" 438111 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-243 430863 431066 431331 "DIRPROD2" 431808 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-242 419571 425578 425631 "DIRPCAT" 426041 NIL DIRPCAT (NIL NIL T) -9 NIL 426881 NIL) (-241 416897 417539 418420 "DIRPCAT-" 418757 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-240 416184 416344 416530 "DIOSP" 416731 T DIOSP (NIL) -7 NIL NIL NIL) (-239 412839 415096 415137 "DIOPS" 415571 NIL DIOPS (NIL T) -9 NIL 415800 NIL) (-238 412388 412502 412693 "DIOPS-" 412698 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-237 411277 411905 411933 "DIFRING" 412052 T DIFRING (NIL) -9 NIL 412135 NIL) (-236 410922 411000 411152 "DIFRING-" 411157 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-235 410630 410675 410716 "DIFFDOM" 410837 NIL DIFFDOM (NIL T) -9 NIL 410905 NIL) (-234 410483 410507 410591 "DIFFDOM-" 410596 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 408121 409413 409454 "DIFEXT" 409817 NIL DIFEXT (NIL T) -9 NIL 410117 NIL) (-232 406406 406834 407500 "DIFEXT-" 407505 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403681 405938 405979 "DIAGG" 405984 NIL DIAGG (NIL T) -9 NIL 406004 NIL) (-230 403065 403222 403474 "DIAGG-" 403479 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398482 402024 402301 "DHMATRIX" 402834 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394094 395003 396013 "DFSFUN" 397492 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389174 393025 393337 "DFLOAT" 393802 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387437 387718 388107 "DFINTTLS" 388882 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384466 385458 385858 "DERHAM" 387103 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382267 384241 384330 "DEQUEUE" 384410 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381521 381654 381837 "DEGRED" 382129 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377951 378696 379542 "DEFINTRF" 380749 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375506 375975 376567 "DEFINTEF" 377470 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374856 375126 375241 "DEFAST" 375411 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368858 374449 374599 "DECIMAL" 374726 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366370 366828 367334 "DDFACT" 368402 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365966 366009 366160 "DBLRESP" 366321 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363834 364196 364557 "DBASE" 365732 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363076 363314 363460 "DATAARY" 363733 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362182 363035 363063 "D03FAFA" 363068 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361289 362141 362169 "D03EEFA" 362174 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359239 359705 360194 "D03AGNT" 360820 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358528 359198 359226 "D02EJFA" 359231 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357817 358487 358515 "D02CJFA" 358520 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357106 357776 357804 "D02BHFA" 357809 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356395 357065 357093 "D02BBFA" 357098 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349592 351181 352787 "D02AGNT" 354809 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347360 347883 348429 "D01WGTS" 349066 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346427 347319 347347 "D01TRNS" 347352 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345495 346386 346414 "D01GBFA" 346419 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344563 345454 345482 "D01FCFA" 345487 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343631 344522 344550 "D01ASFA" 344555 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342699 343590 343618 "D01AQFA" 343623 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341767 342658 342686 "D01APFA" 342691 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340835 341726 341754 "D01ANFA" 341759 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339903 340794 340822 "D01AMFA" 340827 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338971 339862 339890 "D01ALFA" 339895 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338039 338930 338958 "D01AKFA" 338963 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337107 337998 338026 "D01AJFA" 338031 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330402 331955 333516 "D01AGNT" 335566 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329739 329867 330019 "CYCLOTOM" 330270 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326472 327187 327914 "CYCLES" 329032 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325784 325918 326089 "CVMP" 326333 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323625 323883 324252 "CTRIGMNP" 325512 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323061 323419 323492 "CTOR" 323572 T CTOR (NIL) -8 NIL NIL NIL) (-188 322570 322792 322893 "CTORKIND" 322980 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321861 322177 322205 "CTORCAT" 322387 T CTORCAT (NIL) -9 NIL 322500 NIL) (-186 321459 321570 321729 "CTORCAT-" 321734 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320921 321133 321241 "CTORCALL" 321383 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320295 320394 320547 "CSTTOOLS" 320818 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316094 316751 317509 "CRFP" 319607 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315569 315815 315907 "CRCEAST" 316022 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314616 314801 315029 "CRAPACK" 315373 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 314000 314101 314305 "CPMATCH" 314492 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313725 313753 313859 "CPIMA" 313966 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310073 310745 311464 "COORDSYS" 313060 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309485 309606 309748 "CONTOUR" 309951 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305376 307488 307980 "CONTFRAC" 309025 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305256 305277 305305 "CONDUIT" 305342 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304344 304898 304926 "COMRING" 304931 T COMRING (NIL) -9 NIL 304983 NIL) (-173 303398 303702 303886 "COMPPROP" 304180 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303059 303094 303222 "COMPLPAT" 303357 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293350 302868 302977 "COMPLEX" 302982 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292986 293043 293150 "COMPLEX2" 293287 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292325 292446 292606 "COMPILER" 292846 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292043 292078 292176 "COMPFACT" 292284 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276055 286050 286090 "COMPCAT" 287094 NIL COMPCAT (NIL T) -9 NIL 288442 NIL) (-166 265567 268494 272121 "COMPCAT-" 272477 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265296 265324 265427 "COMMUPC" 265533 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265090 265124 265183 "COMMONOP" 265257 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264646 264841 264928 "COMM" 265023 T COMM (NIL) -8 NIL NIL NIL) (-162 264222 264450 264525 "COMMAAST" 264591 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263471 263665 263693 "COMBOPC" 264031 T COMBOPC (NIL) -9 NIL 264206 NIL) (-160 262367 262577 262819 "COMBINAT" 263261 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258824 259398 260025 "COMBF" 261789 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257582 257940 258175 "COLOR" 258609 T COLOR (NIL) -8 NIL NIL NIL) (-157 257058 257303 257395 "COLONAST" 257510 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256698 256745 256870 "CMPLXRT" 257005 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256146 256398 256497 "CLLCTAST" 256619 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251648 252676 253756 "CLIP" 255086 T CLIP (NIL) -7 NIL NIL NIL) (-153 249989 250749 250989 "CLIF" 251475 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246164 248135 248176 "CLAGG" 249105 NIL CLAGG (NIL T) -9 NIL 249641 NIL) (-151 244586 245043 245626 "CLAGG-" 245631 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244130 244215 244355 "CINTSLPE" 244495 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241631 242102 242650 "CHVAR" 243658 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240805 241359 241387 "CHARZ" 241392 T CHARZ (NIL) -9 NIL 241407 NIL) (-147 240559 240599 240677 "CHARPOL" 240759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239617 240204 240232 "CHARNZ" 240279 T CHARNZ (NIL) -9 NIL 240335 NIL) (-145 237523 238271 238624 "CHAR" 239284 T CHAR (NIL) -8 NIL NIL NIL) (-144 237249 237310 237338 "CFCAT" 237449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236490 236601 236784 "CDEN" 237133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232455 235643 235923 "CCLASS" 236230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231706 231863 232040 "CATEGORY" 232298 T -10 (NIL) -8 NIL NIL NIL) (-140 231279 231625 231673 "CATCTOR" 231678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230730 230982 231080 "CATAST" 231201 T CATAST (NIL) -8 NIL NIL NIL) (-138 230206 230451 230543 "CASEAST" 230658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225344 226363 227107 "CARTEN" 229518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224452 224600 224821 "CARTEN2" 225191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222768 223602 223859 "CARD" 224215 T CARD (NIL) -8 NIL NIL NIL) (-134 222344 222572 222647 "CAPSLAST" 222713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221848 222056 222084 "CACHSET" 222216 T CACHSET (NIL) -9 NIL 222294 NIL) (-132 221318 221640 221668 "CABMON" 221718 T CABMON (NIL) -9 NIL 221774 NIL) (-131 220791 221022 221132 "BYTEORD" 221228 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210076 212275 212397 "BTOURN" 212537 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207446 209546 209587 "BTCAT" 209655 NIL BTCAT (NIL T) -9 NIL 209732 NIL) (-125 207113 207193 207342 "BTCAT-" 207347 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202492 206372 206400 "BTAGG" 206514 T BTAGG (NIL) -9 NIL 206624 NIL) (-123 201982 202107 202313 "BTAGG-" 202318 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198977 201260 201475 "BSTREE" 201799 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198115 198241 198425 "BRILL" 198833 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194767 196841 196882 "BRAGG" 197531 NIL BRAGG (NIL T) -9 NIL 197789 NIL) (-119 193296 193702 194257 "BRAGG-" 194262 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186523 192640 192825 "BPADICRT" 193143 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184838 186460 186505 "BPADIC" 186510 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184536 184566 184680 "BOUNDZRO" 184802 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179764 180962 181874 "BOP" 183644 T BOP (NIL) -8 NIL NIL NIL) (-114 177545 177949 178424 "BOP1" 179322 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177246 177307 177335 "BOOLE" 177446 T BOOLE (NIL) -9 NIL 177528 NIL) (-112 176071 176820 176969 "BOOLEAN" 177117 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175350 175754 175808 "BMODULE" 175813 NIL BMODULE (NIL T T) -9 NIL 175878 NIL) (-110 171151 175148 175221 "BITS" 175297 T BITS (NIL) -8 NIL NIL NIL) (-109 170572 170691 170831 "BINDING" 171031 T BINDING (NIL) -8 NIL NIL NIL) (-108 164577 170167 170316 "BINARY" 170443 T BINARY (NIL) -8 NIL NIL NIL) (-107 162357 163832 163873 "BGAGG" 164133 NIL BGAGG (NIL T) -9 NIL 164270 NIL) (-106 162188 162220 162311 "BGAGG-" 162316 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161259 161572 161777 "BFUNCT" 162003 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159949 160127 160415 "BEZOUT" 161083 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156418 158801 159131 "BBTREE" 159652 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156152 156205 156233 "BASTYPE" 156352 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156004 156033 156106 "BASTYPE-" 156111 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155438 155514 155666 "BALFACT" 155915 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154294 154853 155039 "AUTOMOR" 155283 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154020 154025 154051 "ATTREG" 154056 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152272 152717 153069 "ATTRBUT" 153686 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151880 152100 152166 "ATTRAST" 152224 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151416 151529 151555 "ATRIG" 151756 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151225 151266 151353 "ATRIG-" 151358 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150870 151056 151082 "ASTCAT" 151087 T ASTCAT (NIL) -9 NIL 151117 NIL) (-92 150597 150656 150775 "ASTCAT-" 150780 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148746 150373 150461 "ASTACK" 150540 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147251 147548 147913 "ASSOCEQ" 148428 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146283 146910 147034 "ASP9" 147158 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146046 146231 146270 "ASP8" 146275 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144914 145651 145793 "ASP80" 145935 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143812 144549 144681 "ASP7" 144813 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142766 143489 143607 "ASP78" 143725 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141735 142446 142563 "ASP77" 142680 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140647 141373 141504 "ASP74" 141635 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139547 140282 140414 "ASP73" 140546 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138651 139373 139473 "ASP6" 139478 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137598 138328 138446 "ASP55" 138564 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136547 137272 137391 "ASP50" 137510 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135635 136248 136358 "ASP4" 136468 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134723 135336 135446 "ASP49" 135556 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133507 134262 134430 "ASP42" 134612 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132284 133040 133210 "ASP41" 133394 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131234 131961 132079 "ASP35" 132197 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130999 131182 131221 "ASP34" 131226 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130736 130803 130879 "ASP33" 130954 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129630 130371 130503 "ASP31" 130635 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129395 129578 129617 "ASP30" 129622 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129130 129199 129275 "ASP29" 129350 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128895 129078 129117 "ASP28" 129122 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128660 128843 128882 "ASP27" 128887 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127744 128358 128469 "ASP24" 128580 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126821 127546 127658 "ASP20" 127663 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125909 126522 126632 "ASP1" 126742 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124852 125583 125702 "ASP19" 125821 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124589 124656 124732 "ASP12" 124807 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123441 124188 124332 "ASP10" 124476 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121292 123285 123376 "ARRAY2" 123381 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117057 120940 121054 "ARRAY1" 121209 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116089 116262 116483 "ARRAY12" 116880 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110401 112319 112394 "ARR2CAT" 115024 NIL ARR2CAT (NIL T T T) -9 NIL 115782 NIL) (-56 107835 108579 109533 "ARR2CAT-" 109538 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107152 107462 107587 "ARITY" 107728 T ARITY (NIL) -8 NIL NIL NIL) (-54 105928 106080 106379 "APPRULE" 106988 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105579 105627 105746 "APPLYORE" 105874 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104933 105172 105292 "ANY" 105477 T ANY (NIL) -8 NIL NIL NIL) (-51 104211 104334 104491 "ANY1" 104807 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101741 102648 102975 "ANTISYM" 103935 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101233 101448 101544 "ANON" 101663 T ANON (NIL) -8 NIL NIL NIL) (-48 95482 99772 100226 "AN" 100797 T AN (NIL) -8 NIL NIL NIL) (-47 91380 92768 92819 "AMR" 93567 NIL AMR (NIL T T) -9 NIL 94167 NIL) (-46 90492 90713 91076 "AMR-" 91081 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74931 90409 90470 "ALIST" 90475 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71736 74525 74694 "ALGSC" 74849 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68292 68846 69453 "ALGPKG" 71176 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67569 67670 67854 "ALGMFACT" 68178 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63604 64183 64777 "ALGMANIP" 67153 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54974 63230 63380 "ALGFF" 63537 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54170 54301 54480 "ALGFACT" 54832 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53111 53711 53749 "ALGEBRA" 53754 NIL ALGEBRA (NIL T) -9 NIL 53795 NIL) (-37 52829 52888 53020 "ALGEBRA-" 53025 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34892 50801 50853 "ALAGG" 50989 NIL ALAGG (NIL T T) -9 NIL 51150 NIL) (-35 34428 34541 34567 "AHYP" 34768 T AHYP (NIL) -9 NIL NIL NIL) (-34 33359 33607 33633 "AGG" 34132 T AGG (NIL) -9 NIL 34411 NIL) (-33 32793 32955 33169 "AGG-" 33174 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30599 31022 31427 "AF" 32435 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30079 30324 30414 "ADDAST" 30527 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29347 29606 29762 "ACPLOT" 29941 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26474 26512 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3230023 3230028 3230033 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3230008 3230013 3230018 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3229993 3229998 3230003 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3229978 3229983 3229988 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1308 3229121 3229853 3229930 "ZMOD" 3229935 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1307 3228231 3228395 3228604 "ZLINDEP" 3228953 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1306 3217531 3219299 3221271 "ZDSOLVE" 3226361 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1305 3216777 3216918 3217107 "YSTREAM" 3217377 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1304 3216205 3216451 3216564 "YDIAGRAM" 3216686 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1303 3213979 3215506 3215710 "XRPOLY" 3216048 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1302 3210532 3211850 3212425 "XPR" 3213451 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1301 3208253 3209863 3210067 "XPOLY" 3210363 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1300 3205906 3207274 3207329 "XPOLYC" 3207617 NIL XPOLYC (NIL T T) -9 NIL 3207730 NIL) (-1299 3202282 3204423 3204811 "XPBWPOLY" 3205564 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1298 3197977 3200272 3200314 "XF" 3200935 NIL XF (NIL T) -9 NIL 3201335 NIL) (-1297 3197598 3197686 3197855 "XF-" 3197860 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1296 3192794 3194083 3194138 "XFALG" 3196310 NIL XFALG (NIL T T) -9 NIL 3197099 NIL) (-1295 3191927 3192031 3192236 "XEXPPKG" 3192686 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1294 3190036 3191777 3191873 "XDPOLY" 3191878 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1293 3188843 3189443 3189486 "XALG" 3189491 NIL XALG (NIL T) -9 NIL 3189602 NIL) (-1292 3182285 3186820 3187314 "WUTSET" 3188435 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1291 3180541 3181337 3181660 "WP" 3182096 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1290 3180143 3180363 3180433 "WHILEAST" 3180493 T WHILEAST (NIL) -8 NIL NIL NIL) (-1289 3179615 3179860 3179954 "WHEREAST" 3180071 T WHEREAST (NIL) -8 NIL NIL NIL) (-1288 3178501 3178699 3178994 "WFFINTBS" 3179412 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1287 3176405 3176832 3177294 "WEIER" 3178073 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1286 3175451 3175901 3175943 "VSPACE" 3176079 NIL VSPACE (NIL T) -9 NIL 3176153 NIL) (-1285 3175289 3175316 3175407 "VSPACE-" 3175412 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1284 3175098 3175140 3175208 "VOID" 3175243 T VOID (NIL) -8 NIL NIL NIL) (-1283 3173234 3173593 3173999 "VIEW" 3174714 T VIEW (NIL) -7 NIL NIL NIL) (-1282 3169658 3170297 3171034 "VIEWDEF" 3172519 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1281 3158962 3161206 3163379 "VIEW3D" 3167507 T VIEW3D (NIL) -8 NIL NIL NIL) (-1280 3151213 3152873 3154452 "VIEW2D" 3157405 T VIEW2D (NIL) -8 NIL NIL NIL) (-1279 3146566 3150983 3151075 "VECTOR" 3151156 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1278 3145143 3145402 3145720 "VECTOR2" 3146296 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1277 3138585 3142894 3142937 "VECTCAT" 3143932 NIL VECTCAT (NIL T) -9 NIL 3144519 NIL) (-1276 3137599 3137853 3138243 "VECTCAT-" 3138248 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3137053 3137250 3137370 "VARIABLE" 3137514 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1274 3136986 3136991 3137021 "UTYPE" 3137026 T UTYPE (NIL) -9 NIL NIL NIL) (-1273 3135816 3135970 3136232 "UTSODETL" 3136812 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1272 3133256 3133716 3134240 "UTSODE" 3135357 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1271 3125094 3130882 3131371 "UTS" 3132825 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3115881 3121250 3121293 "UTSCAT" 3122405 NIL UTSCAT (NIL T) -9 NIL 3123163 NIL) (-1269 3113229 3113951 3114940 "UTSCAT-" 3114945 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1268 3112856 3112899 3113032 "UTS2" 3113180 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1267 3107082 3109694 3109737 "URAGG" 3111807 NIL URAGG (NIL T) -9 NIL 3112530 NIL) (-1266 3104021 3104884 3106007 "URAGG-" 3106012 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1265 3099730 3102656 3103121 "UPXSSING" 3103685 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1264 3091796 3098977 3099250 "UPXS" 3099515 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1263 3084869 3091700 3091772 "UPXSCONS" 3091777 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1262 3074520 3081315 3081377 "UPXSCCA" 3081951 NIL UPXSCCA (NIL T T) -9 NIL 3082184 NIL) (-1261 3074158 3074243 3074417 "UPXSCCA-" 3074422 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1260 3063661 3070229 3070272 "UPXSCAT" 3070920 NIL UPXSCAT (NIL T) -9 NIL 3071529 NIL) (-1259 3063091 3063170 3063349 "UPXS2" 3063576 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1258 3061745 3061998 3062349 "UPSQFREE" 3062834 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1257 3055170 3058229 3058284 "UPSCAT" 3059364 NIL UPSCAT (NIL T T) -9 NIL 3060129 NIL) (-1256 3054374 3054581 3054908 "UPSCAT-" 3054913 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1255 3040000 3047768 3047811 "UPOLYC" 3049912 NIL UPOLYC (NIL T) -9 NIL 3051133 NIL) (-1254 3031328 3033754 3036901 "UPOLYC-" 3036906 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1253 3030955 3030998 3031131 "UPOLYC2" 3031279 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3022766 3030638 3030767 "UP" 3030874 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1251 3022105 3022212 3022376 "UPMP" 3022655 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1250 3021658 3021739 3021878 "UPDIVP" 3022018 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1249 3020226 3020475 3020791 "UPDECOMP" 3021407 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1248 3019457 3019569 3019755 "UPCDEN" 3020110 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1247 3018976 3019045 3019194 "UP2" 3019382 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1246 3017443 3018180 3018457 "UNISEG" 3018734 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1245 3016658 3016785 3016990 "UNISEG2" 3017286 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1244 3015718 3015898 3016124 "UNIFACT" 3016474 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1243 2999650 3014895 3015146 "ULS" 3015525 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1242 2987648 2999554 2999626 "ULSCONS" 2999631 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1241 2969552 2981539 2981601 "ULSCCAT" 2982239 NIL ULSCCAT (NIL T T) -9 NIL 2982528 NIL) (-1240 2968602 2968847 2969235 "ULSCCAT-" 2969240 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1239 2957889 2964371 2964414 "ULSCAT" 2965277 NIL ULSCAT (NIL T) -9 NIL 2966008 NIL) (-1238 2957319 2957398 2957577 "ULS2" 2957804 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1237 2956438 2956948 2957055 "UINT8" 2957166 T UINT8 (NIL) -8 NIL NIL 2957251) (-1236 2955556 2956066 2956173 "UINT64" 2956284 T UINT64 (NIL) -8 NIL NIL 2956369) (-1235 2954674 2955184 2955291 "UINT32" 2955402 T UINT32 (NIL) -8 NIL NIL 2955487) (-1234 2953792 2954302 2954409 "UINT16" 2954520 T UINT16 (NIL) -8 NIL NIL 2954605) (-1233 2952095 2953052 2953082 "UFD" 2953294 T UFD (NIL) -9 NIL 2953408 NIL) (-1232 2951889 2951935 2952030 "UFD-" 2952035 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1231 2950971 2951154 2951370 "UDVO" 2951695 T UDVO (NIL) -7 NIL NIL NIL) (-1230 2948787 2949196 2949667 "UDPO" 2950535 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1229 2948720 2948725 2948755 "TYPE" 2948760 T TYPE (NIL) -9 NIL NIL NIL) (-1228 2948480 2948675 2948706 "TYPEAST" 2948711 T TYPEAST (NIL) -8 NIL NIL NIL) (-1227 2947451 2947653 2947893 "TWOFACT" 2948274 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1226 2946474 2946860 2947095 "TUPLE" 2947251 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1225 2944165 2944684 2945223 "TUBETOOL" 2945957 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1224 2943014 2943219 2943460 "TUBE" 2943958 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1223 2937743 2941986 2942269 "TS" 2942766 NIL TS (NIL T) -8 NIL NIL NIL) (-1222 2926383 2930502 2930599 "TSETCAT" 2935868 NIL TSETCAT (NIL T T T T) -9 NIL 2937399 NIL) (-1221 2921115 2922715 2924606 "TSETCAT-" 2924611 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1220 2915754 2916601 2917530 "TRMANIP" 2920251 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1219 2915195 2915258 2915421 "TRIMAT" 2915686 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1218 2913061 2913298 2913655 "TRIGMNIP" 2914944 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1217 2912581 2912694 2912724 "TRIGCAT" 2912937 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1216 2912250 2912329 2912470 "TRIGCAT-" 2912475 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1215 2909095 2911108 2911389 "TREE" 2912004 NIL TREE (NIL T) -8 NIL NIL NIL) (-1214 2908369 2908897 2908927 "TRANFUN" 2908962 T TRANFUN (NIL) -9 NIL 2909028 NIL) (-1213 2907648 2907839 2908119 "TRANFUN-" 2908124 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1212 2907452 2907484 2907545 "TOPSP" 2907609 T TOPSP (NIL) -7 NIL NIL NIL) (-1211 2906800 2906915 2907069 "TOOLSIGN" 2907333 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1210 2905434 2905977 2906216 "TEXTFILE" 2906583 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1209 2903346 2903887 2904316 "TEX" 2905027 T TEX (NIL) -8 NIL NIL NIL) (-1208 2903127 2903158 2903230 "TEX1" 2903309 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1207 2902775 2902838 2902928 "TEMUTL" 2903059 T TEMUTL (NIL) -7 NIL NIL NIL) (-1206 2900929 2901209 2901534 "TBCMPPK" 2902498 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1205 2892706 2899089 2899145 "TBAGG" 2899545 NIL TBAGG (NIL T T) -9 NIL 2899756 NIL) (-1204 2887776 2889264 2891018 "TBAGG-" 2891023 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1203 2887160 2887267 2887412 "TANEXP" 2887665 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1202 2886671 2886935 2887025 "TALGOP" 2887105 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1201 2880061 2886528 2886621 "TABLE" 2886626 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1200 2879473 2879572 2879710 "TABLEAU" 2879958 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1199 2874081 2875301 2876549 "TABLBUMP" 2878259 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1198 2873303 2873450 2873631 "SYSTEM" 2873922 T SYSTEM (NIL) -8 NIL NIL NIL) (-1197 2869762 2870461 2871244 "SYSSOLP" 2872554 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1196 2869560 2869717 2869748 "SYSPTR" 2869753 T SYSPTR (NIL) -8 NIL NIL NIL) (-1195 2868596 2869101 2869220 "SYSNNI" 2869406 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869491) (-1194 2867895 2868354 2868433 "SYSINT" 2868493 NIL SYSINT (NIL NIL) -8 NIL NIL 2868538) (-1193 2864227 2865173 2865883 "SYNTAX" 2867207 T SYNTAX (NIL) -8 NIL NIL NIL) (-1192 2861385 2861987 2862619 "SYMTAB" 2863617 T SYMTAB (NIL) -8 NIL NIL NIL) (-1191 2856634 2857536 2858519 "SYMS" 2860424 T SYMS (NIL) -8 NIL NIL NIL) (-1190 2853869 2856092 2856322 "SYMPOLY" 2856439 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1189 2853386 2853461 2853584 "SYMFUNC" 2853781 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1188 2849406 2850698 2851511 "SYMBOL" 2852595 T SYMBOL (NIL) -8 NIL NIL NIL) (-1187 2842945 2844634 2846354 "SWITCH" 2847708 T SWITCH (NIL) -8 NIL NIL NIL) (-1186 2836179 2841766 2842069 "SUTS" 2842700 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2828245 2835426 2835699 "SUPXS" 2835964 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2820004 2827863 2827989 "SUP" 2828154 NIL SUP (NIL T) -8 NIL NIL NIL) (-1183 2819163 2819290 2819507 "SUPFRACF" 2819872 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1182 2818784 2818843 2818956 "SUP2" 2819098 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1181 2817232 2817506 2817862 "SUMRF" 2818483 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1180 2816567 2816633 2816825 "SUMFS" 2817153 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1179 2800534 2815744 2815995 "SULS" 2816374 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1178 2800136 2800356 2800426 "SUCHTAST" 2800486 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1177 2799431 2799661 2799801 "SUCH" 2800044 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1176 2793298 2794337 2795296 "SUBSPACE" 2798519 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1175 2792728 2792818 2792982 "SUBRESP" 2793186 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1174 2786096 2787393 2788704 "STTF" 2791464 NIL STTF (NIL T) -7 NIL NIL NIL) (-1173 2780269 2781389 2782536 "STTFNC" 2784996 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1172 2771582 2773451 2775245 "STTAYLOR" 2778510 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1171 2764712 2771446 2771529 "STRTBL" 2771534 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1170 2760076 2764667 2764698 "STRING" 2764703 T STRING (NIL) -8 NIL NIL NIL) (-1169 2754905 2759419 2759449 "STRICAT" 2759508 T STRICAT (NIL) -9 NIL 2759570 NIL) (-1168 2747658 2752524 2753135 "STREAM" 2754329 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1167 2747168 2747245 2747389 "STREAM3" 2747575 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1166 2746150 2746333 2746568 "STREAM2" 2746981 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1165 2745838 2745890 2745983 "STREAM1" 2746092 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1164 2744854 2745035 2745266 "STINPROD" 2745654 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1163 2744406 2744616 2744646 "STEP" 2744726 T STEP (NIL) -9 NIL 2744804 NIL) (-1162 2743593 2743895 2744043 "STEPAST" 2744280 T STEPAST (NIL) -8 NIL NIL NIL) (-1161 2737025 2743492 2743569 "STBL" 2743574 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1160 2732120 2736216 2736259 "STAGG" 2736412 NIL STAGG (NIL T) -9 NIL 2736501 NIL) (-1159 2729822 2730424 2731296 "STAGG-" 2731301 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1158 2727969 2729592 2729684 "STACK" 2729765 NIL STACK (NIL T) -8 NIL NIL NIL) (-1157 2720664 2726110 2726566 "SREGSET" 2727599 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1156 2713089 2714458 2715971 "SRDCMPK" 2719270 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1155 2705974 2710499 2710529 "SRAGG" 2711832 T SRAGG (NIL) -9 NIL 2712440 NIL) (-1154 2704991 2705246 2705625 "SRAGG-" 2705630 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1153 2699451 2703938 2704359 "SQMATRIX" 2704617 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1152 2693136 2696169 2696896 "SPLTREE" 2698796 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1151 2689099 2689792 2690438 "SPLNODE" 2692562 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1150 2688146 2688379 2688409 "SPFCAT" 2688853 T SPFCAT (NIL) -9 NIL NIL NIL) (-1149 2686883 2687093 2687357 "SPECOUT" 2687904 T SPECOUT (NIL) -7 NIL NIL NIL) (-1148 2677993 2679865 2679895 "SPADXPT" 2684571 T SPADXPT (NIL) -9 NIL 2686735 NIL) (-1147 2677754 2677794 2677863 "SPADPRSR" 2677946 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1146 2675803 2677709 2677740 "SPADAST" 2677745 T SPADAST (NIL) -8 NIL NIL NIL) (-1145 2667748 2669521 2669564 "SPACEC" 2673937 NIL SPACEC (NIL T) -9 NIL 2675753 NIL) (-1144 2665878 2667680 2667729 "SPACE3" 2667734 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1143 2664630 2664801 2665092 "SORTPAK" 2665683 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1142 2662722 2663025 2663437 "SOLVETRA" 2664294 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1141 2661772 2661994 2662255 "SOLVESER" 2662495 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1140 2657076 2657964 2658959 "SOLVERAD" 2660824 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1139 2652891 2653500 2654229 "SOLVEFOR" 2656443 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1138 2647161 2652240 2652337 "SNTSCAT" 2652342 NIL SNTSCAT (NIL T T T T) -9 NIL 2652412 NIL) (-1137 2641267 2645484 2645875 "SMTS" 2646851 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1136 2635952 2641155 2641232 "SMP" 2641237 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1135 2634111 2634412 2634810 "SMITH" 2635649 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1134 2626794 2630991 2631094 "SMATCAT" 2632445 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632995 NIL) (-1133 2623734 2624557 2625735 "SMATCAT-" 2625740 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1132 2621400 2622970 2623013 "SKAGG" 2623274 NIL SKAGG (NIL T) -9 NIL 2623409 NIL) (-1131 2617726 2620873 2621057 "SINT" 2621209 T SINT (NIL) -8 NIL NIL 2621371) (-1130 2617498 2617536 2617602 "SIMPAN" 2617682 T SIMPAN (NIL) -7 NIL NIL NIL) (-1129 2616777 2617033 2617173 "SIG" 2617380 T SIG (NIL) -8 NIL NIL NIL) (-1128 2615615 2615836 2616111 "SIGNRF" 2616536 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1127 2614448 2614599 2614883 "SIGNEF" 2615444 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1126 2613754 2614031 2614155 "SIGAST" 2614346 T SIGAST (NIL) -8 NIL NIL NIL) (-1125 2611444 2611898 2612404 "SHP" 2613295 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1124 2605296 2611345 2611421 "SHDP" 2611426 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1123 2604869 2605061 2605091 "SGROUP" 2605184 T SGROUP (NIL) -9 NIL 2605246 NIL) (-1122 2604727 2604753 2604826 "SGROUP-" 2604831 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1121 2601518 2602216 2602939 "SGCF" 2604026 T SGCF (NIL) -7 NIL NIL NIL) (-1120 2595886 2600965 2601062 "SFRTCAT" 2601067 NIL SFRTCAT (NIL T T T T) -9 NIL 2601106 NIL) (-1119 2589307 2590325 2591461 "SFRGCD" 2594869 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1118 2582433 2583506 2584692 "SFQCMPK" 2588240 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1117 2582053 2582142 2582253 "SFORT" 2582374 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1116 2581171 2581893 2582014 "SEXOF" 2582019 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1115 2580278 2581052 2581120 "SEX" 2581125 T SEX (NIL) -8 NIL NIL NIL) (-1114 2576059 2576774 2576869 "SEXCAT" 2579491 NIL SEXCAT (NIL T T T T T) -9 NIL 2580051 NIL) (-1113 2573212 2575993 2576041 "SET" 2576046 NIL SET (NIL T) -8 NIL NIL NIL) (-1112 2571436 2571925 2572230 "SETMN" 2572953 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1111 2570932 2571084 2571114 "SETCAT" 2571290 T SETCAT (NIL) -9 NIL 2571400 NIL) (-1110 2570624 2570702 2570832 "SETCAT-" 2570837 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1109 2566985 2569085 2569128 "SETAGG" 2569998 NIL SETAGG (NIL T) -9 NIL 2570338 NIL) (-1108 2566443 2566559 2566796 "SETAGG-" 2566801 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1107 2565886 2566139 2566240 "SEQAST" 2566364 T SEQAST (NIL) -8 NIL NIL NIL) (-1106 2565085 2565379 2565440 "SEGXCAT" 2565726 NIL SEGXCAT (NIL T T) -9 NIL 2565846 NIL) (-1105 2564091 2564751 2564933 "SEG" 2564938 NIL SEG (NIL T) -8 NIL NIL NIL) (-1104 2563070 2563284 2563327 "SEGCAT" 2563849 NIL SEGCAT (NIL T) -9 NIL 2564070 NIL) (-1103 2562002 2562433 2562641 "SEGBIND" 2562897 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1102 2561623 2561682 2561795 "SEGBIND2" 2561937 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1101 2561196 2561424 2561501 "SEGAST" 2561568 T SEGAST (NIL) -8 NIL NIL NIL) (-1100 2560415 2560541 2560745 "SEG2" 2561040 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1099 2559825 2560350 2560397 "SDVAR" 2560402 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1098 2552352 2559595 2559725 "SDPOL" 2559730 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1097 2550945 2551211 2551530 "SCPKG" 2552067 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1096 2550109 2550281 2550473 "SCOPE" 2550775 T SCOPE (NIL) -8 NIL NIL NIL) (-1095 2549329 2549463 2549642 "SCACHE" 2549964 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1094 2548975 2549161 2549191 "SASTCAT" 2549196 T SASTCAT (NIL) -9 NIL 2549209 NIL) (-1093 2548462 2548810 2548886 "SAOS" 2548921 T SAOS (NIL) -8 NIL NIL NIL) (-1092 2548027 2548062 2548235 "SAERFFC" 2548421 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1091 2541966 2547924 2548004 "SAE" 2548009 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1090 2541559 2541594 2541753 "SAEFACT" 2541925 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1089 2539880 2540194 2540595 "RURPK" 2541225 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1088 2538517 2538823 2539128 "RULESET" 2539714 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1087 2535740 2536270 2536728 "RULE" 2538198 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1086 2535352 2535534 2535617 "RULECOLD" 2535692 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1085 2535142 2535170 2535241 "RTVALUE" 2535303 T RTVALUE (NIL) -8 NIL NIL NIL) (-1084 2534613 2534859 2534953 "RSTRCAST" 2535070 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1083 2529461 2530256 2531176 "RSETGCD" 2533812 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1082 2518691 2523770 2523867 "RSETCAT" 2527986 NIL RSETCAT (NIL T T T T) -9 NIL 2529083 NIL) (-1081 2516618 2517157 2517981 "RSETCAT-" 2517986 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1080 2509004 2510380 2511900 "RSDCMPK" 2515217 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1079 2506983 2507450 2507524 "RRCC" 2508610 NIL RRCC (NIL T T) -9 NIL 2508954 NIL) (-1078 2506334 2506508 2506787 "RRCC-" 2506792 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1077 2505777 2506030 2506131 "RPTAST" 2506255 T RPTAST (NIL) -8 NIL NIL NIL) (-1076 2479623 2488982 2489049 "RPOLCAT" 2499715 NIL RPOLCAT (NIL T T T) -9 NIL 2502875 NIL) (-1075 2471121 2473461 2476583 "RPOLCAT-" 2476588 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1074 2462052 2469332 2469814 "ROUTINE" 2470661 T ROUTINE (NIL) -8 NIL NIL NIL) (-1073 2458850 2461678 2461818 "ROMAN" 2461934 T ROMAN (NIL) -8 NIL NIL NIL) (-1072 2457094 2457710 2457970 "ROIRC" 2458655 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1071 2453326 2455610 2455640 "RNS" 2455944 T RNS (NIL) -9 NIL 2456218 NIL) (-1070 2451835 2452218 2452752 "RNS-" 2452827 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1069 2451238 2451646 2451676 "RNG" 2451681 T RNG (NIL) -9 NIL 2451702 NIL) (-1068 2450241 2450603 2450805 "RNGBIND" 2451089 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1067 2449640 2450028 2450071 "RMODULE" 2450076 NIL RMODULE (NIL T) -9 NIL 2450103 NIL) (-1066 2448476 2448570 2448906 "RMCAT2" 2449541 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1065 2445326 2447822 2448119 "RMATRIX" 2448238 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1064 2438153 2440413 2440528 "RMATCAT" 2443887 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444869 NIL) (-1063 2437528 2437675 2437982 "RMATCAT-" 2437987 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1062 2436929 2437150 2437193 "RLINSET" 2437387 NIL RLINSET (NIL T) -9 NIL 2437478 NIL) (-1061 2436496 2436571 2436699 "RINTERP" 2436848 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1060 2435554 2436108 2436138 "RING" 2436194 T RING (NIL) -9 NIL 2436286 NIL) (-1059 2435346 2435390 2435487 "RING-" 2435492 NIL RING- (NIL T) -8 NIL NIL NIL) (-1058 2434187 2434424 2434682 "RIDIST" 2435110 T RIDIST (NIL) -7 NIL NIL NIL) (-1057 2425476 2433655 2433861 "RGCHAIN" 2434035 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1056 2424826 2425232 2425273 "RGBCSPC" 2425331 NIL RGBCSPC (NIL T) -9 NIL 2425383 NIL) (-1055 2423984 2424365 2424406 "RGBCMDL" 2424638 NIL RGBCMDL (NIL T) -9 NIL 2424752 NIL) (-1054 2420978 2421592 2422262 "RF" 2423348 NIL RF (NIL T) -7 NIL NIL NIL) (-1053 2420624 2420687 2420790 "RFFACTOR" 2420909 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1052 2420349 2420384 2420481 "RFFACT" 2420583 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1051 2418466 2418830 2419212 "RFDIST" 2419989 T RFDIST (NIL) -7 NIL NIL NIL) (-1050 2417919 2418011 2418174 "RETSOL" 2418368 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1049 2417555 2417635 2417678 "RETRACT" 2417811 NIL RETRACT (NIL T) -9 NIL 2417898 NIL) (-1048 2417404 2417429 2417516 "RETRACT-" 2417521 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1047 2417006 2417226 2417296 "RETAST" 2417356 T RETAST (NIL) -8 NIL NIL NIL) (-1046 2409744 2416659 2416786 "RESULT" 2416901 T RESULT (NIL) -8 NIL NIL NIL) (-1045 2408335 2409013 2409212 "RESRING" 2409647 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1044 2407971 2408020 2408118 "RESLATC" 2408272 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1043 2407676 2407711 2407818 "REPSQ" 2407930 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1042 2405098 2405678 2406280 "REP" 2407096 T REP (NIL) -7 NIL NIL NIL) (-1041 2404795 2404830 2404941 "REPDB" 2405057 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1040 2398695 2400084 2401307 "REP2" 2403607 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1039 2395072 2395753 2396561 "REP1" 2397922 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1038 2387768 2393213 2393669 "REGSET" 2394702 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1037 2386533 2386916 2387166 "REF" 2387553 NIL REF (NIL T) -8 NIL NIL NIL) (-1036 2385910 2386013 2386180 "REDORDER" 2386417 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1035 2381878 2385123 2385350 "RECLOS" 2385738 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1034 2380930 2381111 2381326 "REALSOLV" 2381685 T REALSOLV (NIL) -7 NIL NIL NIL) (-1033 2380776 2380817 2380847 "REAL" 2380852 T REAL (NIL) -9 NIL 2380887 NIL) (-1032 2377259 2378061 2378945 "REAL0Q" 2379941 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1031 2372860 2373848 2374909 "REAL0" 2376240 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1030 2372331 2372577 2372671 "RDUCEAST" 2372788 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1029 2371736 2371808 2372015 "RDIV" 2372253 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1028 2370804 2370978 2371191 "RDIST" 2371558 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1027 2369401 2369688 2370060 "RDETRS" 2370512 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1026 2367213 2367667 2368205 "RDETR" 2368943 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1025 2365838 2366116 2366513 "RDEEFS" 2366929 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1024 2364347 2364653 2365078 "RDEEF" 2365526 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1023 2358408 2361328 2361358 "RCFIELD" 2362653 T RCFIELD (NIL) -9 NIL 2363384 NIL) (-1022 2356472 2356976 2357672 "RCFIELD-" 2357747 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1021 2352741 2354573 2354616 "RCAGG" 2355700 NIL RCAGG (NIL T) -9 NIL 2356165 NIL) (-1020 2352369 2352463 2352626 "RCAGG-" 2352631 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1019 2351704 2351816 2351981 "RATRET" 2352253 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1018 2351257 2351324 2351445 "RATFACT" 2351632 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1017 2350565 2350685 2350837 "RANDSRC" 2351127 T RANDSRC (NIL) -7 NIL NIL NIL) (-1016 2350299 2350343 2350416 "RADUTIL" 2350514 T RADUTIL (NIL) -7 NIL NIL NIL) (-1015 2343413 2349130 2349441 "RADIX" 2350022 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1014 2335032 2343255 2343385 "RADFF" 2343390 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1013 2334679 2334754 2334784 "RADCAT" 2334944 T RADCAT (NIL) -9 NIL NIL NIL) (-1012 2334461 2334509 2334609 "RADCAT-" 2334614 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1011 2332559 2334231 2334323 "QUEUE" 2334404 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1010 2329096 2332492 2332540 "QUAT" 2332545 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1009 2328727 2328770 2328901 "QUATCT2" 2329047 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2322080 2325426 2325468 "QUATCAT" 2326259 NIL QUATCAT (NIL T) -9 NIL 2327025 NIL) (-1007 2318219 2319256 2320646 "QUATCAT-" 2320742 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1006 2315684 2317295 2317338 "QUAGG" 2317719 NIL QUAGG (NIL T) -9 NIL 2317894 NIL) (-1005 2315286 2315506 2315576 "QQUTAST" 2315636 T QQUTAST (NIL) -8 NIL NIL NIL) (-1004 2314299 2314799 2314964 "QFORM" 2315167 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1003 2305263 2310502 2310544 "QFCAT" 2311212 NIL QFCAT (NIL T) -9 NIL 2312213 NIL) (-1002 2300830 2302031 2303625 "QFCAT-" 2303721 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2300461 2300504 2300635 "QFCAT2" 2300781 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1000 2299916 2300026 2300158 "QEQUAT" 2300351 T QEQUAT (NIL) -8 NIL NIL NIL) (-999 2293062 2294135 2295319 "QCMPACK" 2298849 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-998 2290611 2291059 2291487 "QALGSET" 2292717 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-997 2289856 2290030 2290262 "QALGSET2" 2290431 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-996 2288546 2288770 2289087 "PWFFINTB" 2289629 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-995 2286728 2286896 2287250 "PUSHVAR" 2288360 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-994 2282646 2283700 2283741 "PTRANFN" 2285625 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-993 2281048 2281339 2281661 "PTPACK" 2282357 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-992 2280680 2280737 2280846 "PTFUNC2" 2280985 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-991 2275125 2279522 2279563 "PTCAT" 2279859 NIL PTCAT (NIL T) -9 NIL 2280012 NIL) (-990 2274783 2274818 2274942 "PSQFR" 2275084 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-989 2273378 2273676 2274010 "PSEUDLIN" 2274481 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-988 2260141 2262512 2264836 "PSETPK" 2271138 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-987 2253159 2255899 2255995 "PSETCAT" 2259016 NIL PSETCAT (NIL T T T T) -9 NIL 2259830 NIL) (-986 2250995 2251629 2252450 "PSETCAT-" 2252455 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-985 2250344 2250509 2250537 "PSCURVE" 2250805 T PSCURVE (NIL) -9 NIL 2250972 NIL) (-984 2246342 2247858 2247923 "PSCAT" 2248767 NIL PSCAT (NIL T T T) -9 NIL 2249007 NIL) (-983 2245405 2245621 2246021 "PSCAT-" 2246026 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-982 2243764 2244474 2244737 "PRTITION" 2245162 T PRTITION (NIL) -8 NIL NIL NIL) (-981 2243239 2243485 2243577 "PRTDAST" 2243692 T PRTDAST (NIL) -8 NIL NIL NIL) (-980 2232329 2234543 2236731 "PRS" 2241101 NIL PRS (NIL T T) -7 NIL NIL NIL) (-979 2230140 2231679 2231719 "PRQAGG" 2231902 NIL PRQAGG (NIL T) -9 NIL 2232004 NIL) (-978 2229476 2229781 2229809 "PROPLOG" 2229948 T PROPLOG (NIL) -9 NIL 2230063 NIL) (-977 2229080 2229137 2229260 "PROPFUN2" 2229399 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-976 2228395 2228516 2228688 "PROPFUN1" 2228941 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-975 2226576 2227142 2227439 "PROPFRML" 2228131 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-974 2226045 2226152 2226280 "PROPERTY" 2226468 T PROPERTY (NIL) -8 NIL NIL NIL) (-973 2220103 2224211 2225031 "PRODUCT" 2225271 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-972 2217381 2219561 2219795 "PR" 2219914 NIL PR (NIL T T) -8 NIL NIL NIL) (-971 2217177 2217209 2217268 "PRINT" 2217342 T PRINT (NIL) -7 NIL NIL NIL) (-970 2216517 2216634 2216786 "PRIMES" 2217057 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-969 2214582 2214983 2215449 "PRIMELT" 2216096 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-968 2214311 2214360 2214388 "PRIMCAT" 2214512 T PRIMCAT (NIL) -9 NIL NIL NIL) (-967 2210426 2214249 2214294 "PRIMARR" 2214299 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-966 2209433 2209611 2209839 "PRIMARR2" 2210244 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-965 2209076 2209132 2209243 "PREASSOC" 2209371 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-964 2208551 2208684 2208712 "PPCURVE" 2208917 T PPCURVE (NIL) -9 NIL 2209053 NIL) (-963 2208146 2208346 2208429 "PORTNUM" 2208488 T PORTNUM (NIL) -8 NIL NIL NIL) (-962 2205505 2205904 2206496 "POLYROOT" 2207727 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-961 2199687 2205109 2205269 "POLY" 2205378 NIL POLY (NIL T) -8 NIL NIL NIL) (-960 2199070 2199128 2199362 "POLYLIFT" 2199623 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-959 2195345 2195794 2196423 "POLYCATQ" 2198615 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-958 2182057 2187185 2187250 "POLYCAT" 2190764 NIL POLYCAT (NIL T T T) -9 NIL 2192642 NIL) (-957 2175506 2177368 2179752 "POLYCAT-" 2179757 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-956 2175093 2175161 2175281 "POLY2UP" 2175432 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-955 2174725 2174782 2174891 "POLY2" 2175030 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-954 2173410 2173649 2173925 "POLUTIL" 2174499 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-953 2171765 2172042 2172373 "POLTOPOL" 2173132 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-952 2167230 2171701 2171747 "POINT" 2171752 NIL POINT (NIL T) -8 NIL NIL NIL) (-951 2165417 2165774 2166149 "PNTHEORY" 2166875 T PNTHEORY (NIL) -7 NIL NIL NIL) (-950 2163875 2164172 2164571 "PMTOOLS" 2165115 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-949 2163468 2163546 2163663 "PMSYM" 2163791 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-948 2162976 2163045 2163220 "PMQFCAT" 2163393 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-947 2162331 2162441 2162597 "PMPRED" 2162853 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-946 2161724 2161810 2161972 "PMPREDFS" 2162232 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-945 2160388 2160596 2160974 "PMPLCAT" 2161486 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-944 2159920 2159999 2160151 "PMLSAGG" 2160303 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-943 2159393 2159469 2159651 "PMKERNEL" 2159838 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-942 2159010 2159085 2159198 "PMINS" 2159312 NIL PMINS (NIL T) -7 NIL NIL NIL) (-941 2158452 2158521 2158730 "PMFS" 2158935 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-940 2157680 2157798 2158003 "PMDOWN" 2158329 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-939 2156847 2157005 2157186 "PMASS" 2157519 T PMASS (NIL) -7 NIL NIL NIL) (-938 2156120 2156230 2156393 "PMASSFS" 2156734 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-937 2155775 2155843 2155937 "PLOTTOOL" 2156046 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-936 2150382 2151586 2152734 "PLOT" 2154647 T PLOT (NIL) -8 NIL NIL NIL) (-935 2146186 2147230 2148151 "PLOT3D" 2149481 T PLOT3D (NIL) -8 NIL NIL NIL) (-934 2145098 2145275 2145510 "PLOT1" 2145990 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-933 2120489 2125164 2130015 "PLEQN" 2140364 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-932 2119807 2119929 2120109 "PINTERP" 2120354 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-931 2119500 2119547 2119650 "PINTERPA" 2119754 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-930 2118716 2119264 2119351 "PI" 2119391 T PI (NIL) -8 NIL NIL 2119458) (-929 2117013 2117988 2118016 "PID" 2118198 T PID (NIL) -9 NIL 2118332 NIL) (-928 2116764 2116801 2116876 "PICOERCE" 2116970 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-927 2116084 2116223 2116399 "PGROEB" 2116620 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-926 2111671 2112485 2113390 "PGE" 2115199 T PGE (NIL) -7 NIL NIL NIL) (-925 2109794 2110041 2110407 "PGCD" 2111388 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-924 2109132 2109235 2109396 "PFRPAC" 2109678 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-923 2105772 2107680 2108033 "PFR" 2108811 NIL PFR (NIL T) -8 NIL NIL NIL) (-922 2104161 2104405 2104730 "PFOTOOLS" 2105519 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-921 2102694 2102933 2103284 "PFOQ" 2103918 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-920 2101195 2101407 2101763 "PFO" 2102478 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-919 2097748 2101084 2101153 "PF" 2101158 NIL PF (NIL NIL) -8 NIL NIL NIL) (-918 2095082 2096353 2096381 "PFECAT" 2096966 T PFECAT (NIL) -9 NIL 2097350 NIL) (-917 2094527 2094681 2094895 "PFECAT-" 2094900 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-916 2093130 2093382 2093683 "PFBRU" 2094276 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-915 2090996 2091348 2091780 "PFBR" 2092781 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-914 2087042 2088508 2089155 "PERM" 2090382 NIL PERM (NIL T) -8 NIL NIL NIL) (-913 2082276 2083249 2084119 "PERMGRP" 2086205 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-912 2080395 2081355 2081396 "PERMCAT" 2081796 NIL PERMCAT (NIL T) -9 NIL 2082094 NIL) (-911 2080048 2080089 2080213 "PERMAN" 2080348 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-910 2077536 2079713 2079835 "PENDTREE" 2079959 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-909 2075560 2076328 2076369 "PDRING" 2077026 NIL PDRING (NIL T) -9 NIL 2077312 NIL) (-908 2074663 2074881 2075243 "PDRING-" 2075248 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-907 2071878 2072656 2073324 "PDEPROB" 2074015 T PDEPROB (NIL) -8 NIL NIL NIL) (-906 2069423 2069927 2070482 "PDEPACK" 2071343 T PDEPACK (NIL) -7 NIL NIL NIL) (-905 2068335 2068525 2068776 "PDECOMP" 2069222 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-904 2065914 2066757 2066785 "PDECAT" 2067572 T PDECAT (NIL) -9 NIL 2068285 NIL) (-903 2065665 2065698 2065788 "PCOMP" 2065875 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-902 2063843 2064466 2064763 "PBWLB" 2065394 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-901 2056316 2057916 2059254 "PATTERN" 2062526 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-900 2055948 2056005 2056114 "PATTERN2" 2056253 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-899 2053705 2054093 2054550 "PATTERN1" 2055537 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-898 2051073 2051654 2052135 "PATRES" 2053270 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-897 2050637 2050704 2050836 "PATRES2" 2051000 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-896 2048520 2048925 2049332 "PATMATCH" 2050304 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-895 2048030 2048239 2048280 "PATMAB" 2048387 NIL PATMAB (NIL T) -9 NIL 2048470 NIL) (-894 2046548 2046884 2047142 "PATLRES" 2047835 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-893 2046094 2046217 2046258 "PATAB" 2046263 NIL PATAB (NIL T) -9 NIL 2046435 NIL) (-892 2044276 2044671 2045094 "PARTPERM" 2045691 T PARTPERM (NIL) -7 NIL NIL NIL) (-891 2043897 2043960 2044062 "PARSURF" 2044207 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-890 2043529 2043586 2043695 "PARSU2" 2043834 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-889 2043293 2043333 2043400 "PARSER" 2043482 T PARSER (NIL) -7 NIL NIL NIL) (-888 2042914 2042977 2043079 "PARSCURV" 2043224 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-887 2042546 2042603 2042712 "PARSC2" 2042851 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-886 2042185 2042243 2042340 "PARPCURV" 2042482 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-885 2041817 2041874 2041983 "PARPC2" 2042122 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-884 2040878 2041190 2041372 "PARAMAST" 2041655 T PARAMAST (NIL) -8 NIL NIL NIL) (-883 2040398 2040484 2040603 "PAN2EXPR" 2040779 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-882 2039175 2039519 2039747 "PALETTE" 2040190 T PALETTE (NIL) -8 NIL NIL NIL) (-881 2037568 2038180 2038540 "PAIR" 2038861 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-880 2031436 2036825 2037020 "PADICRC" 2037422 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-879 2024663 2030780 2030965 "PADICRAT" 2031283 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-878 2022978 2024600 2024645 "PADIC" 2024650 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-877 2020088 2021652 2021692 "PADICCT" 2022273 NIL PADICCT (NIL NIL) -9 NIL 2022555 NIL) (-876 2019045 2019245 2019513 "PADEPAC" 2019875 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-875 2018257 2018390 2018596 "PADE" 2018907 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-874 2016644 2017465 2017745 "OWP" 2018061 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-873 2016137 2016350 2016447 "OVERSET" 2016567 T OVERSET (NIL) -8 NIL NIL NIL) (-872 2015183 2015742 2015914 "OVAR" 2016005 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-871 2014447 2014568 2014729 "OUT" 2015042 T OUT (NIL) -7 NIL NIL NIL) (-870 2003319 2005556 2007756 "OUTFORM" 2012267 T OUTFORM (NIL) -8 NIL NIL NIL) (-869 2002655 2002916 2003043 "OUTBFILE" 2003212 T OUTBFILE (NIL) -8 NIL NIL NIL) (-868 2001962 2002127 2002155 "OUTBCON" 2002473 T OUTBCON (NIL) -9 NIL 2002639 NIL) (-867 2001563 2001675 2001832 "OUTBCON-" 2001837 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-866 2000943 2001292 2001381 "OSI" 2001494 T OSI (NIL) -8 NIL NIL NIL) (-865 2000473 2000811 2000839 "OSGROUP" 2000844 T OSGROUP (NIL) -9 NIL 2000866 NIL) (-864 1999218 1999445 1999730 "ORTHPOL" 2000220 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-863 1996769 1999053 1999174 "OREUP" 1999179 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-862 1994172 1996460 1996587 "ORESUP" 1996711 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-861 1991700 1992200 1992761 "OREPCTO" 1993661 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-860 1985386 1987587 1987628 "OREPCAT" 1989976 NIL OREPCAT (NIL T) -9 NIL 1991080 NIL) (-859 1982533 1983315 1984373 "OREPCAT-" 1984378 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-858 1981684 1981982 1982010 "ORDSET" 1982319 T ORDSET (NIL) -9 NIL 1982483 NIL) (-857 1981115 1981263 1981487 "ORDSET-" 1981492 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-856 1979680 1980471 1980499 "ORDRING" 1980701 T ORDRING (NIL) -9 NIL 1980826 NIL) (-855 1979325 1979419 1979563 "ORDRING-" 1979568 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-854 1978705 1979168 1979196 "ORDMON" 1979201 T ORDMON (NIL) -9 NIL 1979222 NIL) (-853 1977867 1978014 1978209 "ORDFUNS" 1978554 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-852 1977205 1977624 1977652 "ORDFIN" 1977717 T ORDFIN (NIL) -9 NIL 1977791 NIL) (-851 1973764 1975791 1976200 "ORDCOMP" 1976829 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-850 1973030 1973157 1973343 "ORDCOMP2" 1973624 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-849 1969611 1970521 1971335 "OPTPROB" 1972236 T OPTPROB (NIL) -8 NIL NIL NIL) (-848 1966413 1967052 1967756 "OPTPACK" 1968927 T OPTPACK (NIL) -7 NIL NIL NIL) (-847 1964100 1964866 1964894 "OPTCAT" 1965713 T OPTCAT (NIL) -9 NIL 1966363 NIL) (-846 1963484 1963777 1963882 "OPSIG" 1964015 T OPSIG (NIL) -8 NIL NIL NIL) (-845 1963252 1963291 1963357 "OPQUERY" 1963438 T OPQUERY (NIL) -7 NIL NIL NIL) (-844 1960383 1961563 1962067 "OP" 1962781 NIL OP (NIL T) -8 NIL NIL NIL) (-843 1959757 1959983 1960024 "OPERCAT" 1960236 NIL OPERCAT (NIL T) -9 NIL 1960333 NIL) (-842 1959512 1959568 1959685 "OPERCAT-" 1959690 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-841 1956325 1958309 1958678 "ONECOMP" 1959176 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-840 1955630 1955745 1955919 "ONECOMP2" 1956197 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1955049 1955155 1955285 "OMSERVER" 1955520 T OMSERVER (NIL) -7 NIL NIL NIL) (-838 1951911 1954489 1954529 "OMSAGG" 1954590 NIL OMSAGG (NIL T) -9 NIL 1954654 NIL) (-837 1950534 1950797 1951079 "OMPKG" 1951649 T OMPKG (NIL) -7 NIL NIL NIL) (-836 1949964 1950067 1950095 "OM" 1950394 T OM (NIL) -9 NIL NIL NIL) (-835 1948511 1949513 1949682 "OMLO" 1949845 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-834 1947471 1947618 1947838 "OMEXPR" 1948337 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-833 1946762 1947017 1947153 "OMERR" 1947355 T OMERR (NIL) -8 NIL NIL NIL) (-832 1945913 1946183 1946343 "OMERRK" 1946622 T OMERRK (NIL) -8 NIL NIL NIL) (-831 1945364 1945590 1945698 "OMENC" 1945825 T OMENC (NIL) -8 NIL NIL NIL) (-830 1939259 1940444 1941615 "OMDEV" 1944213 T OMDEV (NIL) -8 NIL NIL NIL) (-829 1938328 1938499 1938693 "OMCONN" 1939085 T OMCONN (NIL) -8 NIL NIL NIL) (-828 1936849 1937825 1937853 "OINTDOM" 1937858 T OINTDOM (NIL) -9 NIL 1937879 NIL) (-827 1934187 1935537 1935874 "OFMONOID" 1936544 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-826 1933598 1934124 1934169 "ODVAR" 1934174 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-825 1931021 1933343 1933498 "ODR" 1933503 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-824 1923602 1930797 1930923 "ODPOL" 1930928 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-823 1917424 1923474 1923579 "ODP" 1923584 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-822 1916190 1916405 1916680 "ODETOOLS" 1917198 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-821 1913157 1913815 1914531 "ODESYS" 1915523 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-820 1908039 1908947 1909972 "ODERTRIC" 1912232 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-819 1907465 1907547 1907741 "ODERED" 1907951 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-818 1904353 1904901 1905578 "ODERAT" 1906888 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-817 1901312 1901777 1902374 "ODEPRRIC" 1903882 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-816 1899255 1899851 1900337 "ODEPROB" 1900846 T ODEPROB (NIL) -8 NIL NIL NIL) (-815 1895775 1896260 1896907 "ODEPRIM" 1898734 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-814 1895024 1895126 1895386 "ODEPAL" 1895667 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-813 1891186 1891977 1892841 "ODEPACK" 1894180 T ODEPACK (NIL) -7 NIL NIL NIL) (-812 1890247 1890354 1890576 "ODEINT" 1891075 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-811 1884348 1885773 1887220 "ODEIFTBL" 1888820 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-810 1879746 1880532 1881484 "ODEEF" 1883507 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-809 1879095 1879184 1879407 "ODECONST" 1879651 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-808 1877220 1877881 1877909 "ODECAT" 1878514 T ODECAT (NIL) -9 NIL 1879045 NIL) (-807 1874075 1876925 1877047 "OCT" 1877130 NIL OCT (NIL T) -8 NIL NIL NIL) (-806 1873713 1873756 1873883 "OCTCT2" 1874026 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-805 1868324 1870759 1870799 "OC" 1871896 NIL OC (NIL T) -9 NIL 1872754 NIL) (-804 1865551 1866299 1867289 "OC-" 1867383 NIL OC- (NIL T T) -8 NIL NIL NIL) (-803 1864903 1865371 1865399 "OCAMON" 1865404 T OCAMON (NIL) -9 NIL 1865425 NIL) (-802 1864434 1864775 1864803 "OASGP" 1864808 T OASGP (NIL) -9 NIL 1864828 NIL) (-801 1863695 1864184 1864212 "OAMONS" 1864252 T OAMONS (NIL) -9 NIL 1864295 NIL) (-800 1863109 1863542 1863570 "OAMON" 1863575 T OAMON (NIL) -9 NIL 1863595 NIL) (-799 1862367 1862885 1862913 "OAGROUP" 1862918 T OAGROUP (NIL) -9 NIL 1862938 NIL) (-798 1862057 1862107 1862195 "NUMTUBE" 1862311 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-797 1855630 1857148 1858684 "NUMQUAD" 1860541 T NUMQUAD (NIL) -7 NIL NIL NIL) (-796 1851386 1852374 1853399 "NUMODE" 1854625 T NUMODE (NIL) -7 NIL NIL NIL) (-795 1848741 1849621 1849649 "NUMINT" 1850572 T NUMINT (NIL) -9 NIL 1851336 NIL) (-794 1847689 1847886 1848104 "NUMFMT" 1848543 T NUMFMT (NIL) -7 NIL NIL NIL) (-793 1834048 1836993 1839525 "NUMERIC" 1845196 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-792 1828418 1833497 1833592 "NTSCAT" 1833597 NIL NTSCAT (NIL T T T T) -9 NIL 1833636 NIL) (-791 1827612 1827777 1827970 "NTPOLFN" 1828257 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-790 1815689 1824437 1825249 "NSUP" 1826833 NIL NSUP (NIL T) -8 NIL NIL NIL) (-789 1815321 1815378 1815487 "NSUP2" 1815626 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-788 1805547 1815095 1815228 "NSMP" 1815233 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-787 1803979 1804280 1804637 "NREP" 1805235 NIL NREP (NIL T) -7 NIL NIL NIL) (-786 1802570 1802822 1803180 "NPCOEF" 1803722 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-785 1801636 1801751 1801967 "NORMRETR" 1802451 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-784 1799677 1799967 1800376 "NORMPK" 1801344 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-783 1799362 1799390 1799514 "NORMMA" 1799643 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-782 1799162 1799319 1799348 "NONE" 1799353 T NONE (NIL) -8 NIL NIL NIL) (-781 1798951 1798980 1799049 "NONE1" 1799126 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-780 1798448 1798510 1798689 "NODE1" 1798883 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-779 1796729 1797580 1797835 "NNI" 1798182 T NNI (NIL) -8 NIL NIL 1798417) (-778 1795149 1795462 1795826 "NLINSOL" 1796397 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-777 1791390 1792385 1793284 "NIPROB" 1794270 T NIPROB (NIL) -8 NIL NIL NIL) (-776 1790147 1790381 1790683 "NFINTBAS" 1791152 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-775 1789321 1789797 1789838 "NETCLT" 1790010 NIL NETCLT (NIL T) -9 NIL 1790092 NIL) (-774 1788029 1788260 1788541 "NCODIV" 1789089 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-773 1787791 1787828 1787903 "NCNTFRAC" 1787986 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-772 1785971 1786335 1786755 "NCEP" 1787416 NIL NCEP (NIL T) -7 NIL NIL NIL) (-771 1784822 1785595 1785623 "NASRING" 1785733 T NASRING (NIL) -9 NIL 1785813 NIL) (-770 1784617 1784661 1784755 "NASRING-" 1784760 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-769 1783724 1784249 1784277 "NARNG" 1784394 T NARNG (NIL) -9 NIL 1784485 NIL) (-768 1783416 1783483 1783617 "NARNG-" 1783622 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-767 1782295 1782502 1782737 "NAGSP" 1783201 T NAGSP (NIL) -7 NIL NIL NIL) (-766 1773567 1775251 1776924 "NAGS" 1780642 T NAGS (NIL) -7 NIL NIL NIL) (-765 1772115 1772423 1772754 "NAGF07" 1773256 T NAGF07 (NIL) -7 NIL NIL NIL) (-764 1766653 1767944 1769251 "NAGF04" 1770828 T NAGF04 (NIL) -7 NIL NIL NIL) (-763 1759621 1761235 1762868 "NAGF02" 1765040 T NAGF02 (NIL) -7 NIL NIL NIL) (-762 1754845 1755945 1757062 "NAGF01" 1758524 T NAGF01 (NIL) -7 NIL NIL NIL) (-761 1748473 1750039 1751624 "NAGE04" 1753280 T NAGE04 (NIL) -7 NIL NIL NIL) (-760 1739642 1741763 1743893 "NAGE02" 1746363 T NAGE02 (NIL) -7 NIL NIL NIL) (-759 1735595 1736542 1737506 "NAGE01" 1738698 T NAGE01 (NIL) -7 NIL NIL NIL) (-758 1733390 1733924 1734482 "NAGD03" 1735057 T NAGD03 (NIL) -7 NIL NIL NIL) (-757 1725140 1727068 1729022 "NAGD02" 1731456 T NAGD02 (NIL) -7 NIL NIL NIL) (-756 1718951 1720376 1721816 "NAGD01" 1723720 T NAGD01 (NIL) -7 NIL NIL NIL) (-755 1715160 1715982 1716819 "NAGC06" 1718134 T NAGC06 (NIL) -7 NIL NIL NIL) (-754 1713625 1713957 1714313 "NAGC05" 1714824 T NAGC05 (NIL) -7 NIL NIL NIL) (-753 1713001 1713120 1713264 "NAGC02" 1713501 T NAGC02 (NIL) -7 NIL NIL NIL) (-752 1711960 1712543 1712583 "NAALG" 1712662 NIL NAALG (NIL T) -9 NIL 1712723 NIL) (-751 1711795 1711824 1711914 "NAALG-" 1711919 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-750 1705745 1706853 1708040 "MULTSQFR" 1710691 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-749 1705064 1705139 1705323 "MULTFACT" 1705657 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-748 1697788 1701701 1701754 "MTSCAT" 1702824 NIL MTSCAT (NIL T T) -9 NIL 1703339 NIL) (-747 1697500 1697554 1697646 "MTHING" 1697728 NIL MTHING (NIL T) -7 NIL NIL NIL) (-746 1697292 1697325 1697385 "MSYSCMD" 1697460 T MSYSCMD (NIL) -7 NIL NIL NIL) (-745 1693374 1696047 1696367 "MSET" 1697005 NIL MSET (NIL T) -8 NIL NIL NIL) (-744 1690443 1692935 1692976 "MSETAGG" 1692981 NIL MSETAGG (NIL T) -9 NIL 1693015 NIL) (-743 1686285 1687822 1688567 "MRING" 1689743 NIL MRING (NIL T T) -8 NIL NIL NIL) (-742 1685851 1685918 1686049 "MRF2" 1686212 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-741 1685469 1685504 1685648 "MRATFAC" 1685810 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-740 1683081 1683376 1683807 "MPRFF" 1685174 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-739 1677378 1682935 1683032 "MPOLY" 1683037 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-738 1676868 1676903 1677111 "MPCPF" 1677337 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-737 1676382 1676425 1676609 "MPC3" 1676819 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-736 1675577 1675658 1675879 "MPC2" 1676297 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-735 1673878 1674215 1674605 "MONOTOOL" 1675237 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-734 1673103 1673420 1673448 "MONOID" 1673667 T MONOID (NIL) -9 NIL 1673814 NIL) (-733 1672649 1672768 1672949 "MONOID-" 1672954 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-732 1662958 1668910 1668969 "MONOGEN" 1669643 NIL MONOGEN (NIL T T) -9 NIL 1670099 NIL) (-731 1660176 1660911 1661911 "MONOGEN-" 1662030 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-730 1659009 1659455 1659483 "MONADWU" 1659875 T MONADWU (NIL) -9 NIL 1660113 NIL) (-729 1658381 1658540 1658788 "MONADWU-" 1658793 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-728 1657740 1657984 1658012 "MONAD" 1658219 T MONAD (NIL) -9 NIL 1658331 NIL) (-727 1657425 1657503 1657635 "MONAD-" 1657640 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-726 1655714 1656338 1656617 "MOEBIUS" 1657178 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-725 1654992 1655396 1655436 "MODULE" 1655441 NIL MODULE (NIL T) -9 NIL 1655480 NIL) (-724 1654560 1654656 1654846 "MODULE-" 1654851 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-723 1652240 1652924 1653251 "MODRING" 1654384 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1649184 1650345 1650866 "MODOP" 1651769 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-721 1647772 1648251 1648528 "MODMONOM" 1649047 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-720 1637816 1646063 1646477 "MODMON" 1647409 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-719 1634972 1636660 1636936 "MODFIELD" 1637691 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-718 1633949 1634253 1634443 "MMLFORM" 1634802 T MMLFORM (NIL) -8 NIL NIL NIL) (-717 1633475 1633518 1633697 "MMAP" 1633900 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-716 1631554 1632321 1632362 "MLO" 1632785 NIL MLO (NIL T) -9 NIL 1633027 NIL) (-715 1628920 1629436 1630038 "MLIFT" 1631035 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-714 1628311 1628395 1628549 "MKUCFUNC" 1628831 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-713 1627910 1627980 1628103 "MKRECORD" 1628234 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-712 1626957 1627119 1627347 "MKFUNC" 1627721 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-711 1626345 1626449 1626605 "MKFLCFN" 1626840 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-710 1625622 1625724 1625909 "MKBCFUNC" 1626238 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-709 1622329 1625176 1625312 "MINT" 1625506 T MINT (NIL) -8 NIL NIL NIL) (-708 1621141 1621384 1621661 "MHROWRED" 1622084 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-707 1616521 1619676 1620081 "MFLOAT" 1620756 T MFLOAT (NIL) -8 NIL NIL NIL) (-706 1615878 1615954 1616125 "MFINFACT" 1616433 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-705 1612193 1613041 1613925 "MESH" 1615014 T MESH (NIL) -7 NIL NIL NIL) (-704 1610583 1610895 1611248 "MDDFACT" 1611880 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-703 1607378 1609742 1609783 "MDAGG" 1610038 NIL MDAGG (NIL T) -9 NIL 1610181 NIL) (-702 1597118 1606671 1606878 "MCMPLX" 1607191 T MCMPLX (NIL) -8 NIL NIL NIL) (-701 1596255 1596401 1596602 "MCDEN" 1596967 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-700 1594145 1594415 1594795 "MCALCFN" 1595985 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-699 1593070 1593310 1593543 "MAYBE" 1593951 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-698 1590682 1591205 1591767 "MATSTOR" 1592541 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-697 1586639 1590054 1590302 "MATRIX" 1590467 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-696 1582405 1583112 1583848 "MATLIN" 1585996 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-695 1572511 1575697 1575774 "MATCAT" 1580654 NIL MATCAT (NIL T T T) -9 NIL 1582071 NIL) (-694 1568867 1569888 1571244 "MATCAT-" 1571249 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-693 1567461 1567614 1567947 "MATCAT2" 1568702 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-692 1565573 1565897 1566281 "MAPPKG3" 1567136 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-691 1564554 1564727 1564949 "MAPPKG2" 1565397 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-690 1563053 1563337 1563664 "MAPPKG1" 1564260 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-689 1562132 1562459 1562636 "MAPPAST" 1562896 T MAPPAST (NIL) -8 NIL NIL NIL) (-688 1561743 1561801 1561924 "MAPHACK3" 1562068 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-687 1561335 1561396 1561510 "MAPHACK2" 1561675 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-686 1560773 1560876 1561018 "MAPHACK1" 1561226 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-685 1558852 1559473 1559777 "MAGMA" 1560501 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-684 1558331 1558576 1558667 "MACROAST" 1558781 T MACROAST (NIL) -8 NIL NIL NIL) (-683 1554749 1556570 1557031 "M3D" 1557903 NIL M3D (NIL T) -8 NIL NIL NIL) (-682 1548824 1553088 1553129 "LZSTAGG" 1553911 NIL LZSTAGG (NIL T) -9 NIL 1554206 NIL) (-681 1544782 1545955 1547412 "LZSTAGG-" 1547417 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-680 1541869 1542673 1543160 "LWORD" 1544327 NIL LWORD (NIL T) -8 NIL NIL NIL) (-679 1541445 1541673 1541748 "LSTAST" 1541814 T LSTAST (NIL) -8 NIL NIL NIL) (-678 1534611 1541216 1541350 "LSQM" 1541355 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-677 1533835 1533974 1534202 "LSPP" 1534466 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-676 1531647 1531948 1532404 "LSMP" 1533524 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-675 1528426 1529100 1529830 "LSMP1" 1530949 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-674 1522272 1527563 1527604 "LSAGG" 1527666 NIL LSAGG (NIL T) -9 NIL 1527744 NIL) (-673 1518967 1519891 1521104 "LSAGG-" 1521109 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-672 1516566 1518111 1518360 "LPOLY" 1518762 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-671 1516148 1516233 1516356 "LPEFRAC" 1516475 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-670 1514469 1515242 1515495 "LO" 1515980 NIL LO (NIL T T T) -8 NIL NIL NIL) (-669 1514121 1514233 1514261 "LOGIC" 1514372 T LOGIC (NIL) -9 NIL 1514453 NIL) (-668 1513983 1514006 1514077 "LOGIC-" 1514082 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-667 1513176 1513316 1513509 "LODOOPS" 1513839 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-666 1510599 1513092 1513158 "LODO" 1513163 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-665 1509137 1509372 1509725 "LODOF" 1510346 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-664 1505341 1507772 1507813 "LODOCAT" 1508251 NIL LODOCAT (NIL T) -9 NIL 1508462 NIL) (-663 1505074 1505132 1505259 "LODOCAT-" 1505264 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-662 1502394 1504915 1505033 "LODO2" 1505038 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-661 1499829 1502331 1502376 "LODO1" 1502381 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-660 1498710 1498875 1499180 "LODEEF" 1499652 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-659 1494013 1496904 1496945 "LNAGG" 1497807 NIL LNAGG (NIL T) -9 NIL 1498242 NIL) (-658 1493160 1493374 1493716 "LNAGG-" 1493721 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-657 1489296 1490085 1490724 "LMOPS" 1492575 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-656 1488699 1489087 1489128 "LMODULE" 1489133 NIL LMODULE (NIL T) -9 NIL 1489159 NIL) (-655 1485897 1488344 1488467 "LMDICT" 1488609 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-654 1485303 1485524 1485565 "LLINSET" 1485756 NIL LLINSET (NIL T) -9 NIL 1485847 NIL) (-653 1485002 1485211 1485271 "LITERAL" 1485276 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-652 1478165 1483936 1484240 "LIST" 1484731 NIL LIST (NIL T) -8 NIL NIL NIL) (-651 1477690 1477764 1477903 "LIST3" 1478085 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-650 1476697 1476875 1477103 "LIST2" 1477508 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-649 1474831 1475143 1475542 "LIST2MAP" 1476344 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-648 1474427 1474664 1474705 "LINSET" 1474710 NIL LINSET (NIL T) -9 NIL 1474744 NIL) (-647 1473088 1473758 1473799 "LINEXP" 1474054 NIL LINEXP (NIL T) -9 NIL 1474203 NIL) (-646 1471735 1471995 1472292 "LINDEP" 1472840 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-645 1468502 1469221 1469998 "LIMITRF" 1470990 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-644 1466805 1467101 1467510 "LIMITPS" 1468197 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-643 1461233 1466316 1466544 "LIE" 1466626 NIL LIE (NIL T T) -8 NIL NIL NIL) (-642 1460181 1460650 1460690 "LIECAT" 1460830 NIL LIECAT (NIL T) -9 NIL 1460981 NIL) (-641 1460022 1460049 1460137 "LIECAT-" 1460142 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-640 1452609 1459562 1459718 "LIB" 1459886 T LIB (NIL) -8 NIL NIL NIL) (-639 1448244 1449127 1450062 "LGROBP" 1451726 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-638 1446242 1446516 1446866 "LF" 1447965 NIL LF (NIL T T) -7 NIL NIL NIL) (-637 1445082 1445774 1445802 "LFCAT" 1446009 T LFCAT (NIL) -9 NIL 1446148 NIL) (-636 1441984 1442614 1443302 "LEXTRIPK" 1444446 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-635 1438728 1439554 1440057 "LEXP" 1441564 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-634 1438204 1438449 1438541 "LETAST" 1438656 T LETAST (NIL) -8 NIL NIL NIL) (-633 1436602 1436915 1437316 "LEADCDET" 1437886 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-632 1435792 1435866 1436095 "LAZM3PK" 1436523 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-631 1430709 1433869 1434407 "LAUPOL" 1435304 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-630 1430288 1430332 1430493 "LAPLACE" 1430659 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-629 1428227 1429389 1429640 "LA" 1430121 NIL LA (NIL T T T) -8 NIL NIL NIL) (-628 1427221 1427805 1427846 "LALG" 1427908 NIL LALG (NIL T) -9 NIL 1427967 NIL) (-627 1426935 1426994 1427130 "LALG-" 1427135 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-626 1426770 1426794 1426835 "KVTFROM" 1426897 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-625 1425693 1426137 1426322 "KTVLOGIC" 1426605 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-624 1425528 1425552 1425593 "KRCFROM" 1425655 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-623 1424432 1424619 1424918 "KOVACIC" 1425328 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-622 1424267 1424291 1424332 "KONVERT" 1424394 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-621 1424102 1424126 1424167 "KOERCE" 1424229 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-620 1421933 1422695 1423072 "KERNEL" 1423758 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-619 1421429 1421510 1421642 "KERNEL2" 1421847 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-618 1415199 1419968 1420022 "KDAGG" 1420399 NIL KDAGG (NIL T T) -9 NIL 1420605 NIL) (-617 1414728 1414852 1415057 "KDAGG-" 1415062 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1407876 1414389 1414544 "KAFILE" 1414606 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-615 1402304 1407387 1407615 "JORDAN" 1407697 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-614 1401683 1401953 1402074 "JOINAST" 1402203 T JOINAST (NIL) -8 NIL NIL NIL) (-613 1401529 1401588 1401643 "JAVACODE" 1401648 T JAVACODE (NIL) -8 NIL NIL NIL) (-612 1397781 1399734 1399788 "IXAGG" 1400717 NIL IXAGG (NIL T T) -9 NIL 1401176 NIL) (-611 1396700 1397006 1397425 "IXAGG-" 1397430 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-610 1392230 1396622 1396681 "IVECTOR" 1396686 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-609 1390996 1391233 1391499 "ITUPLE" 1391997 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-608 1389498 1389675 1389970 "ITRIGMNP" 1390818 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-607 1388243 1388447 1388730 "ITFUN3" 1389274 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-606 1387875 1387932 1388041 "ITFUN2" 1388180 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-605 1387034 1387355 1387529 "ITFORM" 1387721 T ITFORM (NIL) -8 NIL NIL NIL) (-604 1384995 1386054 1386332 "ITAYLOR" 1386789 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-603 1373940 1379132 1380295 "ISUPS" 1383865 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-602 1373044 1373184 1373420 "ISUMP" 1373787 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-601 1368419 1372989 1373030 "ISTRING" 1373035 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-600 1367895 1368140 1368232 "ISAST" 1368347 T ISAST (NIL) -8 NIL NIL NIL) (-599 1367104 1367186 1367402 "IRURPK" 1367809 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-598 1366040 1366241 1366481 "IRSN" 1366884 T IRSN (NIL) -7 NIL NIL NIL) (-597 1364111 1364466 1364895 "IRRF2F" 1365678 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-596 1363858 1363896 1363972 "IRREDFFX" 1364067 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-595 1362473 1362732 1363031 "IROOT" 1363591 NIL IROOT (NIL T) -7 NIL NIL NIL) (-594 1359077 1360157 1360849 "IR" 1361813 NIL IR (NIL T) -8 NIL NIL NIL) (-593 1358282 1358570 1358721 "IRFORM" 1358946 T IRFORM (NIL) -8 NIL NIL NIL) (-592 1355895 1356390 1356956 "IR2" 1357760 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-591 1354995 1355108 1355322 "IR2F" 1355778 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-590 1354786 1354820 1354880 "IPRNTPK" 1354955 T IPRNTPK (NIL) -7 NIL NIL NIL) (-589 1351367 1354675 1354744 "IPF" 1354749 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-588 1349694 1351292 1351349 "IPADIC" 1351354 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-587 1349006 1349254 1349384 "IP4ADDR" 1349584 T IP4ADDR (NIL) -8 NIL NIL NIL) (-586 1348380 1348635 1348767 "IOMODE" 1348894 T IOMODE (NIL) -8 NIL NIL NIL) (-585 1347453 1347977 1348104 "IOBFILE" 1348273 T IOBFILE (NIL) -8 NIL NIL NIL) (-584 1346941 1347357 1347385 "IOBCON" 1347390 T IOBCON (NIL) -9 NIL 1347411 NIL) (-583 1346452 1346510 1346693 "INVLAPLA" 1346877 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-582 1336100 1338454 1340840 "INTTR" 1344116 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-581 1332435 1333177 1334042 "INTTOOLS" 1335285 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-580 1332021 1332112 1332229 "INTSLPE" 1332338 T INTSLPE (NIL) -7 NIL NIL NIL) (-579 1329974 1331944 1332003 "INTRVL" 1332008 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-578 1327576 1328088 1328663 "INTRF" 1329459 NIL INTRF (NIL T) -7 NIL NIL NIL) (-577 1326987 1327084 1327226 "INTRET" 1327474 NIL INTRET (NIL T) -7 NIL NIL NIL) (-576 1324984 1325373 1325843 "INTRAT" 1326595 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-575 1322247 1322830 1323449 "INTPM" 1324469 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-574 1318992 1319591 1320329 "INTPAF" 1321633 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-573 1314171 1315133 1316184 "INTPACK" 1317961 T INTPACK (NIL) -7 NIL NIL NIL) (-572 1311119 1313968 1314077 "INT" 1314082 T INT (NIL) -8 NIL NIL NIL) (-571 1310371 1310523 1310731 "INTHERTR" 1310961 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-570 1309810 1309890 1310078 "INTHERAL" 1310285 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-569 1307656 1308099 1308556 "INTHEORY" 1309373 T INTHEORY (NIL) -7 NIL NIL NIL) (-568 1299062 1300683 1302455 "INTG0" 1306008 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-567 1279635 1284425 1289235 "INTFTBL" 1294272 T INTFTBL (NIL) -8 NIL NIL NIL) (-566 1278884 1279022 1279195 "INTFACT" 1279494 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-565 1276311 1276757 1277314 "INTEF" 1278438 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-564 1274678 1275417 1275445 "INTDOM" 1275746 T INTDOM (NIL) -9 NIL 1275953 NIL) (-563 1274047 1274221 1274463 "INTDOM-" 1274468 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-562 1270435 1272363 1272417 "INTCAT" 1273216 NIL INTCAT (NIL T) -9 NIL 1273537 NIL) (-561 1269907 1270010 1270138 "INTBIT" 1270327 T INTBIT (NIL) -7 NIL NIL NIL) (-560 1268606 1268760 1269067 "INTALG" 1269752 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-559 1268089 1268179 1268336 "INTAF" 1268510 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-558 1261432 1267899 1268039 "INTABL" 1268044 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-557 1260765 1261231 1261296 "INT8" 1261330 T INT8 (NIL) -8 NIL NIL 1261375) (-556 1260097 1260563 1260628 "INT64" 1260662 T INT64 (NIL) -8 NIL NIL 1260707) (-555 1259429 1259895 1259960 "INT32" 1259994 T INT32 (NIL) -8 NIL NIL 1260039) (-554 1258761 1259227 1259292 "INT16" 1259326 T INT16 (NIL) -8 NIL NIL 1259371) (-553 1253641 1256355 1256383 "INS" 1257317 T INS (NIL) -9 NIL 1257982 NIL) (-552 1250881 1251652 1252626 "INS-" 1252699 NIL INS- (NIL T) -8 NIL NIL NIL) (-551 1249656 1249883 1250181 "INPSIGN" 1250634 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-550 1248774 1248891 1249088 "INPRODPF" 1249536 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-549 1247668 1247785 1248022 "INPRODFF" 1248654 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-548 1246668 1246820 1247080 "INNMFACT" 1247504 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-547 1245865 1245962 1246150 "INMODGCD" 1246567 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-546 1244373 1244618 1244942 "INFSP" 1245610 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-545 1243557 1243674 1243857 "INFPROD0" 1244253 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-544 1240412 1241622 1242137 "INFORM" 1243050 T INFORM (NIL) -8 NIL NIL NIL) (-543 1240022 1240082 1240180 "INFORM1" 1240347 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-542 1239545 1239634 1239748 "INFINITY" 1239928 T INFINITY (NIL) -7 NIL NIL NIL) (-541 1238721 1239265 1239366 "INETCLTS" 1239464 T INETCLTS (NIL) -8 NIL NIL NIL) (-540 1237337 1237587 1237908 "INEP" 1238469 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-539 1236586 1237234 1237299 "INDE" 1237304 NIL INDE (NIL T) -8 NIL NIL NIL) (-538 1236150 1236218 1236335 "INCRMAPS" 1236513 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-537 1234968 1235419 1235625 "INBFILE" 1235964 T INBFILE (NIL) -8 NIL NIL NIL) (-536 1230267 1231204 1232148 "INBFF" 1234056 NIL INBFF (NIL T) -7 NIL NIL NIL) (-535 1229175 1229444 1229472 "INBCON" 1229985 T INBCON (NIL) -9 NIL 1230251 NIL) (-534 1228427 1228650 1228926 "INBCON-" 1228931 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-533 1227906 1228151 1228242 "INAST" 1228356 T INAST (NIL) -8 NIL NIL NIL) (-532 1227333 1227585 1227691 "IMPTAST" 1227820 T IMPTAST (NIL) -8 NIL NIL NIL) (-531 1223779 1227177 1227281 "IMATRIX" 1227286 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-530 1222487 1222610 1222926 "IMATQF" 1223635 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-529 1220707 1220934 1221271 "IMATLIN" 1222243 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-528 1215285 1220631 1220689 "ILIST" 1220694 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-527 1213190 1215145 1215258 "IIARRAY2" 1215263 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-526 1208588 1213101 1213165 "IFF" 1213170 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-525 1207935 1208205 1208321 "IFAST" 1208492 T IFAST (NIL) -8 NIL NIL NIL) (-524 1202930 1207227 1207415 "IFARRAY" 1207792 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-523 1202110 1202834 1202907 "IFAMON" 1202912 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-522 1201694 1201759 1201813 "IEVALAB" 1202020 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-521 1201369 1201437 1201597 "IEVALAB-" 1201602 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-520 1201000 1201283 1201346 "IDPO" 1201351 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-519 1200250 1200889 1200964 "IDPOAMS" 1200969 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-518 1199557 1200139 1200214 "IDPOAM" 1200219 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-517 1198616 1198892 1198945 "IDPC" 1199358 NIL IDPC (NIL T T) -9 NIL 1199507 NIL) (-516 1198085 1198508 1198581 "IDPAM" 1198586 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-515 1197461 1197977 1198050 "IDPAG" 1198055 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-514 1197106 1197297 1197372 "IDENT" 1197406 T IDENT (NIL) -8 NIL NIL NIL) (-513 1193361 1194209 1195104 "IDECOMP" 1196263 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-512 1186198 1187284 1188331 "IDEAL" 1192397 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-511 1185358 1185470 1185670 "ICDEN" 1186082 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-510 1184429 1184838 1184985 "ICARD" 1185231 T ICARD (NIL) -8 NIL NIL NIL) (-509 1182489 1182802 1183207 "IBPTOOLS" 1184106 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-508 1178096 1182109 1182222 "IBITS" 1182408 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-507 1174819 1175395 1176090 "IBATOOL" 1177513 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-506 1172598 1173060 1173593 "IBACHIN" 1174354 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-505 1170427 1172444 1172547 "IARRAY2" 1172552 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-504 1166533 1170353 1170410 "IARRAY1" 1170415 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-503 1160642 1164945 1165426 "IAN" 1166072 T IAN (NIL) -8 NIL NIL NIL) (-502 1160153 1160210 1160383 "IALGFACT" 1160579 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-501 1159681 1159794 1159822 "HYPCAT" 1160029 T HYPCAT (NIL) -9 NIL NIL NIL) (-500 1159219 1159336 1159522 "HYPCAT-" 1159527 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-499 1158814 1159014 1159097 "HOSTNAME" 1159156 T HOSTNAME (NIL) -8 NIL NIL NIL) (-498 1158659 1158696 1158737 "HOMOTOP" 1158742 NIL HOMOTOP (NIL T) -9 NIL 1158775 NIL) (-497 1155291 1156669 1156710 "HOAGG" 1157691 NIL HOAGG (NIL T) -9 NIL 1158370 NIL) (-496 1153885 1154284 1154810 "HOAGG-" 1154815 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-495 1147887 1153478 1153628 "HEXADEC" 1153755 T HEXADEC (NIL) -8 NIL NIL NIL) (-494 1146635 1146857 1147120 "HEUGCD" 1147664 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-493 1145711 1146472 1146602 "HELLFDIV" 1146607 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-492 1143890 1145488 1145576 "HEAP" 1145655 NIL HEAP (NIL T) -8 NIL NIL NIL) (-491 1143153 1143442 1143576 "HEADAST" 1143776 T HEADAST (NIL) -8 NIL NIL NIL) (-490 1137019 1143068 1143130 "HDP" 1143135 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-489 1131007 1136654 1136806 "HDMP" 1136920 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-488 1130331 1130471 1130635 "HB" 1130863 T HB (NIL) -7 NIL NIL NIL) (-487 1123717 1130177 1130281 "HASHTBL" 1130286 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-486 1123193 1123438 1123530 "HASAST" 1123645 T HASAST (NIL) -8 NIL NIL NIL) (-485 1120971 1122815 1122997 "HACKPI" 1123031 T HACKPI (NIL) -8 NIL NIL NIL) (-484 1116639 1120824 1120937 "GTSET" 1120942 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-483 1110054 1116517 1116615 "GSTBL" 1116620 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-482 1102332 1109085 1109350 "GSERIES" 1109845 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-481 1101473 1101890 1101918 "GROUP" 1102121 T GROUP (NIL) -9 NIL 1102255 NIL) (-480 1100839 1100998 1101249 "GROUP-" 1101254 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-479 1099206 1099527 1099914 "GROEBSOL" 1100516 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-478 1098120 1098408 1098459 "GRMOD" 1098988 NIL GRMOD (NIL T T) -9 NIL 1099156 NIL) (-477 1097888 1097924 1098052 "GRMOD-" 1098057 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-476 1093178 1094242 1095242 "GRIMAGE" 1096908 T GRIMAGE (NIL) -8 NIL NIL NIL) (-475 1091644 1091905 1092229 "GRDEF" 1092874 T GRDEF (NIL) -7 NIL NIL NIL) (-474 1091088 1091204 1091345 "GRAY" 1091523 T GRAY (NIL) -7 NIL NIL NIL) (-473 1090275 1090681 1090732 "GRALG" 1090885 NIL GRALG (NIL T T) -9 NIL 1090978 NIL) (-472 1089936 1090009 1090172 "GRALG-" 1090177 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-471 1086713 1089521 1089699 "GPOLSET" 1089843 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-470 1086067 1086124 1086382 "GOSPER" 1086650 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-469 1081799 1082505 1083031 "GMODPOL" 1085766 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-468 1080804 1080988 1081226 "GHENSEL" 1081611 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-467 1074960 1075803 1076823 "GENUPS" 1079888 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-466 1074657 1074708 1074797 "GENUFACT" 1074903 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-465 1074069 1074146 1074311 "GENPGCD" 1074575 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-464 1073543 1073578 1073791 "GENMFACT" 1074028 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-463 1072109 1072366 1072673 "GENEEZ" 1073286 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-462 1066257 1071720 1071882 "GDMP" 1072032 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-461 1055600 1060028 1061134 "GCNAALG" 1065240 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-460 1053927 1054789 1054817 "GCDDOM" 1055072 T GCDDOM (NIL) -9 NIL 1055229 NIL) (-459 1053397 1053524 1053739 "GCDDOM-" 1053744 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-458 1052069 1052254 1052558 "GB" 1053176 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-457 1040685 1043015 1045407 "GBINTERN" 1049760 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-456 1038522 1038814 1039235 "GBF" 1040360 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-455 1037303 1037468 1037735 "GBEUCLID" 1038338 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-454 1036652 1036777 1036926 "GAUSSFAC" 1037174 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-453 1035019 1035321 1035635 "GALUTIL" 1036371 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-452 1033327 1033601 1033925 "GALPOLYU" 1034746 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-451 1030692 1030982 1031389 "GALFACTU" 1033024 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-450 1022498 1023997 1025605 "GALFACT" 1029124 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-449 1019886 1020544 1020572 "FVFUN" 1021728 T FVFUN (NIL) -9 NIL 1022448 NIL) (-448 1019152 1019334 1019362 "FVC" 1019653 T FVC (NIL) -9 NIL 1019836 NIL) (-447 1018795 1018977 1019045 "FUNDESC" 1019104 T FUNDESC (NIL) -8 NIL NIL NIL) (-446 1018410 1018592 1018673 "FUNCTION" 1018747 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-445 1016154 1016732 1017198 "FT" 1017964 T FT (NIL) -8 NIL NIL NIL) (-444 1014945 1015455 1015658 "FTEM" 1015971 T FTEM (NIL) -8 NIL NIL NIL) (-443 1013236 1013525 1013922 "FSUPFACT" 1014636 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-442 1011633 1011922 1012254 "FST" 1012924 T FST (NIL) -8 NIL NIL NIL) (-441 1010832 1010938 1011126 "FSRED" 1011515 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-440 1009531 1009787 1010134 "FSPRMELT" 1010547 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-439 1006837 1007275 1007761 "FSPECF" 1009094 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-438 988475 996806 996847 "FS" 1000731 NIL FS (NIL T) -9 NIL 1003020 NIL) (-437 977118 980111 984168 "FS-" 984468 NIL FS- (NIL T T) -8 NIL NIL NIL) (-436 976646 976700 976870 "FSINT" 977059 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-435 974938 975639 975942 "FSERIES" 976425 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-434 973980 974096 974320 "FSCINT" 974818 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-433 970188 972924 972965 "FSAGG" 973335 NIL FSAGG (NIL T) -9 NIL 973594 NIL) (-432 967950 968551 969347 "FSAGG-" 969442 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-431 966992 967135 967362 "FSAGG2" 967803 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-430 964674 964954 965501 "FS2UPS" 966710 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-429 964308 964351 964480 "FS2" 964625 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-428 963186 963357 963659 "FS2EXPXP" 964133 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 962612 962727 962879 "FRUTIL" 963066 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-426 954025 958107 959465 "FR" 961286 NIL FR (NIL T) -8 NIL NIL NIL) (-425 949039 951714 951754 "FRNAALG" 953074 NIL FRNAALG (NIL T) -9 NIL 953672 NIL) (-424 944712 945788 947063 "FRNAALG-" 947813 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-423 944350 944393 944520 "FRNAAF2" 944663 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-422 942725 943199 943495 "FRMOD" 944162 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-421 940468 941100 941418 "FRIDEAL" 942516 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-420 939659 939746 940037 "FRIDEAL2" 940375 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-419 938792 939206 939247 "FRETRCT" 939252 NIL FRETRCT (NIL T) -9 NIL 939428 NIL) (-418 937904 938135 938486 "FRETRCT-" 938491 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-417 934992 936202 936261 "FRAMALG" 937143 NIL FRAMALG (NIL T T) -9 NIL 937435 NIL) (-416 933126 933581 934211 "FRAMALG-" 934434 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-415 927045 932599 932876 "FRAC" 932881 NIL FRAC (NIL T) -8 NIL NIL NIL) (-414 926681 926738 926845 "FRAC2" 926982 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-413 926317 926374 926481 "FR2" 926618 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-412 920830 923723 923751 "FPS" 924870 T FPS (NIL) -9 NIL 925427 NIL) (-411 920279 920388 920552 "FPS-" 920698 NIL FPS- (NIL T) -8 NIL NIL NIL) (-410 917581 919250 919278 "FPC" 919503 T FPC (NIL) -9 NIL 919645 NIL) (-409 917374 917414 917511 "FPC-" 917516 NIL FPC- (NIL T) -8 NIL NIL NIL) (-408 916164 916862 916903 "FPATMAB" 916908 NIL FPATMAB (NIL T) -9 NIL 917060 NIL) (-407 913837 914340 914766 "FPARFRAC" 915801 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-406 909231 909729 910411 "FORTRAN" 913269 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-405 906947 907447 907986 "FORT" 908712 T FORT (NIL) -7 NIL NIL NIL) (-404 904623 905185 905213 "FORTFN" 906273 T FORTFN (NIL) -9 NIL 906897 NIL) (-403 904387 904437 904465 "FORTCAT" 904524 T FORTCAT (NIL) -9 NIL 904586 NIL) (-402 902493 903003 903393 "FORMULA" 904017 T FORMULA (NIL) -8 NIL NIL NIL) (-401 902281 902311 902380 "FORMULA1" 902457 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-400 901804 901856 902029 "FORDER" 902223 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-399 900900 901064 901257 "FOP" 901631 T FOP (NIL) -7 NIL NIL NIL) (-398 899481 900180 900354 "FNLA" 900782 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-397 898210 898625 898653 "FNCAT" 899113 T FNCAT (NIL) -9 NIL 899373 NIL) (-396 897749 898169 898197 "FNAME" 898202 T FNAME (NIL) -8 NIL NIL NIL) (-395 896312 897275 897303 "FMTC" 897308 T FMTC (NIL) -9 NIL 897344 NIL) (-394 895058 896248 896294 "FMONOID" 896299 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-393 891886 893054 893095 "FMONCAT" 894312 NIL FMONCAT (NIL T) -9 NIL 894917 NIL) (-392 891078 891628 891777 "FM" 891782 NIL FM (NIL T T) -8 NIL NIL NIL) (-391 888502 889148 889176 "FMFUN" 890320 T FMFUN (NIL) -9 NIL 891028 NIL) (-390 887771 887952 887980 "FMC" 888270 T FMC (NIL) -9 NIL 888452 NIL) (-389 884850 885710 885764 "FMCAT" 886959 NIL FMCAT (NIL T T) -9 NIL 887454 NIL) (-388 883716 884616 884716 "FM1" 884795 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-387 881490 881906 882400 "FLOATRP" 883267 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-386 875068 879219 879840 "FLOAT" 880889 T FLOAT (NIL) -8 NIL NIL NIL) (-385 872506 873006 873584 "FLOATCP" 874535 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-384 871246 872084 872125 "FLINEXP" 872130 NIL FLINEXP (NIL T) -9 NIL 872223 NIL) (-383 870400 870635 870963 "FLINEXP-" 870968 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-382 869476 869620 869844 "FLASORT" 870252 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-381 866592 867460 867512 "FLALG" 868739 NIL FLALG (NIL T T) -9 NIL 869206 NIL) (-380 860296 864048 864089 "FLAGG" 865351 NIL FLAGG (NIL T) -9 NIL 866003 NIL) (-379 859022 859361 859851 "FLAGG-" 859856 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-378 858064 858207 858434 "FLAGG2" 858875 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-377 854915 855923 855982 "FINRALG" 857110 NIL FINRALG (NIL T T) -9 NIL 857618 NIL) (-376 854075 854304 854643 "FINRALG-" 854648 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-375 853455 853694 853722 "FINITE" 853918 T FINITE (NIL) -9 NIL 854025 NIL) (-374 845812 847999 848039 "FINAALG" 851706 NIL FINAALG (NIL T) -9 NIL 853159 NIL) (-373 841144 842194 843338 "FINAALG-" 844717 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-372 840512 840899 841002 "FILE" 841074 NIL FILE (NIL T) -8 NIL NIL NIL) (-371 839170 839508 839562 "FILECAT" 840246 NIL FILECAT (NIL T T) -9 NIL 840462 NIL) (-370 836886 838414 838442 "FIELD" 838482 T FIELD (NIL) -9 NIL 838562 NIL) (-369 835506 835891 836402 "FIELD-" 836407 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-368 833356 834141 834488 "FGROUP" 835192 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-367 832446 832610 832830 "FGLMICPK" 833188 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-366 828278 832371 832428 "FFX" 832433 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-365 827879 827940 828075 "FFSLPE" 828211 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-364 823869 824651 825447 "FFPOLY" 827115 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-363 823373 823409 823618 "FFPOLY2" 823827 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-362 819219 823292 823355 "FFP" 823360 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-361 814617 819130 819194 "FF" 819199 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-360 809743 813960 814150 "FFNBX" 814471 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-359 804671 808878 809136 "FFNBP" 809597 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-358 799304 803955 804166 "FFNB" 804504 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-357 798136 798334 798649 "FFINTBAS" 799101 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-356 794175 796396 796424 "FFIELDC" 797044 T FFIELDC (NIL) -9 NIL 797420 NIL) (-355 792837 793208 793705 "FFIELDC-" 793710 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-354 792406 792452 792576 "FFHOM" 792779 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-353 790101 790588 791105 "FFF" 791921 NIL FFF (NIL T) -7 NIL NIL NIL) (-352 785719 789843 789944 "FFCGX" 790044 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-351 781341 785451 785558 "FFCGP" 785662 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-350 776524 781068 781176 "FFCG" 781277 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-349 757712 766794 766880 "FFCAT" 772045 NIL FFCAT (NIL T T T) -9 NIL 773496 NIL) (-348 752909 753957 755271 "FFCAT-" 756501 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-347 752320 752363 752598 "FFCAT2" 752860 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 741643 745292 746512 "FEXPR" 751172 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-345 740605 741040 741081 "FEVALAB" 741165 NIL FEVALAB (NIL T) -9 NIL 741426 NIL) (-344 739764 739974 740312 "FEVALAB-" 740317 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-343 738330 739147 739350 "FDIV" 739663 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-342 735350 736091 736206 "FDIVCAT" 737774 NIL FDIVCAT (NIL T T T T) -9 NIL 738211 NIL) (-341 735112 735139 735309 "FDIVCAT-" 735314 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-340 734332 734419 734696 "FDIV2" 735019 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 733306 733627 733829 "FCTRDATA" 734150 T FCTRDATA (NIL) -8 NIL NIL NIL) (-338 731992 732251 732540 "FCPAK1" 733037 T FCPAK1 (NIL) -7 NIL NIL NIL) (-337 731091 731492 731633 "FCOMP" 731883 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-336 714796 718241 721779 "FC" 727573 T FC (NIL) -8 NIL NIL NIL) (-335 707102 711130 711170 "FAXF" 712972 NIL FAXF (NIL T) -9 NIL 713664 NIL) (-334 704379 705036 705861 "FAXF-" 706326 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-333 699431 703755 703931 "FARRAY" 704236 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-332 694325 696392 696445 "FAMR" 697468 NIL FAMR (NIL T T) -9 NIL 697928 NIL) (-331 693215 693517 693952 "FAMR-" 693957 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-330 692384 693137 693190 "FAMONOID" 693195 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-329 690170 690880 690933 "FAMONC" 691874 NIL FAMONC (NIL T T) -9 NIL 692260 NIL) (-328 688834 689924 690061 "FAGROUP" 690066 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-327 686629 686948 687351 "FACUTIL" 688515 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-326 685728 685913 686135 "FACTFUNC" 686439 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-325 678150 685031 685230 "EXPUPXS" 685584 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-324 675633 676173 676759 "EXPRTUBE" 677584 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-323 671904 672496 673226 "EXPRODE" 674972 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-322 657389 670553 670982 "EXPR" 671508 NIL EXPR (NIL T) -8 NIL NIL NIL) (-321 651943 652530 653336 "EXPR2UPS" 656687 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-320 651575 651632 651741 "EXPR2" 651880 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-319 642963 650726 651017 "EXPEXPAN" 651411 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-318 642763 642920 642949 "EXIT" 642954 T EXIT (NIL) -8 NIL NIL NIL) (-317 642243 642487 642578 "EXITAST" 642692 T EXITAST (NIL) -8 NIL NIL NIL) (-316 641870 641932 642045 "EVALCYC" 642175 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-315 641411 641529 641570 "EVALAB" 641740 NIL EVALAB (NIL T) -9 NIL 641844 NIL) (-314 640892 641014 641235 "EVALAB-" 641240 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-313 638260 639562 639590 "EUCDOM" 640145 T EUCDOM (NIL) -9 NIL 640495 NIL) (-312 636665 637107 637697 "EUCDOM-" 637702 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-311 624204 626963 629713 "ESTOOLS" 633935 T ESTOOLS (NIL) -7 NIL NIL NIL) (-310 623836 623893 624002 "ESTOOLS2" 624141 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-309 623587 623629 623709 "ESTOOLS1" 623788 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-308 617624 619232 619260 "ES" 622028 T ES (NIL) -9 NIL 623438 NIL) (-307 612571 613858 615675 "ES-" 615839 NIL ES- (NIL T) -8 NIL NIL NIL) (-306 608945 609706 610486 "ESCONT" 611811 T ESCONT (NIL) -7 NIL NIL NIL) (-305 608690 608722 608804 "ESCONT1" 608907 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 608365 608415 608515 "ES2" 608634 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-303 607995 608053 608162 "ES1" 608301 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-302 607211 607340 607516 "ERROR" 607839 T ERROR (NIL) -7 NIL NIL NIL) (-301 600603 607070 607161 "EQTBL" 607166 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-300 593106 595917 597366 "EQ" 599187 NIL -2075 (NIL T) -8 NIL NIL NIL) (-299 592738 592795 592904 "EQ2" 593043 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-298 588029 589076 590169 "EP" 591677 NIL EP (NIL T) -7 NIL NIL NIL) (-297 586629 586920 587226 "ENV" 587743 T ENV (NIL) -8 NIL NIL NIL) (-296 585723 586277 586305 "ENTIRER" 586310 T ENTIRER (NIL) -9 NIL 586356 NIL) (-295 582417 583905 584266 "EMR" 585531 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-294 581547 581732 581786 "ELTAGG" 582166 NIL ELTAGG (NIL T T) -9 NIL 582377 NIL) (-293 581266 581328 581469 "ELTAGG-" 581474 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-292 581030 581059 581113 "ELTAB" 581197 NIL ELTAB (NIL T T) -9 NIL 581249 NIL) (-291 580156 580302 580501 "ELFUTS" 580881 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-290 579898 579954 579982 "ELEMFUN" 580087 T ELEMFUN (NIL) -9 NIL NIL NIL) (-289 579768 579789 579857 "ELEMFUN-" 579862 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-288 574582 577838 577879 "ELAGG" 578819 NIL ELAGG (NIL T) -9 NIL 579282 NIL) (-287 572867 573301 573964 "ELAGG-" 573969 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-286 572179 572316 572472 "ELABOR" 572731 T ELABOR (NIL) -8 NIL NIL NIL) (-285 570840 571119 571413 "ELABEXPR" 571905 T ELABEXPR (NIL) -8 NIL NIL NIL) (-284 563704 565507 566334 "EFUPXS" 570116 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-283 557154 558955 559765 "EFULS" 562980 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-282 554639 554997 555469 "EFSTRUC" 556786 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-281 544430 545996 547544 "EF" 553154 NIL EF (NIL T T) -7 NIL NIL NIL) (-280 543504 543915 544064 "EAB" 544301 T EAB (NIL) -8 NIL NIL NIL) (-279 542686 543463 543491 "E04UCFA" 543496 T E04UCFA (NIL) -8 NIL NIL NIL) (-278 541868 542645 542673 "E04NAFA" 542678 T E04NAFA (NIL) -8 NIL NIL NIL) (-277 541050 541827 541855 "E04MBFA" 541860 T E04MBFA (NIL) -8 NIL NIL NIL) (-276 540232 541009 541037 "E04JAFA" 541042 T E04JAFA (NIL) -8 NIL NIL NIL) (-275 539416 540191 540219 "E04GCFA" 540224 T E04GCFA (NIL) -8 NIL NIL NIL) (-274 538600 539375 539403 "E04FDFA" 539408 T E04FDFA (NIL) -8 NIL NIL NIL) (-273 537782 538559 538587 "E04DGFA" 538592 T E04DGFA (NIL) -8 NIL NIL NIL) (-272 531955 533307 534671 "E04AGNT" 536438 T E04AGNT (NIL) -7 NIL NIL NIL) (-271 530635 531141 531181 "DVARCAT" 531656 NIL DVARCAT (NIL T) -9 NIL 531855 NIL) (-270 529839 530051 530365 "DVARCAT-" 530370 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-269 522976 529638 529767 "DSMP" 529772 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-268 517757 518921 519989 "DROPT" 521928 T DROPT (NIL) -8 NIL NIL NIL) (-267 517422 517481 517579 "DROPT1" 517692 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-266 512537 513663 514800 "DROPT0" 516305 T DROPT0 (NIL) -7 NIL NIL NIL) (-265 510882 511207 511593 "DRAWPT" 512171 T DRAWPT (NIL) -7 NIL NIL NIL) (-264 505469 506392 507471 "DRAW" 509856 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 505102 505155 505273 "DRAWHACK" 505410 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-262 503833 504102 504393 "DRAWCX" 504831 T DRAWCX (NIL) -7 NIL NIL NIL) (-261 503348 503417 503568 "DRAWCURV" 503759 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-260 493816 495778 497893 "DRAWCFUN" 501253 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-259 490580 492509 492550 "DQAGG" 493179 NIL DQAGG (NIL T) -9 NIL 493453 NIL) (-258 478647 485116 485199 "DPOLCAT" 487051 NIL DPOLCAT (NIL T T T T) -9 NIL 487596 NIL) (-257 473484 474832 476790 "DPOLCAT-" 476795 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-256 466606 473345 473443 "DPMO" 473448 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-255 459631 466386 466553 "DPMM" 466558 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-254 459201 459415 459504 "DOMTMPLT" 459562 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-253 458634 459003 459083 "DOMCTOR" 459141 T DOMCTOR (NIL) -8 NIL NIL NIL) (-252 457846 458114 458265 "DOMAIN" 458503 T DOMAIN (NIL) -8 NIL NIL NIL) (-251 451834 457481 457633 "DMP" 457747 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-250 451434 451490 451634 "DLP" 451772 NIL DLP (NIL T) -7 NIL NIL NIL) (-249 445256 450761 450951 "DLIST" 451276 NIL DLIST (NIL T) -8 NIL NIL NIL) (-248 442053 444109 444150 "DLAGG" 444700 NIL DLAGG (NIL T) -9 NIL 444930 NIL) (-247 440729 441393 441421 "DIVRING" 441513 T DIVRING (NIL) -9 NIL 441596 NIL) (-246 439966 440156 440456 "DIVRING-" 440461 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-245 438068 438425 438831 "DISPLAY" 439580 T DISPLAY (NIL) -7 NIL NIL NIL) (-244 431954 437982 438045 "DIRPROD" 438050 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-243 430802 431005 431270 "DIRPROD2" 431747 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-242 419520 425527 425580 "DIRPCAT" 425990 NIL DIRPCAT (NIL NIL T) -9 NIL 426830 NIL) (-241 416846 417488 418369 "DIRPCAT-" 418706 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-240 416133 416293 416479 "DIOSP" 416680 T DIOSP (NIL) -7 NIL NIL NIL) (-239 412788 415045 415086 "DIOPS" 415520 NIL DIOPS (NIL T) -9 NIL 415749 NIL) (-238 412337 412451 412642 "DIOPS-" 412647 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-237 411226 411854 411882 "DIFRING" 412001 T DIFRING (NIL) -9 NIL 412084 NIL) (-236 410871 410949 411101 "DIFRING-" 411106 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-235 410579 410624 410665 "DIFFDOM" 410786 NIL DIFFDOM (NIL T) -9 NIL 410854 NIL) (-234 410432 410456 410540 "DIFFDOM-" 410545 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 408111 409383 409424 "DIFEXT" 409787 NIL DIFEXT (NIL T) -9 NIL 410081 NIL) (-232 406396 406824 407490 "DIFEXT-" 407495 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403671 405928 405969 "DIAGG" 405974 NIL DIAGG (NIL T) -9 NIL 405994 NIL) (-230 403055 403212 403464 "DIAGG-" 403469 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398472 402014 402291 "DHMATRIX" 402824 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394084 394993 396003 "DFSFUN" 397482 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389164 393015 393327 "DFLOAT" 393792 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387427 387708 388097 "DFINTTLS" 388872 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384456 385448 385848 "DERHAM" 387093 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382257 384231 384320 "DEQUEUE" 384400 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381511 381644 381827 "DEGRED" 382119 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377941 378686 379532 "DEFINTRF" 380739 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375496 375965 376557 "DEFINTEF" 377460 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374846 375116 375231 "DEFAST" 375401 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368848 374439 374589 "DECIMAL" 374716 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366360 366818 367324 "DDFACT" 368392 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365956 365999 366150 "DBLRESP" 366311 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363824 364186 364547 "DBASE" 365722 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363066 363304 363450 "DATAARY" 363723 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362172 363025 363053 "D03FAFA" 363058 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361279 362131 362159 "D03EEFA" 362164 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359229 359695 360184 "D03AGNT" 360810 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358518 359188 359216 "D02EJFA" 359221 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357807 358477 358505 "D02CJFA" 358510 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357096 357766 357794 "D02BHFA" 357799 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356385 357055 357083 "D02BBFA" 357088 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349582 351171 352777 "D02AGNT" 354799 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347350 347873 348419 "D01WGTS" 349056 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346417 347309 347337 "D01TRNS" 347342 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345485 346376 346404 "D01GBFA" 346409 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344553 345444 345472 "D01FCFA" 345477 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343621 344512 344540 "D01ASFA" 344545 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342689 343580 343608 "D01AQFA" 343613 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341757 342648 342676 "D01APFA" 342681 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340825 341716 341744 "D01ANFA" 341749 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339893 340784 340812 "D01AMFA" 340817 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338961 339852 339880 "D01ALFA" 339885 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338029 338920 338948 "D01AKFA" 338953 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337097 337988 338016 "D01AJFA" 338021 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330392 331945 333506 "D01AGNT" 335556 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329729 329857 330009 "CYCLOTOM" 330260 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326462 327177 327904 "CYCLES" 329022 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325774 325908 326079 "CVMP" 326323 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323615 323873 324242 "CTRIGMNP" 325502 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323051 323409 323482 "CTOR" 323562 T CTOR (NIL) -8 NIL NIL NIL) (-188 322560 322782 322883 "CTORKIND" 322970 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321851 322167 322195 "CTORCAT" 322377 T CTORCAT (NIL) -9 NIL 322490 NIL) (-186 321449 321560 321719 "CTORCAT-" 321724 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320911 321123 321231 "CTORCALL" 321373 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320285 320384 320537 "CSTTOOLS" 320808 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316084 316741 317499 "CRFP" 319597 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315559 315805 315897 "CRCEAST" 316012 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314606 314791 315019 "CRAPACK" 315363 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313990 314091 314295 "CPMATCH" 314482 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313715 313743 313849 "CPIMA" 313956 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310063 310735 311454 "COORDSYS" 313050 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309475 309596 309738 "CONTOUR" 309941 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305366 307478 307970 "CONTFRAC" 309015 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305246 305267 305295 "CONDUIT" 305332 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304334 304888 304916 "COMRING" 304921 T COMRING (NIL) -9 NIL 304973 NIL) (-173 303388 303692 303876 "COMPPROP" 304170 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303049 303084 303212 "COMPLPAT" 303347 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293340 302858 302967 "COMPLEX" 302972 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292976 293033 293140 "COMPLEX2" 293277 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292315 292436 292596 "COMPILER" 292836 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292033 292068 292166 "COMPFACT" 292274 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276055 286050 286090 "COMPCAT" 287094 NIL COMPCAT (NIL T) -9 NIL 288442 NIL) (-166 265567 268494 272121 "COMPCAT-" 272477 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265296 265324 265427 "COMMUPC" 265533 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265090 265124 265183 "COMMONOP" 265257 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264646 264841 264928 "COMM" 265023 T COMM (NIL) -8 NIL NIL NIL) (-162 264222 264450 264525 "COMMAAST" 264591 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263471 263665 263693 "COMBOPC" 264031 T COMBOPC (NIL) -9 NIL 264206 NIL) (-160 262367 262577 262819 "COMBINAT" 263261 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258824 259398 260025 "COMBF" 261789 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257582 257940 258175 "COLOR" 258609 T COLOR (NIL) -8 NIL NIL NIL) (-157 257058 257303 257395 "COLONAST" 257510 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256698 256745 256870 "CMPLXRT" 257005 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256146 256398 256497 "CLLCTAST" 256619 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251648 252676 253756 "CLIP" 255086 T CLIP (NIL) -7 NIL NIL NIL) (-153 249989 250749 250989 "CLIF" 251475 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246164 248135 248176 "CLAGG" 249105 NIL CLAGG (NIL T) -9 NIL 249641 NIL) (-151 244586 245043 245626 "CLAGG-" 245631 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244130 244215 244355 "CINTSLPE" 244495 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241631 242102 242650 "CHVAR" 243658 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240805 241359 241387 "CHARZ" 241392 T CHARZ (NIL) -9 NIL 241407 NIL) (-147 240559 240599 240677 "CHARPOL" 240759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239617 240204 240232 "CHARNZ" 240279 T CHARNZ (NIL) -9 NIL 240335 NIL) (-145 237523 238271 238624 "CHAR" 239284 T CHAR (NIL) -8 NIL NIL NIL) (-144 237249 237310 237338 "CFCAT" 237449 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236490 236601 236784 "CDEN" 237133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232455 235643 235923 "CCLASS" 236230 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231706 231863 232040 "CATEGORY" 232298 T -10 (NIL) -8 NIL NIL NIL) (-140 231279 231625 231673 "CATCTOR" 231678 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230730 230982 231080 "CATAST" 231201 T CATAST (NIL) -8 NIL NIL NIL) (-138 230206 230451 230543 "CASEAST" 230658 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225344 226363 227107 "CARTEN" 229518 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224452 224600 224821 "CARTEN2" 225191 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222768 223602 223859 "CARD" 224215 T CARD (NIL) -8 NIL NIL NIL) (-134 222344 222572 222647 "CAPSLAST" 222713 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221848 222056 222084 "CACHSET" 222216 T CACHSET (NIL) -9 NIL 222294 NIL) (-132 221318 221640 221668 "CABMON" 221718 T CABMON (NIL) -9 NIL 221774 NIL) (-131 220791 221022 221132 "BYTEORD" 221228 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219768 220320 220462 "BYTE" 220625 T BYTE (NIL) -8 NIL NIL 220747) (-129 215118 219273 219445 "BYTEBUF" 219616 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212627 214810 214917 "BTREE" 215044 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210076 212275 212397 "BTOURN" 212537 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207446 209546 209587 "BTCAT" 209655 NIL BTCAT (NIL T) -9 NIL 209732 NIL) (-125 207113 207193 207342 "BTCAT-" 207347 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202492 206372 206400 "BTAGG" 206514 T BTAGG (NIL) -9 NIL 206624 NIL) (-123 201982 202107 202313 "BTAGG-" 202318 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198977 201260 201475 "BSTREE" 201799 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198115 198241 198425 "BRILL" 198833 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194767 196841 196882 "BRAGG" 197531 NIL BRAGG (NIL T) -9 NIL 197789 NIL) (-119 193296 193702 194257 "BRAGG-" 194262 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186523 192640 192825 "BPADICRT" 193143 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184838 186460 186505 "BPADIC" 186510 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184536 184566 184680 "BOUNDZRO" 184802 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179764 180962 181874 "BOP" 183644 T BOP (NIL) -8 NIL NIL NIL) (-114 177545 177949 178424 "BOP1" 179322 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177246 177307 177335 "BOOLE" 177446 T BOOLE (NIL) -9 NIL 177528 NIL) (-112 176071 176820 176969 "BOOLEAN" 177117 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175350 175754 175808 "BMODULE" 175813 NIL BMODULE (NIL T T) -9 NIL 175878 NIL) (-110 171151 175148 175221 "BITS" 175297 T BITS (NIL) -8 NIL NIL NIL) (-109 170572 170691 170831 "BINDING" 171031 T BINDING (NIL) -8 NIL NIL NIL) (-108 164577 170167 170316 "BINARY" 170443 T BINARY (NIL) -8 NIL NIL NIL) (-107 162357 163832 163873 "BGAGG" 164133 NIL BGAGG (NIL T) -9 NIL 164270 NIL) (-106 162188 162220 162311 "BGAGG-" 162316 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161259 161572 161777 "BFUNCT" 162003 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159949 160127 160415 "BEZOUT" 161083 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156418 158801 159131 "BBTREE" 159652 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156152 156205 156233 "BASTYPE" 156352 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156004 156033 156106 "BASTYPE-" 156111 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155438 155514 155666 "BALFACT" 155915 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154294 154853 155039 "AUTOMOR" 155283 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154020 154025 154051 "ATTREG" 154056 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152272 152717 153069 "ATTRBUT" 153686 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151880 152100 152166 "ATTRAST" 152224 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151416 151529 151555 "ATRIG" 151756 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151225 151266 151353 "ATRIG-" 151358 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150870 151056 151082 "ASTCAT" 151087 T ASTCAT (NIL) -9 NIL 151117 NIL) (-92 150597 150656 150775 "ASTCAT-" 150780 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148746 150373 150461 "ASTACK" 150540 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147251 147548 147913 "ASSOCEQ" 148428 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146283 146910 147034 "ASP9" 147158 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146046 146231 146270 "ASP8" 146275 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144914 145651 145793 "ASP80" 145935 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143812 144549 144681 "ASP7" 144813 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142766 143489 143607 "ASP78" 143725 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141735 142446 142563 "ASP77" 142680 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140647 141373 141504 "ASP74" 141635 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139547 140282 140414 "ASP73" 140546 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138651 139373 139473 "ASP6" 139478 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137598 138328 138446 "ASP55" 138564 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136547 137272 137391 "ASP50" 137510 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135635 136248 136358 "ASP4" 136468 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134723 135336 135446 "ASP49" 135556 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133507 134262 134430 "ASP42" 134612 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132284 133040 133210 "ASP41" 133394 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131234 131961 132079 "ASP35" 132197 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130999 131182 131221 "ASP34" 131226 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130736 130803 130879 "ASP33" 130954 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129630 130371 130503 "ASP31" 130635 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129395 129578 129617 "ASP30" 129622 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129130 129199 129275 "ASP29" 129350 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128895 129078 129117 "ASP28" 129122 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128660 128843 128882 "ASP27" 128887 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127744 128358 128469 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105579 105627 105746 "APPLYORE" 105874 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104933 105172 105292 "ANY" 105477 T ANY (NIL) -8 NIL NIL NIL) (-51 104211 104334 104491 "ANY1" 104807 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101741 102648 102975 "ANTISYM" 103935 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101233 101448 101544 "ANON" 101663 T ANON (NIL) -8 NIL NIL NIL) (-48 95482 99772 100226 "AN" 100797 T AN (NIL) -8 NIL NIL NIL) (-47 91380 92768 92819 "AMR" 93567 NIL AMR (NIL T T) -9 NIL 94167 NIL) (-46 90492 90713 91076 "AMR-" 91081 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74931 90409 90470 "ALIST" 90475 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71736 74525 74694 "ALGSC" 74849 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68292 68846 69453 "ALGPKG" 71176 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67569 67670 67854 "ALGMFACT" 68178 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63604 64183 64777 "ALGMANIP" 67153 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54974 63230 63380 "ALGFF" 63537 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54170 54301 54480 "ALGFACT" 54832 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53111 53711 53749 "ALGEBRA" 53754 NIL ALGEBRA (NIL T) -9 NIL 53795 NIL) (-37 52829 52888 53020 "ALGEBRA-" 53025 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34892 50801 50853 "ALAGG" 50989 NIL ALAGG (NIL T T) -9 NIL 51150 NIL) (-35 34428 34541 34567 "AHYP" 34768 T AHYP (NIL) -9 NIL NIL NIL) (-34 33359 33607 33633 "AGG" 34132 T AGG (NIL) -9 NIL 34411 NIL) (-33 32793 32955 33169 "AGG-" 33174 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30599 31022 31427 "AF" 32435 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30079 30324 30414 "ADDAST" 30527 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29347 29606 29762 "ACPLOT" 29941 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26474 26512 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 436e055c..39dd22a9 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,466 +1,1007 @@ -(732471 . 3485464571) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1184 *3)) (-4 *3 (-356)) (-5 *1 (-364 *3))))) -(((*1 *2) - (-12 (-5 *2 (-2 (|:| -1534 (-652 *3)) (|:| -2300 (-652 *3)))) - (-5 *1 (-1230 *3)) (-4 *3 (-1111))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-697 (-415 (-572)))) - (-5 *2 - (-652 - (-2 (|:| |outval| *4) (|:| |outmult| (-572)) - (|:| |outvect| (-652 (-697 *4)))))) - (-5 *1 (-787 *4)) (-4 *4 (-13 (-370) (-856)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-779)) (-5 *2 (-1 (-1168 (-961 *4)) (-1168 (-961 *4)))) - (-5 *1 (-1287 *4)) (-4 *4 (-370))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1255 *5)) (-4 *5 (-370)) - (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) - (-5 *1 (-582 *5 *3))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-779)) (-5 *1 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(-652 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -4103 (-652 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2021 (-652 *7))))) (-5 *1 (-676 *5 *6 *7 *3)) (-5 *4 (-652 *7)) (-4 *3 (-695 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -11940,7 +14525,7 @@ (-4 *7 (-13 (-29 *6) (-1214) (-968))) (-4 *6 (-13 (-313) (-1049 (-572)) (-647 (-572)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1279 *7)) (|:| -4103 (-652 (-1279 *7))))) + (-2 (|:| |particular| (-1279 *7)) (|:| -2021 (-652 (-1279 *7))))) (-5 *1 (-810 *6 *7)) (-5 *4 (-1279 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-697 *6)) (-5 *4 (-1188)) @@ -11952,27 +14537,27 @@ (-5 *5 (-1188)) (-4 *7 (-13 (-29 *6) (-1214) (-968))) (-4 *6 (-13 (-313) (-1049 (-572)) (-647 (-572)) (-148))) (-5 *2 - (-2 (|:| |particular| (-1279 *7)) (|:| -4103 (-652 (-1279 *7))))) + (-2 (|:| |particular| (-1279 *7)) (|:| -2021 (-652 (-1279 *7))))) (-5 *1 (-810 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-652 *7)) (-5 *4 (-652 (-115))) (-5 *5 (-1188)) (-4 *7 (-13 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