diff options
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/mset.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/hyper/pages/releaseNotes.ht | 5 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1058 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 224 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 16 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 5732 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 2227 |
8 files changed, 4641 insertions, 4632 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 962dbffc..0695a22f 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,10 @@ 2013-05-17 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/mset.spad.pamphlet (Multiset) [unique]: Rename from + members to avoid semantics clash. + +2013-05-17 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/aggcat.spad.pamphlet: Replace uses of parts by members. 2013-05-17 Gabriel Dos Reis <gdr@integrable-solutions.net> diff --git a/src/algebra/mset.spad.pamphlet b/src/algebra/mset.spad.pamphlet index e4dd72e7..6fd60011 100644 --- a/src/algebra/mset.spad.pamphlet +++ b/src/algebra/mset.spad.pamphlet @@ -30,8 +30,8 @@ Multiset(S: SetCategory): Join(MultisetAggregate S,FiniteAggregate S,ShallowlyMu ++ multiset(s) creates a multiset with singleton s. multiset: List S -> % ++ multiset(ls) creates a multiset with elements from \spad{ls}. - members: % -> List S - ++ members(ms) returns a list of the elements of \spad{ms} + unique: % -> List S + ++ \spad{unique ms} returns a list of the elements of \spad{ms} ++ {\em without} their multiplicity. See also \spadfun{parts}. remove: (S,%,Integer) -> % ++ remove(x,ms,number) removes at most \spad{number} copies of @@ -99,7 +99,7 @@ Multiset(S: SetCategory): Join(MultisetAggregate S,FiniteAggregate S,ShallowlyMu convert [convert('multiset)@InputForm, convert(parts ms)@InputForm] - members(ms:%):List S == keys ms.table + unique(ms:%):List S == keys ms.table coerce(ms:%):OutputForm == l: List OutputForm := empty() diff --git a/src/hyper/pages/releaseNotes.ht b/src/hyper/pages/releaseNotes.ht index 2188cc87..2735563d 100644 --- a/src/hyper/pages/releaseNotes.ht +++ b/src/hyper/pages/releaseNotes.ht @@ -60,7 +60,10 @@ contains additions of new features and domains including: The category KeyedDictionary now extends EltableAggregate. The category TableAggregate now extends FiniteAggregate. - + + The operation members from Multiset has been renamed to unique, to + avoid semantics confusion with an operation of same name exported + by the domain FiniteAggregate. \endscroll \autobuttons diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 81be998a..52ed26e0 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(1962315 . 3577834557) +(1962312 . 3577838827) (-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 NIL (-19 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."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T)) +((-3994 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T)) NIL (-30) ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3093) +(-32 R -3094) ((|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| (QUOTE (-951 (-485))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -3996))) +((|HasAttribute| |#1| (QUOTE -3997))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -3093 UP UPUP -2615) +(-40 -3094 UP UPUP -2616) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) -(-41 R -3093) +(-41 R -3094) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-258)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) +((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-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."))) -((-3996 . T) (-3997 . T)) -((OR (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) +((-3997 . T) (-3998 . T)) +((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\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| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\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| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-3993 . T)) +((-3994 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -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 -3093) +(-54 |Base| R -3094) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -158,11 +158,11 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. 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.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -170,7 +170,7 @@ NIL NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-61 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) @@ -178,7 +178,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-312)))) (-62 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}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-63 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) @@ -202,11 +202,11 @@ NIL NIL (-68) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-3996 . T) ((-3998 "*") . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T)) +((-3997 . T) ((-3999 "*") . T) (-3994 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3993 . T) (-3996 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3984 . T)) NIL (-69 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-3993 . T)) +((-3994 . T)) NIL (-70 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -222,23 +222,23 @@ NIL NIL (-73 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-74 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 -((|HasAttribute| |#1| (QUOTE (-3998 "*")))) +((|HasAttribute| |#1| (QUOTE (-3999 "*")))) (-75 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) NIL NIL (-76 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) -((-3997 . T)) +((-3998 . T)) NIL (-77) ((|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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) (-78) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) @@ -254,11 +254,11 @@ NIL NIL (-81) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) (-82 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-83 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -280,22 +280,22 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-88 -3093 UP) +(-88 -3094 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 (-89 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-90 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-89 |#1|) (QUOTE (-934))) (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757)))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) (-91 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3998))) (-92 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -306,7 +306,7 @@ NIL NIL (-94 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"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-95 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) @@ -314,7 +314,7 @@ NIL NIL (-96) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-97 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) @@ -322,15 +322,15 @@ NIL NIL (-98 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-99 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-100 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."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-101) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) @@ -338,7 +338,7 @@ NIL NIL (-102) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (-103) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) @@ -358,13 +358,13 @@ NIL NIL (-107) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-3998 "*") . T)) +(((-3999 "*") . T)) NIL -(-108 |minix| -2622 R) +(-108 |minix| -2623 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) NIL NIL -(-109 |minix| -2622 S T$) +(-109 |minix| -2623 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -386,7 +386,7 @@ NIL NIL (-114) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3997 . T) (-3987 . T) (-3998 . T)) ((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (-115 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) @@ -402,7 +402,7 @@ NIL NIL (-118) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-3993 . T)) +((-3994 . T)) NIL (-119 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -410,9 +410,9 @@ NIL NIL (-120) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-3993 . T)) +((-3994 . T)) NIL -(-121 -3093 UP UPUP) +(-121 -3094 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 @@ -423,14 +423,14 @@ NIL (-123 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -3996))) +((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -3997))) (-124 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-125 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-3991 . T) (-3990 . T) (-3993 . T)) +((-3992 . T) (-3991 . T) (-3994 . T)) NIL (-126) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -452,7 +452,7 @@ 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 -(-131 R -3093) +(-131 R -3094) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -483,10 +483,10 @@ NIL (-138 S 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| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\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| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) +((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) (-139 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})"))) -((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-140 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."))) @@ -498,8 +498,8 @@ NIL NIL (-142 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}."))) -((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-974))) (-12 (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3995)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-147) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -522,7 +522,7 @@ NIL NIL (-148 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-149) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -576,7 +576,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-162 R -3093) +(-162 R -3094) ((|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 @@ -604,23 +604,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-169 -3093 UP UPUP R) +(-169 -3094 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 -(-170 -3093 FP) +(-170 -3094 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-171) ((|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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) (-172) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-173 R -3093) +(-173 R -3094) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -634,19 +634,19 @@ NIL NIL (-176 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-177 |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}."))) -((-3993 . T)) +((-3994 . T)) NIL -(-178 R -3093) +(-178 R -3094) ((|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 (-179) ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}."))) -((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-180) ((|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)}.}"))) @@ -654,19 +654,19 @@ NIL NIL (-181 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}"))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3998 . T) (-3997 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) (-182 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 NIL (-183 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."))) -((-3997 . T)) +((-3998 . T)) NIL (-184 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-3993 . T)) +((-3994 . T)) NIL (-185 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -678,7 +678,7 @@ NIL NIL (-187 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-188 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -690,7 +690,7 @@ NIL NIL (-190) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-3993 . T)) +((-3994 . T)) NIL (-191) ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) @@ -699,28 +699,28 @@ NIL (-192 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -3996))) +((|HasAttribute| |#1| (QUOTE -3997))) (-193 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-3997 . T)) +((-3998 . T)) NIL (-194) ((|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 -(-195 S -2622 R) +(-195 S -2623 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3993)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) -(-196 -2622 R) +((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) +(-196 -2623 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) -((-3990 |has| |#2| (-962)) (-3991 |has| |#2| (-962)) (-3993 |has| |#2| (-6 -3993)) (-3996 . T)) +((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . T)) NIL -(-197 -2622 R) +(-197 -2623 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."))) -((-3990 |has| |#2| (-962)) (-3991 |has| |#2| (-962)) (-3993 |has| |#2| (-6 -3993)) (-3996 . 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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 @@ -734,7 +734,7 @@ NIL NIL (-201) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-202 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -742,7 +742,7 @@ NIL NIL (-203 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}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-204 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'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}"))) @@ -750,12 +750,12 @@ NIL NIL (-205 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-206 |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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . 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T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-207) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) 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((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} := 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| (QUOTE (-190)))) (-213 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} := 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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-214 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|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}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-215 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -834,8 +834,8 @@ NIL NIL (-226 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"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#3| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#3| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#3| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#3| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#3| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#3| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-227 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.")) (|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 @@ -848,11 +848,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-230 R -3093) +(-230 R -3094) ((|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 -(-231 R -3093) +(-231 R -3094) ((|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 @@ -878,7 +878,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) (-237 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-3997 . T)) +((-3998 . T)) NIL (-238 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -899,14 +899,14 @@ NIL (-242 S |Dom| |Im|) ((|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!| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2| |#3|) "\\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| ((|#3| $ |#2|) "\\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| ((|#3| $ |#2| |#3|) "\\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 -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3998))) (-243 |Dom| |Im|) ((|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 -(-244 S R |Mod| -2038 -3519 |exactQuo|) +(-244 S R |Mod| -2038 -3520 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-245 S) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) @@ -914,7 +914,7 @@ NIL NIL (-246) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-247) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -926,7 +926,7 @@ NIL NIL (-249 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-3993 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3990 |has| |#1| (-962)) (-3991 |has| |#1| (-962))) +((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-962)) (-3992 |has| |#1| (-962))) ((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) (-250 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) @@ -934,8 +934,8 @@ NIL NIL (-251 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) (-252) ((|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 @@ -948,11 +948,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-255 -3093 S) +(-255 -3094 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 -(-256 E -3093) +(-256 E -3094) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -962,7 +962,7 @@ NIL NIL (-258) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-259 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -972,7 +972,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-261 -3093) +(-261 -3094) ((|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 @@ -986,11 +986,11 @@ NIL NIL (-264 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))}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-330)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) (-265 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."))) -((-3993 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) +((-3994 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) ((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) (-266 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}."))) @@ -1000,7 +1000,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-268 R -3093) +(-268 R -3094) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1010,8 +1010,8 @@ NIL NIL (-270 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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-271 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1022,7 +1022,7 @@ NIL NIL (-273 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-717)))) (-274 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1038,19 +1038,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) (-277 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-278 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."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-279 S -3093) +(-279 S -3094) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-320)))) -(-280 -3093) +(-280 -3094) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-281 E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) @@ -1060,7 +1060,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-283 -3093 UP UPUP R) +(-283 -3094 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1068,11 +1068,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-285 S -3093 UP UPUP R) +(-285 S -3094 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-286 -3093 UP UPUP R) +(-286 -3094 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1086,15 +1086,15 @@ NIL NIL (-289 |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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) -(-290 S -3093 UP UPUP) +(-290 S -3094 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-312)))) -(-291 -3093 UP UPUP) +(-291 -3094 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-292 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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}."))) @@ -1102,15 +1102,15 @@ NIL NIL (-293 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) (-294 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-295 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-296 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) @@ -1126,43 +1126,43 @@ NIL NIL (-299) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL -(-300 R UP -3093) +(-300 R UP -3094) ((|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 (-301 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) (-302 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-303 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-304 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-305 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-306 -3093 GF) +(-306 -3094 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-307 -3093 FP FPP) +(-307 -3094 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-308 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-309 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) @@ -1170,7 +1170,7 @@ NIL NIL (-310 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-3993 . T)) +((-3994 . T)) NIL (-311 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1178,7 +1178,7 @@ NIL NIL (-312) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-313 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1194,7 +1194,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-496)))) (-316 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) +((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) NIL (-317 A S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) @@ -1202,7 +1202,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-72)))) (-318 S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#1| $) "\\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| |#1|) $) "\\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})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\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|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds 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|) |#1|) $) "\\spad{any?(p,u)} tests if \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) -((-3996 . T)) +((-3997 . T)) NIL (-319 S) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1218,15 +1218,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) (-322 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-323 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) (-324 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-3996 . T)) +((-3997 . T)) NIL (-325 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1234,7 +1234,7 @@ NIL NIL (-326 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) NIL (-327 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1250,7 +1250,7 @@ NIL NIL (-330) ((|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}."))) -((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3980 . T) (-3988 . T) (-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-331 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1262,15 +1262,15 @@ NIL NIL (-333 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-334 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-146)))) (-335 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-336 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1290,13 +1290,13 @@ NIL NIL (-340 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL -(-341 -3093 UP UPUP R) +(-341 -3094 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-342 -3093 UP) +(-342 -3094 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1310,19 +1310,19 @@ NIL NIL (-345) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-346 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3987))) +((|HasAttribute| |#1| (QUOTE -3980)) (|HasAttribute| |#1| (QUOTE -3988))) (-347) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-348 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-456 (-1091) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-392)))) (-349 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."))) @@ -1330,8 +1330,8 @@ NIL NIL (-350 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-3983 -12 (|has| |#1| (-6 -3994)) (|has| |#1| (-392)) (|has| |#1| (-6 -3983))) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +((-3984 -12 (|has| |#1| (-6 -3995)) (|has| |#1| (-392)) (|has| |#1| (-6 -3984))) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-351 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1342,7 +1342,7 @@ NIL NIL (-353 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-354 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1352,15 +1352,15 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-356 R -3093 UP A) +(-356 R -3094 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-3993 . T)) +((-3994 . T)) NIL (-357 R1 F1 U1 A1 R2 F2 U2 A2) ((|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 -(-358 R -3093 UP A |ibasis|) +(-358 R -3094 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) @@ -1374,7 +1374,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-361 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\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."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) +((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) NIL (-362 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)}."))) @@ -1386,7 +1386,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (-364 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-3993 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) +((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) NIL (-365 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1406,33 +1406,33 @@ NIL ((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) (-369 S) ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3997 . T) (-3987 . T) (-3998 . T)) NIL (-370 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-371 R -3093) +(-371 R -3094) ((|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 (-372 R E) ((|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"))) -((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983)))) -(-373 R -3093) +((-3984 -12 (|has| |#1| (-6 -3984)) (|has| |#2| (-6 -3984))) (-3991 . T) (-3992 . T) (-3994 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#2| (QUOTE -3984)))) +(-373 R -3094) ((|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 -(-374 R -3093) +(-374 R -3094) ((|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 -(-375 R -3093) +(-375 R -3094) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-376 R -3093) +(-376 R -3094) ((|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 @@ -1440,7 +1440,7 @@ 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 -(-378 R -3093 UP) +(-378 R -3094 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| (QUOTE (-951 (-48))))) @@ -1460,7 +1460,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-383 R UP -3093) +(-383 R UP -3094) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1498,16 +1498,16 @@ NIL NIL (-392) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-393 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-3993 |has| (-350 (-858 |#1|)) (-496)) (-3991 . T) (-3990 . T)) +((-3994 |has| (-350 (-858 |#1|)) (-496)) (-3992 . T) (-3991 . T)) ((|HasCategory| (-350 (-858 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-350 (-858 |#1|)) (QUOTE (-496)))) (-394 |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"))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-395 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1534,7 +1534,7 @@ NIL NIL (-401 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-402 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1542,7 +1542,7 @@ NIL NIL (-403 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) (-404 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) @@ -1572,7 +1572,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-411 |lv| -3093 R) +(-411 |lv| -3094 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1582,23 +1582,23 @@ NIL NIL (-413) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-3993 . T)) +((-3994 . T)) NIL (-414 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . 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T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) (-416 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)}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) (-417) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-418) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1606,29 +1606,29 @@ NIL NIL (-419 |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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) (-420) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-421 |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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-422 -2622 S) +(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-422 -2623 S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. 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(|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) (-428 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 -((|HasAttribute| |#1| (QUOTE -3996)) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) +((|HasAttribute| |#1| (QUOTE -3997)) (|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-429 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|) |#1| $) "\\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| |#1|) $) "\\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| |#1|) $) "\\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|) |#1| $) "\\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|) |#1|) $) "\\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|) |#1|) $) "\\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|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1664,33 +1664,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-434 -3093 UP |AlExt| |AlPol|) +(-434 -3094 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-435) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) (-436 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-437 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-438 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 -(-439 R UP -3093) +(-439 R UP -3094) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-440 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) (-441 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1704,7 +1704,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-444 -3093 |Expon| |VarSet| |DPoly|) +(-444 -3094 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (QUOTE (-554 (-1091))))) @@ -1714,7 +1714,7 @@ NIL NIL (-446 T$) ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) -(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3057 (|f| |x| |x|) |x|))) . T)) +(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3058 (|f| |x| |x|) |x|))) . T)) NIL (-447) ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) @@ -1762,7 +1762,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-717)))) (-458 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-459) ((|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'."))) @@ -1770,16 +1770,16 @@ NIL NIL (-460 |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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-320)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-320))) (|HasCategory| (-518 |#1|) (QUOTE (-118)))) (-461 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -3997))) +((|HasAttribute| |#3| (QUOTE -3998))) (-462 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "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. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -3997))) +((|HasAttribute| |#7| (QUOTE -3998))) (-463) ((|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 @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) -(-471 K -3093 |Par|) +(-471 K -3094 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -1836,7 +1836,7 @@ 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 -(-477 K -3093 |Par|) +(-477 K -3094 |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 @@ -1866,11 +1866,11 @@ NIL NIL (-484) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-485) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-486) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -1890,13 +1890,13 @@ NIL NIL (-490 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) -(-491 R -3093) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +(-491 R -3094) ((|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 -(-492 R0 -3093 UP UPUP R) +(-492 R0 -3094 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 @@ -1906,7 +1906,7 @@ NIL NIL (-494 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-495 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."))) @@ -1914,9 +1914,9 @@ NIL NIL (-496) ((|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."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL -(-497 R -3093) +(-497 R -3094) ((|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|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#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 @@ -1924,7 +1924,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-499 R -3093 L) +(-499 R -3094 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| #1="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| #1#)) (|:| |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| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="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|)) #4#) |#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 -601) (|devaluate| |#2|)))) @@ -1932,23 +1932,23 @@ 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 -(-501 -3093 UP UPUP R) +(-501 -3094 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 -(-502 -3093 UP) +(-502 -3094 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 -(-503 R -3093 L) +(-503 R -3094 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| #1="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| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) -(-504 R -3093) +(-504 R -3094) ((|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| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-570))))) -(-505 -3093 UP) +(-505 -3094 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -1956,27 +1956,27 @@ 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 -(-507 -3093) +(-507 -3094) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-508 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."))) -((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-509) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-510 R -3093) +(-510 R -3094) ((|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| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496)))) -(-511 -3093 UP) +(-511 -3094 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|)) #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|)) #1#) |#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|)) #1#) |#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|)) #1#) |#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 -(-512 R -3093) +(-512 R -3094) ((|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 @@ -1998,25 +1998,25 @@ NIL NIL (-517 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-518 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) (-519) ((|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 -(-520 -3093) +(-520 -3094) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-951 (-1091))))) -(-521 E -3093) +(-521 E -3094) ((|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 -(-522 R -3093) +(-522 R -3094) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2054,11 +2054,11 @@ NIL NIL (-531 |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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) (-532 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-496)))) (-533) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2072,7 +2072,7 @@ 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 -(-536 R -3093 FG) +(-536 R -3094 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2083,7 +2083,7 @@ NIL (-538 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 -((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#3| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#3| (QUOTE (-1014)))) (-539 |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|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\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| ((|#1| $) "\\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| ((|#1| $) "\\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|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2094,7 +2094,7 @@ NIL NIL (-541 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) +((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) ((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-542) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) @@ -2122,15 +2122,15 @@ NIL NIL (-548 |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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (-549 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 NIL (-550 |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| |#2| "failed") |#1| $) "\\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| |#2| "failed") |#1| $) "\\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| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-3997 . T)) +((-3998 . T)) NIL (-551 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) @@ -2148,7 +2148,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-555 -3093 UP) +(-555 -3094 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2166,7 +2166,7 @@ NIL NIL (-559 A R S) ((|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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-756)))) (-560 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) @@ -2174,15 +2174,15 @@ NIL NIL (-561 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-3993 . T)) +((-3994 . T)) NIL -(-562 R -3093) +(-562 R -3094) ((|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 (-563 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T)) +((-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3994 . T)) ((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (-564 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\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 \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) @@ -2198,13 +2198,13 @@ NIL NIL (-567 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-3993 . T)) +((-3994 . T)) NIL (-568 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-569 R -3093) +(-569 R -3094) ((|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 @@ -2212,17 +2212,17 @@ 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 -(-571 |lv| -3093) +(-571 |lv| -3094) ((|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 (-572) ((|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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773))))) (-573 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)."))) -((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) +((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) ((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-574 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) @@ -2230,7 +2230,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-575 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) NIL (-576 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|) #1="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|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) @@ -2247,10 +2247,10 @@ NIL (-579 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2561 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) +((-2562 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) (-580 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-578 |#2|) (QUOTE (-1014))))) (-581 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) @@ -2258,7 +2258,7 @@ NIL NIL (-582 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-583 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2266,7 +2266,7 @@ NIL NIL (-584 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. 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."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-585 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) @@ -2290,7 +2290,7 @@ NIL NIL (-590 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72)))) (-591 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) @@ -2303,30 +2303,30 @@ NIL (-593 A S) ((|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| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\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{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}..) )}.") (($ |#2| $ (|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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3998))) (-594 S) ((|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{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{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}) == 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| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL (-595 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) ((|HasCategory| |#1| (QUOTE (-715)))) -(-596 R -3093 L) +(-596 R -3094 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 -(-597 A -2493) +(-597 A -2494) ((|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}}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) (-598 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) (-599 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) (-600 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2334,9 +2334,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-601 A) ((|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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL -(-602 -3093 UP) +(-602 -3094 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)))) @@ -2358,7 +2358,7 @@ NIL NIL (-607 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) (-608 A S) ((|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| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2366,13 +2366,13 @@ NIL NIL (-609 S) ((|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}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL -(-610 -3093 |Row| |Col| M) +(-610 -3094 |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| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |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| #1#)) (|:| |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 -(-611 -3093) +(-611 -3094) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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 @@ -2382,8 +2382,8 @@ NIL NIL (-613 |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."))) -((-3993 . T) (-3996 . T) (-3990 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +((-3994 . T) (-3997 . T) (-3991 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) (-614) ((|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 @@ -2439,10 +2439,10 @@ NIL (-627 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. 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.")) (|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.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) NIL -((|HasAttribute| |#2| (QUOTE (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496)))) +((|HasAttribute| |#2| (QUOTE (-3999 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496)))) (-628 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. 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.")) (|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.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) @@ -2454,8 +2454,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496)))) (-631 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."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3998 . T) (-3997 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-632 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2470,7 +2470,7 @@ NIL NIL (-635 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-3997 . T)) +((-3998 . T)) NIL (-636 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2480,7 +2480,7 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-638 OV E -3093 PG) +(-638 OV E -3094 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL @@ -2504,7 +2504,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-644 S -2670 I) +(-644 S -2671 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2514,7 +2514,7 @@ NIL NIL (-646 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-647 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2524,25 +2524,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-649 R |Mod| -2038 -3519 |exactQuo|) +(-649 R |Mod| -2038 -3520 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-650 R P) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-651 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-652 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-653 R |Mod| -2038 -3519 |exactQuo|) +(-653 R |Mod| -2038 -3520 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-3993 . T)) +((-3994 . T)) NIL (-654 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2550,11 +2550,11 @@ NIL NIL (-655 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL -(-656 -3093) +(-656 -3094) ((|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]]}."))) -((-3993 . T)) +((-3994 . T)) NIL (-657 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2578,7 +2578,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320)))) (-662 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-663 S) ((|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| (($) "1 is the multiplicative identity."))) @@ -2590,13 +2590,13 @@ NIL NIL (-665 T$) ((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL (-666 T$) ((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-667 -3093 UP) +(-667 -3094 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 @@ -2614,8 +2614,8 @@ NIL NIL (-671 |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."))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-672 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2630,15 +2630,15 @@ NIL NIL (-675 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757)))) (-676 S) -((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) +((-3997 . T) (-3987 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-677 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-3986 . T) (-3997 . T)) +((-3987 . T) (-3998 . T)) NIL (-678) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) @@ -2650,7 +2650,7 @@ NIL NIL (-680 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|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}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-681 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2666,7 +2666,7 @@ NIL NIL (-684 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-685 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) @@ -2688,11 +2688,11 @@ 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 -(-690 -3093) +(-690 -3094) ((|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 -(-691 P -3093) +(-691 P -3094) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL @@ -2700,7 +2700,7 @@ NIL NIL NIL NIL -(-693 UP -3093) +(-693 UP -3094) ((|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 @@ -2710,9 +2710,9 @@ NIL NIL (-695) ((|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."))) -(((-3998 "*") . T)) +(((-3999 "*") . T)) NIL -(-696 R -3093) +(-696 R -3094) ((|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 @@ -2732,7 +2732,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-701 -3093 |ExtF| |SUEx| |ExtP| |n|) +(-701 -3094 |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 @@ -2746,12 +2746,12 @@ NIL NIL (-704 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . 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T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-2562 (|HasCategory| |#1| (QUOTE (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-905 (-485))))))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-705 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-706 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 @@ -2762,7 +2762,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-708 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular 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} \\indented{1}{[2] \\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)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\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.}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-709 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -2814,7 +2814,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) (-721 R) ((|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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-722) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -2822,67 +2822,67 @@ NIL NIL (-723 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (-724 OR R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-725 R -3093 L) +(-725 R -3094 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-726 R -3093) +(-726 R -3094) ((|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| #1="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| #1#) (|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| #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| #2#) (|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 -(-727 R -3093) +(-727 R -3094) ((|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 -(-728 -3093 UP UPUP R) +(-728 -3094 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 -(-729 -3093 UP L LQ) +(-729 -3094 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL -(-730 -3093 UP L LQ) +(-730 -3094 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-731 -3093 UP) +(-731 -3094 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|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-732 -3093 L UP A LO) +(-732 -3094 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 -(-733 -3093 UP) +(-733 -3094 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-734 -3093 LO) +(-734 -3094 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 -(-735 -3093 LODO) +(-735 -3094 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. 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(-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (-737 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-738 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-3998 "*") |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 . T) (-3991 . T) (-3990 . T)) +(((-3999 "*") |has| |#2| (-312)) (-3990 |has| |#2| (-312)) (-3995 |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 . T) (-3992 . T) (-3991 . T)) ((|HasCategory| |#2| (QUOTE (-312)))) (-739 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -2894,19 +2894,19 @@ NIL ((|HasCategory| |#1| (QUOTE (-757)))) (-741) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-742 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' 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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) (-743 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3997 . T) (-3987 . T) (-3998 . T)) NIL (-744 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."))) -((-3993 |has| |#1| (-756))) +((-3994 |has| |#1| (-756))) ((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) (-745 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) @@ -2914,7 +2914,7 @@ NIL NIL (-746 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) (-747 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}."))) @@ -2934,7 +2934,7 @@ NIL NIL (-751 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-3993 |has| |#1| (-756))) +((-3994 |has| |#1| (-756))) ((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) (-752 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) @@ -2944,7 +2944,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-754 -2622 S) +(-754 -2623 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 @@ -2954,7 +2954,7 @@ NIL NIL (-756) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-3993 . T)) +((-3994 . T)) NIL (-757) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) @@ -2978,19 +2978,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) (-762 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(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 right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes 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}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(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.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\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| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} 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''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(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}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-763 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) -(-764 R |sigma| -3245) +(-764 R |sigma| -3246) ((|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."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) -(-765 |x| R |sigma| -3245) +(-765 |x| R |sigma| -3246) ((|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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) (-766 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) @@ -3034,7 +3034,7 @@ NIL NIL (-776 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (-777 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3046,19 +3046,19 @@ NIL NIL (-779 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-780 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-781 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-1067))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-258))) (|HasCategory| (-779 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))))) (-782 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-783 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) @@ -3123,7 +3123,7 @@ NIL (-798 |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 (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2561 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) +((-12 (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2562 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-799 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL @@ -3136,7 +3136,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) (|One| (($) "1")) (|Zero| (($) "0"))) NIL NIL -(-802 R -2670) +(-802 R -2671) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3160,17 +3160,17 @@ NIL ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-808 UP -3093) +(-808 UP -3094) ((|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 (-809 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-810 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3993 . T)) +((-3994 . T)) NIL (-811 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) @@ -3186,7 +3186,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-814 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-3993 . T)) +((-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) (-815 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) @@ -3194,7 +3194,7 @@ NIL NIL (-816 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not 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.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(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."))) -((-3993 . T)) +((-3994 . T)) NIL (-817 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3202,7 +3202,7 @@ NIL NIL (-818 |p|) ((|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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) (-819 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."))) @@ -3218,9 +3218,9 @@ NIL ((|HasCategory| |#1| (QUOTE (-118)))) (-822) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL -(-823 R0 -3093 UP UPUP R) +(-823 R0 -3094 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 @@ -3234,7 +3234,7 @@ NIL NIL (-826 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-827 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3248,13 +3248,13 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-830 -3093) +(-830 -3094) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL (-831) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-3998 "*") . T)) +(((-3999 "*") . T)) NIL (-832 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) @@ -3262,13 +3262,13 @@ NIL NIL (-833) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL -(-834 |xx| -3093) +(-834 |xx| -3094) ((|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 -(-835 -3093 P) +(-835 -3094 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3296,7 +3296,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-842 R -3093) +(-842 R -3094) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3304,7 +3304,7 @@ 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 -(-844 S R -3093) +(-844 S R -3094) ((|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 @@ -3324,11 +3324,11 @@ 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 -797) (|devaluate| |#1|)))) -(-849 -2670) +(-849 -2671) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-850 R -3093 -2670) +(-850 R -3094 -2671) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3350,7 +3350,7 @@ NIL NIL (-855 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-856 |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}."))) @@ -3362,8 +3362,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-756)))) (-858 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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1091) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1091) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-859 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3375,12 +3375,12 @@ NIL (-861 S R E |VarSet|) ((|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| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\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.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\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| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |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| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|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| $)) $ $ |#4|) "\\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| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\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| |#4| "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| |#2|) $) "\\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| $) $ |#4|) "\\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| |#4|) (|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)}.") (($ $ |#4| (|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| |#4|)) "\\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|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) +((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (-862 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL -(-863 E V R P -3093) +(-863 E V R P -3094) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3388,7 +3388,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-865 E V R P -3093) +(-865 E V R P -3094) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-392)))) @@ -3402,15 +3402,15 @@ NIL NIL (-868 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) (-869 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL (-870 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-871 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -3420,7 +3420,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-873 -3093) +(-873 -3094) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3434,7 +3434,7 @@ NIL NIL (-876 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"))) -((-3993 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) +((-3994 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) ((OR (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-877) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) @@ -3458,7 +3458,7 @@ NIL NIL (-882 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-883 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3478,7 +3478,7 @@ NIL NIL (-887 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-888) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3490,7 +3490,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-496)))) (-890 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-3996 . T)) +((-3997 . T)) NIL (-891 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) @@ -3506,7 +3506,7 @@ NIL NIL (-894 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-895 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3524,7 +3524,7 @@ 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 -(-899 K R UP -3093) +(-899 K R UP -3094) ((|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 @@ -3550,7 +3550,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) (-905 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-906 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) @@ -3566,11 +3566,11 @@ NIL NIL (-909 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-910 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.}"))) -((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484)))) (-911 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3578,7 +3578,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-246)))) (-912 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-913 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3586,7 +3586,7 @@ NIL NIL (-914 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-915 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) @@ -3596,13 +3596,13 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-917 -3093 UP UPUP |radicnd| |n|) +(-917 -3094 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (-918 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) (-919) ((|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}."))) @@ -3623,7 +3623,7 @@ NIL (-923 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-1014)))) (-924 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -3634,21 +3634,21 @@ NIL NIL (-926) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) +((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) NIL -(-927 R -3093) +(-927 R -3094) ((|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 -(-928 R -3093) +(-928 R -3094) ((|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 -(-929 -3093 UP) +(-929 -3094 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 -(-930 -3093 UP) +(-930 -3094 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 @@ -3682,9 +3682,9 @@ NIL NIL (-938 |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"))) -((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) +((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) ((OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) -(-939 -3093 L) +(-939 -3094 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 @@ -3694,7 +3694,7 @@ NIL NIL (-941 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) (-942) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) @@ -3703,7 +3703,7 @@ NIL (-943 R) ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-3998 "*")))) +((|HasAttribute| |#1| (QUOTE (-3999 "*")))) (-944 R) ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -3720,9 +3720,9 @@ 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 -(-948 -3093 |Expon| |VarSet| |FPol| |LFPol|) +(-948 -3094 |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"))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-949) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) @@ -3766,7 +3766,7 @@ NIL NIL (-959 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) (-960) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) @@ -3778,9 +3778,9 @@ NIL NIL (-962) ((|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."))) -((-3993 . T)) +((-3994 . T)) NIL -(-963 |xx| -3093) +(-963 |xx| -3094) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3794,11 +3794,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146)))) (-966 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) -((-3996 . T) (-3991 . T) (-3990 . T)) +((-3997 . T) (-3992 . T) (-3991 . T)) NIL (-967 |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}."))) -((-3996 . T) (-3991 . T) (-3990 . T)) +((-3997 . T) (-3992 . T) (-3991 . T)) ((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) (-968 |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}."))) @@ -3826,7 +3826,7 @@ NIL NIL (-974) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-975 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -3834,7 +3834,7 @@ NIL NIL (-976) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-977 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) @@ -3842,7 +3842,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-905 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-1091))))) (-978 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\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}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\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.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\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}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\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| (($ $ |#3|) "\\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| ((|#3| $) "\\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}}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-979) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -3866,7 +3866,7 @@ NIL NIL (-984 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\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)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-985 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\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.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -3880,7 +3880,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-988 |Base| R -3093) +(-988 |Base| R -3094) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -3888,7 +3888,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-990 |Base| R -3093) +(-990 |Base| R -3094) ((|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 @@ -3898,7 +3898,7 @@ NIL NIL (-992 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."))) -((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (-993 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) @@ -3930,8 +3930,8 @@ NIL NIL (-1000 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"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-1001 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -3970,7 +3970,7 @@ NIL NIL (-1010 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)}}"))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3997 . T) (-3987 . T) (-3998 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-1011 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3978,7 +3978,7 @@ NIL NIL (-1012 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-3986 . T)) +((-3987 . T)) NIL (-1013 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4014,7 +4014,7 @@ NIL NIL (-1021 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\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}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-1022) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4022,11 +4022,11 @@ NIL NIL (-1023 T$) ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL (-1024 T$) ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL (-1025 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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(-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (-1028 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4052,7 +4052,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1031 R -3093) +(-1031 R -3094) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) |#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|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4066,23 +4066,23 @@ NIL NIL (-1034) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1035 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-1036 S) ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) -((-3997 . T)) +((-3998 . T)) NIL (-1037 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) +((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3999 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) (-1038 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) -((-3996 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3997 . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1039 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4090,17 +4090,17 @@ NIL NIL (-1040 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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-1041 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) (-1042 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}"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL -(-1043 UP -3093) +(-1043 UP -3094) ((|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 @@ -4154,19 +4154,19 @@ NIL NIL (-1056 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72)))) (-1057 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3996 . T) (-3990 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +((-3994 . T) (-3986 |has| |#2| (-6 (-3999 "*"))) (-3997 . T) (-3991 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) (-1058 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1059) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-1060 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4174,7 +4174,7 @@ NIL NIL (-1061 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) (-1062) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) @@ -4182,7 +4182,7 @@ NIL NIL (-1063 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}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-1064 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) @@ -4194,8 +4194,8 @@ NIL NIL (-1066 |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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) (-1067) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4210,7 +4210,7 @@ NIL NIL (-1070 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."))) -((-3997 . T)) +((-3998 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72)))) (-1071 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) @@ -4226,12 +4226,12 @@ NIL NIL (-1074) ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (-1075 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773))))) (-1076 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4262,9 +4262,9 @@ NIL NIL (-1083 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-3998 "*") OR (-2563 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-741))) (|has| |#1| (-146)) (-2563 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-822)))) (-3989 OR (-2563 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-741))) (|has| |#1| (-496)) (-2563 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-822)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . 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T)) +((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-1087 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| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4286,12 +4286,12 @@ NIL NIL (-1089 |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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1090 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1091) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL @@ -4302,8 +4302,8 @@ NIL NIL (-1093 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . 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T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) (-1094) ((|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| #1="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| #1#))) "\\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| #1#))) "\\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| #1#)) $) "\\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 @@ -4342,8 +4342,8 @@ NIL NIL (-1103 |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}"))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3997 . T) (-3998 . T)) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) (-1104 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4362,7 +4362,7 @@ NIL NIL (-1108 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}."))) -((-3996 . T) (-3997 . T)) +((-3997 . T) (-3998 . T)) NIL (-1109 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4398,7 +4398,7 @@ NIL NIL (-1117 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) (-1118 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) @@ -4408,7 +4408,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1120 R -3093) +(-1120 R -3094) ((|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 @@ -4416,13 +4416,13 @@ 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 -(-1122 R -3093) +(-1122 R -3094) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) (-1123 |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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) (-1124 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) @@ -4430,7 +4430,7 @@ NIL ((|HasCategory| |#4| (QUOTE (-320)))) (-1125 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-1126 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}."))) @@ -4444,7 +4444,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) -(-1129 -3093) +(-1129 -3094) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4470,7 +4470,7 @@ NIL NIL (-1135) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1136) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4490,15 +4490,15 @@ NIL NIL (-1140 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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"\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL (-1142 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent 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 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1143 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) @@ -4506,12 +4506,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-1144 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1145 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4526,8 +4526,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-756)))) (-1149 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4554,7 +4554,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067)))) (-1156 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-1157 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."))) @@ -4563,10 +4563,10 @@ NIL (-1158 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) +((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) (-1159 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1160 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4574,15 +4574,15 @@ NIL NIL (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1162 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL (-1163 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux 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),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and 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 and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1164 S |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) @@ -4590,28 +4590,28 @@ NIL NIL (-1165 |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1166 |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)}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-1167 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((-3998 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3990 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) ((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) (-1168 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3998))) (-1169 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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!| ((|#1| $ |#1|) "\\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| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\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| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "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}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL (-1170 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) (-1171 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -4619,16 +4619,16 @@ NIL (-1172 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| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) +((|HasCategory| |#2| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) (-1173 |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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1174 |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 -(-1175 -3093 UP L UTS) +(-1175 -3094 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 (-496)))) @@ -4646,11 +4646,11 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1179 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) NIL (-1180 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-1181 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4682,13 +4682,13 @@ NIL NIL (-1188 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-3991 . T) (-3990 . T)) +((-3992 . T) (-3991 . T)) NIL (-1189 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1190 K R UP -3093) +(-1190 K R UP -3094) ((|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 @@ -4702,56 +4702,56 @@ NIL NIL (-1193 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (-1194 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. 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. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-3997 . T) (-3996 . T)) +((-3998 . T) (-3997 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) (-1195 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1196 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) +((-3994 . T) (-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3990))) (-1197 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1198 S -3093) +(-1198 S -3094) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) -(-1199 -3093) +(-1199 -3094) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL (-1200 |vl| R) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) +((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-1201 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-350 (-485))))) (|HasAttribute| |#2| (QUOTE -3989))) +((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-350 (-485))))) (|HasAttribute| |#2| (QUOTE -3990))) (-1202 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989))) +((-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3990))) (-1203 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) +((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) NIL (-1204 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989))) +((-3994 . T) (-3995 |has| |#1| (-6 -3995)) (-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3990))) (-1205 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) +((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3990))) (-1206) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL @@ -4770,7 +4770,7 @@ NIL NIL (-1210 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) NIL NIL NIL @@ -4788,4 +4788,4 @@ NIL NIL NIL NIL -((-3 NIL 1962295 1962300 1962305 1962310) (-2 NIL 1962275 1962280 1962285 1962290) (-1 NIL 1962255 1962260 1962265 1962270) (0 NIL 1962235 1962240 1962245 1962250) (-1210 "ZMOD.spad" 1962044 1962057 1962173 1962230) (-1209 "ZLINDEP.spad" 1961142 1961153 1962034 1962039) (-1208 "ZDSOLVE.spad" 1951103 1951125 1961132 1961137) (-1207 "YSTREAM.spad" 1950598 1950609 1951093 1951098) (-1206 "YDIAGRAM.spad" 1950232 1950241 1950588 1950593) (-1205 "XRPOLY.spad" 1949452 1949472 1950088 1950157) (-1204 "XPR.spad" 1947247 1947260 1949170 1949269) (-1203 "XPOLYC.spad" 1946566 1946582 1947173 1947242) (-1202 "XPOLY.spad" 1946121 1946132 1946422 1946491) (-1201 "XPBWPOLY.spad" 1944592 1944612 1945927 1945996) (-1200 "XFALG.spad" 1941640 1941656 1944518 1944587) (-1199 "XF.spad" 1940103 1940118 1941542 1941635) (-1198 "XF.spad" 1938546 1938563 1939987 1939992) (-1197 "XEXPPKG.spad" 1937805 1937831 1938536 1938541) (-1196 "XDPOLY.spad" 1937419 1937435 1937661 1937730) (-1195 "XALG.spad" 1937087 1937098 1937375 1937414) (-1194 "WUTSET.spad" 1933090 1933107 1936721 1936748) (-1193 "WP.spad" 1932297 1932341 1932948 1933015) (-1192 "WHILEAST.spad" 1932095 1932104 1932287 1932292) (-1191 "WHEREAST.spad" 1931766 1931775 1932085 1932090) (-1190 "WFFINTBS.spad" 1929429 1929451 1931756 1931761) (-1189 "WEIER.spad" 1927651 1927662 1929419 1929424) (-1188 "VSPACE.spad" 1927324 1927335 1927619 1927646) (-1187 "VSPACE.spad" 1927017 1927030 1927314 1927319) (-1186 "VOID.spad" 1926694 1926703 1927007 1927012) (-1185 "VIEWDEF.spad" 1921895 1921904 1926684 1926689) (-1184 "VIEW3D.spad" 1905856 1905865 1921885 1921890) (-1183 "VIEW2D.spad" 1893755 1893764 1905846 1905851) (-1182 "VIEW.spad" 1891475 1891484 1893745 1893750) (-1181 "VECTOR2.spad" 1890114 1890127 1891465 1891470) (-1180 "VECTOR.spad" 1888833 1888844 1889084 1889111) (-1179 "VECTCAT.spad" 1886745 1886756 1888801 1888828) (-1178 "VECTCAT.spad" 1884466 1884479 1886524 1886529) (-1177 "VARIABLE.spad" 1884246 1884261 1884456 1884461) (-1176 "UTYPE.spad" 1883890 1883899 1884236 1884241) (-1175 "UTSODETL.spad" 1883185 1883209 1883846 1883851) (-1174 "UTSODE.spad" 1881401 1881421 1883175 1883180) (-1173 "UTSCAT.spad" 1878880 1878896 1881299 1881396) (-1172 "UTSCAT.spad" 1876027 1876045 1878448 1878453) (-1171 "UTS2.spad" 1875622 1875657 1876017 1876022) (-1170 "UTS.spad" 1870634 1870662 1874154 1874251) (-1169 "URAGG.spad" 1865355 1865366 1870624 1870629) (-1168 "URAGG.spad" 1860040 1860053 1865311 1865316) (-1167 "UPXSSING.spad" 1857808 1857834 1859244 1859377) (-1166 "UPXSCONS.spad" 1855626 1855646 1855999 1856148) (-1165 "UPXSCCA.spad" 1854197 1854217 1855472 1855621) (-1164 "UPXSCCA.spad" 1852910 1852932 1854187 1854192) (-1163 "UPXSCAT.spad" 1851499 1851515 1852756 1852905) (-1162 "UPXS2.spad" 1851042 1851095 1851489 1851494) (-1161 "UPXS.spad" 1848397 1848425 1849233 1849382) (-1160 "UPSQFREE.spad" 1846812 1846826 1848387 1848392) (-1159 "UPSCAT.spad" 1844607 1844631 1846710 1846807) (-1158 "UPSCAT.spad" 1842103 1842129 1844208 1844213) (-1157 "UPOLYC2.spad" 1841574 1841593 1842093 1842098) (-1156 "UPOLYC.spad" 1836654 1836665 1841416 1841569) (-1155 "UPOLYC.spad" 1831652 1831665 1836416 1836421) (-1154 "UPMP.spad" 1830584 1830597 1831642 1831647) (-1153 "UPDIVP.spad" 1830149 1830163 1830574 1830579) (-1152 "UPDECOMP.spad" 1828410 1828424 1830139 1830144) (-1151 "UPCDEN.spad" 1827627 1827643 1828400 1828405) (-1150 "UP2.spad" 1826991 1827012 1827617 1827622) (-1149 "UP.spad" 1824461 1824476 1824848 1825001) (-1148 "UNISEG2.spad" 1823958 1823971 1824417 1824422) (-1147 "UNISEG.spad" 1823311 1823322 1823877 1823882) (-1146 "UNIFACT.spad" 1822414 1822426 1823301 1823306) (-1145 "ULSCONS.spad" 1816260 1816280 1816630 1816779) (-1144 "ULSCCAT.spad" 1813997 1814017 1816106 1816255) (-1143 "ULSCCAT.spad" 1811842 1811864 1813953 1813958) (-1142 "ULSCAT.spad" 1810082 1810098 1811688 1811837) (-1141 "ULS2.spad" 1809596 1809649 1810072 1810077) (-1140 "ULS.spad" 1801629 1801657 1802574 1802997) (-1139 "UINT8.spad" 1801506 1801515 1801619 1801624) (-1138 "UINT64.spad" 1801382 1801391 1801496 1801501) (-1137 "UINT32.spad" 1801258 1801267 1801372 1801377) (-1136 "UINT16.spad" 1801134 1801143 1801248 1801253) (-1135 "UFD.spad" 1800199 1800208 1801060 1801129) (-1134 "UFD.spad" 1799326 1799337 1800189 1800194) (-1133 "UDVO.spad" 1798207 1798216 1799316 1799321) (-1132 "UDPO.spad" 1795788 1795799 1798163 1798168) (-1131 "TYPEAST.spad" 1795707 1795716 1795778 1795783) (-1130 "TYPE.spad" 1795639 1795648 1795697 1795702) (-1129 "TWOFACT.spad" 1794291 1794306 1795629 1795634) (-1128 "TUPLE.spad" 1793798 1793809 1794203 1794208) (-1127 "TUBETOOL.spad" 1790665 1790674 1793788 1793793) (-1126 "TUBE.spad" 1789312 1789329 1790655 1790660) (-1125 "TSETCAT.spad" 1777383 1777400 1789280 1789307) (-1124 "TSETCAT.spad" 1765440 1765459 1777339 1777344) (-1123 "TS.spad" 1764068 1764084 1765034 1765131) (-1122 "TRMANIP.spad" 1758432 1758449 1763756 1763761) (-1121 "TRIMAT.spad" 1757395 1757420 1758422 1758427) (-1120 "TRIGMNIP.spad" 1755922 1755939 1757385 1757390) (-1119 "TRIGCAT.spad" 1755434 1755443 1755912 1755917) (-1118 "TRIGCAT.spad" 1754944 1754955 1755424 1755429) (-1117 "TREE.spad" 1753584 1753595 1754616 1754643) (-1116 "TRANFUN.spad" 1753423 1753432 1753574 1753579) (-1115 "TRANFUN.spad" 1753260 1753271 1753413 1753418) (-1114 "TOPSP.spad" 1752934 1752943 1753250 1753255) (-1113 "TOOLSIGN.spad" 1752597 1752608 1752924 1752929) (-1112 "TEXTFILE.spad" 1751158 1751167 1752587 1752592) (-1111 "TEX1.spad" 1750714 1750725 1751148 1751153) (-1110 "TEX.spad" 1747908 1747917 1750704 1750709) (-1109 "TBCMPPK.spad" 1746009 1746032 1747898 1747903) (-1108 "TBAGG.spad" 1745252 1745275 1745977 1746004) (-1107 "TBAGG.spad" 1744515 1744540 1745242 1745247) (-1106 "TANEXP.spad" 1743923 1743934 1744505 1744510) (-1105 "TALGOP.spad" 1743647 1743658 1743913 1743918) (-1104 "TABLEAU.spad" 1743128 1743139 1743637 1743642) (-1103 "TABLE.spad" 1741403 1741426 1741673 1741700) (-1102 "TABLBUMP.spad" 1738182 1738193 1741393 1741398) (-1101 "SYSTEM.spad" 1737410 1737419 1738172 1738177) (-1100 "SYSSOLP.spad" 1734893 1734904 1737400 1737405) (-1099 "SYSPTR.spad" 1734792 1734801 1734883 1734888) (-1098 "SYSNNI.spad" 1734015 1734026 1734782 1734787) (-1097 "SYSINT.spad" 1733419 1733430 1734005 1734010) (-1096 "SYNTAX.spad" 1729753 1729762 1733409 1733414) (-1095 "SYMTAB.spad" 1727821 1727830 1729743 1729748) (-1094 "SYMS.spad" 1723850 1723859 1727811 1727816) (-1093 "SYMPOLY.spad" 1722983 1722994 1723065 1723192) (-1092 "SYMFUNC.spad" 1722484 1722495 1722973 1722978) (-1091 "SYMBOL.spad" 1719979 1719988 1722474 1722479) (-1090 "SUTS.spad" 1717092 1717120 1718511 1718608) (-1089 "SUPXS.spad" 1714434 1714462 1715283 1715432) (-1088 "SUPFRACF.spad" 1713539 1713557 1714424 1714429) (-1087 "SUP2.spad" 1712931 1712944 1713529 1713534) (-1086 "SUP.spad" 1710015 1710026 1710788 1710941) (-1085 "SUMRF.spad" 1708989 1709000 1710005 1710010) (-1084 "SUMFS.spad" 1708618 1708635 1708979 1708984) (-1083 "SULS.spad" 1700638 1700666 1701596 1702019) (-1082 "syntax.spad" 1700407 1700416 1700628 1700633) (-1081 "SUCH.spad" 1700097 1700112 1700397 1700402) (-1080 "SUBSPACE.spad" 1692228 1692243 1700087 1700092) (-1079 "SUBRESP.spad" 1691398 1691412 1692184 1692189) (-1078 "STTFNC.spad" 1687866 1687882 1691388 1691393) (-1077 "STTF.spad" 1683965 1683981 1687856 1687861) (-1076 "STTAYLOR.spad" 1676642 1676653 1683872 1683877) (-1075 "STRTBL.spad" 1675029 1675046 1675178 1675205) (-1074 "STRING.spad" 1673897 1673906 1674282 1674309) (-1073 "STREAM3.spad" 1673470 1673485 1673887 1673892) (-1072 "STREAM2.spad" 1672598 1672611 1673460 1673465) (-1071 "STREAM1.spad" 1672304 1672315 1672588 1672593) (-1070 "STREAM.spad" 1669300 1669311 1671907 1671922) (-1069 "STINPROD.spad" 1668236 1668252 1669290 1669295) (-1068 "STEPAST.spad" 1667470 1667479 1668226 1668231) (-1067 "STEP.spad" 1666787 1666796 1667460 1667465) (-1066 "STBL.spad" 1665165 1665193 1665332 1665359) (-1065 "STAGG.spad" 1663864 1663875 1665155 1665160) (-1064 "STAGG.spad" 1662561 1662574 1663854 1663859) (-1063 "STACK.spad" 1661983 1661994 1662233 1662260) (-1062 "SRING.spad" 1661743 1661752 1661973 1661978) (-1061 "SREGSET.spad" 1659475 1659492 1661377 1661404) (-1060 "SRDCMPK.spad" 1658052 1658072 1659465 1659470) (-1059 "SRAGG.spad" 1653235 1653244 1658020 1658047) (-1058 "SRAGG.spad" 1648438 1648449 1653225 1653230) (-1057 "SQMATRIX.spad" 1646115 1646133 1647031 1647118) (-1056 "SPLTREE.spad" 1640857 1640870 1645653 1645680) (-1055 "SPLNODE.spad" 1637477 1637490 1640847 1640852) (-1054 "SPFCAT.spad" 1636286 1636295 1637467 1637472) (-1053 "SPECOUT.spad" 1634838 1634847 1636276 1636281) (-1052 "SPADXPT.spad" 1626929 1626938 1634828 1634833) (-1051 "spad-parser.spad" 1626394 1626403 1626919 1626924) (-1050 "SPADAST.spad" 1626095 1626104 1626384 1626389) (-1049 "SPACEC.spad" 1610310 1610321 1626085 1626090) (-1048 "SPACE3.spad" 1610086 1610097 1610300 1610305) (-1047 "SORTPAK.spad" 1609635 1609648 1610042 1610047) (-1046 "SOLVETRA.spad" 1607398 1607409 1609625 1609630) (-1045 "SOLVESER.spad" 1605854 1605865 1607388 1607393) (-1044 "SOLVERAD.spad" 1601880 1601891 1605844 1605849) (-1043 "SOLVEFOR.spad" 1600342 1600360 1601870 1601875) (-1042 "SNTSCAT.spad" 1599942 1599959 1600310 1600337) (-1041 "SMTS.spad" 1598259 1598285 1599536 1599633) (-1040 "SMP.spad" 1596067 1596087 1596457 1596584) (-1039 "SMITH.spad" 1594912 1594937 1596057 1596062) (-1038 "SMATCAT.spad" 1593030 1593060 1594856 1594907) (-1037 "SMATCAT.spad" 1591080 1591112 1592908 1592913) (-1036 "aggcat.spad" 1590756 1590767 1591060 1591075) (-1035 "SKAGG.spad" 1589725 1589736 1590724 1590751) (-1034 "SINT.spad" 1589024 1589033 1589591 1589720) (-1033 "SIMPAN.spad" 1588752 1588761 1589014 1589019) (-1032 "SIGNRF.spad" 1587877 1587888 1588742 1588747) (-1031 "SIGNEF.spad" 1587163 1587180 1587867 1587872) (-1030 "syntax.spad" 1586580 1586589 1587153 1587158) (-1029 "SIG.spad" 1585942 1585951 1586570 1586575) (-1028 "SHP.spad" 1583886 1583901 1585898 1585903) (-1027 "SHDP.spad" 1573379 1573406 1573896 1573993) (-1026 "SGROUP.spad" 1572987 1572996 1573369 1573374) (-1025 "SGROUP.spad" 1572593 1572604 1572977 1572982) (-1024 "catdef.spad" 1572303 1572315 1572414 1572588) (-1023 "catdef.spad" 1571859 1571871 1572124 1572298) (-1022 "SGCF.spad" 1564998 1565007 1571849 1571854) (-1021 "SFRTCAT.spad" 1563944 1563961 1564966 1564993) (-1020 "SFRGCD.spad" 1563007 1563027 1563934 1563939) (-1019 "SFQCMPK.spad" 1557820 1557840 1562997 1563002) (-1018 "SEXOF.spad" 1557663 1557703 1557810 1557815) (-1017 "SEXCAT.spad" 1555491 1555531 1557653 1557658) (-1016 "SEX.spad" 1555383 1555392 1555481 1555486) (-1015 "SETMN.spad" 1553843 1553860 1555373 1555378) (-1014 "SETCAT.spad" 1553328 1553337 1553833 1553838) (-1013 "SETCAT.spad" 1552811 1552822 1553318 1553323) (-1012 "SETAGG.spad" 1549360 1549371 1552791 1552806) (-1011 "SETAGG.spad" 1545917 1545930 1549350 1549355) (-1010 "SET.spad" 1544226 1544237 1545323 1545362) (-1009 "syntax.spad" 1543929 1543938 1544216 1544221) (-1008 "SEGXCAT.spad" 1543085 1543098 1543919 1543924) (-1007 "SEGCAT.spad" 1542010 1542021 1543075 1543080) (-1006 "SEGBIND2.spad" 1541708 1541721 1542000 1542005) (-1005 "SEGBIND.spad" 1541466 1541477 1541655 1541660) (-1004 "SEGAST.spad" 1541196 1541205 1541456 1541461) (-1003 "SEG2.spad" 1540631 1540644 1541152 1541157) (-1002 "SEG.spad" 1540444 1540455 1540550 1540555) (-1001 "SDVAR.spad" 1539720 1539731 1540434 1540439) (-1000 "SDPOL.spad" 1537412 1537423 1537703 1537830) (-999 "SCPKG.spad" 1535502 1535512 1537402 1537407) (-998 "SCOPE.spad" 1534680 1534688 1535492 1535497) (-997 "SCACHE.spad" 1533377 1533387 1534670 1534675) (-996 "SASTCAT.spad" 1533287 1533295 1533367 1533372) (-995 "SAOS.spad" 1533160 1533168 1533277 1533282) (-994 "SAERFFC.spad" 1532874 1532893 1533150 1533155) (-993 "SAEFACT.spad" 1532576 1532595 1532864 1532869) (-992 "SAE.spad" 1530227 1530242 1530837 1530972) (-991 "RURPK.spad" 1527887 1527902 1530217 1530222) (-990 "RULESET.spad" 1527341 1527364 1527877 1527882) (-989 "RULECOLD.spad" 1527194 1527206 1527331 1527336) (-988 "RULE.spad" 1525443 1525466 1527184 1527189) (-987 "RTVALUE.spad" 1525179 1525187 1525433 1525438) (-986 "syntax.spad" 1524897 1524905 1525169 1525174) (-985 "RSETGCD.spad" 1521340 1521359 1524887 1524892) (-984 "RSETCAT.spad" 1511309 1511325 1521308 1521335) (-983 "RSETCAT.spad" 1501298 1501316 1511299 1511304) (-982 "RSDCMPK.spad" 1499799 1499818 1501288 1501293) (-981 "RRCC.spad" 1498184 1498213 1499789 1499794) (-980 "RRCC.spad" 1496567 1496598 1498174 1498179) (-979 "RPTAST.spad" 1496270 1496278 1496557 1496562) (-978 "RPOLCAT.spad" 1475775 1475789 1496138 1496265) (-977 "RPOLCAT.spad" 1455073 1455089 1475438 1475443) (-976 "ROMAN.spad" 1454402 1454410 1454939 1455068) (-975 "ROIRC.spad" 1453483 1453514 1454392 1454397) (-974 "RNS.spad" 1452460 1452468 1453385 1453478) (-973 "RNS.spad" 1451523 1451533 1452450 1452455) (-972 "RNGBIND.spad" 1450684 1450697 1451478 1451483) (-971 "RNG.spad" 1450293 1450301 1450674 1450679) (-970 "RNG.spad" 1449900 1449910 1450283 1450288) (-969 "RMODULE.spad" 1449682 1449692 1449890 1449895) (-968 "RMCAT2.spad" 1449103 1449159 1449672 1449677) (-967 "RMATRIX.spad" 1447913 1447931 1448255 1448294) (-966 "RMATCAT.spad" 1443551 1443581 1447869 1447908) (-965 "RMATCAT.spad" 1439079 1439111 1443399 1443404) (-964 "RLINSET.spad" 1438784 1438794 1439069 1439074) (-963 "RINTERP.spad" 1438673 1438692 1438774 1438779) (-962 "RING.spad" 1438144 1438152 1438653 1438668) (-961 "RING.spad" 1437623 1437633 1438134 1438139) (-960 "RIDIST.spad" 1437016 1437024 1437613 1437618) (-959 "RGCHAIN.spad" 1435571 1435586 1436464 1436491) (-958 "RGBCSPC.spad" 1435361 1435372 1435561 1435566) (-957 "RGBCMDL.spad" 1434924 1434935 1435351 1435356) (-956 "RFFACTOR.spad" 1434387 1434397 1434914 1434919) (-955 "RFFACT.spad" 1434123 1434134 1434377 1434382) 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"GAUSSFAC.spad" 611811 611819 612488 612493) (-385 "GALUTIL.spad" 610137 610147 611767 611772) (-384 "GALPOLYU.spad" 608591 608604 610127 610132) (-383 "GALFACTU.spad" 606804 606823 608581 608586) (-382 "GALFACT.spad" 597017 597028 606794 606799) (-381 "FUNDESC.spad" 596695 596703 597007 597012) (-380 "FUNCTION.spad" 596544 596556 596685 596690) (-379 "FT.spad" 594844 594852 596534 596539) (-378 "FSUPFACT.spad" 593758 593777 594794 594799) (-377 "FST.spad" 591844 591852 593748 593753) (-376 "FSRED.spad" 591324 591340 591834 591839) (-375 "FSPRMELT.spad" 590190 590206 591281 591286) (-374 "FSPECF.spad" 588281 588297 590180 590185) (-373 "FSINT.spad" 587941 587957 588271 588276) (-372 "FSERIES.spad" 587132 587144 587761 587860) (-371 "FSCINT.spad" 586449 586465 587122 587127) (-370 "FSAGG2.spad" 585184 585200 586439 586444) (-369 "FSAGG.spad" 584301 584311 585140 585179) (-368 "FSAGG.spad" 583380 583392 584221 584226) (-367 "FS2UPS.spad" 577895 577929 583370 583375) (-366 "FS2EXPXP.spad" 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"FPC.spad" 531447 531455 532303 532396) (-344 "FPC.spad" 530579 530589 531437 531442) (-343 "FPATMAB.spad" 530341 530351 530569 530574) (-342 "FPARFRAC.spad" 529183 529200 530331 530336) (-341 "FORDER.spad" 528874 528898 529173 529178) (-340 "FNLA.spad" 528298 528320 528842 528869) (-339 "FNCAT.spad" 526893 526901 528288 528293) (-338 "FNAME.spad" 526785 526793 526883 526888) (-337 "FMONOID.spad" 526466 526476 526741 526746) (-336 "FMONCAT.spad" 523635 523645 526456 526461) (-335 "FMCAT.spad" 521311 521329 523603 523630) (-334 "FM1.spad" 520676 520688 521245 521272) (-333 "FM.spad" 520291 520303 520530 520557) (-332 "FLOATRP.spad" 518034 518048 520281 520286) (-331 "FLOATCP.spad" 515473 515487 518024 518029) (-330 "FLOAT.spad" 512564 512572 515339 515468) (-329 "FLINEXP.spad" 512286 512296 512554 512559) (-328 "FLINEXP.spad" 511965 511977 512235 512240) (-327 "FLASORT.spad" 511291 511303 511955 511960) (-326 "FLALG.spad" 508961 508980 511217 511286) (-325 "FLAGG2.spad" 507678 507694 508951 508956) (-324 "FLAGG.spad" 504744 504754 507658 507673) (-323 "FLAGG.spad" 501711 501723 504627 504632) (-322 "FINRALG.spad" 499796 499809 501667 501706) (-321 "FINRALG.spad" 497807 497822 499680 499685) (-320 "FINITE.spad" 496959 496967 497797 497802) (-319 "FINITE.spad" 496109 496119 496949 496954) (-318 "aggcat.spad" 494275 494285 496089 496104) (-317 "FINAGG.spad" 492416 492428 494232 494237) (-316 "FINAALG.spad" 481601 481611 492358 492411) (-315 "FINAALG.spad" 470798 470810 481557 481562) (-314 "FILECAT.spad" 469332 469349 470788 470793) (-313 "FILE.spad" 468915 468925 469322 469327) (-312 "FIELD.spad" 468321 468329 468817 468910) (-311 "FIELD.spad" 467813 467823 468311 468316) (-310 "FGROUP.spad" 466476 466486 467793 467808) (-309 "FGLMICPK.spad" 465271 465286 466466 466471) (-308 "FFX.spad" 464657 464672 464990 465083) (-307 "FFSLPE.spad" 464168 464189 464647 464652) (-306 "FFPOLY2.spad" 463228 463245 464158 464163) (-305 "FFPOLY.spad" 454570 454581 463218 463223) (-304 "FFP.spad" 453978 453998 454289 454382) (-303 "FFNBX.spad" 452501 452521 453697 453790) (-302 "FFNBP.spad" 451025 451042 452220 452313) (-301 "FFNB.spad" 449493 449514 450709 450802) (-300 "FFINTBAS.spad" 447007 447026 449483 449488) (-299 "FFIELDC.spad" 444592 444600 446909 447002) (-298 "FFIELDC.spad" 442263 442273 444582 444587) (-297 "FFHOM.spad" 441035 441052 442253 442258) (-296 "FFF.spad" 438478 438489 441025 441030) (-295 "FFCGX.spad" 437336 437356 438197 438290) (-294 "FFCGP.spad" 436236 436256 437055 437148) (-293 "FFCG.spad" 435031 435052 435920 436013) (-292 "FFCAT2.spad" 434778 434818 435021 435026) (-291 "FFCAT.spad" 427943 427965 434617 434773) (-290 "FFCAT.spad" 421187 421211 427863 427868) (-289 "FF.spad" 420638 420654 420871 420964) (-288 "FEVALAB.spad" 420346 420356 420628 420633) (-287 "FEVALAB.spad" 419830 419842 420114 420119) (-286 "FDIVCAT.spad" 417926 417950 419820 419825) (-285 "FDIVCAT.spad" 416020 416046 417916 417921) (-284 "FDIV2.spad" 415676 415716 416010 416015) (-283 "FDIV.spad" 415134 415158 415666 415671) (-282 "FCTRDATA.spad" 414142 414150 415124 415129) (-281 "FCOMP.spad" 413521 413531 414132 414137) (-280 "FAXF.spad" 406556 406570 413423 413516) (-279 "FAXF.spad" 399643 399659 406512 406517) (-278 "FARRAY.spad" 397835 397845 398868 398895) (-277 "FAMR.spad" 395979 395991 397733 397830) (-276 "FAMR.spad" 394107 394121 395863 395868) (-275 "FAMONOID.spad" 393791 393801 394061 394066) (-274 "FAMONC.spad" 392111 392123 393781 393786) (-273 "FAGROUP.spad" 391751 391761 392007 392034) (-272 "FACUTIL.spad" 389963 389980 391741 391746) (-271 "FACTFUNC.spad" 389165 389175 389953 389958) (-270 "EXPUPXS.spad" 386057 386080 387356 387505) (-269 "EXPRTUBE.spad" 383345 383353 386047 386052) (-268 "EXPRODE.spad" 380513 380529 383335 383340) (-267 "EXPR2UPS.spad" 376635 376648 380503 380508) (-266 "EXPR2.spad" 376340 376352 376625 376630) (-265 "EXPR.spad" 371985 371995 372699 372986) (-264 "EXPEXPAN.spad" 368930 368955 369562 369655) (-263 "EXITAST.spad" 368666 368674 368920 368925) (-262 "EXIT.spad" 368337 368345 368656 368661) (-261 "EVALCYC.spad" 367797 367811 368327 368332) (-260 "EVALAB.spad" 367377 367387 367787 367792) (-259 "EVALAB.spad" 366955 366967 367367 367372) (-258 "EUCDOM.spad" 364545 364553 366881 366950) (-257 "EUCDOM.spad" 362197 362207 364535 364540) (-256 "ES2.spad" 361710 361726 362187 362192) (-255 "ES1.spad" 361280 361296 361700 361705) (-254 "ES.spad" 354151 354159 361270 361275) (-253 "ES.spad" 346943 346953 354064 354069) (-252 "ERROR.spad" 344270 344278 346933 346938) (-251 "EQTBL.spad" 342606 342628 342815 342842) (-250 "EQ2.spad" 342324 342336 342596 342601) (-249 "EQ.spad" 337230 337240 340025 340131) (-248 "EP.spad" 333556 333566 337220 337225) (-247 "ENV.spad" 332234 332242 333546 333551) (-246 "ENTIRER.spad" 331902 331910 332178 332229) (-245 "ENTIRER.spad" 331614 331624 331892 331897) (-244 "EMR.spad" 330902 330943 331540 331609) (-243 "ELTAGG.spad" 329156 329175 330892 330897) (-242 "ELTAGG.spad" 327374 327395 329112 329117) (-241 "ELTAB.spad" 326849 326862 327364 327369) (-240 "ELFUTS.spad" 326284 326303 326839 326844) (-239 "ELEMFUN.spad" 325973 325981 326274 326279) (-238 "ELEMFUN.spad" 325660 325670 325963 325968) (-237 "ELAGG.spad" 323631 323641 325640 325655) (-236 "ELAGG.spad" 321539 321551 323550 323555) (-235 "ELABOR.spad" 320885 320893 321529 321534) (-234 "ELABEXPR.spad" 319817 319825 320875 320880) (-233 "EFUPXS.spad" 316593 316623 319773 319778) (-232 "EFULS.spad" 313429 313452 316549 316554) (-231 "EFSTRUC.spad" 311444 311460 313419 313424) (-230 "EF.spad" 306220 306236 311434 311439) (-229 "EAB.spad" 304520 304528 306210 306215) (-228 "DVARCAT.spad" 301526 301536 304510 304515) (-227 "DVARCAT.spad" 298530 298542 301516 301521) (-226 "DSMP.spad" 296263 296277 296568 296695) (-225 "DSEXT.spad" 295565 295575 296253 296258) (-224 "DSEXT.spad" 294787 294799 295477 295482) (-223 "DROPT1.spad" 294452 294462 294777 294782) (-222 "DROPT0.spad" 289317 289325 294442 294447) (-221 "DROPT.spad" 283276 283284 289307 289312) (-220 "DRAWPT.spad" 281449 281457 283266 283271) (-219 "DRAWHACK.spad" 280757 280767 281439 281444) (-218 "DRAWCX.spad" 278235 278243 280747 280752) (-217 "DRAWCURV.spad" 277782 277797 278225 278230) (-216 "DRAWCFUN.spad" 267314 267322 277772 277777) (-215 "DRAW.spad" 260190 260203 267304 267309) (-214 "DQAGG.spad" 258368 258378 260158 260185) (-213 "DPOLCAT.spad" 253725 253741 258236 258363) (-212 "DPOLCAT.spad" 249168 249186 253681 253686) (-211 "DPMO.spad" 241871 241887 242009 242215) (-210 "DPMM.spad" 234587 234605 234712 234918) (-209 "DOMTMPLT.spad" 234358 234366 234577 234582) (-208 "DOMCTOR.spad" 234113 234121 234348 234353) (-207 "DOMAIN.spad" 233224 233232 234103 234108) (-206 "DMP.spad" 230817 230832 231387 231514) (-205 "DMEXT.spad" 230684 230694 230785 230812) (-204 "DLP.spad" 230044 230054 230674 230679) (-203 "DLIST.spad" 228665 228675 229269 229296) (-202 "DLAGG.spad" 227082 227092 228655 228660) (-201 "DIVRING.spad" 226624 226632 227026 227077) (-200 "DIVRING.spad" 226210 226220 226614 226619) (-199 "DISPLAY.spad" 224400 224408 226200 226205) (-198 "DIRPROD2.spad" 223218 223236 224390 224395) (-197 "DIRPROD.spad" 212588 212604 213228 213325) (-196 "DIRPCAT.spad" 211871 211887 212486 212583) (-195 "DIRPCAT.spad" 210780 210798 211397 211402) (-194 "DIOSP.spad" 209605 209613 210770 210775) (-193 "DIOPS.spad" 208601 208611 209585 209600) (-192 "DIOPS.spad" 207571 207583 208557 208562) (-191 "catdef.spad" 207429 207437 207561 207566) (-190 "DIFRING.spad" 207267 207275 207409 207424) (-189 "DIFFSPC.spad" 206846 206854 207257 207262) (-188 "DIFFSPC.spad" 206423 206433 206836 206841) (-187 "DIFFMOD.spad" 205912 205922 206391 206418) (-186 "DIFFDOM.spad" 205077 205088 205902 205907) (-185 "DIFFDOM.spad" 204240 204253 205067 205072) (-184 "DIFEXT.spad" 204059 204069 204220 204235) (-183 "DIAGG.spad" 203689 203699 204039 204054) (-182 "DIAGG.spad" 203327 203339 203679 203684) (-181 "DHMATRIX.spad" 201704 201714 202849 202876) (-180 "DFSFUN.spad" 195344 195352 201694 201699) (-179 "DFLOAT.spad" 191951 191959 195234 195339) (-178 "DFINTTLS.spad" 190182 190198 191941 191946) (-177 "DERHAM.spad" 188096 188128 190162 190177) (-176 "DEQUEUE.spad" 187485 187495 187768 187795) (-175 "DEGRED.spad" 187102 187116 187475 187480) (-174 "DEFINTRF.spad" 184684 184694 187092 187097) (-173 "DEFINTEF.spad" 183222 183238 184674 184679) (-172 "DEFAST.spad" 182606 182614 183212 183217) (-171 "DECIMAL.spad" 180835 180843 181196 181289) (-170 "DDFACT.spad" 178656 178673 180825 180830) (-169 "DBLRESP.spad" 178256 178280 178646 178651) (-168 "DBASIS.spad" 177882 177897 178246 178251) (-167 "DBASE.spad" 176546 176556 177872 177877) (-166 "DATAARY.spad" 176032 176045 176536 176541) (-165 "CYCLOTOM.spad" 175538 175546 176022 176027) (-164 "CYCLES.spad" 172330 172338 175528 175533) (-163 "CVMP.spad" 171747 171757 172320 172325) (-162 "CTRIGMNP.spad" 170247 170263 171737 171742) (-161 "CTORKIND.spad" 169850 169858 170237 170242) (-160 "CTORCAT.spad" 169091 169099 169840 169845) (-159 "CTORCAT.spad" 168330 168340 169081 169086) (-158 "CTORCALL.spad" 167919 167929 168320 168325) (-157 "CTOR.spad" 167610 167618 167909 167914) (-156 "CSTTOOLS.spad" 166855 166868 167600 167605) (-155 "CRFP.spad" 160627 160640 166845 166850) (-154 "CRCEAST.spad" 160347 160355 160617 160622) (-153 "CRAPACK.spad" 159414 159424 160337 160342) (-152 "CPMATCH.spad" 158915 158930 159336 159341) (-151 "CPIMA.spad" 158620 158639 158905 158910) (-150 "COORDSYS.spad" 153629 153639 158610 158615) (-149 "CONTOUR.spad" 153056 153064 153619 153624) (-148 "CONTFRAC.spad" 148806 148816 152958 153051) (-147 "CONDUIT.spad" 148564 148572 148796 148801) (-146 "COMRING.spad" 148238 148246 148502 148559) (-145 "COMPPROP.spad" 147756 147764 148228 148233) (-144 "COMPLPAT.spad" 147523 147538 147746 147751) (-143 "COMPLEX2.spad" 147238 147250 147513 147518) (-142 "COMPLEX.spad" 142944 142954 143188 143446) (-141 "COMPILER.spad" 142493 142501 142934 142939) (-140 "COMPFACT.spad" 142095 142109 142483 142488) (-139 "COMPCAT.spad" 140170 140180 141832 142090) (-138 "COMPCAT.spad" 137986 137998 139650 139655) (-137 "COMMUPC.spad" 137734 137752 137976 137981) (-136 "COMMONOP.spad" 137267 137275 137724 137729) (-135 "COMMAAST.spad" 137030 137038 137257 137262) (-134 "COMM.spad" 136841 136849 137020 137025) (-133 "COMBOPC.spad" 135764 135772 136831 136836) (-132 "COMBINAT.spad" 134531 134541 135754 135759) (-131 "COMBF.spad" 131953 131969 134521 134526) (-130 "COLOR.spad" 130790 130798 131943 131948) (-129 "COLONAST.spad" 130456 130464 130780 130785) (-128 "CMPLXRT.spad" 130167 130184 130446 130451) (-127 "CLLCTAST.spad" 129829 129837 130157 130162) (-126 "CLIP.spad" 125937 125945 129819 129824) (-125 "CLIF.spad" 124592 124608 125893 125932) (-124 "CLAGG.spad" 121129 121139 124582 124587) (-123 "CLAGG.spad" 117550 117562 121005 121010) (-122 "CINTSLPE.spad" 116905 116918 117540 117545) (-121 "CHVAR.spad" 115043 115065 116895 116900) (-120 "CHARZ.spad" 114958 114966 115023 115038) (-119 "CHARPOL.spad" 114484 114494 114948 114953) (-118 "CHARNZ.spad" 114246 114254 114464 114479) (-117 "CHAR.spad" 111614 111622 114236 114241) (-116 "CFCAT.spad" 110942 110950 111604 111609) (-115 "CDEN.spad" 110162 110176 110932 110937) (-114 "CCLASS.spad" 108342 108350 109604 109643) (-113 "CATEGORY.spad" 107416 107424 108332 108337) (-112 "CATCTOR.spad" 107307 107315 107406 107411) (-111 "CATAST.spad" 106933 106941 107297 107302) (-110 "CASEAST.spad" 106647 106655 106923 106928) (-109 "CARTEN2.spad" 106037 106064 106637 106642) (-108 "CARTEN.spad" 101789 101813 106027 106032) (-107 "CARD.spad" 99084 99092 101763 101784) (-106 "CAPSLAST.spad" 98866 98874 99074 99079) (-105 "CACHSET.spad" 98490 98498 98856 98861) (-104 "CABMON.spad" 98045 98053 98480 98485) (-103 "BYTEORD.spad" 97720 97728 98035 98040) (-102 "BYTEBUF.spad" 95767 95775 96973 97000) (-101 "BYTE.spad" 95242 95250 95757 95762) (-100 "BTREE.spad" 94380 94390 94914 94941) (-99 "BTOURN.spad" 93451 93460 94052 94079) (-98 "BTCAT.spad" 93009 93018 93419 93446) (-97 "BTCAT.spad" 92587 92598 92999 93004) (-96 "BTAGG.spad" 92054 92061 92555 92582) (-95 "BTAGG.spad" 91541 91550 92044 92049) (-94 "BSTREE.spad" 90348 90357 91213 91240) (-93 "BRILL.spad" 88554 88564 90338 90343) (-92 "BRAGG.spad" 87511 87520 88544 88549) (-91 "BRAGG.spad" 86432 86443 87467 87472) (-90 "BPADICRT.spad" 84492 84503 84738 84831) (-89 "BPADIC.spad" 84165 84176 84418 84487) (-88 "BOUNDZRO.spad" 83822 83838 84155 84160) (-87 "BOP1.spad" 81281 81290 83812 83817) (-86 "BOP.spad" 76424 76431 81271 81276) (-85 "BOOLEAN.spad" 75973 75980 76414 76419) (-84 "BOOLE.spad" 75624 75631 75963 75968) (-83 "BOOLE.spad" 75273 75282 75614 75619) (-82 "BMODULE.spad" 74986 74997 75241 75268) (-81 "BITS.spad" 74418 74425 74632 74659) (-80 "catdef.spad" 74301 74311 74408 74413) (-79 "catdef.spad" 74052 74062 74291 74296) (-78 "BINDING.spad" 73474 73481 74042 74047) (-77 "BINARY.spad" 71709 71716 72064 72157) (-76 "BGAGG.spad" 71029 71038 71689 71704) (-75 "BGAGG.spad" 70357 70368 71019 71024) (-74 "BEZOUT.spad" 69498 69524 70307 70312) (-73 "BBTREE.spad" 66441 66450 69170 69197) (-72 "BASTYPE.spad" 65941 65948 66431 66436) (-71 "BASTYPE.spad" 65439 65448 65931 65936) (-70 "BALFACT.spad" 64899 64911 65429 65434) (-69 "AUTOMOR.spad" 64350 64359 64879 64894) (-68 "ATTREG.spad" 61336 61343 64114 64345) (-67 "ATTRAST.spad" 61053 61060 61326 61331) (-66 "ATRIG.spad" 60523 60530 61043 61048) (-65 "ATRIG.spad" 59991 60000 60513 60518) (-64 "ASTCAT.spad" 59895 59902 59981 59986) (-63 "ASTCAT.spad" 59797 59806 59885 59890) (-62 "ASTACK.spad" 59201 59210 59469 59496) (-61 "ASSOCEQ.spad" 58035 58046 59157 59162) (-60 "ARRAY2.spad" 57558 57567 57707 57734) (-59 "ARRAY12.spad" 56271 56282 57548 57553) (-58 "ARRAY1.spad" 55150 55159 55496 55523) (-57 "ARR2CAT.spad" 51190 51211 55118 55145) (-56 "ARR2CAT.spad" 47250 47273 51180 51185) (-55 "ARITY.spad" 46622 46629 47240 47245) (-54 "APPRULE.spad" 45906 45928 46612 46617) (-53 "APPLYORE.spad" 45525 45538 45896 45901) (-52 "ANY1.spad" 44596 44605 45515 45520) (-51 "ANY.spad" 43447 43454 44586 44591) (-50 "ANTISYM.spad" 41892 41908 43427 43442) (-49 "ANON.spad" 41601 41608 41882 41887) (-48 "AN.spad" 40069 40076 41432 41525) (-47 "AMR.spad" 38254 38265 39967 40064) (-46 "AMR.spad" 36302 36315 38017 38022) (-45 "ALIST.spad" 33540 33561 33890 33917) (-44 "ALGSC.spad" 32675 32701 33412 33465) (-43 "ALGPKG.spad" 28458 28469 32631 32636) (-42 "ALGMFACT.spad" 27651 27665 28448 28453) (-41 "ALGMANIP.spad" 25152 25167 27495 27500) (-40 "ALGFF.spad" 22970 22997 23187 23343) (-39 "ALGFACT.spad" 22089 22099 22960 22965) (-38 "ALGEBRA.spad" 21922 21931 22045 22084) (-37 "ALGEBRA.spad" 21787 21798 21912 21917) (-36 "ALAGG.spad" 21303 21324 21755 21782) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-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 1962292 1962297 1962302 1962307) (-2 NIL 1962272 1962277 1962282 1962287) (-1 NIL 1962252 1962257 1962262 1962267) (0 NIL 1962232 1962237 1962242 1962247) (-1210 "ZMOD.spad" 1962041 1962054 1962170 1962227) (-1209 "ZLINDEP.spad" 1961139 1961150 1962031 1962036) (-1208 "ZDSOLVE.spad" 1951100 1951122 1961129 1961134) (-1207 "YSTREAM.spad" 1950595 1950606 1951090 1951095) (-1206 "YDIAGRAM.spad" 1950229 1950238 1950585 1950590) (-1205 "XRPOLY.spad" 1949449 1949469 1950085 1950154) (-1204 "XPR.spad" 1947244 1947257 1949167 1949266) (-1203 "XPOLYC.spad" 1946563 1946579 1947170 1947239) (-1202 "XPOLY.spad" 1946118 1946129 1946419 1946488) (-1201 "XPBWPOLY.spad" 1944589 1944609 1945924 1945993) (-1200 "XFALG.spad" 1941637 1941653 1944515 1944584) (-1199 "XF.spad" 1940100 1940115 1941539 1941632) (-1198 "XF.spad" 1938543 1938560 1939984 1939989) (-1197 "XEXPPKG.spad" 1937802 1937828 1938533 1938538) (-1196 "XDPOLY.spad" 1937416 1937432 1937658 1937727) (-1195 "XALG.spad" 1937084 1937095 1937372 1937411) (-1194 "WUTSET.spad" 1933087 1933104 1936718 1936745) (-1193 "WP.spad" 1932294 1932338 1932945 1933012) (-1192 "WHILEAST.spad" 1932092 1932101 1932284 1932289) (-1191 "WHEREAST.spad" 1931763 1931772 1932082 1932087) (-1190 "WFFINTBS.spad" 1929426 1929448 1931753 1931758) (-1189 "WEIER.spad" 1927648 1927659 1929416 1929421) (-1188 "VSPACE.spad" 1927321 1927332 1927616 1927643) (-1187 "VSPACE.spad" 1927014 1927027 1927311 1927316) (-1186 "VOID.spad" 1926691 1926700 1927004 1927009) (-1185 "VIEWDEF.spad" 1921892 1921901 1926681 1926686) (-1184 "VIEW3D.spad" 1905853 1905862 1921882 1921887) (-1183 "VIEW2D.spad" 1893752 1893761 1905843 1905848) (-1182 "VIEW.spad" 1891472 1891481 1893742 1893747) (-1181 "VECTOR2.spad" 1890111 1890124 1891462 1891467) (-1180 "VECTOR.spad" 1888830 1888841 1889081 1889108) (-1179 "VECTCAT.spad" 1886742 1886753 1888798 1888825) (-1178 "VECTCAT.spad" 1884463 1884476 1886521 1886526) (-1177 "VARIABLE.spad" 1884243 1884258 1884453 1884458) (-1176 "UTYPE.spad" 1883887 1883896 1884233 1884238) (-1175 "UTSODETL.spad" 1883182 1883206 1883843 1883848) (-1174 "UTSODE.spad" 1881398 1881418 1883172 1883177) (-1173 "UTSCAT.spad" 1878877 1878893 1881296 1881393) (-1172 "UTSCAT.spad" 1876024 1876042 1878445 1878450) (-1171 "UTS2.spad" 1875619 1875654 1876014 1876019) (-1170 "UTS.spad" 1870631 1870659 1874151 1874248) (-1169 "URAGG.spad" 1865352 1865363 1870621 1870626) (-1168 "URAGG.spad" 1860037 1860050 1865308 1865313) (-1167 "UPXSSING.spad" 1857805 1857831 1859241 1859374) (-1166 "UPXSCONS.spad" 1855623 1855643 1855996 1856145) (-1165 "UPXSCCA.spad" 1854194 1854214 1855469 1855618) (-1164 "UPXSCCA.spad" 1852907 1852929 1854184 1854189) (-1163 "UPXSCAT.spad" 1851496 1851512 1852753 1852902) (-1162 "UPXS2.spad" 1851039 1851092 1851486 1851491) (-1161 "UPXS.spad" 1848394 1848422 1849230 1849379) (-1160 "UPSQFREE.spad" 1846809 1846823 1848384 1848389) (-1159 "UPSCAT.spad" 1844604 1844628 1846707 1846804) (-1158 "UPSCAT.spad" 1842100 1842126 1844205 1844210) (-1157 "UPOLYC2.spad" 1841571 1841590 1842090 1842095) (-1156 "UPOLYC.spad" 1836651 1836662 1841413 1841566) (-1155 "UPOLYC.spad" 1831649 1831662 1836413 1836418) (-1154 "UPMP.spad" 1830581 1830594 1831639 1831644) (-1153 "UPDIVP.spad" 1830146 1830160 1830571 1830576) (-1152 "UPDECOMP.spad" 1828407 1828421 1830136 1830141) (-1151 "UPCDEN.spad" 1827624 1827640 1828397 1828402) (-1150 "UP2.spad" 1826988 1827009 1827614 1827619) (-1149 "UP.spad" 1824458 1824473 1824845 1824998) (-1148 "UNISEG2.spad" 1823955 1823968 1824414 1824419) (-1147 "UNISEG.spad" 1823308 1823319 1823874 1823879) (-1146 "UNIFACT.spad" 1822411 1822423 1823298 1823303) (-1145 "ULSCONS.spad" 1816257 1816277 1816627 1816776) (-1144 "ULSCCAT.spad" 1813994 1814014 1816103 1816252) (-1143 "ULSCCAT.spad" 1811839 1811861 1813950 1813955) (-1142 "ULSCAT.spad" 1810079 1810095 1811685 1811834) (-1141 "ULS2.spad" 1809593 1809646 1810069 1810074) (-1140 "ULS.spad" 1801626 1801654 1802571 1802994) (-1139 "UINT8.spad" 1801503 1801512 1801616 1801621) (-1138 "UINT64.spad" 1801379 1801388 1801493 1801498) (-1137 "UINT32.spad" 1801255 1801264 1801369 1801374) (-1136 "UINT16.spad" 1801131 1801140 1801245 1801250) (-1135 "UFD.spad" 1800196 1800205 1801057 1801126) (-1134 "UFD.spad" 1799323 1799334 1800186 1800191) (-1133 "UDVO.spad" 1798204 1798213 1799313 1799318) (-1132 "UDPO.spad" 1795785 1795796 1798160 1798165) (-1131 "TYPEAST.spad" 1795704 1795713 1795775 1795780) (-1130 "TYPE.spad" 1795636 1795645 1795694 1795699) (-1129 "TWOFACT.spad" 1794288 1794303 1795626 1795631) (-1128 "TUPLE.spad" 1793795 1793806 1794200 1794205) (-1127 "TUBETOOL.spad" 1790662 1790671 1793785 1793790) (-1126 "TUBE.spad" 1789309 1789326 1790652 1790657) (-1125 "TSETCAT.spad" 1777380 1777397 1789277 1789304) (-1124 "TSETCAT.spad" 1765437 1765456 1777336 1777341) (-1123 "TS.spad" 1764065 1764081 1765031 1765128) (-1122 "TRMANIP.spad" 1758429 1758446 1763753 1763758) (-1121 "TRIMAT.spad" 1757392 1757417 1758419 1758424) (-1120 "TRIGMNIP.spad" 1755919 1755936 1757382 1757387) (-1119 "TRIGCAT.spad" 1755431 1755440 1755909 1755914) (-1118 "TRIGCAT.spad" 1754941 1754952 1755421 1755426) (-1117 "TREE.spad" 1753581 1753592 1754613 1754640) (-1116 "TRANFUN.spad" 1753420 1753429 1753571 1753576) (-1115 "TRANFUN.spad" 1753257 1753268 1753410 1753415) (-1114 "TOPSP.spad" 1752931 1752940 1753247 1753252) (-1113 "TOOLSIGN.spad" 1752594 1752605 1752921 1752926) (-1112 "TEXTFILE.spad" 1751155 1751164 1752584 1752589) (-1111 "TEX1.spad" 1750711 1750722 1751145 1751150) (-1110 "TEX.spad" 1747905 1747914 1750701 1750706) (-1109 "TBCMPPK.spad" 1746006 1746029 1747895 1747900) (-1108 "TBAGG.spad" 1745249 1745272 1745974 1746001) (-1107 "TBAGG.spad" 1744512 1744537 1745239 1745244) (-1106 "TANEXP.spad" 1743920 1743931 1744502 1744507) (-1105 "TALGOP.spad" 1743644 1743655 1743910 1743915) (-1104 "TABLEAU.spad" 1743125 1743136 1743634 1743639) (-1103 "TABLE.spad" 1741400 1741423 1741670 1741697) (-1102 "TABLBUMP.spad" 1738179 1738190 1741390 1741395) (-1101 "SYSTEM.spad" 1737407 1737416 1738169 1738174) (-1100 "SYSSOLP.spad" 1734890 1734901 1737397 1737402) (-1099 "SYSPTR.spad" 1734789 1734798 1734880 1734885) (-1098 "SYSNNI.spad" 1734012 1734023 1734779 1734784) (-1097 "SYSINT.spad" 1733416 1733427 1734002 1734007) (-1096 "SYNTAX.spad" 1729750 1729759 1733406 1733411) (-1095 "SYMTAB.spad" 1727818 1727827 1729740 1729745) (-1094 "SYMS.spad" 1723847 1723856 1727808 1727813) (-1093 "SYMPOLY.spad" 1722980 1722991 1723062 1723189) (-1092 "SYMFUNC.spad" 1722481 1722492 1722970 1722975) (-1091 "SYMBOL.spad" 1719976 1719985 1722471 1722476) (-1090 "SUTS.spad" 1717089 1717117 1718508 1718605) (-1089 "SUPXS.spad" 1714431 1714459 1715280 1715429) (-1088 "SUPFRACF.spad" 1713536 1713554 1714421 1714426) (-1087 "SUP2.spad" 1712928 1712941 1713526 1713531) (-1086 "SUP.spad" 1710012 1710023 1710785 1710938) (-1085 "SUMRF.spad" 1708986 1708997 1710002 1710007) (-1084 "SUMFS.spad" 1708615 1708632 1708976 1708981) (-1083 "SULS.spad" 1700635 1700663 1701593 1702016) (-1082 "syntax.spad" 1700404 1700413 1700625 1700630) (-1081 "SUCH.spad" 1700094 1700109 1700394 1700399) (-1080 "SUBSPACE.spad" 1692225 1692240 1700084 1700089) (-1079 "SUBRESP.spad" 1691395 1691409 1692181 1692186) (-1078 "STTFNC.spad" 1687863 1687879 1691385 1691390) (-1077 "STTF.spad" 1683962 1683978 1687853 1687858) (-1076 "STTAYLOR.spad" 1676639 1676650 1683869 1683874) (-1075 "STRTBL.spad" 1675026 1675043 1675175 1675202) (-1074 "STRING.spad" 1673894 1673903 1674279 1674306) (-1073 "STREAM3.spad" 1673467 1673482 1673884 1673889) (-1072 "STREAM2.spad" 1672595 1672608 1673457 1673462) (-1071 "STREAM1.spad" 1672301 1672312 1672585 1672590) (-1070 "STREAM.spad" 1669297 1669308 1671904 1671919) (-1069 "STINPROD.spad" 1668233 1668249 1669287 1669292) (-1068 "STEPAST.spad" 1667467 1667476 1668223 1668228) (-1067 "STEP.spad" 1666784 1666793 1667457 1667462) (-1066 "STBL.spad" 1665162 1665190 1665329 1665356) (-1065 "STAGG.spad" 1663861 1663872 1665152 1665157) (-1064 "STAGG.spad" 1662558 1662571 1663851 1663856) (-1063 "STACK.spad" 1661980 1661991 1662230 1662257) (-1062 "SRING.spad" 1661740 1661749 1661970 1661975) (-1061 "SREGSET.spad" 1659472 1659489 1661374 1661401) (-1060 "SRDCMPK.spad" 1658049 1658069 1659462 1659467) (-1059 "SRAGG.spad" 1653232 1653241 1658017 1658044) (-1058 "SRAGG.spad" 1648435 1648446 1653222 1653227) (-1057 "SQMATRIX.spad" 1646112 1646130 1647028 1647115) (-1056 "SPLTREE.spad" 1640854 1640867 1645650 1645677) (-1055 "SPLNODE.spad" 1637474 1637487 1640844 1640849) (-1054 "SPFCAT.spad" 1636283 1636292 1637464 1637469) (-1053 "SPECOUT.spad" 1634835 1634844 1636273 1636278) (-1052 "SPADXPT.spad" 1626926 1626935 1634825 1634830) (-1051 "spad-parser.spad" 1626391 1626400 1626916 1626921) (-1050 "SPADAST.spad" 1626092 1626101 1626381 1626386) (-1049 "SPACEC.spad" 1610307 1610318 1626082 1626087) (-1048 "SPACE3.spad" 1610083 1610094 1610297 1610302) (-1047 "SORTPAK.spad" 1609632 1609645 1610039 1610044) (-1046 "SOLVETRA.spad" 1607395 1607406 1609622 1609627) (-1045 "SOLVESER.spad" 1605851 1605862 1607385 1607390) (-1044 "SOLVERAD.spad" 1601877 1601888 1605841 1605846) (-1043 "SOLVEFOR.spad" 1600339 1600357 1601867 1601872) (-1042 "SNTSCAT.spad" 1599939 1599956 1600307 1600334) (-1041 "SMTS.spad" 1598256 1598282 1599533 1599630) (-1040 "SMP.spad" 1596064 1596084 1596454 1596581) (-1039 "SMITH.spad" 1594909 1594934 1596054 1596059) (-1038 "SMATCAT.spad" 1593027 1593057 1594853 1594904) (-1037 "SMATCAT.spad" 1591077 1591109 1592905 1592910) (-1036 "aggcat.spad" 1590753 1590764 1591057 1591072) (-1035 "SKAGG.spad" 1589722 1589733 1590721 1590748) (-1034 "SINT.spad" 1589021 1589030 1589588 1589717) (-1033 "SIMPAN.spad" 1588749 1588758 1589011 1589016) (-1032 "SIGNRF.spad" 1587874 1587885 1588739 1588744) (-1031 "SIGNEF.spad" 1587160 1587177 1587864 1587869) (-1030 "syntax.spad" 1586577 1586586 1587150 1587155) (-1029 "SIG.spad" 1585939 1585948 1586567 1586572) (-1028 "SHP.spad" 1583883 1583898 1585895 1585900) (-1027 "SHDP.spad" 1573376 1573403 1573893 1573990) (-1026 "SGROUP.spad" 1572984 1572993 1573366 1573371) (-1025 "SGROUP.spad" 1572590 1572601 1572974 1572979) (-1024 "catdef.spad" 1572300 1572312 1572411 1572585) (-1023 "catdef.spad" 1571856 1571868 1572121 1572295) (-1022 "SGCF.spad" 1564995 1565004 1571846 1571851) (-1021 "SFRTCAT.spad" 1563941 1563958 1564963 1564990) (-1020 "SFRGCD.spad" 1563004 1563024 1563931 1563936) (-1019 "SFQCMPK.spad" 1557817 1557837 1562994 1562999) (-1018 "SEXOF.spad" 1557660 1557700 1557807 1557812) (-1017 "SEXCAT.spad" 1555488 1555528 1557650 1557655) (-1016 "SEX.spad" 1555380 1555389 1555478 1555483) (-1015 "SETMN.spad" 1553840 1553857 1555370 1555375) (-1014 "SETCAT.spad" 1553325 1553334 1553830 1553835) (-1013 "SETCAT.spad" 1552808 1552819 1553315 1553320) (-1012 "SETAGG.spad" 1549357 1549368 1552788 1552803) (-1011 "SETAGG.spad" 1545914 1545927 1549347 1549352) (-1010 "SET.spad" 1544223 1544234 1545320 1545359) (-1009 "syntax.spad" 1543926 1543935 1544213 1544218) (-1008 "SEGXCAT.spad" 1543082 1543095 1543916 1543921) (-1007 "SEGCAT.spad" 1542007 1542018 1543072 1543077) (-1006 "SEGBIND2.spad" 1541705 1541718 1541997 1542002) (-1005 "SEGBIND.spad" 1541463 1541474 1541652 1541657) (-1004 "SEGAST.spad" 1541193 1541202 1541453 1541458) (-1003 "SEG2.spad" 1540628 1540641 1541149 1541154) (-1002 "SEG.spad" 1540441 1540452 1540547 1540552) (-1001 "SDVAR.spad" 1539717 1539728 1540431 1540436) (-1000 "SDPOL.spad" 1537409 1537420 1537700 1537827) (-999 "SCPKG.spad" 1535499 1535509 1537399 1537404) (-998 "SCOPE.spad" 1534677 1534685 1535489 1535494) (-997 "SCACHE.spad" 1533374 1533384 1534667 1534672) (-996 "SASTCAT.spad" 1533284 1533292 1533364 1533369) (-995 "SAOS.spad" 1533157 1533165 1533274 1533279) (-994 "SAERFFC.spad" 1532871 1532890 1533147 1533152) (-993 "SAEFACT.spad" 1532573 1532592 1532861 1532866) (-992 "SAE.spad" 1530224 1530239 1530834 1530969) (-991 "RURPK.spad" 1527884 1527899 1530214 1530219) (-990 "RULESET.spad" 1527338 1527361 1527874 1527879) (-989 "RULECOLD.spad" 1527191 1527203 1527328 1527333) (-988 "RULE.spad" 1525440 1525463 1527181 1527186) (-987 "RTVALUE.spad" 1525176 1525184 1525430 1525435) (-986 "syntax.spad" 1524894 1524902 1525166 1525171) (-985 "RSETGCD.spad" 1521337 1521356 1524884 1524889) (-984 "RSETCAT.spad" 1511306 1511322 1521305 1521332) (-983 "RSETCAT.spad" 1501295 1501313 1511296 1511301) (-982 "RSDCMPK.spad" 1499796 1499815 1501285 1501290) (-981 "RRCC.spad" 1498181 1498210 1499786 1499791) (-980 "RRCC.spad" 1496564 1496595 1498171 1498176) (-979 "RPTAST.spad" 1496267 1496275 1496554 1496559) (-978 "RPOLCAT.spad" 1475772 1475786 1496135 1496262) (-977 "RPOLCAT.spad" 1455070 1455086 1475435 1475440) (-976 "ROMAN.spad" 1454399 1454407 1454936 1455065) (-975 "ROIRC.spad" 1453480 1453511 1454389 1454394) (-974 "RNS.spad" 1452457 1452465 1453382 1453475) (-973 "RNS.spad" 1451520 1451530 1452447 1452452) (-972 "RNGBIND.spad" 1450681 1450694 1451475 1451480) (-971 "RNG.spad" 1450290 1450298 1450671 1450676) (-970 "RNG.spad" 1449897 1449907 1450280 1450285) (-969 "RMODULE.spad" 1449679 1449689 1449887 1449892) (-968 "RMCAT2.spad" 1449100 1449156 1449669 1449674) (-967 "RMATRIX.spad" 1447910 1447928 1448252 1448291) (-966 "RMATCAT.spad" 1443548 1443578 1447866 1447905) (-965 "RMATCAT.spad" 1439076 1439108 1443396 1443401) (-964 "RLINSET.spad" 1438781 1438791 1439066 1439071) (-963 "RINTERP.spad" 1438670 1438689 1438771 1438776) (-962 "RING.spad" 1438141 1438149 1438650 1438665) (-961 "RING.spad" 1437620 1437630 1438131 1438136) (-960 "RIDIST.spad" 1437013 1437021 1437610 1437615) (-959 "RGCHAIN.spad" 1435568 1435583 1436461 1436488) (-958 "RGBCSPC.spad" 1435358 1435369 1435558 1435563) (-957 "RGBCMDL.spad" 1434921 1434932 1435348 1435353) (-956 "RFFACTOR.spad" 1434384 1434394 1434911 1434916) (-955 "RFFACT.spad" 1434120 1434131 1434374 1434379) (-954 "RFDIST.spad" 1433117 1433125 1434110 1434115) (-953 "RF.spad" 1430792 1430802 1433107 1433112) (-952 "RETSOL.spad" 1430212 1430224 1430782 1430787) (-951 "RETRACT.spad" 1429641 1429651 1430202 1430207) (-950 "RETRACT.spad" 1429068 1429080 1429631 1429636) (-949 "RETAST.spad" 1428881 1428889 1429058 1429063) (-948 "RESRING.spad" 1428229 1428275 1428819 1428876) (-947 "RESLATC.spad" 1427554 1427564 1428219 1428224) (-946 "REPSQ.spad" 1427286 1427296 1427544 1427549) (-945 "REPDB.spad" 1426994 1427004 1427276 1427281) (-944 "REP2.spad" 1416709 1416719 1426836 1426841) (-943 "REP1.spad" 1410930 1410940 1416659 1416664) (-942 "REP.spad" 1408485 1408493 1410920 1410925) (-941 "REGSET.spad" 1406311 1406327 1408119 1408146) (-940 "REF.spad" 1405830 1405840 1406301 1406306) (-939 "REDORDER.spad" 1405037 1405053 1405820 1405825) (-938 "RECLOS.spad" 1403934 1403953 1404637 1404730) (-937 "REALSOLV.spad" 1403075 1403083 1403924 1403929) (-936 "REAL0Q.spad" 1400374 1400388 1403065 1403070) (-935 "REAL0.spad" 1397219 1397233 1400364 1400369) (-934 "REAL.spad" 1397092 1397100 1397209 1397214) (-933 "RDUCEAST.spad" 1396814 1396822 1397082 1397087) (-932 "RDIV.spad" 1396470 1396494 1396804 1396809) (-931 "RDIST.spad" 1396038 1396048 1396460 1396465) (-930 "RDETRS.spad" 1394903 1394920 1396028 1396033) (-929 "RDETR.spad" 1393043 1393060 1394893 1394898) (-928 "RDEEFS.spad" 1392143 1392159 1393033 1393038) (-927 "RDEEF.spad" 1391154 1391170 1392133 1392138) (-926 "RCFIELD.spad" 1388373 1388381 1391056 1391149) (-925 "RCFIELD.spad" 1385678 1385688 1388363 1388368) (-924 "RCAGG.spad" 1383615 1383625 1385668 1385673) (-923 "RCAGG.spad" 1381479 1381491 1383534 1383539) (-922 "RATRET.spad" 1380840 1380850 1381469 1381474) (-921 "RATFACT.spad" 1380533 1380544 1380830 1380835) (-920 "RANDSRC.spad" 1379853 1379861 1380523 1380528) (-919 "RADUTIL.spad" 1379610 1379618 1379843 1379848) (-918 "RADIX.spad" 1376655 1376668 1378200 1378293) (-917 "RADFF.spad" 1374572 1374608 1374690 1374846) (-916 "RADCAT.spad" 1374168 1374176 1374562 1374567) (-915 "RADCAT.spad" 1373762 1373772 1374158 1374163) (-914 "QUEUE.spad" 1373176 1373186 1373434 1373461) (-913 "QUATCT2.spad" 1372797 1372815 1373166 1373171) (-912 "QUATCAT.spad" 1370968 1370978 1372727 1372792) (-911 "QUATCAT.spad" 1368904 1368916 1370665 1370670) (-910 "QUAT.spad" 1367511 1367521 1367853 1367918) (-909 "QUAGG.spad" 1366345 1366355 1367479 1367506) (-908 "QQUTAST.spad" 1366114 1366122 1366335 1366340) (-907 "QFORM.spad" 1365733 1365747 1366104 1366109) (-906 "QFCAT2.spad" 1365426 1365442 1365723 1365728) (-905 "QFCAT.spad" 1364129 1364139 1365328 1365421) (-904 "QFCAT.spad" 1362465 1362477 1363666 1363671) (-903 "QEQUAT.spad" 1362024 1362032 1362455 1362460) (-902 "QCMPACK.spad" 1356939 1356958 1362014 1362019) (-901 "QALGSET2.spad" 1354935 1354953 1356929 1356934) (-900 "QALGSET.spad" 1351040 1351072 1354849 1354854) (-899 "PWFFINTB.spad" 1348456 1348477 1351030 1351035) (-898 "PUSHVAR.spad" 1347795 1347814 1348446 1348451) (-897 "PTRANFN.spad" 1343931 1343941 1347785 1347790) (-896 "PTPACK.spad" 1341019 1341029 1343921 1343926) (-895 "PTFUNC2.spad" 1340842 1340856 1341009 1341014) (-894 "PTCAT.spad" 1340097 1340107 1340810 1340837) (-893 "PSQFR.spad" 1339412 1339436 1340087 1340092) (-892 "PSEUDLIN.spad" 1338298 1338308 1339402 1339407) (-891 "PSETPK.spad" 1325003 1325019 1338176 1338181) (-890 "PSETCAT.spad" 1319403 1319426 1324983 1324998) (-889 "PSETCAT.spad" 1313777 1313802 1319359 1319364) (-888 "PSCURVE.spad" 1312776 1312784 1313767 1313772) (-887 "PSCAT.spad" 1311559 1311588 1312674 1312771) (-886 "PSCAT.spad" 1310432 1310463 1311549 1311554) (-885 "PRTITION.spad" 1309130 1309138 1310422 1310427) (-884 "PRTDAST.spad" 1308849 1308857 1309120 1309125) (-883 "PRS.spad" 1298467 1298484 1308805 1308810) (-882 "PRQAGG.spad" 1297902 1297912 1298435 1298462) (-881 "PROPLOG.spad" 1297506 1297514 1297892 1297897) (-880 "PROPFUN2.spad" 1297129 1297142 1297496 1297501) (-879 "PROPFUN1.spad" 1296535 1296546 1297119 1297124) (-878 "PROPFRML.spad" 1295103 1295114 1296525 1296530) (-877 "PROPERTY.spad" 1294599 1294607 1295093 1295098) (-876 "PRODUCT.spad" 1292296 1292308 1292580 1292635) (-875 "PRINT.spad" 1292048 1292056 1292286 1292291) (-874 "PRIMES.spad" 1290309 1290319 1292038 1292043) (-873 "PRIMELT.spad" 1288430 1288444 1290299 1290304) (-872 "PRIMCAT.spad" 1288073 1288081 1288420 1288425) (-871 "PRIMARR2.spad" 1286840 1286852 1288063 1288068) (-870 "PRIMARR.spad" 1285895 1285905 1286065 1286092) (-869 "PREASSOC.spad" 1285277 1285289 1285885 1285890) (-868 "PR.spad" 1283795 1283807 1284494 1284621) (-867 "PPCURVE.spad" 1282932 1282940 1283785 1283790) (-866 "PORTNUM.spad" 1282723 1282731 1282922 1282927) (-865 "POLYROOT.spad" 1281572 1281594 1282679 1282684) (-864 "POLYLIFT.spad" 1280837 1280860 1281562 1281567) (-863 "POLYCATQ.spad" 1278963 1278985 1280827 1280832) (-862 "POLYCAT.spad" 1272465 1272486 1278831 1278958) (-861 "POLYCAT.spad" 1265487 1265510 1271855 1271860) (-860 "POLY2UP.spad" 1264939 1264953 1265477 1265482) (-859 "POLY2.spad" 1264536 1264548 1264929 1264934) (-858 "POLY.spad" 1262204 1262214 1262719 1262846) (-857 "POLUTIL.spad" 1261169 1261198 1262160 1262165) (-856 "POLTOPOL.spad" 1259917 1259932 1261159 1261164) (-855 "POINT.spad" 1258800 1258810 1258887 1258914) (-854 "PNTHEORY.spad" 1255502 1255510 1258790 1258795) (-853 "PMTOOLS.spad" 1254277 1254291 1255492 1255497) (-852 "PMSYM.spad" 1253826 1253836 1254267 1254272) (-851 "PMQFCAT.spad" 1253417 1253431 1253816 1253821) (-850 "PMPREDFS.spad" 1252879 1252901 1253407 1253412) (-849 "PMPRED.spad" 1252366 1252380 1252869 1252874) (-848 "PMPLCAT.spad" 1251443 1251461 1252295 1252300) (-847 "PMLSAGG.spad" 1251028 1251042 1251433 1251438) (-846 "PMKERNEL.spad" 1250607 1250619 1251018 1251023) (-845 "PMINS.spad" 1250187 1250197 1250597 1250602) (-844 "PMFS.spad" 1249764 1249782 1250177 1250182) (-843 "PMDOWN.spad" 1249054 1249068 1249754 1249759) (-842 "PMASSFS.spad" 1248029 1248045 1249044 1249049) (-841 "PMASS.spad" 1247047 1247055 1248019 1248024) (-840 "PLOTTOOL.spad" 1246827 1246835 1247037 1247042) (-839 "PLOT3D.spad" 1243291 1243299 1246817 1246822) (-838 "PLOT1.spad" 1242464 1242474 1243281 1243286) (-837 "PLOT.spad" 1237387 1237395 1242454 1242459) (-836 "PLEQN.spad" 1224789 1224816 1237377 1237382) (-835 "PINTERPA.spad" 1224573 1224589 1224779 1224784) (-834 "PINTERP.spad" 1224195 1224214 1224563 1224568) (-833 "PID.spad" 1223169 1223177 1224121 1224190) (-832 "PICOERCE.spad" 1222826 1222836 1223159 1223164) (-831 "PI.spad" 1222443 1222451 1222800 1222821) (-830 "PGROEB.spad" 1221052 1221066 1222433 1222438) (-829 "PGE.spad" 1212725 1212733 1221042 1221047) (-828 "PGCD.spad" 1211679 1211696 1212715 1212720) (-827 "PFRPAC.spad" 1210828 1210838 1211669 1211674) (-826 "PFR.spad" 1207531 1207541 1210730 1210823) (-825 "PFOTOOLS.spad" 1206789 1206805 1207521 1207526) (-824 "PFOQ.spad" 1206159 1206177 1206779 1206784) (-823 "PFO.spad" 1205578 1205605 1206149 1206154) (-822 "PFECAT.spad" 1203288 1203296 1205504 1205573) (-821 "PFECAT.spad" 1201026 1201036 1203244 1203249) (-820 "PFBRU.spad" 1198914 1198926 1201016 1201021) (-819 "PFBR.spad" 1196474 1196497 1198904 1198909) (-818 "PF.spad" 1196048 1196060 1196279 1196372) (-817 "PERMGRP.spad" 1190818 1190828 1196038 1196043) (-816 "PERMCAT.spad" 1189479 1189489 1190798 1190813) (-815 "PERMAN.spad" 1188035 1188049 1189469 1189474) (-814 "PERM.spad" 1183845 1183855 1187868 1187883) (-813 "PENDTREE.spad" 1183259 1183269 1183539 1183544) (-812 "PDSPC.spad" 1182072 1182082 1183249 1183254) (-811 "PDSPC.spad" 1180883 1180895 1182062 1182067) (-810 "PDRING.spad" 1180725 1180735 1180863 1180878) (-809 "PDMOD.spad" 1180541 1180553 1180693 1180720) (-808 "PDECOMP.spad" 1180011 1180028 1180531 1180536) (-807 "PDDOM.spad" 1179449 1179462 1180001 1180006) (-806 "PDDOM.spad" 1178885 1178900 1179439 1179444) (-805 "PCOMP.spad" 1178738 1178751 1178875 1178880) (-804 "PBWLB.spad" 1177336 1177353 1178728 1178733) (-803 "PATTERN2.spad" 1177074 1177086 1177326 1177331) (-802 "PATTERN1.spad" 1175418 1175434 1177064 1177069) (-801 "PATTERN.spad" 1169993 1170003 1175408 1175413) (-800 "PATRES2.spad" 1169665 1169679 1169983 1169988) (-799 "PATRES.spad" 1167248 1167260 1169655 1169660) (-798 "PATMATCH.spad" 1165489 1165520 1167000 1167005) (-797 "PATMAB.spad" 1164918 1164928 1165479 1165484) (-796 "PATLRES.spad" 1164004 1164018 1164908 1164913) (-795 "PATAB.spad" 1163768 1163778 1163994 1163999) (-794 "PARTPERM.spad" 1161824 1161832 1163758 1163763) (-793 "PARSURF.spad" 1161258 1161286 1161814 1161819) (-792 "PARSU2.spad" 1161055 1161071 1161248 1161253) (-791 "script-parser.spad" 1160575 1160583 1161045 1161050) (-790 "PARSCURV.spad" 1160009 1160037 1160565 1160570) (-789 "PARSC2.spad" 1159800 1159816 1159999 1160004) (-788 "PARPCURV.spad" 1159262 1159290 1159790 1159795) (-787 "PARPC2.spad" 1159053 1159069 1159252 1159257) (-786 "PARAMAST.spad" 1158181 1158189 1159043 1159048) (-785 "PAN2EXPR.spad" 1157593 1157601 1158171 1158176) (-784 "PALETTE.spad" 1156707 1156715 1157583 1157588) (-783 "PAIR.spad" 1155781 1155794 1156350 1156355) (-782 "PADICRC.spad" 1153186 1153204 1154349 1154442) (-781 "PADICRAT.spad" 1151246 1151258 1151459 1151552) (-780 "PADICCT.spad" 1149795 1149807 1151172 1151241) (-779 "PADIC.spad" 1149498 1149510 1149721 1149790) (-778 "PADEPAC.spad" 1148187 1148206 1149488 1149493) (-777 "PADE.spad" 1146939 1146955 1148177 1148182) (-776 "OWP.spad" 1146187 1146217 1146797 1146864) (-775 "OVERSET.spad" 1145760 1145768 1146177 1146182) (-774 "OVAR.spad" 1145541 1145564 1145750 1145755) (-773 "OUTFORM.spad" 1134949 1134957 1145531 1145536) (-772 "OUTBFILE.spad" 1134383 1134391 1134939 1134944) (-771 "OUTBCON.spad" 1133453 1133461 1134373 1134378) (-770 "OUTBCON.spad" 1132521 1132531 1133443 1133448) (-769 "OUT.spad" 1131639 1131647 1132511 1132516) (-768 "OSI.spad" 1131114 1131122 1131629 1131634) (-767 "OSGROUP.spad" 1131032 1131040 1131104 1131109) (-766 "ORTHPOL.spad" 1129543 1129553 1130975 1130980) (-765 "OREUP.spad" 1129037 1129065 1129264 1129303) (-764 "ORESUP.spad" 1128379 1128403 1128758 1128797) (-763 "OREPCTO.spad" 1126268 1126280 1128299 1128304) (-762 "OREPCAT.spad" 1120455 1120465 1126224 1126263) (-761 "OREPCAT.spad" 1114532 1114544 1120303 1120308) (-760 "ORDTYPE.spad" 1113769 1113777 1114522 1114527) (-759 "ORDTYPE.spad" 1113004 1113014 1113759 1113764) (-758 "ORDSTRCT.spad" 1112790 1112805 1112953 1112958) (-757 "ORDSET.spad" 1112490 1112498 1112780 1112785) (-756 "ORDRING.spad" 1112307 1112315 1112470 1112485) (-755 "ORDMON.spad" 1112162 1112170 1112297 1112302) (-754 "ORDFUNS.spad" 1111294 1111310 1112152 1112157) (-753 "ORDFIN.spad" 1111114 1111122 1111284 1111289) (-752 "ORDCOMP2.spad" 1110407 1110419 1111104 1111109) (-751 "ORDCOMP.spad" 1108933 1108943 1110015 1110044) (-750 "OPSIG.spad" 1108595 1108603 1108923 1108928) (-749 "OPQUERY.spad" 1108176 1108184 1108585 1108590) (-748 "OPERCAT.spad" 1107642 1107652 1108166 1108171) (-747 "OPERCAT.spad" 1107106 1107118 1107632 1107637) (-746 "OP.spad" 1106848 1106858 1106928 1106995) (-745 "ONECOMP2.spad" 1106272 1106284 1106838 1106843) (-744 "ONECOMP.spad" 1105078 1105088 1105880 1105909) (-743 "OMSAGG.spad" 1104866 1104876 1105034 1105073) (-742 "OMLO.spad" 1104299 1104311 1104752 1104791) (-741 "OINTDOM.spad" 1104062 1104070 1104225 1104294) (-740 "OFMONOID.spad" 1102201 1102211 1104018 1104023) (-739 "ODVAR.spad" 1101462 1101472 1102191 1102196) (-738 "ODR.spad" 1101106 1101132 1101274 1101423) (-737 "ODPOL.spad" 1098754 1098764 1099094 1099221) (-736 "ODP.spad" 1088391 1088411 1088764 1088861) (-735 "ODETOOLS.spad" 1087040 1087059 1088381 1088386) (-734 "ODESYS.spad" 1084734 1084751 1087030 1087035) (-733 "ODERTRIC.spad" 1080767 1080784 1084691 1084696) (-732 "ODERED.spad" 1080166 1080190 1080757 1080762) (-731 "ODERAT.spad" 1077799 1077816 1080156 1080161) (-730 "ODEPRRIC.spad" 1074892 1074914 1077789 1077794) (-729 "ODEPRIM.spad" 1072290 1072312 1074882 1074887) (-728 "ODEPAL.spad" 1071676 1071700 1072280 1072285) (-727 "ODEINT.spad" 1071111 1071127 1071666 1071671) (-726 "ODEEF.spad" 1066606 1066622 1071101 1071106) (-725 "ODECONST.spad" 1066151 1066169 1066596 1066601) (-724 "OCTCT2.spad" 1065792 1065810 1066141 1066146) (-723 "OCT.spad" 1064107 1064117 1064821 1064860) (-722 "OCAMON.spad" 1063955 1063963 1064097 1064102) (-721 "OC.spad" 1061751 1061761 1063911 1063950) (-720 "OC.spad" 1059286 1059298 1061448 1061453) (-719 "OASGP.spad" 1059101 1059109 1059276 1059281) (-718 "OAMONS.spad" 1058623 1058631 1059091 1059096) (-717 "OAMON.spad" 1058381 1058389 1058613 1058618) (-716 "OAMON.spad" 1058137 1058147 1058371 1058376) (-715 "OAGROUP.spad" 1057675 1057683 1058127 1058132) (-714 "OAGROUP.spad" 1057211 1057221 1057665 1057670) (-713 "NUMTUBE.spad" 1056802 1056818 1057201 1057206) (-712 "NUMQUAD.spad" 1044778 1044786 1056792 1056797) (-711 "NUMODE.spad" 1036130 1036138 1044768 1044773) (-710 "NUMFMT.spad" 1034970 1034978 1036120 1036125) (-709 "NUMERIC.spad" 1027085 1027095 1034776 1034781) (-708 "NTSCAT.spad" 1025593 1025609 1027053 1027080) (-707 "NTPOLFN.spad" 1025170 1025180 1025536 1025541) (-706 "NSUP2.spad" 1024562 1024574 1025160 1025165) (-705 "NSUP.spad" 1017999 1018009 1022419 1022572) (-704 "NSMP.spad" 1014911 1014930 1015203 1015330) (-703 "NREP.spad" 1013313 1013327 1014901 1014906) (-702 "NPCOEF.spad" 1012559 1012579 1013303 1013308) (-701 "NORMRETR.spad" 1012157 1012196 1012549 1012554) (-700 "NORMPK.spad" 1010099 1010118 1012147 1012152) (-699 "NORMMA.spad" 1009787 1009813 1010089 1010094) (-698 "NONE1.spad" 1009463 1009473 1009777 1009782) (-697 "NONE.spad" 1009204 1009212 1009453 1009458) (-696 "NODE1.spad" 1008691 1008707 1009194 1009199) (-695 "NNI.spad" 1007586 1007594 1008665 1008686) (-694 "NLINSOL.spad" 1006212 1006222 1007576 1007581) (-693 "NFINTBAS.spad" 1003772 1003789 1006202 1006207) (-692 "NETCLT.spad" 1003746 1003757 1003762 1003767) (-691 "NCODIV.spad" 1001970 1001986 1003736 1003741) (-690 "NCNTFRAC.spad" 1001612 1001626 1001960 1001965) (-689 "NCEP.spad" 999778 999792 1001602 1001607) (-688 "NASRING.spad" 999382 999390 999768 999773) (-687 "NASRING.spad" 998984 998994 999372 999377) (-686 "NARNG.spad" 998384 998392 998974 998979) (-685 "NARNG.spad" 997782 997792 998374 998379) (-684 "NAALG.spad" 997347 997357 997750 997777) (-683 "NAALG.spad" 996932 996944 997337 997342) (-682 "MULTSQFR.spad" 993890 993907 996922 996927) (-681 "MULTFACT.spad" 993273 993290 993880 993885) (-680 "MTSCAT.spad" 991367 991388 993171 993268) (-679 "MTHING.spad" 991026 991036 991357 991362) (-678 "MSYSCMD.spad" 990460 990468 991016 991021) (-677 "MSETAGG.spad" 990305 990315 990428 990455) (-676 "MSET.spad" 988254 988264 989999 990038) (-675 "MRING.spad" 985231 985243 987962 988029) (-674 "MRF2.spad" 984793 984807 985221 985226) (-673 "MRATFAC.spad" 984339 984356 984783 984788) (-672 "MPRFF.spad" 982379 982398 984329 984334) (-671 "MPOLY.spad" 980183 980198 980542 980669) (-670 "MPCPF.spad" 979447 979466 980173 980178) (-669 "MPC3.spad" 979264 979304 979437 979442) (-668 "MPC2.spad" 978918 978951 979254 979259) (-667 "MONOTOOL.spad" 977269 977286 978908 978913) (-666 "catdef.spad" 976702 976713 976923 977264) (-665 "catdef.spad" 976100 976111 976356 976697) (-664 "MONOID.spad" 975421 975429 976090 976095) (-663 "MONOID.spad" 974740 974750 975411 975416) (-662 "MONOGEN.spad" 973488 973501 974600 974735) (-661 "MONOGEN.spad" 972258 972273 973372 973377) (-660 "MONADWU.spad" 970338 970346 972248 972253) (-659 "MONADWU.spad" 968416 968426 970328 970333) (-658 "MONAD.spad" 967576 967584 968406 968411) (-657 "MONAD.spad" 966734 966744 967566 967571) (-656 "MOEBIUS.spad" 965470 965484 966714 966729) (-655 "MODULE.spad" 965340 965350 965438 965465) (-654 "MODULE.spad" 965230 965242 965330 965335) (-653 "MODRING.spad" 964565 964604 965210 965225) (-652 "MODOP.spad" 963222 963234 964387 964454) (-651 "MODMONOM.spad" 962953 962971 963212 963217) (-650 "MODMON.spad" 960023 960035 960738 960891) (-649 "MODFIELD.spad" 959385 959424 959925 960018) (-648 "MMLFORM.spad" 958245 958253 959375 959380) (-647 "MMAP.spad" 957987 958021 958235 958240) (-646 "MLO.spad" 956446 956456 957943 957982) (-645 "MLIFT.spad" 955058 955075 956436 956441) (-644 "MKUCFUNC.spad" 954593 954611 955048 955053) (-643 "MKRECORD.spad" 954181 954194 954583 954588) (-642 "MKFUNC.spad" 953588 953598 954171 954176) (-641 "MKFLCFN.spad" 952556 952566 953578 953583) (-640 "MKBCFUNC.spad" 952051 952069 952546 952551) (-639 "MHROWRED.spad" 950562 950572 952041 952046) (-638 "MFINFACT.spad" 949962 949984 950552 950557) (-637 "MESH.spad" 947757 947765 949952 949957) (-636 "MDDFACT.spad" 945976 945986 947747 947752) (-635 "MDAGG.spad" 945267 945277 945956 945971) (-634 "MCDEN.spad" 944477 944489 945257 945262) (-633 "MAYBE.spad" 943777 943788 944467 944472) (-632 "MATSTOR.spad" 941093 941103 943767 943772) (-631 "MATRIX.spad" 939872 939882 940356 940383) (-630 "MATLIN.spad" 937240 937264 939756 939761) (-629 "MATCAT2.spad" 936522 936570 937230 937235) (-628 "MATCAT.spad" 928218 928240 936490 936517) (-627 "MATCAT.spad" 919786 919810 928060 928065) (-626 "MAPPKG3.spad" 918701 918715 919776 919781) (-625 "MAPPKG2.spad" 918039 918051 918691 918696) (-624 "MAPPKG1.spad" 916867 916877 918029 918034) (-623 "MAPPAST.spad" 916206 916214 916857 916862) (-622 "MAPHACK3.spad" 916018 916032 916196 916201) (-621 "MAPHACK2.spad" 915787 915799 916008 916013) (-620 "MAPHACK1.spad" 915431 915441 915777 915782) (-619 "MAGMA.spad" 913237 913254 915421 915426) (-618 "MACROAST.spad" 912832 912840 913227 913232) (-617 "LZSTAGG.spad" 910086 910096 912822 912827) (-616 "LZSTAGG.spad" 907338 907350 910076 910081) (-615 "LWORD.spad" 904083 904100 907328 907333) (-614 "LSTAST.spad" 903867 903875 904073 904078) (-613 "LSQM.spad" 902145 902159 902539 902590) (-612 "LSPP.spad" 901680 901697 902135 902140) (-611 "LSMP1.spad" 899523 899537 901670 901675) (-610 "LSMP.spad" 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(-589 "LLINSET.spad" 874840 874850 875123 875128) (-588 "LITERAL.spad" 874746 874757 874830 874835) (-587 "LIST3.spad" 874057 874071 874736 874741) (-586 "LIST2MAP.spad" 870984 870996 874047 874052) (-585 "LIST2.spad" 869686 869698 870974 870979) (-584 "LIST.spad" 867568 867578 868911 868938) (-583 "LINSET.spad" 867347 867357 867558 867563) (-582 "LINFORM.spad" 866810 866822 867315 867342) (-581 "LINEXP.spad" 865553 865563 866800 866805) (-580 "LINELT.spad" 864924 864936 865436 865463) (-579 "LINDEP.spad" 863773 863785 864836 864841) (-578 "LINBASIS.spad" 863409 863424 863763 863768) (-577 "LIMITRF.spad" 861356 861366 863399 863404) (-576 "LIMITPS.spad" 860266 860279 861346 861351) (-575 "LIECAT.spad" 859750 859760 860192 860261) (-574 "LIECAT.spad" 859262 859274 859706 859711) (-573 "LIE.spad" 857266 857278 858540 858682) (-572 "LIB.spad" 855425 855433 855871 855898) (-571 "LGROBP.spad" 852778 852797 855415 855420) (-570 "LFCAT.spad" 851837 851845 852768 852773) (-569 "LF.spad" 850792 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 4e68d5a8..44e0d10c 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(200821 . 3577834560) +(200821 . 3577838831) ((((-773)) . T)) ((((-773)) . T)) ((((-773)) . T)) @@ -49,27 +49,27 @@ (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) (((-1147 (-485)) $) . T) ((|#1| |#2|) . T)) -((((-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) (((-1147 (-485)) $) . T) ((|#1| |#2|) . T)) +((((-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) ((($) . T)) @@ -548,7 +548,7 @@ (((|#1|) . T)) ((((-474)) |has| |#2| (-554 (-474))) (((-801 (-330))) |has| |#2| (-554 (-801 (-330)))) (((-801 (-485))) |has| |#2| (-554 (-801 (-485))))) ((($) . T)) -(((|#2| (-197 (-3958 |#1|) (-695))) . T)) +(((|#2| (-197 (-3959 |#1|) (-695))) . T)) (((|#2|) . T)) ((((-773)) . T)) ((($) . T) (((-485)) . T) (((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) . T)) @@ -563,7 +563,7 @@ ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) -(((|#2| (-197 (-3958 |#1|) (-695))) . T)) +(((|#2| (-197 (-3959 |#1|) (-695))) . T)) (((|#2|) . T)) ((($) . T) (((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) . T) (((-485)) |has| |#2| (-581 (-485)))) (((|#2|) . T) (((-485)) |has| |#2| (-581 (-485)))) @@ -576,7 +576,7 @@ (|has| |#2| (-822)) ((((-350 (-485))) |has| |#2| (-951 (-350 (-485)))) (((-485)) |has| |#2| (-951 (-485))) ((|#2|) . T) (((-774 |#1|)) . T)) ((((-485)) . T) (((-350 (-485))) OR (|has| |#2| (-38 (-350 (-485)))) (|has| |#2| (-951 (-350 (-485))))) ((|#2|) . T) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822))) (((-774 |#1|)) . T)) -(((|#2| (-197 (-3958 |#1|) (-695)) (-774 |#1|)) . T)) +(((|#2| (-197 (-3959 |#1|) (-695)) (-774 |#1|)) . T)) ((((-773)) . T)) ((((-447)) . T)) ((((-157)) . T) (((-773)) . T)) @@ -746,20 +746,20 @@ ((((-85)) |has| |#1| (-1014)) (((-773)) OR (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-312)) (|has| |#1| (-413)) (|has| |#1| (-664)) (|has| |#1| (-810 (-1091))) (|has| |#1| (-962)) (|has| |#1| (-1026)) (|has| |#1| (-1014)))) (OR (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-312)) (|has| |#1| (-413)) (|has| |#1| (-664)) (|has| |#1| (-810 (-1091))) (|has| |#1| (-962)) (|has| |#1| (-1026)) (|has| |#1| (-1014))) ((((-1091) |#1|) |has| |#1| (-456 (-1091) |#1|))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((((-773)) . T)) ((((-1096)) . T)) @@ -1362,20 +1362,20 @@ ((($) |has| |#1| (-15 * (|#1| (-350 (-485)) |#1|)))) (|has| |#1| (-15 * (|#1| (-350 (-485)) |#1|))) (((|#1|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#4|) . T)) @@ -1401,24 +1401,24 @@ ((((-1096)) . T)) ((((-773)) . T) (((-1096)) . T)) ((((-1096)) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((((-474)) |has| |#2| (-554 (-474))) (((-801 (-330))) |has| |#2| (-554 (-801 (-330)))) (((-801 (-485))) |has| |#2| (-554 (-801 (-485))))) ((($) . T)) -(((|#2| (-422 (-3958 |#1|) (-695))) . T)) +(((|#2| (-422 (-3959 |#1|) (-695))) . T)) (((|#2|) . T)) ((((-773)) . T)) ((($) . T) (((-485)) . T) (((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) . T)) @@ -1433,7 +1433,7 @@ ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) ((((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822)))) -(((|#2| (-422 (-3958 |#1|) (-695))) . T)) +(((|#2| (-422 (-3959 |#1|) (-695))) . T)) (((|#2|) . T)) ((($) . T) (((-350 (-485))) |has| |#2| (-38 (-350 (-485)))) ((|#2|) . T) (((-485)) |has| |#2| (-581 (-485)))) (((|#2|) . T) (((-485)) |has| |#2| (-581 (-485)))) @@ -1446,7 +1446,7 @@ (|has| |#2| (-822)) ((((-350 (-485))) |has| |#2| (-951 (-350 (-485)))) (((-485)) |has| |#2| (-951 (-485))) ((|#2|) . T) (((-774 |#1|)) . T)) ((((-485)) . T) (((-350 (-485))) OR (|has| |#2| (-38 (-350 (-485)))) (|has| |#2| (-951 (-350 (-485))))) ((|#2|) . T) (($) OR (|has| |#2| (-392)) (|has| |#2| (-496)) (|has| |#2| (-822))) (((-774 |#1|)) . T)) -(((|#2| (-422 (-3958 |#1|) (-695)) (-774 |#1|)) . T)) +(((|#2| (-422 (-3959 |#1|) (-695)) (-774 |#1|)) . T)) (OR (|has| |#2| (-21)) (|has| |#2| (-146)) (|has| |#2| (-312)) (|has| |#2| (-962))) (OR (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-104)) (|has| |#2| (-146)) (|has| |#2| (-312)) (|has| |#2| (-718)) (|has| |#2| (-962))) (OR (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-104)) (|has| |#2| (-146)) (|has| |#2| (-312)) (|has| |#2| (-320)) (|has| |#2| (-664)) (|has| |#2| (-718)) (|has| |#2| (-757)) (|has| |#2| (-962)) (|has| |#2| (-1014))) @@ -1689,20 +1689,20 @@ ((((-773)) . T)) ((((-773)) . T)) ((((-773)) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((($) . T)) ((($ $) . T)) @@ -1830,22 +1830,22 @@ ((((-101)) . T) (((-542)) . T)) ((((-101)) . T) (((-542)) . T)) ((((-101)) . T) (((-542)) . T) (((-773)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) ((((-1074) |#1|) . T)) ((((-1074) |#1|) . T)) ((((-1074) |#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T) ((|#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)))) ((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)))) ((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T) ((|#1|) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)))) ((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)))) ((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) ((((-1074) |#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) ((((-1074) |#1|) . T)) ((((-773)) . T)) -((((-338) (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) +((((-338) (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) ((((-474)) |has| |#1| (-554 (-474))) (((-801 (-330))) |has| |#1| (-554 (-801 (-330)))) (((-801 (-485))) |has| |#1| (-554 (-801 (-485))))) (((|#1|) . T)) ((((-773)) . T)) @@ -1898,20 +1898,20 @@ ((((-773)) . T) (((-1096)) . T)) ((((-1096)) . T)) ((((-773)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) ((((-773)) . T)) ((((-1074) (-51)) . T)) ((((-1074) (-51)) . T)) ((((-1091) (-51)) . T) (((-1074) (-51)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T) (((-51)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))))) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T) (((-51)) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) ((((-1074) (-51)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))) . T)) ((((-1074) (-51)) . T)) ((((-485) |#1|) |has| |#2| (-361 |#1|))) (((|#1|) OR (|has| |#2| (-316 |#1|)) (|has| |#2| (-361 |#1|)))) @@ -2066,7 +2066,7 @@ (((|#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -(((|#2|) |has| |#2| (-6 (-3998 "*")))) +(((|#2|) |has| |#2| (-6 (-3999 "*")))) (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3311,14 +3311,14 @@ ((((-773)) . T)) ((((-1055 |#1| |#2|)) . T)) ((((-474)) |has| |#2| (-554 (-474)))) -(((|#2|) |has| |#2| (-6 (-3998 "*")))) +(((|#2|) |has| |#2| (-6 (-3999 "*")))) (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) ((((-631 |#2|)) . T) (((-773)) . T)) ((($) . T) (((-485)) . T) ((|#2|) . T)) -(((|#2|) OR (|has| |#2| (-6 (-3998 "*"))) (|has| |#2| (-146)))) -(((|#2|) OR (|has| |#2| (-6 (-3998 "*"))) (|has| |#2| (-146)))) +(((|#2|) OR (|has| |#2| (-6 (-3999 "*"))) (|has| |#2| (-146)))) +(((|#2|) OR (|has| |#2| (-6 (-3999 "*"))) (|has| |#2| (-146)))) (((|#2|) . T)) ((((-1091)) |has| |#2| (-810 (-1091)))) ((((-1091)) OR (|has| |#2| (-810 (-1091))) (|has| |#2| (-812 (-1091))))) @@ -3360,20 +3360,20 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((((-1096)) . T)) ((((-773)) . T) (((-1096)) . T)) @@ -3406,20 +3406,20 @@ ((((-485) (-117)) . T) (((-1147 (-485)) $) . T)) ((((-117)) . T)) ((((-117)) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) ((((-773)) . T)) ((((-1074) |#1|) . T)) ((((-1074) |#1|) . T)) ((((-1074) |#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T) ((|#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)))) ((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)))) ((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T) ((|#1|) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)))) ((|#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) |has| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)))) ((|#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014)))) ((((-1074) |#1|) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) -((((-2 (|:| -3861 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) +((((-2 (|:| -3862 (-1074)) (|:| |entry| |#1|))) . T)) ((((-1074) |#1|) . T)) ((((-773)) . T)) ((((-773)) . T)) @@ -3621,20 +3621,20 @@ ((((-773)) . T)) ((((-773)) . T)) ((((-773)) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) ((((-773)) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((((-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) +((((-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) (((|#1| |#2|) . T)) ((((-773)) . T)) (((|#1|) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index c85732ec..735a3b1e 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3577834556) -(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3577838826) +(4000 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -629,12 +629,12 @@ |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| |derivationCoordinates| |generator| |one?| |monoidOperation| |neutralValue| |splitSquarefree| |normalDenom| |reshape| |totalfract| |pushdterm| |pushucoef| - |pushuconst| |numberOfMonomials| |multiset| |systemCommand| |mergeDifference| - |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| - |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |antiCommutator| - |commutator| |associator| |complexEigenvalues| |complexEigenvectors| - |isConnected?| |connectTo| |shift| |normalizedAssociate| |normalize| - |outputArgs| |normInvertible?| |normFactors| |npcoef| |listexp| + |pushuconst| |numberOfMonomials| |unique| |multiset| |systemCommand| + |mergeDifference| |squareFreePrim| |compdegd| |univcase| |consnewpol| + |nsqfree| |intChoose| |coefChoose| |myDegree| |normDeriv2| |plenaryPower| + |antiCommutator| |commutator| |associator| |complexEigenvalues| + |complexEigenvectors| |isConnected?| |connectTo| |shift| |normalizedAssociate| + |normalize| |outputArgs| |normInvertible?| |normFactors| |npcoef| |listexp| |characteristicPolynomial| |realEigenvalues| |realEigenvectors| |halfExtendedResultant2| |halfExtendedResultant1| |extendedResultant| |subResultantsChain| |lazyPseudoQuotient| |lazyPseudoRemainder| |bernoulliB| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 77f72e64..86111471 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,687 +1,687 @@ -(2826158 . 3577834564) -((-1733 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1731 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3789 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-1147 (-485)) |#2|) 44 T ELT)) (-2298 (($ $) 80 T ELT)) (-3843 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3420 (((-485) (-1 (-85) |#2|) $) 27 T ELT) (((-485) |#2| $) NIL T ELT) (((-485) |#2| $ (-485)) 96 T ELT)) (-3519 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2609 (((-584 |#2|) $) 13 T ELT)) (-3327 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3959 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2305 (($ |#2| $ (-485)) NIL T ELT) (($ $ $ (-485)) 67 T ELT)) 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T) ((-76 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1014)) (|has| |#2| (-72))) ((-553 (-773)) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-1014)) (|has| |#2| (-553 (-773)))) ((-124 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-554 (-474)) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-554 (-474))) ((-183 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-193 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-1147 (-485)) $) . T) ((-241 |#1| |#2|) . T) ((-243 (-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1014))) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-237 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-318 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-324 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-429 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-429 |#2|) . T) ((-539 (-485) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-539 |#1| |#2|) . T) ((-456 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1014))) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-550 |#1| |#2|) . T) ((-594 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-609 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-757) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-757)) ((-760) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-757)) ((-924 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1014) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-757)) (|has| |#2| (-1014))) ((-1036 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1065 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1108 |#1| |#2|) . T) ((-1130) . T) ((-1169 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) -((-3947 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ |#2|) 10 T ELT))) -(((-37 |#1| |#2|) (-10 -7 (-15 -3947 (|#1| |#2|)) (-15 -3947 (|#1| (-485))) (-15 -3947 ((-773) |#1|))) (-38 |#2|) (-146)) (T -37)) +((-1224 (*1 *2 *3 *1) (-12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014)) (-5 *2 (-633 (-2 (|:| -3862 *3) (|:| |entry| *4))))))) +(-13 (-1108 |t#1| |t#2|) (-609 (-2 (|:| -3862 |t#1|) (|:| |entry| |t#2|))) (-10 -8 (-15 -1224 ((-633 (-2 (|:| -3862 |t#1|) (|:| |entry| |t#2|))) |t#1| $)))) +(((-34) . T) ((-76 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1014)) (|has| |#2| (-72))) ((-553 (-773)) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-1014)) (|has| |#2| (-553 (-773)))) ((-124 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-554 (-474)) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-554 (-474))) ((-183 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-193 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-1147 (-485)) $) . T) ((-241 |#1| |#2|) . T) ((-243 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-237 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-318 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-324 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-429 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-429 |#2|) . T) ((-539 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-539 |#1| |#2|) . T) ((-456 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-550 |#1| |#2|) . T) ((-594 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-609 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-757) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) ((-760) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) ((-924 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1014) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| |#2| (-1014))) ((-1036 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1065 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1108 |#1| |#2|) . T) ((-1130) . T) ((-1169 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . 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T) ((-186 $) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-184 |#1|) . T) ((-190) OR (|has| |#1| (-299)) (|has| |#1| (-190))) ((-189) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-201) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-239) |has| |#1| (-1116)) ((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-258) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-260 |#1|) |has| |#1| (-260 |#1|)) ((-312) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-345) |has| |#1| (-299)) ((-320) OR (|has| |#1| (-299)) (|has| |#1| (-320))) ((-299) |has| |#1| (-299)) ((-322 |#1| (-1086 |#1|)) . T) ((-353 |#1| (-1086 |#1|)) . T) ((-288 |#1|) . T) ((-329 |#1|) . T) ((-343 |#1|) . T) ((-355 |#1|) . T) ((-392) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-433) |has| |#1| (-1116)) ((-456 (-1091) |#1|) |has| |#1| (-456 (-1091) |#1|)) ((-456 |#1| |#1|) |has| |#1| (-260 |#1|)) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-591 (-485)) |has| |#1| (-581 (-485))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-583 |#1|) . T) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-581 (-485)) |has| |#1| (-581 (-485))) ((-581 |#1|) . T) ((-655 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-655 |#1|) . T) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-662 |#1| (-1086 |#1|)) . T) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-810 (-1091)) |has| |#1| (-810 (-1091))) ((-812 (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-797 (-330)) |has| |#1| (-797 (-330))) ((-797 (-485)) |has| |#1| (-797 (-485))) ((-795 |#1|) . T) ((-822) -12 (|has| |#1| (-258)) (|has| |#1| (-822))) ((-833) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-916) -12 (|has| |#1| (-916)) (|has| |#1| (-1116))) ((-951 (-350 (-485))) |has| |#1| (-951 (-350 (-485)))) ((-951 (-485)) |has| |#1| (-951 (-485))) ((-951 |#1|) . T) ((-964 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-964 |#1|) . T) ((-964 $) . T) ((-969 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-969 |#1|) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . 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T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) (-12 (|has| |#2| (-190)) (|has| |#2| (-962)))) ((-184 |#2|) |has| |#2| (-962)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-962))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) (-12 (|has| |#2| (-190)) (|has| |#2| (-962)))) ((-225 |#2|) |has| |#2| (-962)) ((-241 (-485) |#2|) . T) ((-243 (-485) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-320) |has| |#2| (-320)) ((-318 |#2|) . T) ((-329 |#2|) |has| |#2| (-962)) ((-355 |#2|) |has| |#2| (-1014)) ((-429 |#2|) . T) ((-539 (-485) |#2|) . T) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-589 (-485)) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-589 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-589 $) |has| |#2| (-962)) ((-591 (-485)) -12 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-591 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-591 $) |has| |#2| (-962)) ((-583 |#2|) OR (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-581 (-485)) -12 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-581 |#2|) |has| |#2| (-962)) ((-655 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-664) |has| |#2| (-962)) ((-717) |has| |#2| (-718)) ((-718) |has| |#2| (-718)) ((-719) |has| |#2| (-718)) ((-722) |has| |#2| (-718)) ((-757) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-760) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-807 $ (-1091)) OR (-12 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-810 (-1091)) -12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962))) ((-812 (-1091)) OR (-12 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-951 (-350 (-485))) -12 (|has| |#2| (-951 (-350 (-485)))) (|has| |#2| (-1014))) ((-951 (-485)) -12 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014))) ((-951 |#2|) |has| |#2| (-1014)) ((-964 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-969 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-962) |has| |#2| (-962)) ((-971) |has| |#2| (-962)) ((-1026) |has| |#2| (-962)) ((-1062) |has| |#2| (-962)) ((-1014) OR (|has| |#2| (-1014)) (|has| |#2| (-962)) (|has| |#2| (-757)) (|has| |#2| (-718)) (|has| |#2| (-664)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1130) . 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T) ((-23) . T) ((-47 |#1| (-485)) . T) ((-25) . T) ((-38 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-350 (-485)))) ((-66) |has| |#1| (-38 (-350 (-485)))) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-741))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-556 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-556 (-485)) . T) ((-556 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-1091)))) ((-556 |#1|) |has| |#1| (-146)) ((-556 |#2|) . 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T) ((-146) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-554 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-554 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-554 (-474)) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-474)))) ((-554 (-801 (-330))) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-801 (-330))))) ((-554 (-801 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-801 (-485))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-312)) ((-190) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-312)) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-350 (-485)))) ((-241 (-485) |#1|) . T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-485) (-1026)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-456 (-1091) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-591 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-312)) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-312)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-581 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-312)) ((-655 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-312)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-664) . 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"XFALG" 2798328 XFALG (NIL T T) -9 NIL 2799112 NIL) (-1199 2789652 2792385 2792427 "XF" 2793045 XF (NIL T) -9 NIL 2793441 NIL) (-1198 2789370 2789480 2789647 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2788597 2788719 2788923 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2786339 2788497 2788592 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2784920 2785715 2785757 "XALG" 2785762 XALG (NIL T) -9 NIL 2785871 NIL) (-1194 2778630 2783330 2783808 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2776873 2777875 2778196 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2776472 2776744 2776813 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2775959 2776262 2776355 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2775036 2775246 2775541 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2773332 2773795 2774257 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2772221 2772806 2772848 "VSPACE" 2772984 VSPACE (NIL T) -9 NIL 2773058 NIL) (-1187 2772092 2772125 2772216 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2771935 2771989 2772057 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2768918 2769713 2770450 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2760016 2762617 2764790 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2753593 2755484 2757063 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2752077 2752472 2752878 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2750904 2751185 2751501 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2746192 2750731 2750823 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2739428 2743865 2743908 "VECTCAT" 2744896 VECTCAT (NIL T) -9 NIL 2745480 NIL) (-1178 2738707 2739033 2739423 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2738201 2738443 2738563 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2738134 2738139 2738169 "UTYPE" 2738174 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2737121 2737297 2737558 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2734972 2735480 2736004 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2724854 2730824 2730866 "UTSCAT" 2731964 UTSCAT (NIL T) -9 NIL 2732721 NIL) (-1172 2722919 2723862 2724849 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2722593 2722642 2722773 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2714304 2720789 2721268 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2708303 2711112 2711155 "URAGG" 2713225 URAGG (NIL T) -9 NIL 2713947 NIL) (-1168 2706318 2707280 2708298 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2702025 2705294 2705756 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2694454 2701949 2702020 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2683105 2690592 2690653 "UPXSCCA" 2691221 UPXSCCA (NIL T T) -9 NIL 2691453 NIL) (-1164 2682826 2682928 2683100 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2671378 2678590 2678632 "UPXSCAT" 2679272 UPXSCAT (NIL T) -9 NIL 2679880 NIL) (-1162 2670891 2670976 2671153 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2662577 2670482 2670744 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2661472 2661742 2662092 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2654175 2657660 2657714 "UPSCAT" 2658783 UPSCAT (NIL T T) -9 NIL 2659547 NIL) (-1158 2653595 2653847 2654170 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2653269 2653318 2653449 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2637399 2646353 2646395 "UPOLYC" 2648473 UPOLYC (NIL T) -9 NIL 2649693 NIL) (-1155 2631454 2634302 2637394 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2630890 2631015 2631178 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2630524 2630611 2630750 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2629337 2629604 2629908 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2628670 2628800 2628985 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2628262 2628337 2628484 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2619026 2628028 2628156 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2618388 2618525 2618730 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2616989 2617836 2618112 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2616218 2616415 2616640 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2603028 2616142 2616213 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2582834 2596069 2596130 "ULSCCAT" 2596761 ULSCCAT (NIL T T) -9 NIL 2597048 NIL) (-1143 2582169 2582455 2582829 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2570541 2577675 2577717 "ULSCAT" 2578570 ULSCAT (NIL T) -9 NIL 2579300 NIL) (-1141 2570054 2570139 2570316 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2552171 2569553 2569794 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2551205 2551898 2552012 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2552123) (-1138 2550238 2550931 2551045 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2551156) (-1137 2549271 2549964 2550078 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2550189) (-1136 2548304 2548997 2549111 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2549222) (-1135 2546311 2547532 2547562 "UFD" 2547773 UFD (NIL) -9 NIL 2547886 NIL) (-1134 2546155 2546212 2546306 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2545407 2545614 2545830 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2543627 2544080 2544545 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2543352 2543592 2543622 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2543290 2543295 2543325 "TYPE" 2543330 TYPE (NIL) -9 NIL 2543337 NIL) (-1129 2542449 2542669 2542909 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2541627 2542058 2542293 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2539781 2540354 2540893 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2538815 2539051 2539287 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2527314 2531630 2531726 "TSETCAT" 2536941 TSETCAT (NIL T T T T) -9 NIL 2538442 NIL) (-1124 2523651 2525467 2527309 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2518043 2522877 2523159 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2513380 2514393 2515322 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2512877 2512952 2513115 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2510953 2511243 2511598 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2510437 2510586 2510616 "TRIGCAT" 2510829 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2510188 2510291 2510432 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2507353 2509294 2509575 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2506459 2507155 2507185 "TRANFUN" 2507220 TRANFUN (NIL) -9 NIL 2507286 NIL) (-1115 2505923 2506174 2506454 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2505760 2505798 2505859 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2505217 2505348 2505499 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2503958 2504615 2504851 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2503770 2503807 2503879 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2501984 2502630 2503059 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2500364 2500701 2501023 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2489271 2498144 2498200 "TBAGG" 2498517 TBAGG (NIL T T) -9 NIL 2498727 NIL) (-1107 2484782 2486969 2489266 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2484259 2484384 2484529 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2483769 2484089 2484179 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2483266 2483383 2483521 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2474589 2483194 2483261 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2470342 2471637 2472882 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2469711 2469870 2470051 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2466865 2467618 2468401 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2466639 2466829 2466860 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2465593 2466278 2466404 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2466590) (-1097 2464857 2465405 2465484 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2465544) (-1096 2461680 2462839 2463539 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2459363 2460046 2460680 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2455441 2456487 2457464 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2452540 2455096 2455325 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2452136 2452223 2452345 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2448760 2450234 2451053 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2441720 2447957 2448250 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2433406 2441311 2441573 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2432685 2432824 2433041 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2432369 2432434 2432545 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2423092 2432081 2432206 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2421822 2422120 2422475 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2421227 2421305 2421496 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2403379 2420726 2420967 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2402978 2403250 2403319 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2402314 2402595 2402735 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2396916 2398175 2399128 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2396448 2396548 2396712 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2391559 2392841 2393988 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2386017 2387488 2388799 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2378932 2380996 2382787 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2369905 2378870 2378927 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2364771 2369619 2369734 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2364358 2364441 2364585 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2363509 2363710 2363945 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2363249 2363307 2363400 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2355991 2361454 2362060 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2355167 2355372 2355603 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2354412 2354783 2354930 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2353900 2354142 2354172 "STEP" 2354266 STEP (NIL) -9 NIL 2354337 NIL) (-1066 2345213 2353818 2353895 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2339432 2344011 2344054 "STAGG" 2344481 STAGG (NIL T) -9 NIL 2344655 NIL) (-1064 2337811 2338559 2339427 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2336140 2337638 2337730 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2335420 2335959 2335989 "SRING" 2335994 SRING (NIL) -9 NIL 2336014 NIL) (-1061 2328195 2333958 2334397 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2321969 2323408 2324912 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2314524 2319264 2319294 "SRAGG" 2320593 SRAGG (NIL) -9 NIL 2321197 NIL) (-1058 2313821 2314141 2314519 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2308029 2313143 2313566 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2302381 2305397 2306133 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2298810 2299629 2300266 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2297785 2298090 2298120 "SPFCAT" 2298564 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2296722 2296974 2297238 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2287480 2289754 2289784 "SPADXPT" 2294421 SPADXPT (NIL) -9 NIL 2296545 NIL) (-1051 2287282 2287328 2287397 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2284938 2287246 2287277 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2276612 2278701 2278743 "SPACEC" 2283058 SPACEC (NIL T) -9 NIL 2284863 NIL) (-1048 2274441 2276559 2276607 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2273377 2273566 2273856 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2271781 2272114 2272525 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2271046 2271280 2271541 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2267226 2268186 2269181 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2263584 2264283 2265012 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2257504 2262906 2263002 "SNTSCAT" 2263007 SNTSCAT (NIL T T T T) -9 NIL 2263077 NIL) (-1041 2251325 2256145 2256535 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2245097 2251244 2251320 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2243529 2243860 2244258 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2235269 2240095 2240197 "SMATCAT" 2241540 SMATCAT (NIL NIL T T T) -9 NIL 2242088 NIL) (-1037 2233110 2234094 2235264 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2231217 2232568 2232611 "SMAGG" 2232696 SMAGG (NIL T) -9 NIL 2232771 NIL) (-1035 2228942 2230384 2230427 "SKAGG" 2230688 SKAGG (NIL T) -9 NIL 2230824 NIL) (-1034 2224988 2228762 2228873 "SINT" NIL SINT (NIL) -8 NIL NIL 2228914) (-1033 2224798 2224842 2224908 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2223873 2224105 2224373 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2222877 2223039 2223315 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2222223 2222563 2222686 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2221569 2221876 2222016 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2219680 2220172 2220678 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2213273 2219599 2219675 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2212776 2213013 2213043 "SGROUP" 2213136 SGROUP (NIL) -9 NIL 2213198 NIL) (-1025 2212666 2212698 2212771 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2212304 2212344 2212385 "SGPOPC" 2212390 SGPOPC (NIL T) -9 NIL 2212591 NIL) (-1023 2211838 2212115 2212221 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2209261 2210030 2210752 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2203280 2208682 2208778 "SFRTCAT" 2208783 SFRTCAT (NIL T T T T) -9 NIL 2208821 NIL) (-1020 2197672 2198785 2199912 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2191848 2193009 2194173 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2190820 2191722 2191843 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2186428 2187323 2187418 "SEXCAT" 2190031 SEXCAT (NIL T T T T T) -9 NIL 2190582 NIL) (-1016 2185401 2186355 2186423 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2183792 2184377 2184679 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2183315 2183500 2183530 "SETCAT" 2183647 SETCAT (NIL) -9 NIL 2183731 NIL) (-1013 2183147 2183211 2183310 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2179374 2181601 2181644 "SETAGG" 2182512 SETAGG (NIL T) -9 NIL 2182850 NIL) (-1011 2178980 2179132 2179369 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2176106 2178927 2178975 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2175572 2175882 2175982 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2174699 2175065 2175126 "SEGXCAT" 2175412 SEGXCAT (NIL T T) -9 NIL 2175532 NIL) (-1007 2173624 2173892 2173935 "SEGCAT" 2174457 SEGCAT (NIL T) -9 NIL 2174678 NIL) (-1006 2173304 2173369 2173482 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2172370 2172840 2173048 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2171948 2172227 2172303 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2171313 2171449 2171653 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2170379 2171126 2171308 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2169632 2170327 2170374 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2161117 2169499 2169627 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2159977 2160267 2160584 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2159283 2159495 2159683 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2158633 2158790 2158966 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2158206 2158437 2158465 "SASTCAT" 2158470 SASTCAT (NIL) -9 NIL 2158483 NIL) (-995 2157673 2158098 2158172 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2157276 2157317 2157488 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2156907 2156948 2157105 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2149988 2156824 2156902 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2148638 2148967 2149363 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2147399 2147760 2148060 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2147023 2147244 2147325 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2144483 2145117 2145570 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2144322 2144355 2144423 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2143813 2144116 2144207 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2139441 2140309 2141220 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2128394 2133796 2133890 "RSETCAT" 2137946 RSETCAT (NIL T T T T) -9 NIL 2139034 NIL) (-983 2126932 2127574 2128389 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2120706 2122151 2123658 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2118588 2119145 2119217 "RRCC" 2120290 RRCC (NIL T T) -9 NIL 2120631 NIL) (-980 2118113 2118312 2118583 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2117583 2117893 2117991 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2090135 2100848 2100912 "RPOLCAT" 2111386 RPOLCAT (NIL T T T) -9 NIL 2114531 NIL) (-977 2084234 2087057 2090130 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2080401 2083982 2084120 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2078729 2079468 2079724 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2074372 2077184 2077212 "RNS" 2077474 RNS (NIL) -9 NIL 2077726 NIL) (-973 2073275 2073762 2074299 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2072393 2072794 2072994 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2071531 2072093 2072121 "RNG" 2072181 RNG (NIL) -9 NIL 2072235 NIL) (-970 2071420 2071454 2071526 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2070682 2071187 2071227 "RMODULE" 2071232 RMODULE (NIL T) -9 NIL 2071258 NIL) (-968 2069621 2069727 2070057 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2066620 2069211 2069504 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2059415 2061754 2061866 "RMATCAT" 2065171 RMATCAT (NIL NIL NIL T T T) -9 NIL 2066137 NIL) (-965 2058932 2059111 2059410 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2058500 2058711 2058752 "RLINSET" 2058813 RLINSET (NIL T) -9 NIL 2058857 NIL) (-963 2058145 2058226 2058352 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2056991 2057722 2057750 "RING" 2057805 RING (NIL) -9 NIL 2057897 NIL) (-961 2056836 2056892 2056986 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2055890 2056157 2056413 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2047030 2055518 2055719 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2046255 2046766 2046805 "RGBCSPC" 2046862 RGBCSPC (NIL T) -9 NIL 2046913 NIL) (-957 2045289 2045775 2045814 "RGBCMDL" 2046042 RGBCMDL (NIL T) -9 NIL 2046156 NIL) (-956 2045001 2045070 2045171 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2044764 2044805 2044900 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2043188 2043618 2043998 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2040775 2041443 2042111 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2040325 2040423 2040583 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2039947 2040045 2040086 "RETRACT" 2040217 RETRACT (NIL T) -9 NIL 2040304 NIL) (-950 2039827 2039858 2039942 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2039429 2039701 2039768 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2037909 2038800 2038997 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2037600 2037661 2037757 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2037343 2037384 2037489 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2037078 2037119 2037228 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2032149 2033600 2034815 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2029248 2030006 2030814 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2027217 2027839 2028439 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2020005 2025768 2026204 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2019317 2019597 2019746 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2018802 2018917 2019082 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2014395 2018205 2018426 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2013627 2013826 2014039 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2010917 2011755 2012637 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 2007499 2008535 2009594 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 2007335 2007388 2007416 "REAL" 2007421 REAL (NIL) -9 NIL 2007456 NIL) (-933 2006825 2007129 2007220 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 2006305 2006383 2006588 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 2005538 2005730 2005941 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 2004426 2004723 2005090 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 2002693 2003163 2003696 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 2001615 2001892 2002279 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 2000442 2000751 2001170 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1993790 1997302 1997330 "RCFIELD" 1998607 RCFIELD (NIL) -9 NIL 1999337 NIL) (-925 1992408 1993020 1993717 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1988612 1990500 1990541 "RCAGG" 1991608 RCAGG (NIL T) -9 NIL 1992069 NIL) (-923 1988339 1988449 1988607 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1987784 1987913 1988074 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1987401 1987480 1987599 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1986816 1986966 1987116 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1986598 1986648 1986719 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1979040 1985716 1986024 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1968742 1978907 1979035 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1968376 1968469 1968497 "RADCAT" 1968654 RADCAT (NIL) -9 NIL NIL NIL) (-915 1968214 1968274 1968371 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1966486 1968045 1968134 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1966167 1966216 1966343 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1958454 1962538 1962578 "QUATCAT" 1963356 QUATCAT (NIL T) -9 NIL 1964120 NIL) (-911 1955704 1956984 1958360 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1951544 1955654 1955699 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1949064 1950559 1950600 "QUAGG" 1950975 QUAGG (NIL T) -9 NIL 1951151 NIL) (-908 1948666 1948938 1949005 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1947672 1948302 1948465 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1947353 1947402 1947529 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1936953 1943122 1943162 "QFCAT" 1943820 QFCAT (NIL T) -9 NIL 1944813 NIL) (-904 1933837 1935276 1936859 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1933383 1933517 1933647 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1927579 1928740 1929902 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1926998 1927178 1927410 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1924820 1925348 1925771 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1923719 1923961 1924278 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1922080 1922278 1922631 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1917836 1919052 1919093 "PTRANFN" 1920977 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1916483 1916828 1917149 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1916176 1916239 1916346 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1910383 1914935 1914975 "PTCAT" 1915267 PTCAT (NIL T) -9 NIL 1915420 NIL) (-893 1910076 1910117 1910241 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1908955 1909271 1909605 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1897834 1900395 1902704 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1890874 1893617 1893711 "PSETCAT" 1896685 PSETCAT (NIL T T T T) -9 NIL 1897494 NIL) (-889 1889324 1890058 1890869 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1888643 1888838 1888866 "PSCURVE" 1889134 PSCURVE (NIL) -9 NIL 1889301 NIL) (-887 1884245 1886065 1886129 "PSCAT" 1886964 PSCAT (NIL T T T) -9 NIL 1887203 NIL) (-886 1883559 1883841 1884240 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1881956 1882871 1883134 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1881447 1881750 1881841 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1872467 1874889 1877077 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1870343 1871748 1871788 "PRQAGG" 1871971 PRQAGG (NIL T) -9 NIL 1872074 NIL) (-881 1869516 1869962 1869990 "PROPLOG" 1870129 PROPLOG (NIL) -9 NIL 1870243 NIL) (-880 1869191 1869254 1869377 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1868627 1868766 1868938 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1866875 1867638 1867935 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1866427 1866559 1866687 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1860868 1865367 1866187 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1860697 1860735 1860794 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1860136 1860276 1860427 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1858604 1859023 1859489 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1858321 1858382 1858410 "PRIMCAT" 1858534 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1857492 1857688 1857916 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1853545 1857442 1857487 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1853244 1853306 1853417 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1850380 1852893 1853126 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1849831 1849988 1850016 "PPCURVE" 1850221 PPCURVE (NIL) -9 NIL 1850357 NIL) (-866 1849444 1849689 1849772 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1847200 1847621 1848213 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1846643 1846707 1846940 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1843363 1843849 1844460 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1828954 1835083 1835147 "POLYCAT" 1838632 POLYCAT (NIL T T T) -9 NIL 1840509 NIL) (-861 1824464 1826611 1828949 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1824121 1824195 1824314 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1823814 1823877 1823984 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1817177 1823547 1823706 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1816064 1816327 1816603 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1814668 1814981 1815311 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1810002 1814618 1814663 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1808490 1808901 1809276 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1807247 1807556 1807952 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1806918 1807002 1807119 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1806497 1806572 1806746 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1805983 1806079 1806239 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1805455 1805575 1805729 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1804350 1804568 1804945 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1803961 1804046 1804198 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1803512 1803594 1803775 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1803204 1803285 1803398 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1802717 1802792 1803000 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1802065 1802193 1802395 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1801427 1801561 1801724 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1800731 1800913 1801094 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1800454 1800528 1800622 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1797022 1798211 1799127 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1796106 1796307 1796542 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1791671 1793055 1794197 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1771592 1776479 1781326 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1771332 1771385 1771488 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1770773 1770907 1771087 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1768782 1770003 1770031 "PID" 1770228 PID (NIL) -9 NIL 1770355 NIL) (-832 1768570 1768613 1768688 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1767757 1768417 1768504 "PI" NIL PI (NIL) -8 NIL NIL 1768544) (-830 1767209 1767360 1767536 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1763537 1764495 1765400 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1761901 1762190 1762556 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1761343 1761458 1761619 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1757884 1760212 1760565 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1756490 1756770 1757095 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1755255 1755509 1755857 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1753965 1754192 1754544 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1750975 1752535 1752563 "PFECAT" 1753156 PFECAT (NIL) -9 NIL 1753533 NIL) (-821 1750598 1750763 1750970 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1749422 1749704 1750005 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1747604 1747991 1748421 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1743574 1747530 1747599 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1739477 1740624 1741491 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1737409 1738498 1738539 "PERMCAT" 1738938 PERMCAT (NIL T) -9 NIL 1739235 NIL) (-815 1737105 1737152 1737275 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1733554 1735235 1735880 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1731023 1733309 1733430 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1729892 1730155 1730196 "PDSPC" 1730729 PDSPC (NIL T) -9 NIL 1730974 NIL) (-811 1729259 1729525 1729887 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1727894 1728887 1728928 "PDRING" 1728933 PDRING (NIL T) -9 NIL 1728960 NIL) (-809 1726604 1727393 1727446 "PDMOD" 1727451 PDMOD (NIL T T) -9 NIL 1727554 NIL) (-808 1725697 1725909 1726158 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1725302 1725369 1725423 "PDDOM" 1725588 PDDOM (NIL T T) -9 NIL 1725668 NIL) (-806 1725154 1725190 1725297 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1724940 1724979 1725068 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1723257 1724011 1724310 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1722946 1723009 1723118 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1721084 1721514 1721965 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1714704 1716533 1717825 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1714335 1714408 1714540 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1712037 1712717 1713198 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1710241 1710669 1711072 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1709687 1709935 1709976 "PATMAB" 1710083 PATMAB (NIL T) -9 NIL 1710166 NIL) (-796 1708334 1708738 1708995 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1707872 1708003 1708044 "PATAB" 1708049 PATAB (NIL T) -9 NIL 1708221 NIL) (-794 1706415 1706852 1707275 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1706093 1706168 1706270 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1705782 1705845 1705954 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1705587 1705633 1705700 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1705265 1705340 1705442 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1704954 1705017 1705126 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1704645 1704715 1704812 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1704334 1704397 1704506 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1703495 1703874 1704053 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1703102 1703200 1703319 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1702070 1702495 1702714 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1700735 1701389 1701749 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1693825 1700139 1700333 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1686246 1693323 1693507 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1682971 1684886 1684926 "PADICCT" 1685507 PADICCT (NIL NIL) -9 NIL 1685789 NIL) (-779 1680961 1682921 1682966 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1680123 1680333 1680599 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1679465 1679608 1679812 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1677846 1678873 1679151 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1677370 1677629 1677726 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1676429 1677107 1677279 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1666851 1669720 1671919 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1666243 1666557 1666683 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1665520 1665715 1665743 "OUTBCON" 1666061 OUTBCON (NIL) -9 NIL 1666227 NIL) (-770 1665228 1665358 1665515 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1664609 1664754 1664915 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1663980 1664407 1664496 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1663395 1663810 1663838 "OSGROUP" 1663843 OSGROUP (NIL) -9 NIL 1663865 NIL) (-766 1662359 1662620 1662905 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1659628 1662234 1662354 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1656769 1659379 1659505 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1654787 1655315 1655875 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1648129 1650669 1650709 "OREPCAT" 1653030 OREPCAT (NIL T) -9 NIL 1654132 NIL) (-761 1646155 1647089 1648124 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1645352 1645623 1645651 "ORDTYPE" 1645956 ORDTYPE (NIL) -9 NIL 1646114 NIL) (-759 1644886 1645097 1645347 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1644348 1644724 1644881 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1643842 1644205 1644233 "ORDSET" 1644238 ORDSET (NIL) -9 NIL 1644260 NIL) (-756 1642407 1643429 1643457 "ORDRING" 1643462 ORDRING (NIL) -9 NIL 1643490 NIL) (-755 1641655 1642212 1642240 "ORDMON" 1642245 ORDMON (NIL) -9 NIL 1642266 NIL) (-754 1640959 1641121 1641313 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1640170 1640678 1640706 "ORDFIN" 1640771 ORDFIN (NIL) -9 NIL 1640845 NIL) (-752 1639564 1639703 1639889 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1636239 1638532 1638938 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1635646 1636001 1636106 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1635454 1635499 1635565 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1634755 1635031 1635072 "OPERCAT" 1635283 OPERCAT (NIL T) -9 NIL 1635379 NIL) (-747 1634567 1634634 1634750 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1631933 1633369 1633865 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1631354 1631481 1631655 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1628255 1630493 1630859 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1625021 1627648 1627688 "OMSAGG" 1627749 OMSAGG (NIL T) -9 NIL 1627813 NIL) (-742 1623433 1624692 1624860 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1621629 1622870 1622898 "OINTDOM" 1622903 OINTDOM (NIL) -9 NIL 1622924 NIL) (-740 1619059 1620631 1620960 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1618313 1619009 1619054 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1615515 1618154 1618308 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1607052 1615386 1615510 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1600616 1606943 1607047 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1599588 1599825 1600098 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1597222 1597892 1598596 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1592999 1593959 1594982 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1592507 1592595 1592789 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1589956 1590538 1591211 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1587351 1587859 1588455 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1584348 1584887 1585533 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1583703 1583811 1584069 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1582861 1582986 1583207 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1579145 1579941 1580854 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1578585 1578680 1578902 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1578266 1578315 1578442 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1574869 1578065 1578184 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1574029 1574651 1574679 "OCAMON" 1574684 OCAMON (NIL) -9 NIL 1574705 NIL) (-721 1568241 1571055 1571095 "OC" 1572190 OC (NIL T) -9 NIL 1573046 NIL) (-720 1566241 1567167 1568147 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1565657 1566075 1566103 "OASGP" 1566108 OASGP (NIL) -9 NIL 1566128 NIL) (-718 1564720 1565369 1565397 "OAMONS" 1565437 OAMONS (NIL) -9 NIL 1565480 NIL) (-717 1563865 1564446 1564474 "OAMON" 1564531 OAMON (NIL) -9 NIL 1564582 NIL) (-716 1563761 1563793 1563860 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1562512 1563286 1563314 "OAGROUP" 1563460 OAGROUP (NIL) -9 NIL 1563552 NIL) (-714 1562303 1562390 1562507 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1562043 1562099 1562187 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1557105 1558668 1560195 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1553800 1554834 1555869 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1552910 1553143 1553361 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1541771 1544799 1547247 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1535792 1541194 1541288 "NTSCAT" 1541293 NTSCAT (NIL T T T T) -9 NIL 1541331 NIL) (-707 1535133 1535312 1535505 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1534826 1534889 1534996 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1522493 1532446 1533256 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1511502 1522358 1522488 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1510222 1510547 1510904 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1509058 1509322 1509680 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1508225 1508358 1508574 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1506543 1506862 1507268 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1506256 1506290 1506414 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1506075 1506110 1506179 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1505851 1506041 1506070 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1505415 1505482 1505659 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1503701 1504778 1505033 "NNI" NIL NNI (NIL) -8 NIL NIL 1505380) (-694 1502429 1502766 1503130 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1501406 1501658 1501960 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1500493 1501058 1501099 "NETCLT" 1501270 NETCLT (NIL T) -9 NIL 1501351 NIL) (-691 1499397 1499664 1499945 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1499196 1499239 1499314 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1497727 1498115 1498535 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1496360 1497326 1497354 "NASRING" 1497464 NASRING (NIL) -9 NIL 1497544 NIL) (-687 1496205 1496261 1496355 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1495134 1495812 1495840 "NARNG" 1495957 NARNG (NIL) -9 NIL 1496048 NIL) (-685 1494910 1494995 1495129 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1493676 1494430 1494470 "NAALG" 1494549 NAALG (NIL T) -9 NIL 1494610 NIL) (-683 1493546 1493581 1493671 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1488525 1489710 1490896 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1487920 1488007 1488191 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1479930 1484424 1484476 "MTSCAT" 1485536 MTSCAT (NIL T T) -9 NIL 1486050 NIL) (-679 1479696 1479756 1479848 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1479522 1479561 1479621 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1476388 1479054 1479095 "MSETAGG" 1479100 MSETAGG (NIL T) -9 NIL 1479134 NIL) (-676 1472675 1475431 1475752 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1468949 1470772 1471512 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1468586 1468659 1468788 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1468239 1468280 1468424 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1466104 1466441 1466872 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1459502 1466003 1466099 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1459027 1459068 1459276 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1458586 1458635 1458818 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1457860 1457953 1458172 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1456477 1456838 1457228 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1455998 1456065 1456104 "MONOPC" 1456164 MONOPC (NIL T) -9 NIL 1456383 NIL) (-665 1455449 1455785 1455913 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1454591 1454970 1454998 "MONOID" 1455216 MONOID (NIL) -9 NIL 1455360 NIL) (-663 1454250 1454400 1454586 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1443188 1450058 1450117 "MONOGEN" 1450791 MONOGEN (NIL T T) -9 NIL 1451247 NIL) (-661 1441200 1442086 1443069 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1439914 1440458 1440486 "MONADWU" 1440877 MONADWU (NIL) -9 NIL 1441112 NIL) (-659 1439462 1439662 1439909 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1438739 1439040 1439068 "MONAD" 1439275 MONAD (NIL) -9 NIL 1439387 NIL) (-657 1438506 1438602 1438734 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1436896 1437666 1437945 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1436030 1436557 1436597 "MODULE" 1436602 MODULE (NIL T) -9 NIL 1436640 NIL) (-654 1435709 1435835 1436025 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1433420 1434306 1434620 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1430599 1432016 1432529 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1429233 1429807 1430083 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1418452 1427898 1428311 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1415408 1417452 1417721 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1414492 1414859 1415049 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1414061 1414110 1414289 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1411886 1412882 1412922 "MLO" 1413339 MLO (NIL T) -9 NIL 1413579 NIL) (-645 1409767 1410294 1410889 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1409235 1409331 1409485 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1408905 1408981 1409104 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1408117 1408303 1408531 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1407610 1407726 1407882 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1406982 1407096 1407281 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1406009 1406282 1406559 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1405442 1405530 1405701 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1402600 1403479 1404358 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1401267 1401615 1401968 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1397928 1400372 1400413 "MDAGG" 1400670 MDAGG (NIL T) -9 NIL 1400815 NIL) (-634 1397202 1397366 1397566 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1396280 1396566 1396796 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1394377 1394954 1395515 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1390283 1393967 1394214 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1386632 1387401 1388135 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1385385 1385554 1385883 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1375016 1378472 1378548 "MATCAT" 1383536 MATCAT (NIL T T T) -9 NIL 1384982 NIL) (-627 1372297 1373603 1375011 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1370698 1371058 1371442 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1369831 1370028 1370250 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1368582 1368908 1369235 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1367744 1368146 1368322 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1367413 1367477 1367600 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1367061 1367134 1367248 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1366596 1366711 1366853 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1364805 1365573 1365874 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1364299 1364601 1364691 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1357812 1362614 1362655 "LZSTAGG" 1363432 LZSTAGG (NIL T) -9 NIL 1363722 NIL) (-616 1354931 1356365 1357807 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1352318 1353284 1353767 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1351899 1352178 1352252 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1344216 1351760 1351894 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1343579 1343724 1343952 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1341063 1341761 1342473 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1339175 1339498 1339946 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1332479 1338225 1338266 "LSAGG" 1338328 LSAGG (NIL T) -9 NIL 1338406 NIL) (-608 1330173 1331272 1332474 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1327653 1329522 1329771 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1327320 1327411 1327534 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1326991 1327070 1327098 "LOGIC" 1327209 LOGIC (NIL) -9 NIL 1327291 NIL) (-604 1326886 1326915 1326986 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1326205 1326363 1326556 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1324990 1325239 1325590 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1320812 1323611 1323651 "LODOCAT" 1324083 LODOCAT (NIL T) -9 NIL 1324294 NIL) (-600 1320605 1320681 1320807 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1317605 1320482 1320600 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1314703 1317555 1317600 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1311790 1314633 1314698 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1310843 1311018 1311320 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1308975 1310105 1310358 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1304074 1307134 1307175 "LNAGG" 1308037 LNAGG (NIL T) -9 NIL 1308472 NIL) (-593 1303461 1303728 1304069 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1300033 1300974 1301611 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1299295 1299800 1299840 "LMODULE" 1299845 LMODULE (NIL T) -9 NIL 1299871 NIL) (-590 1296645 1299031 1299154 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1296213 1296424 1296465 "LLINSET" 1296526 LLINSET (NIL T) -9 NIL 1296570 NIL) (-588 1295889 1296149 1296208 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1295488 1295568 1295707 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1293939 1294287 1294686 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1293110 1293306 1293534 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1286328 1292366 1292620 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1285905 1286138 1286179 "LINSET" 1286184 LINSET (NIL T) -9 NIL 1286217 NIL) (-582 1284806 1285528 1285695 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1283072 1283827 1283867 "LINEXP" 1284353 LINEXP (NIL T) -9 NIL 1284626 NIL) (-580 1281694 1282681 1282862 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1280521 1280793 1281095 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1279734 1280323 1280433 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1277284 1278006 1278756 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1275914 1276211 1276602 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1274707 1275309 1275349 "LIECAT" 1275489 LIECAT (NIL T) -9 NIL 1275640 NIL) (-574 1274581 1274614 1274702 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1268837 1274271 1274499 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1259272 1268513 1268669 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1255724 1256673 1257608 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1254348 1255256 1255284 "LFCAT" 1255491 LFCAT (NIL) -9 NIL 1255630 NIL) (-569 1252587 1252917 1253262 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1250104 1250769 1251450 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1247116 1248094 1248597 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1246607 1246910 1247001 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1245314 1245638 1246038 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1244580 1244665 1244891 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1239583 1243148 1243684 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1239208 1239258 1239418 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1237979 1238752 1238792 "LALG" 1238853 LALG (NIL T) -9 NIL 1238911 NIL) (-560 1237762 1237839 1237974 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1235615 1237030 1237281 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1235444 1235474 1235515 "KVTFROM" 1235577 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1234260 1234975 1235164 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1234089 1234119 1234160 "KRCFROM" 1234222 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1233191 1233388 1233683 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1233020 1233050 1233091 "KONVERT" 1233153 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1232849 1232879 1232920 "KOERCE" 1232982 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1232419 1232512 1232644 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1230472 1231366 1231738 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1221649 1228256 1228310 "KDAGG" 1228686 KDAGG (NIL T T) -9 NIL 1228912 NIL) (-549 1221114 1221346 1221644 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1214112 1220906 1221052 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1213762 1214044 1214107 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1212732 1213231 1213480 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1211858 1212307 1212512 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1210722 1211214 1211514 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1210004 1210403 1210564 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1209714 1209950 1209999 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1203969 1209404 1209632 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1203387 1203720 1203840 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1199553 1201564 1201618 "IXAGG" 1202545 IXAGG (NIL T T) -9 NIL 1203002 NIL) (-538 1198759 1199130 1199548 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1197726 1198001 1198264 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1196388 1196595 1196888 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1195339 1195561 1195844 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1195014 1195077 1195200 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1194276 1194648 1194822 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1192252 1193552 1193826 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1181800 1187569 1188726 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1181045 1181197 1181433 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1180536 1180839 1180930 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1179829 1179920 1180133 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1178961 1179186 1179426 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1177374 1177755 1178183 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1177159 1177203 1177279 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1176009 1176306 1176601 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1175282 1175633 1175784 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1174485 1174616 1174829 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1172640 1173137 1173681 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1169721 1170989 1171678 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1169546 1169586 1169646 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1165544 1169472 1169541 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1163547 1165483 1165539 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1162918 1163217 1163347 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1162371 1162659 1162791 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1161452 1162077 1162203 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1160862 1161356 1161384 "IOBCON" 1161389 IOBCON (NIL) -9 NIL 1161410 NIL) (-512 1160433 1160497 1160679 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1152477 1154848 1157173 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1149588 1150371 1151235 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1149265 1149362 1149479 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1146707 1149201 1149260 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1144819 1145348 1145915 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1144321 1144435 1144575 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1142705 1143111 1143573 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1140484 1141078 1141689 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1137857 1138467 1139187 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1137261 1137419 1137627 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1136780 1136866 1137054 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1134985 1135506 1135963 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1128067 1129720 1131449 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1127433 1127595 1127768 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1125306 1125770 1126314 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1123432 1124382 1124410 "INTDOM" 1124709 INTDOM (NIL) -9 NIL 1124914 NIL) (-495 1122985 1123187 1123427 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1118792 1121264 1121318 "INTCAT" 1122114 INTCAT (NIL T) -9 NIL 1122430 NIL) (-493 1118357 1118477 1118604 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1117197 1117369 1117675 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1116770 1116866 1117023 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1108072 1116677 1116765 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1107370 1107925 1107990 "INT8" NIL INT8 (NIL) -8 NIL NIL 1108024) (-488 1106667 1107222 1107287 "INT64" NIL INT64 (NIL) -8 NIL NIL 1107321) (-487 1105964 1106519 1106584 "INT32" NIL INT32 (NIL) -8 NIL NIL 1106618) (-486 1105261 1105816 1105881 "INT16" NIL INT16 (NIL) -8 NIL NIL 1105915) (-485 1101724 1105180 1105256 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1095781 1099264 1099292 "INS" 1100222 INS (NIL) -9 NIL 1100881 NIL) (-483 1093843 1094761 1095708 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1092902 1093125 1093400 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1092116 1092257 1092454 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1091106 1091247 1091484 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1090258 1090422 1090682 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1089538 1089653 1089841 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1088277 1088546 1088870 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1087557 1087698 1087881 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1087220 1087292 1087390 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1084298 1085784 1086307 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1083897 1084004 1084118 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1083053 1083698 1083799 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1081903 1082171 1082492 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1080893 1081833 1081898 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1080518 1080598 1080715 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1079432 1079977 1080181 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1075527 1076582 1077525 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1074381 1074704 1074732 "INBCON" 1075245 INBCON (NIL) -9 NIL 1075511 NIL) (-465 1073835 1074100 1074376 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1073329 1073631 1073721 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1072786 1073095 1073200 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1071626 1071765 1072080 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1070050 1070317 1070654 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1064893 1069981 1070045 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1064273 1064607 1064722 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1059252 1063711 1063897 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1058282 1059174 1059247 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1057854 1057931 1057985 "IEVALAB" 1058192 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1057609 1057689 1057849 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1056994 1057221 1057378 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1055987 1056914 1056989 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1055050 1055907 1055982 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1054132 1054779 1054916 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1052495 1053066 1053117 "IDPC" 1053623 IDPC (NIL T T) -9 NIL 1053936 NIL) (-449 1051783 1052417 1052490 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1050953 1051705 1051778 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1050646 1050859 1050919 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1050350 1050390 1050429 "IDEMOPC" 1050434 IDEMOPC (NIL T) -9 NIL 1050571 NIL) (-445 1047421 1048302 1049194 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1041047 1042324 1043363 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1040309 1040439 1040638 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1039482 1039981 1040119 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1037871 1038202 1038593 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1033812 1037827 1037866 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1031070 1031694 1032389 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1029296 1029776 1030309 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1027278 1029202 1029291 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1023311 1027216 1027273 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1016890 1022275 1022743 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1016458 1016521 1016694 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1015950 1016099 1016127 "HYPCAT" 1016334 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1015606 1015759 1015945 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1015219 1015464 1015547 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1015052 1015101 1015142 "HOMOTOP" 1015147 HOMOTOP (NIL T) -9 NIL 1015180 NIL) (-429 1011630 1013000 1013041 "HOAGG" 1014012 HOAGG (NIL T) -9 NIL 1014731 NIL) (-428 1010702 1011137 1011625 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 1003902 1010427 1010575 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 1002837 1003095 1003358 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 1001772 1002702 1002832 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 1000138 1001605 1001693 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 999453 999805 999938 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 993060 999386 999448 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 986199 992796 992947 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 985652 985809 985972 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 976971 985569 985647 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 976462 976765 976856 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 974012 976249 976428 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 969558 973895 974007 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 960854 969455 969553 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 952791 960223 960478 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 951815 952324 952352 "GROUP" 952555 GROUP (NIL) -9 NIL 952689 NIL) (-412 951358 951559 951810 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 950030 950369 950756 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 948852 949209 949260 "GRMOD" 949789 GRMOD (NIL T T) -9 NIL 949955 NIL) (-409 948671 948719 948847 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 944794 946005 947005 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 943516 943840 944155 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 943069 943197 943338 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 942142 942641 942692 "GRALG" 942845 GRALG (NIL T T) -9 NIL 942935 NIL) (-404 941861 941962 942137 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 938742 941554 941719 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 938155 938218 938475 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 934009 934905 935430 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 933184 933386 933624 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 928187 929114 930133 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 927935 927992 928081 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 927417 927506 927671 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 926926 926967 927180 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 925727 926010 926314 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 919002 925417 925578 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 908785 913792 914896 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 906837 907940 907968 "GCDDOM" 908223 GCDDOM (NIL) -9 NIL 908380 NIL) (-391 906460 906617 906832 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 897253 899723 902111 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 895388 895713 896131 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 894329 894518 894785 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 893200 893407 893711 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 892663 892805 892953 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 891275 891623 891936 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 889820 890141 890463 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 887446 887802 888207 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 880698 882359 883937 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 880350 880571 880639 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 879974 880195 880276 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 878071 878754 879214 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 876664 876971 877363 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 875319 875678 876002 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 874622 874746 874933 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 873596 873862 874209 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 871254 871784 872266 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 870837 870897 871066 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 869137 870051 870354 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 868285 868419 868642 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 867456 867617 867844 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 863572 866351 866392 "FSAGG" 866762 FSAGG (NIL T) -9 NIL 867023 NIL) (-368 861926 862685 863477 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 859882 860178 860722 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 858929 859111 859411 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 858610 858659 858786 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 838766 848267 848308 "FS" 852178 FS (NIL T) -9 NIL 854456 NIL) (-363 830997 834490 838469 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 830531 830658 830810 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 825054 828212 828252 "FRNAALG" 829572 FRNAALG (NIL T) -9 NIL 830170 NIL) (-360 821795 823046 824304 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 821476 821525 821652 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 819963 820520 820814 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 819249 819342 819629 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 817083 817849 818165 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 816192 816635 816676 "FRETRCT" 816681 FRETRCT (NIL T) -9 NIL 816852 NIL) (-354 815565 815843 816187 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 812309 813829 813888 "FRAMALG" 814770 FRAMALG (NIL T T) -9 NIL 815062 NIL) (-352 810905 811456 812086 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 810598 810661 810768 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 804239 810403 810593 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 803932 803995 804102 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 796240 800811 802139 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 790018 793521 793549 "FPS" 794668 FPS (NIL) -9 NIL 795224 NIL) (-346 789575 789708 789872 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 786385 788428 788456 "FPC" 788681 FPC (NIL) -9 NIL 788823 NIL) (-344 786231 786283 786380 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 785008 785717 785758 "FPATMAB" 785763 FPATMAB (NIL T) -9 NIL 785915 NIL) (-342 783438 784034 784381 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 783013 783071 783244 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 781516 782411 782585 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 780131 780636 780664 "FNCAT" 781121 FNCAT (NIL) -9 NIL 781378 NIL) (-338 779588 780098 780126 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 778175 779537 779583 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 774763 776121 776162 "FMONCAT" 777379 FMONCAT (NIL T) -9 NIL 777983 NIL) (-335 771621 772699 772752 "FMCAT" 773933 FMCAT (NIL T T) -9 NIL 774425 NIL) (-334 770321 771444 771543 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 769369 770169 770316 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 767556 768008 768502 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 765491 766027 766605 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 758877 763828 764442 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 757358 758459 758499 "FLINEXP" 758504 FLINEXP (NIL T) -9 NIL 758597 NIL) (-328 756767 757026 757353 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 755982 756141 756362 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 752865 753944 753996 "FLALG" 755223 FLALG (NIL T T) -9 NIL 755690 NIL) (-325 752036 752197 752424 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 745577 749435 749476 "FLAGG" 750731 FLAGG (NIL T) -9 NIL 751378 NIL) (-323 744685 745089 745572 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 741246 742510 742569 "FINRALG" 743697 FINRALG (NIL T T) -9 NIL 744205 NIL) (-321 740637 740902 741241 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 739935 740231 740259 "FINITE" 740455 FINITE (NIL) -9 NIL 740562 NIL) (-319 739843 739869 739930 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 737300 738521 738562 "FINAGG" 739192 FINAGG (NIL T) -9 NIL 739504 NIL) (-317 736740 736999 737295 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 728701 731292 731332 "FINAALG" 734984 FINAALG (NIL T) -9 NIL 736422 NIL) (-315 724968 726213 727336 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 723520 723939 723993 "FILECAT" 724677 FILECAT (NIL T T) -9 NIL 724893 NIL) (-313 722871 723345 723448 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 720119 721997 722025 "FIELD" 722065 FIELD (NIL) -9 NIL 722145 NIL) (-311 719144 719605 720114 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 717148 718094 718440 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 716391 716572 716791 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 711661 716329 716386 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 711323 711390 711525 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 710863 710905 711114 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 707543 708420 709197 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 702827 707475 707538 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 697506 702316 702506 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 691987 696787 697045 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 686194 691438 691649 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 685217 685427 685742 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 680657 683362 683390 "FFIELDC" 684009 FFIELDC (NIL) -9 NIL 684384 NIL) (-298 679726 680166 680652 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 679341 679399 679523 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 677485 678008 678525 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 672579 677284 677385 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 667679 672368 672475 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 662345 667470 667578 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 661799 661848 662083 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 640374 651408 651494 "FFCAT" 656644 FFCAT (NIL T T T) -9 NIL 658080 NIL) (-290 636614 637840 639146 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 631457 636545 636609 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 630349 630818 630859 "FEVALAB" 630943 FEVALAB (NIL T) -9 NIL 631204 NIL) (-287 629754 630006 630344 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 626581 627492 627607 "FDIVCAT" 629174 FDIVCAT (NIL T T T T) -9 NIL 629610 NIL) (-285 626375 626407 626576 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 625682 625775 626052 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 624168 625166 625369 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 623261 623645 623847 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 622383 622872 623012 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 613970 618613 618653 "FAXF" 620454 FAXF (NIL T) -9 NIL 621144 NIL) (-279 611886 612690 613505 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 606922 611408 611582 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 601380 603803 603855 "FAMR" 604866 FAMR (NIL T T) -9 NIL 605325 NIL) (-276 600579 600944 601375 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 599600 600521 600574 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 597194 598073 598126 "FAMONC" 599067 FAMONC (NIL T T) -9 NIL 599452 NIL) (-273 595750 597052 597189 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 593830 594191 594593 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 593107 593304 593526 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 584967 592554 592753 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 582986 583556 584142 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 579888 580530 581250 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 575045 575752 576557 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 574734 574797 574906 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 559527 573783 574209 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 550054 558847 559135 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 549548 549850 549940 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 549324 549514 549543 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 549013 549081 549194 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 548530 548672 548713 "EVALAB" 548883 EVALAB (NIL T) -9 NIL 548987 NIL) (-259 548158 548304 548525 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 545201 546796 546824 "EUCDOM" 547378 EUCDOM (NIL) -9 NIL 547727 NIL) (-257 544128 544621 545196 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 543853 543909 544009 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 543541 543605 543714 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 537312 539212 539240 "ES" 541982 ES (NIL) -9 NIL 543366 NIL) (-253 533827 535359 537151 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 533175 533328 533504 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524500 533105 533170 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524189 524252 524361 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 517816 520941 522374 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514119 515215 516308 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 512948 513298 513603 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 511833 512564 512592 "ENTIRER" 512597 ENTIRER (NIL) -9 NIL 512641 NIL) (-245 511722 511756 511828 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508355 510152 510501 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507447 507658 507712 "ELTAGG" 508092 ELTAGG (NIL T T) -9 NIL 508303 NIL) (-242 507227 507301 507442 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 506973 507008 507062 "ELTAB" 507146 ELTAB (NIL T T) -9 NIL 507198 NIL) (-240 506224 506394 506593 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 505948 506022 506050 "ELEMFUN" 506155 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 505848 505875 505943 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500394 503867 503908 "ELAGG" 504845 ELAGG (NIL T) -9 NIL 505308 NIL) (-236 499192 499730 500389 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498610 498777 498933 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497523 497842 498121 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 490916 492914 493741 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 484895 486891 487701 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482709 483115 483586 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473709 475622 477163 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 472822 473323 473472 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471520 472194 472234 "DVARCAT" 472517 DVARCAT (NIL T) -9 NIL 472657 NIL) (-227 470939 471203 471515 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463006 470807 470934 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461344 462135 462176 "DSEXT" 462539 DSEXT (NIL T) -9 NIL 462833 NIL) (-224 460149 460673 461339 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 459873 459938 460036 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456024 457240 458371 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451670 453025 454089 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450345 450706 451092 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450031 450090 450208 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449006 449304 449594 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448591 448666 448816 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441004 443116 445231 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436521 437540 438619 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433251 435148 435189 "DQAGG" 435818 DQAGG (NIL T) -9 NIL 436091 NIL) (-213 419794 427434 427516 "DPOLCAT" 429353 DPOLCAT (NIL T T T T) -9 NIL 429896 NIL) (-212 416202 417850 419789 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409360 416100 416197 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402427 409189 409355 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402020 402280 402369 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401434 401882 401962 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400720 401045 401196 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393859 400456 400607 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391608 392925 392965 "DMEXT" 392970 DMEXT (NIL T) -9 NIL 393145 NIL) (-204 391264 391326 391470 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384761 390749 390939 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381431 383584 383625 "DLAGG" 384175 DLAGG (NIL T) -9 NIL 384404 NIL) (-201 379782 380653 380681 "DIVRING" 380773 DIVRING (NIL) -9 NIL 380856 NIL) (-200 379233 379477 379777 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377661 378078 378484 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376698 376919 377184 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370325 376630 376693 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358777 365085 365138 "DIRPCAT" 365394 DIRPCAT (NIL NIL T) -9 NIL 366269 NIL) (-195 356783 357553 358440 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 356230 356396 356582 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352780 355097 355138 "DIOPS" 355570 DIOPS (NIL T) -9 NIL 355796 NIL) (-192 352440 352584 352775 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351447 352193 352221 "DIOID" 352226 DIOID (NIL) -9 NIL 352248 NIL) (-190 350275 351104 351132 "DIFRING" 351137 DIFRING (NIL) -9 NIL 351158 NIL) (-189 349911 350009 350037 "DIFFSPC" 350156 DIFFSPC (NIL) -9 NIL 350231 NIL) (-188 349652 349754 349906 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348555 349180 349220 "DIFFMOD" 349225 DIFFMOD (NIL T) -9 NIL 349322 NIL) (-186 348239 348296 348337 "DIFFDOM" 348458 DIFFDOM (NIL T) -9 NIL 348526 NIL) (-185 348120 348150 348234 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345793 347314 347354 "DIFEXT" 347359 DIFEXT (NIL T) -9 NIL 347511 NIL) (-183 342958 345275 345316 "DIAGG" 345321 DIAGG (NIL T) -9 NIL 345341 NIL) (-182 342514 342704 342953 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337860 341704 341981 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 334318 335371 336381 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328868 333472 333799 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 327434 327726 328101 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324554 325806 326202 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 322446 324385 324474 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321829 321974 322156 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 319147 319871 320671 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 317256 317714 318276 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316639 316972 317086 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309839 316364 316512 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307759 308269 308773 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 307398 307447 307598 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306657 307219 307310 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304681 305123 305483 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303973 304262 304408 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 303424 303570 303722 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300786 301579 302306 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 300225 300371 300542 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 298297 298608 298975 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297854 298109 298210 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 297055 297438 297466 "CTORCAT" 297647 CTORCAT (NIL) -9 NIL 297759 NIL) (-159 296758 296892 297050 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 296251 296508 296616 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295667 296098 296171 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 295126 295243 295396 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 291520 292276 293031 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 291011 291314 291405 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 290230 290439 290667 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289734 289839 290043 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 289487 289521 289627 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 286426 287188 287906 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285945 286087 286226 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281838 284408 284900 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281712 281739 281767 "CONDUIT" 281804 CONDUIT (NIL) -9 NIL NIL NIL) (-146 280591 281322 281350 "COMRING" 281355 COMRING (NIL) -9 NIL 281405 NIL) (-145 279756 280123 280301 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 279452 279493 279621 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 279145 279208 279315 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267987 279095 279140 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 267448 267587 267747 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 267201 267242 267340 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248632 260882 260922 "COMPCAT" 261923 COMPCAT (NIL T) -9 NIL 263265 NIL) (-138 241170 244683 248276 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240929 240963 241065 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240759 240798 240856 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 240340 240619 240693 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239917 240158 240245 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 239112 239360 239388 "COMBOPC" 239726 COMBOPC (NIL) -9 NIL 239901 NIL) (-132 238176 238428 238670 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 235108 235792 236415 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233988 234439 234674 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 233479 233782 233873 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 233166 233219 233344 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232636 232946 233044 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 229156 230226 231306 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 227451 228436 228674 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 223567 225571 225612 "CLAGG" 226538 CLAGG (NIL T) -9 NIL 227071 NIL) (-123 222460 222987 223562 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 222089 222180 222320 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 220026 220533 221081 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218987 219718 219746 "CHARZ" 219751 CHARZ (NIL) -9 NIL 219765 NIL) (-119 218781 218827 218905 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217620 218383 218411 "CHARNZ" 218472 CHARNZ (NIL) -9 NIL 218520 NIL) (-117 215098 216195 216718 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214806 214885 214913 "CFCAT" 215024 CFCAT (NIL) -9 NIL NIL NIL) (-115 214149 214278 214460 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 210310 213562 213842 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 209688 209875 210052 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 209216 209635 209683 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 208689 208998 209095 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 208180 208483 208574 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 207429 207589 207810 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 203529 204786 205494 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201895 202926 203177 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 201476 201755 201829 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200910 201163 201191 "CACHSET" 201323 CACHSET (NIL) -9 NIL 201401 NIL) (-104 200262 200677 200705 "CABMON" 200755 CABMON (NIL) -9 NIL 200811 NIL) (-103 199792 200056 200166 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 195198 199460 199621 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 194168 194872 195007 "BYTE" NIL BYTE (NIL) -8 NIL NIL 195170) (-100 191811 193935 194041 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 189425 191565 191673 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 186795 188827 188866 "BTCAT" 188933 BTCAT (NIL T) -9 NIL 189014 NIL) (-97 186546 186644 186790 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 181787 185738 185764 "BTAGG" 185875 BTAGG (NIL) -9 NIL 185983 NIL) (-95 181418 181579 181782 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 178674 180910 181100 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 177944 178096 178274 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 174481 176650 176689 "BRAGG" 177330 BRAGG (NIL T) -9 NIL 177587 NIL) (-91 173436 173931 174476 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 165970 172941 173122 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 163962 165922 165965 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 163695 163731 163842 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 161934 162367 162815 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 157900 159316 160206 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 156776 157667 157789 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 156362 156519 156545 "BOOLE" 156653 BOOLE (NIL) -9 NIL 156734 NIL) (-83 156155 156236 156357 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 155293 155820 155870 "BMODULE" 155875 BMODULE (NIL T T) -9 NIL 155939 NIL) (-81 151082 155150 155219 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 150895 150935 150974 "BINOPC" 150979 BINOPC (NIL T) -9 NIL 151024 NIL) (-79 150437 150710 150812 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 149958 150102 150240 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 143164 149688 149833 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140912 142384 142423 "BGAGG" 142679 BGAGG (NIL T) -9 NIL 142806 NIL) (-75 140781 140819 140907 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 139632 139833 140118 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 136464 138812 139117 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 136049 136142 136168 "BASTYPE" 136339 BASTYPE (NIL) -9 NIL 136435 NIL) (-71 135819 135915 136044 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 135334 135422 135572 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 134233 134908 135093 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 133970 133975 134001 "ATTREG" 134006 ATTREG (NIL) -9 NIL NIL NIL) (-67 133575 133847 133912 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 133075 133224 133250 "ATRIG" 133451 ATRIG (NIL) -9 NIL NIL NIL) (-65 132930 132983 133070 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 132500 132731 132757 "ASTCAT" 132762 ASTCAT (NIL) -9 NIL 132792 NIL) (-63 132299 132376 132495 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 130630 132132 132220 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 129437 129750 130115 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 127397 129367 129432 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 126588 126779 127000 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 122347 126319 126433 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 116765 118663 118738 "ARR2CAT" 121250 ARR2CAT (NIL T T T) -9 NIL 121971 NIL) (-56 115726 116208 116760 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 115094 115465 115587 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 114026 114194 114490 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 113727 113781 113899 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 113110 113256 113412 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 112515 112805 112925 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 110083 111244 111567 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 109608 109868 109964 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 103303 108670 109112 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 98837 100500 100550 "AMR" 101288 AMR (NIL T T) -9 NIL 101885 NIL) (-46 98191 98471 98832 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79737 98125 98186 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 76140 79413 79582 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 73150 73810 74417 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 72529 72642 72826 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68941 69566 70158 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 58430 68634 68784 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57747 57901 58079 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 56460 57255 57293 "ALGEBRA" 57298 ALGEBRA (NIL T) -9 NIL 57338 NIL) (-37 56246 56323 56455 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34174 53353 53405 "ALAGG" 53540 ALAGG (NIL T T) -9 NIL 53698 NIL) (-35 33674 33823 33849 "AHYP" 34050 AHYP (NIL) -9 NIL NIL NIL) (-34 32970 33151 33177 "AGG" 33458 AGG (NIL) -9 NIL 33645 NIL) (-33 32813 32871 32965 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30952 31412 31812 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30447 30750 30839 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29817 30112 30268 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17375 26654 26692 "ACFS" 27299 ACFS (NIL T) -9 NIL 27538 NIL) (-28 15998 16608 17370 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11550 13929 13955 "ACF" 14834 ACF (NIL) -9 NIL 15246 NIL) (-26 10646 11052 11545 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10148 10388 10414 "ABELSG" 10506 ABELSG (NIL) -9 NIL 10571 NIL) (-24 10046 10077 10143 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9201 9575 9601 "ABELMON" 9826 ABELMON (NIL) -9 NIL 9959 NIL) (-22 8883 9023 9196 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8095 8578 8604 "ABELGRP" 8676 ABELGRP (NIL) -9 NIL 8751 NIL) (-20 7648 7844 8090 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6875 6914 "A1AGG" 6919 A1AGG (NIL T) -9 NIL 6953 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL))
\ No newline at end of file +((-3 2826179 2826184 2826189 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2826164 2826169 2826174 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2826149 2826154 2826159 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2826134 2826139 2826144 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1210 2825113 2826052 2826129 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1209 2824328 2824507 2824726 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1208 2815487 2817356 2819290 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2814875 2815028 2815217 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2814337 2814640 2814753 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2811897 2813799 2814002 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2808661 2810314 2810885 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2805918 2807648 2807702 "XPOLYC" 2807987 XPOLYC (NIL T T) -9 NIL 2808100 NIL) (-1202 2803437 2805422 2805625 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2799685 2802296 2802684 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2794532 2796165 2796219 "XFALG" 2798364 XFALG (NIL T T) -9 NIL 2799148 NIL) (-1199 2789688 2792421 2792463 "XF" 2793081 XF (NIL T) -9 NIL 2793477 NIL) (-1198 2789406 2789516 2789683 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2788633 2788755 2788959 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2786375 2788533 2788628 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2784956 2785751 2785793 "XALG" 2785798 XALG (NIL T) -9 NIL 2785907 NIL) (-1194 2778666 2783366 2783844 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2776909 2777911 2778232 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2776508 2776780 2776849 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2775995 2776298 2776391 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2775072 2775282 2775577 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2773368 2773831 2774293 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2772257 2772842 2772884 "VSPACE" 2773020 VSPACE (NIL T) -9 NIL 2773094 NIL) (-1187 2772128 2772161 2772252 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2771971 2772025 2772093 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2768954 2769749 2770486 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2760052 2762653 2764826 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2753629 2755520 2757099 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2752113 2752508 2752914 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2750940 2751221 2751537 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2746228 2750767 2750859 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2739464 2743901 2743944 "VECTCAT" 2744932 VECTCAT (NIL T) -9 NIL 2745516 NIL) (-1178 2738743 2739069 2739459 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2738237 2738479 2738599 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2738170 2738175 2738205 "UTYPE" 2738210 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2737157 2737333 2737594 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2735008 2735516 2736040 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2724890 2730860 2730902 "UTSCAT" 2732000 UTSCAT (NIL T) -9 NIL 2732757 NIL) (-1172 2722955 2723898 2724885 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2722629 2722678 2722809 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2714340 2720825 2721304 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2708339 2711148 2711191 "URAGG" 2713261 URAGG (NIL T) -9 NIL 2713983 NIL) (-1168 2706354 2707316 2708334 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2702061 2705330 2705792 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2694490 2701985 2702056 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2683141 2690628 2690689 "UPXSCCA" 2691257 UPXSCCA (NIL T T) -9 NIL 2691489 NIL) (-1164 2682862 2682964 2683136 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2671414 2678626 2678668 "UPXSCAT" 2679308 UPXSCAT (NIL T) -9 NIL 2679916 NIL) (-1162 2670927 2671012 2671189 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2662613 2670518 2670780 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2661508 2661778 2662128 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2654211 2657696 2657750 "UPSCAT" 2658819 UPSCAT (NIL T T) -9 NIL 2659583 NIL) (-1158 2653631 2653883 2654206 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2653305 2653354 2653485 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2637435 2646389 2646431 "UPOLYC" 2648509 UPOLYC (NIL T) -9 NIL 2649729 NIL) (-1155 2631490 2634338 2637430 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2630926 2631051 2631214 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2630560 2630647 2630786 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2629373 2629640 2629944 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2628706 2628836 2629021 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2628298 2628373 2628520 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2619062 2628064 2628192 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2618424 2618561 2618766 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2617025 2617872 2618148 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2616254 2616451 2616676 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2603064 2616178 2616249 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2582870 2596105 2596166 "ULSCCAT" 2596797 ULSCCAT (NIL T T) -9 NIL 2597084 NIL) (-1143 2582205 2582491 2582865 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2570577 2577711 2577753 "ULSCAT" 2578606 ULSCAT (NIL T) -9 NIL 2579336 NIL) (-1141 2570090 2570175 2570352 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2552207 2569589 2569830 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2551241 2551934 2552048 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2552159) (-1138 2550274 2550967 2551081 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2551192) (-1137 2549307 2550000 2550114 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2550225) (-1136 2548340 2549033 2549147 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2549258) (-1135 2546347 2547568 2547598 "UFD" 2547809 UFD (NIL) -9 NIL 2547922 NIL) (-1134 2546191 2546248 2546342 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2545443 2545650 2545866 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2543663 2544116 2544581 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2543388 2543628 2543658 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2543326 2543331 2543361 "TYPE" 2543366 TYPE (NIL) -9 NIL 2543373 NIL) (-1129 2542485 2542705 2542945 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2541663 2542094 2542329 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2539817 2540390 2540929 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2538851 2539087 2539323 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2527350 2531666 2531762 "TSETCAT" 2536977 TSETCAT (NIL T T T T) -9 NIL 2538478 NIL) (-1124 2523687 2525503 2527345 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2518079 2522913 2523195 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2513416 2514429 2515358 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2512913 2512988 2513151 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2510989 2511279 2511634 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2510473 2510622 2510652 "TRIGCAT" 2510865 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2510224 2510327 2510468 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2507389 2509330 2509611 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2506495 2507191 2507221 "TRANFUN" 2507256 TRANFUN (NIL) -9 NIL 2507322 NIL) (-1115 2505959 2506210 2506490 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2505796 2505834 2505895 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2505253 2505384 2505535 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2503994 2504651 2504887 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2503806 2503843 2503915 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2502020 2502666 2503095 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2500400 2500737 2501059 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2489307 2498180 2498236 "TBAGG" 2498553 TBAGG (NIL T T) -9 NIL 2498763 NIL) (-1107 2484818 2487005 2489302 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2484295 2484420 2484565 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2483805 2484125 2484215 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2483302 2483419 2483557 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2474625 2483230 2483297 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2470378 2471673 2472918 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2469747 2469906 2470087 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2466901 2467654 2468437 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2466675 2466865 2466896 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2465629 2466314 2466440 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2466626) (-1097 2464893 2465441 2465520 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2465580) (-1096 2461716 2462875 2463575 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2459399 2460082 2460716 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2455477 2456523 2457500 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2452576 2455132 2455361 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2452172 2452259 2452381 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2448796 2450270 2451089 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2441756 2447993 2448286 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2433442 2441347 2441609 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2432721 2432860 2433077 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2432405 2432470 2432581 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2423128 2432117 2432242 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2421858 2422156 2422511 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2421263 2421341 2421532 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2403415 2420762 2421003 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2403014 2403286 2403355 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2402350 2402631 2402771 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2396952 2398211 2399164 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2396484 2396584 2396748 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2391595 2392877 2394024 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2386053 2387524 2388835 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2378968 2381032 2382823 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2369941 2378906 2378963 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2364807 2369655 2369770 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2364394 2364477 2364621 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2363545 2363746 2363981 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2363285 2363343 2363436 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2356027 2361490 2362096 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2355203 2355408 2355639 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2354448 2354819 2354966 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2353936 2354178 2354208 "STEP" 2354302 STEP (NIL) -9 NIL 2354373 NIL) (-1066 2345249 2353854 2353931 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2339468 2344047 2344090 "STAGG" 2344517 STAGG (NIL T) -9 NIL 2344691 NIL) (-1064 2337847 2338595 2339463 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2336176 2337674 2337766 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2335456 2335995 2336025 "SRING" 2336030 SRING (NIL) -9 NIL 2336050 NIL) (-1061 2328231 2333994 2334433 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2322005 2323444 2324948 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2314560 2319300 2319330 "SRAGG" 2320629 SRAGG (NIL) -9 NIL 2321233 NIL) (-1058 2313857 2314177 2314555 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2308065 2313179 2313602 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2302417 2305433 2306169 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2298846 2299665 2300302 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2297821 2298126 2298156 "SPFCAT" 2298600 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2296758 2297010 2297274 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2287516 2289790 2289820 "SPADXPT" 2294457 SPADXPT (NIL) -9 NIL 2296581 NIL) (-1051 2287318 2287364 2287433 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2284974 2287282 2287313 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2276648 2278737 2278779 "SPACEC" 2283094 SPACEC (NIL T) -9 NIL 2284899 NIL) (-1048 2274477 2276595 2276643 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2273413 2273602 2273892 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2271817 2272150 2272561 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2271082 2271316 2271577 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2267262 2268222 2269217 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2263620 2264319 2265048 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2257540 2262942 2263038 "SNTSCAT" 2263043 SNTSCAT (NIL T T T T) -9 NIL 2263113 NIL) (-1041 2251361 2256181 2256571 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2245133 2251280 2251356 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2243565 2243896 2244294 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2235305 2240131 2240233 "SMATCAT" 2241576 SMATCAT (NIL NIL T T T) -9 NIL 2242124 NIL) (-1037 2233146 2234130 2235300 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2231253 2232604 2232647 "SMAGG" 2232732 SMAGG (NIL T) -9 NIL 2232807 NIL) (-1035 2228978 2230420 2230463 "SKAGG" 2230724 SKAGG (NIL T) -9 NIL 2230860 NIL) (-1034 2225024 2228798 2228909 "SINT" NIL SINT (NIL) -8 NIL NIL 2228950) (-1033 2224834 2224878 2224944 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2223909 2224141 2224409 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2222913 2223075 2223351 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2222259 2222599 2222722 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2221605 2221912 2222052 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2219716 2220208 2220714 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2213309 2219635 2219711 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2212812 2213049 2213079 "SGROUP" 2213172 SGROUP (NIL) -9 NIL 2213234 NIL) (-1025 2212702 2212734 2212807 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2212340 2212380 2212421 "SGPOPC" 2212426 SGPOPC (NIL T) -9 NIL 2212627 NIL) (-1023 2211874 2212151 2212257 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2209297 2210066 2210788 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2203316 2208718 2208814 "SFRTCAT" 2208819 SFRTCAT (NIL T T T T) -9 NIL 2208857 NIL) (-1020 2197708 2198821 2199948 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2191884 2193045 2194209 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2190856 2191758 2191879 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2186464 2187359 2187454 "SEXCAT" 2190067 SEXCAT (NIL T T T T T) -9 NIL 2190618 NIL) (-1016 2185437 2186391 2186459 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2183828 2184413 2184715 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2183351 2183536 2183566 "SETCAT" 2183683 SETCAT (NIL) -9 NIL 2183767 NIL) (-1013 2183183 2183247 2183346 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2179410 2181637 2181680 "SETAGG" 2182548 SETAGG (NIL T) -9 NIL 2182886 NIL) (-1011 2179016 2179168 2179405 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2176142 2178963 2179011 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2175608 2175918 2176018 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2174735 2175101 2175162 "SEGXCAT" 2175448 SEGXCAT (NIL T T) -9 NIL 2175568 NIL) (-1007 2173660 2173928 2173971 "SEGCAT" 2174493 SEGCAT (NIL T) -9 NIL 2174714 NIL) (-1006 2173340 2173405 2173518 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2172406 2172876 2173084 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2171984 2172263 2172339 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2171349 2171485 2171689 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2170415 2171162 2171344 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2169668 2170363 2170410 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2161153 2169535 2169663 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2160013 2160303 2160620 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2159319 2159531 2159719 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2158669 2158826 2159002 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2158242 2158473 2158501 "SASTCAT" 2158506 SASTCAT (NIL) -9 NIL 2158519 NIL) (-995 2157709 2158134 2158208 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2157312 2157353 2157524 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2156943 2156984 2157141 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2150024 2156860 2156938 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2148674 2149003 2149399 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2147435 2147796 2148096 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2147059 2147280 2147361 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2144519 2145153 2145606 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2144358 2144391 2144459 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2143849 2144152 2144243 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2139477 2140345 2141256 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2128430 2133832 2133926 "RSETCAT" 2137982 RSETCAT (NIL T T T T) -9 NIL 2139070 NIL) (-983 2126968 2127610 2128425 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2120742 2122187 2123694 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2118624 2119181 2119253 "RRCC" 2120326 RRCC (NIL T T) -9 NIL 2120667 NIL) (-980 2118149 2118348 2118619 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2117619 2117929 2118027 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2090171 2100884 2100948 "RPOLCAT" 2111422 RPOLCAT (NIL T T T) -9 NIL 2114567 NIL) (-977 2084270 2087093 2090166 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2080437 2084018 2084156 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2078765 2079504 2079760 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2074408 2077220 2077248 "RNS" 2077510 RNS (NIL) -9 NIL 2077762 NIL) (-973 2073311 2073798 2074335 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2072429 2072830 2073030 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2071567 2072129 2072157 "RNG" 2072217 RNG (NIL) -9 NIL 2072271 NIL) (-970 2071456 2071490 2071562 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2070718 2071223 2071263 "RMODULE" 2071268 RMODULE (NIL T) -9 NIL 2071294 NIL) (-968 2069657 2069763 2070093 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2066656 2069247 2069540 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2059451 2061790 2061902 "RMATCAT" 2065207 RMATCAT (NIL NIL NIL T T T) -9 NIL 2066173 NIL) (-965 2058968 2059147 2059446 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2058536 2058747 2058788 "RLINSET" 2058849 RLINSET (NIL T) -9 NIL 2058893 NIL) (-963 2058181 2058262 2058388 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2057027 2057758 2057786 "RING" 2057841 RING (NIL) -9 NIL 2057933 NIL) (-961 2056872 2056928 2057022 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2055926 2056193 2056449 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2047066 2055554 2055755 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2046291 2046802 2046841 "RGBCSPC" 2046898 RGBCSPC (NIL T) -9 NIL 2046949 NIL) (-957 2045325 2045811 2045850 "RGBCMDL" 2046078 RGBCMDL (NIL T) -9 NIL 2046192 NIL) (-956 2045037 2045106 2045207 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2044800 2044841 2044936 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2043224 2043654 2044034 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2040811 2041479 2042147 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2040361 2040459 2040619 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2039983 2040081 2040122 "RETRACT" 2040253 RETRACT (NIL T) -9 NIL 2040340 NIL) (-950 2039863 2039894 2039978 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2039465 2039737 2039804 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2037945 2038836 2039033 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2037636 2037697 2037793 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2037379 2037420 2037525 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2037114 2037155 2037264 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2032185 2033636 2034851 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2029284 2030042 2030850 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2027253 2027875 2028475 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2020041 2025804 2026240 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2019353 2019633 2019782 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2018838 2018953 2019118 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2014431 2018241 2018462 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2013663 2013862 2014075 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2010953 2011791 2012673 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 2007535 2008571 2009630 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 2007371 2007424 2007452 "REAL" 2007457 REAL (NIL) -9 NIL 2007492 NIL) (-933 2006861 2007165 2007256 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 2006341 2006419 2006624 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 2005574 2005766 2005977 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 2004462 2004759 2005126 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 2002729 2003199 2003732 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 2001651 2001928 2002315 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 2000478 2000787 2001206 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1993826 1997338 1997366 "RCFIELD" 1998643 RCFIELD (NIL) -9 NIL 1999373 NIL) (-925 1992444 1993056 1993753 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1988648 1990536 1990577 "RCAGG" 1991644 RCAGG (NIL T) -9 NIL 1992105 NIL) (-923 1988375 1988485 1988643 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1987820 1987949 1988110 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1987437 1987516 1987635 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1986852 1987002 1987152 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1986634 1986684 1986755 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1979076 1985752 1986060 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1968778 1978943 1979071 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1968412 1968505 1968533 "RADCAT" 1968690 RADCAT (NIL) -9 NIL NIL NIL) (-915 1968250 1968310 1968407 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1966522 1968081 1968170 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1966203 1966252 1966379 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1958490 1962574 1962614 "QUATCAT" 1963392 QUATCAT (NIL T) -9 NIL 1964156 NIL) (-911 1955740 1957020 1958396 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1951580 1955690 1955735 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1949100 1950595 1950636 "QUAGG" 1951011 QUAGG (NIL T) -9 NIL 1951187 NIL) (-908 1948702 1948974 1949041 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1947708 1948338 1948501 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1947389 1947438 1947565 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1936989 1943158 1943198 "QFCAT" 1943856 QFCAT (NIL T) -9 NIL 1944849 NIL) (-904 1933873 1935312 1936895 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1933419 1933553 1933683 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1927615 1928776 1929938 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1927034 1927214 1927446 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1924856 1925384 1925807 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1923755 1923997 1924314 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1922116 1922314 1922667 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1917872 1919088 1919129 "PTRANFN" 1921013 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1916519 1916864 1917185 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1916212 1916275 1916382 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1910419 1914971 1915011 "PTCAT" 1915303 PTCAT (NIL T) -9 NIL 1915456 NIL) (-893 1910112 1910153 1910277 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1908991 1909307 1909641 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1897870 1900431 1902740 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1890910 1893653 1893747 "PSETCAT" 1896721 PSETCAT (NIL T T T T) -9 NIL 1897530 NIL) (-889 1889360 1890094 1890905 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1888679 1888874 1888902 "PSCURVE" 1889170 PSCURVE (NIL) -9 NIL 1889337 NIL) (-887 1884281 1886101 1886165 "PSCAT" 1887000 PSCAT (NIL T T T) -9 NIL 1887239 NIL) (-886 1883595 1883877 1884276 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1881992 1882907 1883170 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1881483 1881786 1881877 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1872503 1874925 1877113 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1870379 1871784 1871824 "PRQAGG" 1872007 PRQAGG (NIL T) -9 NIL 1872110 NIL) (-881 1869552 1869998 1870026 "PROPLOG" 1870165 PROPLOG (NIL) -9 NIL 1870279 NIL) (-880 1869227 1869290 1869413 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1868663 1868802 1868974 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1866911 1867674 1867971 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1866463 1866595 1866723 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1860904 1865403 1866223 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1860733 1860771 1860830 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1860172 1860312 1860463 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1858640 1859059 1859525 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1858357 1858418 1858446 "PRIMCAT" 1858570 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1857528 1857724 1857952 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1853581 1857478 1857523 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1853280 1853342 1853453 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1850416 1852929 1853162 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1849867 1850024 1850052 "PPCURVE" 1850257 PPCURVE (NIL) -9 NIL 1850393 NIL) (-866 1849480 1849725 1849808 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1847236 1847657 1848249 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1846679 1846743 1846976 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1843399 1843885 1844496 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1828990 1835119 1835183 "POLYCAT" 1838668 POLYCAT (NIL T T T) -9 NIL 1840545 NIL) (-861 1824500 1826647 1828985 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1824157 1824231 1824350 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1823850 1823913 1824020 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1817213 1823583 1823742 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1816100 1816363 1816639 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1814704 1815017 1815347 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1810038 1814654 1814699 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1808526 1808937 1809312 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1807283 1807592 1807988 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1806954 1807038 1807155 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1806533 1806608 1806782 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1806019 1806115 1806275 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1805491 1805611 1805765 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1804386 1804604 1804981 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1803997 1804082 1804234 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1803548 1803630 1803811 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1803240 1803321 1803434 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1802753 1802828 1803036 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1802101 1802229 1802431 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1801463 1801597 1801760 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1800767 1800949 1801130 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1800490 1800564 1800658 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1797058 1798247 1799163 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1796142 1796343 1796578 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1791707 1793091 1794233 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1771628 1776515 1781362 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1771368 1771421 1771524 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1770809 1770943 1771123 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1768818 1770039 1770067 "PID" 1770264 PID (NIL) -9 NIL 1770391 NIL) (-832 1768606 1768649 1768724 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1767793 1768453 1768540 "PI" NIL PI (NIL) -8 NIL NIL 1768580) (-830 1767245 1767396 1767572 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1763573 1764531 1765436 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1761937 1762226 1762592 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1761379 1761494 1761655 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1757920 1760248 1760601 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1756526 1756806 1757131 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1755291 1755545 1755893 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1754001 1754228 1754580 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1751011 1752571 1752599 "PFECAT" 1753192 PFECAT (NIL) -9 NIL 1753569 NIL) (-821 1750634 1750799 1751006 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1749458 1749740 1750041 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1747640 1748027 1748457 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1743610 1747566 1747635 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1739513 1740660 1741527 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1737445 1738534 1738575 "PERMCAT" 1738974 PERMCAT (NIL T) -9 NIL 1739271 NIL) (-815 1737141 1737188 1737311 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1733590 1735271 1735916 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1731059 1733345 1733466 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1729928 1730191 1730232 "PDSPC" 1730765 PDSPC (NIL T) -9 NIL 1731010 NIL) (-811 1729295 1729561 1729923 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1727930 1728923 1728964 "PDRING" 1728969 PDRING (NIL T) -9 NIL 1728996 NIL) (-809 1726640 1727429 1727482 "PDMOD" 1727487 PDMOD (NIL T T) -9 NIL 1727590 NIL) (-808 1725733 1725945 1726194 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1725338 1725405 1725459 "PDDOM" 1725624 PDDOM (NIL T T) -9 NIL 1725704 NIL) (-806 1725190 1725226 1725333 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1724976 1725015 1725104 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1723293 1724047 1724346 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1722982 1723045 1723154 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1721120 1721550 1722001 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1714740 1716569 1717861 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1714371 1714444 1714576 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1712073 1712753 1713234 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1710277 1710705 1711108 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1709723 1709971 1710012 "PATMAB" 1710119 PATMAB (NIL T) -9 NIL 1710202 NIL) (-796 1708370 1708774 1709031 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1707908 1708039 1708080 "PATAB" 1708085 PATAB (NIL T) -9 NIL 1708257 NIL) (-794 1706451 1706888 1707311 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1706129 1706204 1706306 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1705818 1705881 1705990 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1705623 1705669 1705736 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1705301 1705376 1705478 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1704990 1705053 1705162 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1704681 1704751 1704848 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1704370 1704433 1704542 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1703531 1703910 1704089 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1703138 1703236 1703355 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1702106 1702531 1702750 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1700771 1701425 1701785 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1693861 1700175 1700369 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1686282 1693359 1693543 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1683007 1684922 1684962 "PADICCT" 1685543 PADICCT (NIL NIL) -9 NIL 1685825 NIL) (-779 1680997 1682957 1683002 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1680159 1680369 1680635 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1679501 1679644 1679848 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1677882 1678909 1679187 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1677406 1677665 1677762 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1676465 1677143 1677315 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1666887 1669756 1671955 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1666279 1666593 1666719 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1665556 1665751 1665779 "OUTBCON" 1666097 OUTBCON (NIL) -9 NIL 1666263 NIL) (-770 1665264 1665394 1665551 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1664645 1664790 1664951 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1664016 1664443 1664532 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1663431 1663846 1663874 "OSGROUP" 1663879 OSGROUP (NIL) -9 NIL 1663901 NIL) (-766 1662395 1662656 1662941 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1659664 1662270 1662390 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1656805 1659415 1659541 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1654823 1655351 1655911 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1648165 1650705 1650745 "OREPCAT" 1653066 OREPCAT (NIL T) -9 NIL 1654168 NIL) (-761 1646191 1647125 1648160 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1645388 1645659 1645687 "ORDTYPE" 1645992 ORDTYPE (NIL) -9 NIL 1646150 NIL) (-759 1644922 1645133 1645383 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1644384 1644760 1644917 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1643878 1644241 1644269 "ORDSET" 1644274 ORDSET (NIL) -9 NIL 1644296 NIL) (-756 1642443 1643465 1643493 "ORDRING" 1643498 ORDRING (NIL) -9 NIL 1643526 NIL) (-755 1641691 1642248 1642276 "ORDMON" 1642281 ORDMON (NIL) -9 NIL 1642302 NIL) (-754 1640995 1641157 1641349 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1640206 1640714 1640742 "ORDFIN" 1640807 ORDFIN (NIL) -9 NIL 1640881 NIL) (-752 1639600 1639739 1639925 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1636275 1638568 1638974 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1635682 1636037 1636142 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1635490 1635535 1635601 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1634791 1635067 1635108 "OPERCAT" 1635319 OPERCAT (NIL T) -9 NIL 1635415 NIL) (-747 1634603 1634670 1634786 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1631969 1633405 1633901 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1631390 1631517 1631691 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1628291 1630529 1630895 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1625057 1627684 1627724 "OMSAGG" 1627785 OMSAGG (NIL T) -9 NIL 1627849 NIL) (-742 1623469 1624728 1624896 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1621665 1622906 1622934 "OINTDOM" 1622939 OINTDOM (NIL) -9 NIL 1622960 NIL) (-740 1619095 1620667 1620996 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1618349 1619045 1619090 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1615551 1618190 1618344 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1607088 1615422 1615546 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1600652 1606979 1607083 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1599624 1599861 1600134 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1597258 1597928 1598632 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1593035 1593995 1595018 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1592543 1592631 1592825 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1589992 1590574 1591247 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1587387 1587895 1588491 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1584384 1584923 1585569 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1583739 1583847 1584105 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1582897 1583022 1583243 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1579181 1579977 1580890 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1578621 1578716 1578938 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1578302 1578351 1578478 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1574905 1578101 1578220 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1574065 1574687 1574715 "OCAMON" 1574720 OCAMON (NIL) -9 NIL 1574741 NIL) (-721 1568277 1571091 1571131 "OC" 1572226 OC (NIL T) -9 NIL 1573082 NIL) (-720 1566277 1567203 1568183 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1565693 1566111 1566139 "OASGP" 1566144 OASGP (NIL) -9 NIL 1566164 NIL) (-718 1564756 1565405 1565433 "OAMONS" 1565473 OAMONS (NIL) -9 NIL 1565516 NIL) (-717 1563901 1564482 1564510 "OAMON" 1564567 OAMON (NIL) -9 NIL 1564618 NIL) (-716 1563797 1563829 1563896 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1562548 1563322 1563350 "OAGROUP" 1563496 OAGROUP (NIL) -9 NIL 1563588 NIL) (-714 1562339 1562426 1562543 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1562079 1562135 1562223 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1557141 1558704 1560231 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1553836 1554870 1555905 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1552946 1553179 1553397 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1541807 1544835 1547283 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1535828 1541230 1541324 "NTSCAT" 1541329 NTSCAT (NIL T T T T) -9 NIL 1541367 NIL) (-707 1535169 1535348 1535541 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1534862 1534925 1535032 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1522529 1532482 1533292 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1511538 1522394 1522524 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1510258 1510583 1510940 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1509094 1509358 1509716 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1508261 1508394 1508610 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1506579 1506898 1507304 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1506292 1506326 1506450 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1506111 1506146 1506215 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1505887 1506077 1506106 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1505451 1505518 1505695 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1503737 1504814 1505069 "NNI" NIL NNI (NIL) -8 NIL NIL 1505416) (-694 1502465 1502802 1503166 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1501442 1501694 1501996 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1500529 1501094 1501135 "NETCLT" 1501306 NETCLT (NIL T) -9 NIL 1501387 NIL) (-691 1499433 1499700 1499981 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1499232 1499275 1499350 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1497763 1498151 1498571 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1496396 1497362 1497390 "NASRING" 1497500 NASRING (NIL) -9 NIL 1497580 NIL) (-687 1496241 1496297 1496391 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1495170 1495848 1495876 "NARNG" 1495993 NARNG (NIL) -9 NIL 1496084 NIL) (-685 1494946 1495031 1495165 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1493712 1494466 1494506 "NAALG" 1494585 NAALG (NIL T) -9 NIL 1494646 NIL) (-683 1493582 1493617 1493707 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1488561 1489746 1490932 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1487956 1488043 1488227 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1479966 1484460 1484512 "MTSCAT" 1485572 MTSCAT (NIL T T) -9 NIL 1486086 NIL) (-679 1479732 1479792 1479884 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1479558 1479597 1479657 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1476424 1479090 1479131 "MSETAGG" 1479136 MSETAGG (NIL T) -9 NIL 1479170 NIL) (-676 1472675 1475467 1475788 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1468949 1470772 1471512 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1468586 1468659 1468788 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1468239 1468280 1468424 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1466104 1466441 1466872 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1459502 1466003 1466099 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1459027 1459068 1459276 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1458586 1458635 1458818 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1457860 1457953 1458172 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1456477 1456838 1457228 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1455998 1456065 1456104 "MONOPC" 1456164 MONOPC (NIL T) -9 NIL 1456383 NIL) (-665 1455449 1455785 1455913 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1454591 1454970 1454998 "MONOID" 1455216 MONOID (NIL) -9 NIL 1455360 NIL) (-663 1454250 1454400 1454586 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1443188 1450058 1450117 "MONOGEN" 1450791 MONOGEN (NIL T T) -9 NIL 1451247 NIL) (-661 1441200 1442086 1443069 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1439914 1440458 1440486 "MONADWU" 1440877 MONADWU (NIL) -9 NIL 1441112 NIL) (-659 1439462 1439662 1439909 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1438739 1439040 1439068 "MONAD" 1439275 MONAD (NIL) -9 NIL 1439387 NIL) (-657 1438506 1438602 1438734 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1436896 1437666 1437945 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1436030 1436557 1436597 "MODULE" 1436602 MODULE (NIL T) -9 NIL 1436640 NIL) (-654 1435709 1435835 1436025 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1433420 1434306 1434620 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1430599 1432016 1432529 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1429233 1429807 1430083 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1418452 1427898 1428311 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1415408 1417452 1417721 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1414492 1414859 1415049 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1414061 1414110 1414289 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1411886 1412882 1412922 "MLO" 1413339 MLO (NIL T) -9 NIL 1413579 NIL) (-645 1409767 1410294 1410889 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1409235 1409331 1409485 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1408905 1408981 1409104 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1408117 1408303 1408531 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1407610 1407726 1407882 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1406982 1407096 1407281 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1406009 1406282 1406559 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1405442 1405530 1405701 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1402600 1403479 1404358 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1401267 1401615 1401968 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1397928 1400372 1400413 "MDAGG" 1400670 MDAGG (NIL T) -9 NIL 1400815 NIL) (-634 1397202 1397366 1397566 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1396280 1396566 1396796 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1394377 1394954 1395515 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1390283 1393967 1394214 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1386632 1387401 1388135 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1385385 1385554 1385883 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1375016 1378472 1378548 "MATCAT" 1383536 MATCAT (NIL T T T) -9 NIL 1384982 NIL) (-627 1372297 1373603 1375011 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1370698 1371058 1371442 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1369831 1370028 1370250 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1368582 1368908 1369235 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1367744 1368146 1368322 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1367413 1367477 1367600 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1367061 1367134 1367248 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1366596 1366711 1366853 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1364805 1365573 1365874 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1364299 1364601 1364691 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1357812 1362614 1362655 "LZSTAGG" 1363432 LZSTAGG (NIL T) -9 NIL 1363722 NIL) (-616 1354931 1356365 1357807 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1352318 1353284 1353767 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1351899 1352178 1352252 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1344216 1351760 1351894 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1343579 1343724 1343952 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1341063 1341761 1342473 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1339175 1339498 1339946 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1332479 1338225 1338266 "LSAGG" 1338328 LSAGG (NIL T) -9 NIL 1338406 NIL) (-608 1330173 1331272 1332474 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1327653 1329522 1329771 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1327320 1327411 1327534 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1326991 1327070 1327098 "LOGIC" 1327209 LOGIC (NIL) -9 NIL 1327291 NIL) (-604 1326886 1326915 1326986 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1326205 1326363 1326556 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1324990 1325239 1325590 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1320812 1323611 1323651 "LODOCAT" 1324083 LODOCAT (NIL T) -9 NIL 1324294 NIL) (-600 1320605 1320681 1320807 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1317605 1320482 1320600 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1314703 1317555 1317600 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1311790 1314633 1314698 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1310843 1311018 1311320 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1308975 1310105 1310358 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1304074 1307134 1307175 "LNAGG" 1308037 LNAGG (NIL T) -9 NIL 1308472 NIL) (-593 1303461 1303728 1304069 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1300033 1300974 1301611 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1299295 1299800 1299840 "LMODULE" 1299845 LMODULE (NIL T) -9 NIL 1299871 NIL) (-590 1296645 1299031 1299154 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1296213 1296424 1296465 "LLINSET" 1296526 LLINSET (NIL T) -9 NIL 1296570 NIL) (-588 1295889 1296149 1296208 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1295488 1295568 1295707 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1293939 1294287 1294686 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1293110 1293306 1293534 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1286328 1292366 1292620 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1285905 1286138 1286179 "LINSET" 1286184 LINSET (NIL T) -9 NIL 1286217 NIL) (-582 1284806 1285528 1285695 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1283072 1283827 1283867 "LINEXP" 1284353 LINEXP (NIL T) -9 NIL 1284626 NIL) (-580 1281694 1282681 1282862 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1280521 1280793 1281095 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1279734 1280323 1280433 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1277284 1278006 1278756 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1275914 1276211 1276602 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1274707 1275309 1275349 "LIECAT" 1275489 LIECAT (NIL T) -9 NIL 1275640 NIL) (-574 1274581 1274614 1274702 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1268837 1274271 1274499 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1259272 1268513 1268669 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1255724 1256673 1257608 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1254348 1255256 1255284 "LFCAT" 1255491 LFCAT (NIL) -9 NIL 1255630 NIL) (-569 1252587 1252917 1253262 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1250104 1250769 1251450 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1247116 1248094 1248597 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1246607 1246910 1247001 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1245314 1245638 1246038 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1244580 1244665 1244891 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1239583 1243148 1243684 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1239208 1239258 1239418 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1237979 1238752 1238792 "LALG" 1238853 LALG (NIL T) -9 NIL 1238911 NIL) (-560 1237762 1237839 1237974 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1235615 1237030 1237281 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1235444 1235474 1235515 "KVTFROM" 1235577 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1234260 1234975 1235164 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1234089 1234119 1234160 "KRCFROM" 1234222 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1233191 1233388 1233683 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1233020 1233050 1233091 "KONVERT" 1233153 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1232849 1232879 1232920 "KOERCE" 1232982 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1232419 1232512 1232644 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1230472 1231366 1231738 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1221649 1228256 1228310 "KDAGG" 1228686 KDAGG (NIL T T) -9 NIL 1228912 NIL) (-549 1221114 1221346 1221644 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1214112 1220906 1221052 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1213762 1214044 1214107 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1212732 1213231 1213480 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1211858 1212307 1212512 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1210722 1211214 1211514 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1210004 1210403 1210564 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1209714 1209950 1209999 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1203969 1209404 1209632 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1203387 1203720 1203840 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1199553 1201564 1201618 "IXAGG" 1202545 IXAGG (NIL T T) -9 NIL 1203002 NIL) (-538 1198759 1199130 1199548 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1197726 1198001 1198264 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1196388 1196595 1196888 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1195339 1195561 1195844 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1195014 1195077 1195200 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1194276 1194648 1194822 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1192252 1193552 1193826 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1181800 1187569 1188726 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1181045 1181197 1181433 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1180536 1180839 1180930 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1179829 1179920 1180133 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1178961 1179186 1179426 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1177374 1177755 1178183 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1177159 1177203 1177279 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1176009 1176306 1176601 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1175282 1175633 1175784 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1174485 1174616 1174829 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1172640 1173137 1173681 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1169721 1170989 1171678 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1169546 1169586 1169646 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1165544 1169472 1169541 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1163547 1165483 1165539 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1162918 1163217 1163347 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1162371 1162659 1162791 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1161452 1162077 1162203 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1160862 1161356 1161384 "IOBCON" 1161389 IOBCON (NIL) -9 NIL 1161410 NIL) (-512 1160433 1160497 1160679 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1152477 1154848 1157173 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1149588 1150371 1151235 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1149265 1149362 1149479 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1146707 1149201 1149260 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1144819 1145348 1145915 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1144321 1144435 1144575 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1142705 1143111 1143573 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1140484 1141078 1141689 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1137857 1138467 1139187 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1137261 1137419 1137627 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1136780 1136866 1137054 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1134985 1135506 1135963 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1128067 1129720 1131449 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1127433 1127595 1127768 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1125306 1125770 1126314 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1123432 1124382 1124410 "INTDOM" 1124709 INTDOM (NIL) -9 NIL 1124914 NIL) (-495 1122985 1123187 1123427 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1118792 1121264 1121318 "INTCAT" 1122114 INTCAT (NIL T) -9 NIL 1122430 NIL) (-493 1118357 1118477 1118604 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1117197 1117369 1117675 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1116770 1116866 1117023 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1108072 1116677 1116765 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1107370 1107925 1107990 "INT8" NIL INT8 (NIL) -8 NIL NIL 1108024) (-488 1106667 1107222 1107287 "INT64" NIL INT64 (NIL) -8 NIL NIL 1107321) (-487 1105964 1106519 1106584 "INT32" NIL INT32 (NIL) -8 NIL NIL 1106618) (-486 1105261 1105816 1105881 "INT16" NIL INT16 (NIL) -8 NIL NIL 1105915) (-485 1101724 1105180 1105256 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1095781 1099264 1099292 "INS" 1100222 INS (NIL) -9 NIL 1100881 NIL) (-483 1093843 1094761 1095708 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1092902 1093125 1093400 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1092116 1092257 1092454 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1091106 1091247 1091484 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1090258 1090422 1090682 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1089538 1089653 1089841 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1088277 1088546 1088870 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1087557 1087698 1087881 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1087220 1087292 1087390 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1084298 1085784 1086307 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1083897 1084004 1084118 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1083053 1083698 1083799 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1081903 1082171 1082492 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1080893 1081833 1081898 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1080518 1080598 1080715 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1079432 1079977 1080181 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1075527 1076582 1077525 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1074381 1074704 1074732 "INBCON" 1075245 INBCON (NIL) -9 NIL 1075511 NIL) (-465 1073835 1074100 1074376 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1073329 1073631 1073721 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1072786 1073095 1073200 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1071626 1071765 1072080 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1070050 1070317 1070654 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1064893 1069981 1070045 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1064273 1064607 1064722 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1059252 1063711 1063897 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1058282 1059174 1059247 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1057854 1057931 1057985 "IEVALAB" 1058192 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1057609 1057689 1057849 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1056994 1057221 1057378 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1055987 1056914 1056989 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1055050 1055907 1055982 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1054132 1054779 1054916 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1052495 1053066 1053117 "IDPC" 1053623 IDPC (NIL T T) -9 NIL 1053936 NIL) (-449 1051783 1052417 1052490 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1050953 1051705 1051778 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1050646 1050859 1050919 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1050350 1050390 1050429 "IDEMOPC" 1050434 IDEMOPC (NIL T) -9 NIL 1050571 NIL) (-445 1047421 1048302 1049194 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1041047 1042324 1043363 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1040309 1040439 1040638 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1039482 1039981 1040119 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1037871 1038202 1038593 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1033812 1037827 1037866 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1031070 1031694 1032389 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1029296 1029776 1030309 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1027278 1029202 1029291 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1023311 1027216 1027273 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1016890 1022275 1022743 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1016458 1016521 1016694 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1015950 1016099 1016127 "HYPCAT" 1016334 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1015606 1015759 1015945 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1015219 1015464 1015547 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1015052 1015101 1015142 "HOMOTOP" 1015147 HOMOTOP (NIL T) -9 NIL 1015180 NIL) (-429 1011630 1013000 1013041 "HOAGG" 1014012 HOAGG (NIL T) -9 NIL 1014731 NIL) (-428 1010702 1011137 1011625 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 1003902 1010427 1010575 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 1002837 1003095 1003358 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 1001772 1002702 1002832 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 1000138 1001605 1001693 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 999453 999805 999938 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 993060 999386 999448 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 986199 992796 992947 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 985652 985809 985972 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 976971 985569 985647 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 976462 976765 976856 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 974012 976249 976428 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 969558 973895 974007 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 960854 969455 969553 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 952791 960223 960478 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 951815 952324 952352 "GROUP" 952555 GROUP (NIL) -9 NIL 952689 NIL) (-412 951358 951559 951810 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 950030 950369 950756 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 948852 949209 949260 "GRMOD" 949789 GRMOD (NIL T T) -9 NIL 949955 NIL) (-409 948671 948719 948847 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 944794 946005 947005 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 943516 943840 944155 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 943069 943197 943338 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 942142 942641 942692 "GRALG" 942845 GRALG (NIL T T) -9 NIL 942935 NIL) (-404 941861 941962 942137 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 938742 941554 941719 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 938155 938218 938475 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 934009 934905 935430 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 933184 933386 933624 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 928187 929114 930133 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 927935 927992 928081 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 927417 927506 927671 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 926926 926967 927180 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 925727 926010 926314 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 919002 925417 925578 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 908785 913792 914896 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 906837 907940 907968 "GCDDOM" 908223 GCDDOM (NIL) -9 NIL 908380 NIL) (-391 906460 906617 906832 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 897253 899723 902111 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 895388 895713 896131 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 894329 894518 894785 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 893200 893407 893711 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 892663 892805 892953 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 891275 891623 891936 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 889820 890141 890463 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 887446 887802 888207 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 880698 882359 883937 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 880350 880571 880639 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 879974 880195 880276 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 878071 878754 879214 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 876664 876971 877363 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 875319 875678 876002 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 874622 874746 874933 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 873596 873862 874209 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 871254 871784 872266 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 870837 870897 871066 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 869137 870051 870354 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 868285 868419 868642 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 867456 867617 867844 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 863572 866351 866392 "FSAGG" 866762 FSAGG (NIL T) -9 NIL 867023 NIL) (-368 861926 862685 863477 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 859882 860178 860722 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 858929 859111 859411 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 858610 858659 858786 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 838766 848267 848308 "FS" 852178 FS (NIL T) -9 NIL 854456 NIL) (-363 830997 834490 838469 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 830531 830658 830810 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 825054 828212 828252 "FRNAALG" 829572 FRNAALG (NIL T) -9 NIL 830170 NIL) (-360 821795 823046 824304 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 821476 821525 821652 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 819963 820520 820814 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 819249 819342 819629 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 817083 817849 818165 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 816192 816635 816676 "FRETRCT" 816681 FRETRCT (NIL T) -9 NIL 816852 NIL) (-354 815565 815843 816187 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 812309 813829 813888 "FRAMALG" 814770 FRAMALG (NIL T T) -9 NIL 815062 NIL) (-352 810905 811456 812086 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 810598 810661 810768 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 804239 810403 810593 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 803932 803995 804102 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 796240 800811 802139 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 790018 793521 793549 "FPS" 794668 FPS (NIL) -9 NIL 795224 NIL) (-346 789575 789708 789872 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 786385 788428 788456 "FPC" 788681 FPC (NIL) -9 NIL 788823 NIL) (-344 786231 786283 786380 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 785008 785717 785758 "FPATMAB" 785763 FPATMAB (NIL T) -9 NIL 785915 NIL) (-342 783438 784034 784381 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 783013 783071 783244 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 781516 782411 782585 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 780131 780636 780664 "FNCAT" 781121 FNCAT (NIL) -9 NIL 781378 NIL) (-338 779588 780098 780126 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 778175 779537 779583 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 774763 776121 776162 "FMONCAT" 777379 FMONCAT (NIL T) -9 NIL 777983 NIL) (-335 771621 772699 772752 "FMCAT" 773933 FMCAT (NIL T T) -9 NIL 774425 NIL) (-334 770321 771444 771543 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 769369 770169 770316 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 767556 768008 768502 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 765491 766027 766605 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 758877 763828 764442 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 757358 758459 758499 "FLINEXP" 758504 FLINEXP (NIL T) -9 NIL 758597 NIL) (-328 756767 757026 757353 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 755982 756141 756362 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 752865 753944 753996 "FLALG" 755223 FLALG (NIL T T) -9 NIL 755690 NIL) (-325 752036 752197 752424 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 745577 749435 749476 "FLAGG" 750731 FLAGG (NIL T) -9 NIL 751378 NIL) (-323 744685 745089 745572 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 741246 742510 742569 "FINRALG" 743697 FINRALG (NIL T T) -9 NIL 744205 NIL) (-321 740637 740902 741241 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 739935 740231 740259 "FINITE" 740455 FINITE (NIL) -9 NIL 740562 NIL) (-319 739843 739869 739930 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 737300 738521 738562 "FINAGG" 739192 FINAGG (NIL T) -9 NIL 739504 NIL) (-317 736740 736999 737295 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 728701 731292 731332 "FINAALG" 734984 FINAALG (NIL T) -9 NIL 736422 NIL) (-315 724968 726213 727336 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 723520 723939 723993 "FILECAT" 724677 FILECAT (NIL T T) -9 NIL 724893 NIL) (-313 722871 723345 723448 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 720119 721997 722025 "FIELD" 722065 FIELD (NIL) -9 NIL 722145 NIL) (-311 719144 719605 720114 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 717148 718094 718440 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 716391 716572 716791 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 711661 716329 716386 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 711323 711390 711525 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 710863 710905 711114 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 707543 708420 709197 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 702827 707475 707538 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 697506 702316 702506 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 691987 696787 697045 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 686194 691438 691649 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 685217 685427 685742 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 680657 683362 683390 "FFIELDC" 684009 FFIELDC (NIL) -9 NIL 684384 NIL) (-298 679726 680166 680652 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 679341 679399 679523 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 677485 678008 678525 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 672579 677284 677385 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 667679 672368 672475 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 662345 667470 667578 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 661799 661848 662083 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 640374 651408 651494 "FFCAT" 656644 FFCAT (NIL T T T) -9 NIL 658080 NIL) (-290 636614 637840 639146 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 631457 636545 636609 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 630349 630818 630859 "FEVALAB" 630943 FEVALAB (NIL T) -9 NIL 631204 NIL) (-287 629754 630006 630344 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 626581 627492 627607 "FDIVCAT" 629174 FDIVCAT (NIL T T T T) -9 NIL 629610 NIL) (-285 626375 626407 626576 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 625682 625775 626052 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 624168 625166 625369 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 623261 623645 623847 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 622383 622872 623012 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 613970 618613 618653 "FAXF" 620454 FAXF (NIL T) -9 NIL 621144 NIL) (-279 611886 612690 613505 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 606922 611408 611582 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 601380 603803 603855 "FAMR" 604866 FAMR (NIL T T) -9 NIL 605325 NIL) (-276 600579 600944 601375 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 599600 600521 600574 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 597194 598073 598126 "FAMONC" 599067 FAMONC (NIL T T) -9 NIL 599452 NIL) (-273 595750 597052 597189 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 593830 594191 594593 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 593107 593304 593526 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 584967 592554 592753 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 582986 583556 584142 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 579888 580530 581250 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 575045 575752 576557 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 574734 574797 574906 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 559527 573783 574209 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 550054 558847 559135 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 549548 549850 549940 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 549324 549514 549543 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 549013 549081 549194 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 548530 548672 548713 "EVALAB" 548883 EVALAB (NIL T) -9 NIL 548987 NIL) (-259 548158 548304 548525 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 545201 546796 546824 "EUCDOM" 547378 EUCDOM (NIL) -9 NIL 547727 NIL) (-257 544128 544621 545196 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 543853 543909 544009 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 543541 543605 543714 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 537312 539212 539240 "ES" 541982 ES (NIL) -9 NIL 543366 NIL) (-253 533827 535359 537151 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 533175 533328 533504 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524500 533105 533170 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524189 524252 524361 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 517816 520941 522374 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514119 515215 516308 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 512948 513298 513603 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 511833 512564 512592 "ENTIRER" 512597 ENTIRER (NIL) -9 NIL 512641 NIL) (-245 511722 511756 511828 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508355 510152 510501 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507447 507658 507712 "ELTAGG" 508092 ELTAGG (NIL T T) -9 NIL 508303 NIL) (-242 507227 507301 507442 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 506973 507008 507062 "ELTAB" 507146 ELTAB (NIL T T) -9 NIL 507198 NIL) (-240 506224 506394 506593 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 505948 506022 506050 "ELEMFUN" 506155 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 505848 505875 505943 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500394 503867 503908 "ELAGG" 504845 ELAGG (NIL T) -9 NIL 505308 NIL) (-236 499192 499730 500389 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498610 498777 498933 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497523 497842 498121 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 490916 492914 493741 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 484895 486891 487701 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482709 483115 483586 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473709 475622 477163 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 472822 473323 473472 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471520 472194 472234 "DVARCAT" 472517 DVARCAT (NIL T) -9 NIL 472657 NIL) (-227 470939 471203 471515 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463006 470807 470934 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461344 462135 462176 "DSEXT" 462539 DSEXT (NIL T) -9 NIL 462833 NIL) (-224 460149 460673 461339 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 459873 459938 460036 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456024 457240 458371 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451670 453025 454089 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450345 450706 451092 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450031 450090 450208 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449006 449304 449594 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448591 448666 448816 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441004 443116 445231 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436521 437540 438619 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433251 435148 435189 "DQAGG" 435818 DQAGG (NIL T) -9 NIL 436091 NIL) (-213 419794 427434 427516 "DPOLCAT" 429353 DPOLCAT (NIL T T T T) -9 NIL 429896 NIL) (-212 416202 417850 419789 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409360 416100 416197 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402427 409189 409355 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402020 402280 402369 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401434 401882 401962 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400720 401045 401196 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393859 400456 400607 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391608 392925 392965 "DMEXT" 392970 DMEXT (NIL T) -9 NIL 393145 NIL) (-204 391264 391326 391470 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384761 390749 390939 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381431 383584 383625 "DLAGG" 384175 DLAGG (NIL T) -9 NIL 384404 NIL) (-201 379782 380653 380681 "DIVRING" 380773 DIVRING (NIL) -9 NIL 380856 NIL) (-200 379233 379477 379777 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377661 378078 378484 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376698 376919 377184 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370325 376630 376693 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358777 365085 365138 "DIRPCAT" 365394 DIRPCAT (NIL NIL T) -9 NIL 366269 NIL) (-195 356783 357553 358440 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 356230 356396 356582 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352780 355097 355138 "DIOPS" 355570 DIOPS (NIL T) -9 NIL 355796 NIL) (-192 352440 352584 352775 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351447 352193 352221 "DIOID" 352226 DIOID (NIL) -9 NIL 352248 NIL) (-190 350275 351104 351132 "DIFRING" 351137 DIFRING (NIL) -9 NIL 351158 NIL) (-189 349911 350009 350037 "DIFFSPC" 350156 DIFFSPC (NIL) -9 NIL 350231 NIL) (-188 349652 349754 349906 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348555 349180 349220 "DIFFMOD" 349225 DIFFMOD (NIL T) -9 NIL 349322 NIL) (-186 348239 348296 348337 "DIFFDOM" 348458 DIFFDOM (NIL T) -9 NIL 348526 NIL) (-185 348120 348150 348234 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345793 347314 347354 "DIFEXT" 347359 DIFEXT (NIL T) -9 NIL 347511 NIL) (-183 342958 345275 345316 "DIAGG" 345321 DIAGG (NIL T) -9 NIL 345341 NIL) (-182 342514 342704 342953 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337860 341704 341981 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 334318 335371 336381 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328868 333472 333799 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 327434 327726 328101 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324554 325806 326202 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 322446 324385 324474 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321829 321974 322156 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 319147 319871 320671 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 317256 317714 318276 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316639 316972 317086 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309839 316364 316512 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307759 308269 308773 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 307398 307447 307598 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306657 307219 307310 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304681 305123 305483 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303973 304262 304408 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 303424 303570 303722 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300786 301579 302306 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 300225 300371 300542 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 298297 298608 298975 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297854 298109 298210 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 297055 297438 297466 "CTORCAT" 297647 CTORCAT (NIL) -9 NIL 297759 NIL) (-159 296758 296892 297050 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 296251 296508 296616 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295667 296098 296171 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 295126 295243 295396 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 291520 292276 293031 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 291011 291314 291405 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 290230 290439 290667 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289734 289839 290043 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 289487 289521 289627 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 286426 287188 287906 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285945 286087 286226 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281838 284408 284900 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281712 281739 281767 "CONDUIT" 281804 CONDUIT (NIL) -9 NIL NIL NIL) (-146 280591 281322 281350 "COMRING" 281355 COMRING (NIL) -9 NIL 281405 NIL) (-145 279756 280123 280301 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 279452 279493 279621 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 279145 279208 279315 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267987 279095 279140 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 267448 267587 267747 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 267201 267242 267340 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248632 260882 260922 "COMPCAT" 261923 COMPCAT (NIL T) -9 NIL 263265 NIL) (-138 241170 244683 248276 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240929 240963 241065 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240759 240798 240856 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 240340 240619 240693 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239917 240158 240245 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 239112 239360 239388 "COMBOPC" 239726 COMBOPC (NIL) -9 NIL 239901 NIL) (-132 238176 238428 238670 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 235108 235792 236415 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233988 234439 234674 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 233479 233782 233873 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 233166 233219 233344 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232636 232946 233044 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 229156 230226 231306 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 227451 228436 228674 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 223567 225571 225612 "CLAGG" 226538 CLAGG (NIL T) -9 NIL 227071 NIL) (-123 222460 222987 223562 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 222089 222180 222320 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 220026 220533 221081 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218987 219718 219746 "CHARZ" 219751 CHARZ (NIL) -9 NIL 219765 NIL) (-119 218781 218827 218905 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217620 218383 218411 "CHARNZ" 218472 CHARNZ (NIL) -9 NIL 218520 NIL) (-117 215098 216195 216718 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214806 214885 214913 "CFCAT" 215024 CFCAT (NIL) -9 NIL NIL NIL) (-115 214149 214278 214460 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 210310 213562 213842 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 209688 209875 210052 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 209216 209635 209683 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 208689 208998 209095 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 208180 208483 208574 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 207429 207589 207810 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 203529 204786 205494 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201895 202926 203177 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 201476 201755 201829 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200910 201163 201191 "CACHSET" 201323 CACHSET (NIL) -9 NIL 201401 NIL) (-104 200262 200677 200705 "CABMON" 200755 CABMON (NIL) -9 NIL 200811 NIL) (-103 199792 200056 200166 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 195198 199460 199621 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 194168 194872 195007 "BYTE" NIL BYTE (NIL) -8 NIL NIL 195170) (-100 191811 193935 194041 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 189425 191565 191673 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 186795 188827 188866 "BTCAT" 188933 BTCAT (NIL T) -9 NIL 189014 NIL) (-97 186546 186644 186790 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 181787 185738 185764 "BTAGG" 185875 BTAGG (NIL) -9 NIL 185983 NIL) (-95 181418 181579 181782 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 178674 180910 181100 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 177944 178096 178274 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 174481 176650 176689 "BRAGG" 177330 BRAGG (NIL T) -9 NIL 177587 NIL) (-91 173436 173931 174476 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 165970 172941 173122 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 163962 165922 165965 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 163695 163731 163842 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 161934 162367 162815 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 157900 159316 160206 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 156776 157667 157789 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 156362 156519 156545 "BOOLE" 156653 BOOLE (NIL) -9 NIL 156734 NIL) (-83 156155 156236 156357 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 155293 155820 155870 "BMODULE" 155875 BMODULE (NIL T T) -9 NIL 155939 NIL) (-81 151082 155150 155219 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 150895 150935 150974 "BINOPC" 150979 BINOPC (NIL T) -9 NIL 151024 NIL) (-79 150437 150710 150812 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 149958 150102 150240 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 143164 149688 149833 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140912 142384 142423 "BGAGG" 142679 BGAGG (NIL T) -9 NIL 142806 NIL) (-75 140781 140819 140907 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 139632 139833 140118 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 136464 138812 139117 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 136049 136142 136168 "BASTYPE" 136339 BASTYPE (NIL) -9 NIL 136435 NIL) (-71 135819 135915 136044 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 135334 135422 135572 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 134233 134908 135093 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 133970 133975 134001 "ATTREG" 134006 ATTREG (NIL) -9 NIL NIL NIL) (-67 133575 133847 133912 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 133075 133224 133250 "ATRIG" 133451 ATRIG (NIL) -9 NIL NIL NIL) (-65 132930 132983 133070 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 132500 132731 132757 "ASTCAT" 132762 ASTCAT (NIL) -9 NIL 132792 NIL) (-63 132299 132376 132495 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 130630 132132 132220 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 129437 129750 130115 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 127397 129367 129432 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 126588 126779 127000 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 122347 126319 126433 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 116765 118663 118738 "ARR2CAT" 121250 ARR2CAT (NIL T T T) -9 NIL 121971 NIL) (-56 115726 116208 116760 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 115094 115465 115587 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 114026 114194 114490 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 113727 113781 113899 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 113110 113256 113412 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 112515 112805 112925 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 110083 111244 111567 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 109608 109868 109964 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 103303 108670 109112 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 98837 100500 100550 "AMR" 101288 AMR (NIL T T) -9 NIL 101885 NIL) (-46 98191 98471 98832 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79737 98125 98186 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 76140 79413 79582 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 73150 73810 74417 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 72529 72642 72826 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68941 69566 70158 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 58430 68634 68784 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57747 57901 58079 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 56460 57255 57293 "ALGEBRA" 57298 ALGEBRA (NIL T) -9 NIL 57338 NIL) (-37 56246 56323 56455 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34174 53353 53405 "ALAGG" 53540 ALAGG (NIL T T) -9 NIL 53698 NIL) (-35 33674 33823 33849 "AHYP" 34050 AHYP (NIL) -9 NIL NIL NIL) (-34 32970 33151 33177 "AGG" 33458 AGG (NIL) -9 NIL 33645 NIL) (-33 32813 32871 32965 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30952 31412 31812 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30447 30750 30839 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29817 30112 30268 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17375 26654 26692 "ACFS" 27299 ACFS (NIL T) -9 NIL 27538 NIL) (-28 15998 16608 17370 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11550 13929 13955 "ACF" 14834 ACF (NIL) -9 NIL 15246 NIL) (-26 10646 11052 11545 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10148 10388 10414 "ABELSG" 10506 ABELSG (NIL) -9 NIL 10571 NIL) (-24 10046 10077 10143 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9201 9575 9601 "ABELMON" 9826 ABELMON (NIL) -9 NIL 9959 NIL) (-22 8883 9023 9196 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8095 8578 8604 "ABELGRP" 8676 ABELGRP (NIL) -9 NIL 8751 NIL) (-20 7648 7844 8090 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6875 6914 "A1AGG" 6919 A1AGG (NIL T) -9 NIL 6953 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 3fc80efb..87cb9bc1 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,5 +1,5 @@ -(631528 . 3577834557) +(631530 . 3577838828) (((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-1180 (-350 (-485)))) (-5 *1 (-1209 *4))))) @@ -36,7 +36,7 @@ ((*1 *1 *2) (OR (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) - (-12 (-2561 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) + (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) @@ -101,7 +101,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-348 *1)) (-4 *1 (-1135)))) ((*1 *2 *3) (-12 (-4 *4 (-496)) (-5 *2 (-348 *3)) (-5 *1 (-1160 *4 *3)) - (-4 *3 (-13 (-1156 *4) (-496) (-10 -8 (-15 -3145 ($ $ $))))))) + (-4 *3 (-13 (-1156 *4) (-496) (-10 -8 (-15 -3146 ($ $ $))))))) ((*1 *2 *3) (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *5 (-584 (-1091))) @@ -154,26 +154,26 @@ (((*1 *2 *3) (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *5 (-584 (-1091))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3225 (-584 (-858 *4)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3226 (-584 (-858 *4)))))) (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-584 (-1091))))) ((*1 *2 *3 *4 *4 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3225 (-584 (-858 *5)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-1208 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3225 (-584 (-858 *5)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-1208 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3225 (-584 (-858 *5)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-1208 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-756) (-258) (-120) (-934))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3225 (-584 (-858 *4)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3226 (-584 (-858 *4)))))) (-5 *1 (-1208 *4 *5 *6)) (-5 *3 (-584 (-858 *4))) (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091)))))) (((*1 *2 *3 *4 *4) @@ -248,7 +248,7 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-336 *2)) (-4 *2 (-1014)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-336 *2)) (-4 *2 (-1014)))) ((*1 *1 *2 *1) - (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *6 (-196 (-3958 *3) (-695))) + (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *6 (-196 (-3959 *3) (-695))) (-14 *7 (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *6)) (-2 (|:| -2401 *5) (|:| -2402 *6)))) @@ -319,7 +319,7 @@ (-14 *3 (-584 (-1091))))) ((*1 *1 *1) (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-962)) (-4 *3 (-1014)))) ((*1 *1 *1) - (-12 (-14 *2 (-584 (-1091))) (-4 *3 (-146)) (-4 *5 (-196 (-3958 *2) (-695))) + (-12 (-14 *2 (-584 (-1091))) (-4 *3 (-146)) (-4 *5 (-196 (-3959 *2) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *4) (|:| -2402 *5)) (-2 (|:| -2401 *4) (|:| -2402 *5)))) @@ -536,7 +536,7 @@ (-4 *6 (-718)) (-4 *2 (-13 (-1014) - (-10 -8 (-15 -3840 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-695)))))) + (-10 -8 (-15 -3841 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-695)))))) (-5 *1 (-864 *6 *7 *8 *5 *2)) (-4 *5 (-862 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-870 *5)) (-4 *5 (-1130)) (-4 *6 (-1130)) @@ -552,7 +552,7 @@ (-4 *5 (-718)) (-4 *6 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) (-15 -3832 ((-3 $ "failed") (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) (-15 -3833 ((-3 $ "failed") (-1091)))))) (-5 *1 (-898 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-496)) (-4 *6 (-496)) (-4 *2 (-905 *6)) @@ -634,7 +634,7 @@ (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-1200 *3 *4)) (-4 *3 (-757)) (-4 *4 (-962)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-1204 *3 *4)) (-4 *4 (-755))))) -(((*1 *2 *1) (-12 (|has| *1 (-6 -3996)) (-4 *1 (-34)) (-5 *2 (-695)))) +(((*1 *2 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-34)) (-5 *2 (-695)))) ((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-209)))) ((*1 *2 *1) (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-5 *2 (-695)))) ((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-885)))) @@ -871,7 +871,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| -3955 *3) (|:| -3939 *4)))) (-4 *3 (-962)) + (-12 (-5 *2 (-584 (-2 (|:| -3956 *3) (|:| -3940 *4)))) (-4 *3 (-962)) (-4 *4 (-664)) (-5 *1 (-675 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-688)))) ((*1 *2 *3) (-12 (-5 *2 (-697)) (-5 *1 (-698 *3)) (-4 *3 (-1130)))) @@ -1000,7 +1000,7 @@ ((*1 *1 *1) (-4 *1 (-239))) ((*1 *2 *3) (-12 (-5 *3 (-348 *4)) (-4 *4 (-496)) - (-5 *2 (-584 (-2 (|:| -3955 (-695)) (|:| |logand| *4)))) (-5 *1 (-271 *4)))) + (-5 *2 (-584 (-2 (|:| -3956 (-695)) (|:| |logand| *4)))) (-5 *1 (-271 *4)))) ((*1 *2 *1) (-12 (-5 *2 (-607 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-757)) (-4 *4 (-13 (-146) (-655 (-350 (-485))))) (-14 *5 (-831)))) @@ -1136,7 +1136,7 @@ (((*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-1191))))) (((*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-1191))))) (((*1 *2 *3) - (-12 (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *2 (-2 (|:| -2013 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3)))) @@ -1160,7 +1160,7 @@ (-12 (-4 *3 (-1135)) (-4 *4 (-1156 *3)) (-4 *5 (-1156 (-350 *4))) (-5 *2 (-1180 *1)) (-4 *1 (-291 *3 *4 *5)))) ((*1 *2) - (-12 (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *2 (-2 (|:| -2013 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3)))) @@ -1284,14 +1284,14 @@ (((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179)) + (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179)) (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179)) (|:| |deltaX| (-179)) (|:| |deltaY| (-179)))) (-5 *1 (-221)))) ((*1 *2 *3 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179)) + (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179)) (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179)) (|:| |deltaX| (-179)) (|:| |deltaY| (-179)))) (-5 *3 (-584 (-221))) (-5 *1 (-222)))) @@ -1302,14 +1302,14 @@ ((*1 *2 *1 *3) (-12 (-5 *3 - (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179)) + (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179)) (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179)) (|:| |deltaX| (-179)) (|:| |deltaY| (-179)))) (-5 *2 (-1186)) (-5 *1 (-1184)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179)) + (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179)) (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179)) (|:| |deltaX| (-179)) (|:| |deltaY| (-179)))) (-5 *1 (-1184)))) @@ -1373,9 +1373,9 @@ (-5 *2 (-1180 (-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179)) - (|:| |deltaY| (-179)) (|:| -3851 (-485)) (|:| -3849 (-485)) - (|:| |spline| (-485)) (|:| -3880 (-485)) (|:| |axesColor| (-784)) - (|:| -3852 (-485)) (|:| |unitsColor| (-784)) (|:| |showing| (-485))))) + (|:| |deltaY| (-179)) (|:| -3852 (-485)) (|:| -3850 (-485)) + (|:| |spline| (-485)) (|:| -3881 (-485)) (|:| |axesColor| (-784)) + (|:| -3853 (-485)) (|:| |unitsColor| (-784)) (|:| |showing| (-485))))) (-5 *1 (-1183))))) (((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1093 (-350 (-485)))) (-5 *1 (-164)))) ((*1 *2 *1) (-12 (-5 *2 (-1180 (-3 (-408) "undefined"))) (-5 *1 (-1183))))) @@ -1424,13 +1424,13 @@ (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1130)) (-4 *2 (-1130)) (-5 *1 (-59 *5 *2)))) ((*1 *2 *3 *1 *2 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1014)) (|has| *1 (-6 -3996)) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1014)) (|has| *1 (-6 -3997)) (-4 *1 (-124 *2)) (-4 *2 (-1130)))) ((*1 *2 *3 *1 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3997)) (-4 *1 (-124 *2)) (-4 *2 (-1130)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3997)) (-4 *1 (-124 *2)) (-4 *2 (-1130)))) ((*1 *2 *3) (-12 (-4 *4 (-962)) (-5 *2 (-2 (|:| -2005 (-1086 *4)) (|:| |deg| (-831)))) @@ -1527,7 +1527,7 @@ (-12 (-5 *1 (-167 *2)) (-4 *2 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 ((-1186) $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 ((-1186) $)) (-15 -1964 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-249 *2)) (-4 *2 (-25)) (-4 *2 (-1130)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-25)) (-4 *2 (-1130)))) @@ -1558,7 +1558,7 @@ (-12 (-5 *1 (-167 *2)) (-4 *2 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 ((-1186) $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 ((-1186) $)) (-15 -1964 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130)))) @@ -1886,8 +1886,8 @@ (-12 (-4 *3 (-29 (-485))) (-4 *3 (-872)) (-4 *3 (-1116)) (-4 *3 (-38 (-350 (-485)))))) (-12 (-5 *2 (-1091)) (-4 *1 (-1142 *3)) (-4 *3 (-962)) - (-12 (|has| *3 (-15 -3082 ((-584 *2) *3))) - (|has| *3 (-15 -3813 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) + (-12 (|has| *3 (-15 -3083 ((-584 *2) *3))) + (|has| *3 (-15 -3814 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1142 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-350 (-485)))))) ((*1 *1 *1) @@ -1901,8 +1901,8 @@ (-12 (-4 *3 (-29 (-485))) (-4 *3 (-872)) (-4 *3 (-1116)) (-4 *3 (-38 (-350 (-485)))))) (-12 (-5 *2 (-1091)) (-4 *1 (-1163 *3)) (-4 *3 (-962)) - (-12 (|has| *3 (-15 -3082 ((-584 *2) *3))) - (|has| *3 (-15 -3813 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) + (-12 (|has| *3 (-15 -3083 ((-584 *2) *3))) + (|has| *3 (-15 -3814 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1163 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-350 (-485)))))) ((*1 *1 *1 *2) @@ -1914,8 +1914,8 @@ (-12 (-4 *3 (-29 (-485))) (-4 *3 (-872)) (-4 *3 (-1116)) (-4 *3 (-38 (-350 (-485)))))) (-12 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-962)) - (-12 (|has| *3 (-15 -3082 ((-584 *2) *3))) - (|has| *3 (-15 -3813 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) + (-12 (|has| *3 (-15 -3083 ((-584 *2) *3))) + (|has| *3 (-15 -3814 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-350 (-485))))))) (((*1 *2 *1 *3) @@ -2000,13 +2000,13 @@ (-12 (-5 *3 (-1091)) (-5 *2 (-203 (-1074))) (-5 *1 (-167 *4)) (-4 *4 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ *3)) (-15 -3618 ((-1186) $)) + (-10 -8 (-15 -3802 ((-1074) $ *3)) (-15 -3619 ((-1186) $)) (-15 -1964 ((-1186) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-903)) (-5 *1 (-167 *3)) (-4 *3 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 ((-1186) $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 ((-1186) $)) (-15 -1964 ((-1186) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-695)) (-5 *1 (-203 *4)) (-4 *4 (-757)))) @@ -2081,47 +2081,47 @@ (((*1 *1 *1) (-12 (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) (((*1 *2 *1) (-12 (-4 *1 (-1169 *3)) (-4 *3 (-1130)) (-5 *2 (-695))))) (((*1 *1 *1) (-12 (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-202 *2)) (-4 *2 (-1130)))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-202 *2)) (-4 *2 (-1130)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)))) - ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) -(((*1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) + ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130)))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) +(((*1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-485)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1130)) (-4 *4 (-324 *2)) (-4 *5 (-324 *2)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "right") (|has| *1 (-6 -3997)) (-4 *1 (-92 *3)) (-4 *3 (-1130)))) + (-12 (-5 *2 "right") (|has| *1 (-6 -3998)) (-4 *1 (-92 *3)) (-4 *3 (-1130)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "left") (|has| *1 (-6 -3997)) (-4 *1 (-92 *3)) (-4 *3 (-1130)))) + (-12 (-5 *2 "left") (|has| *1 (-6 -3998)) (-4 *1 (-92 *3)) (-4 *3 (-1130)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -3997)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014)) + (-12 (|has| *1 (-6 -3998)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1130)))) ((*1 *2 *1 *3 *2) (-12 (-5 *2 (-51)) (-5 *3 (-1091)) (-5 *1 (-572)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 (-1147 (-485))) (|has| *1 (-6 -3997)) (-4 *1 (-594 *2)) + (-12 (-5 *3 (-1147 (-485))) (|has| *1 (-6 -3998)) (-4 *1 (-594 *2)) (-4 *2 (-1130)))) ((*1 *1 *1 *2 *2 *1) (-12 (-5 *2 (-584 (-485))) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "value") (|has| *1 (-6 -3997)) (-4 *1 (-924 *2)) + (-12 (-5 *3 "value") (|has| *1 (-6 -3998)) (-4 *1 (-924 *2)) (-4 *2 (-1130)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "last") (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) + (-12 (-5 *3 "last") (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "rest") (|has| *1 (-6 -3997)) (-4 *1 (-1169 *3)) + (-12 (-5 *2 "rest") (|has| *1 (-6 -3998)) (-4 *1 (-1169 *3)) (-4 *3 (-1130)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "first") (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) + (-12 (-5 *3 "first") (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) (((*1 *1 *1 *2 *1) (-12 (-5 *2 (-485)) (-5 *1 (-1070 *3)) (-4 *3 (-1130)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-485)) (|has| *1 (-6 -3997)) (-4 *1 (-1169 *3)) + (-12 (-5 *2 (-485)) (|has| *1 (-6 -3998)) (-4 *1 (-1169 *3)) (-4 *3 (-1130))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-13 (-951 (-485)) (-581 (-485)) (-392))) @@ -2218,7 +2218,7 @@ (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-485)))) - (-4 *4 (-13 (-1156 *3) (-496) (-10 -8 (-15 -3145 ($ $ $))))) (-4 *3 (-496)) + (-4 *4 (-13 (-1156 *3) (-496) (-10 -8 (-15 -3146 ($ $ $))))) (-4 *3 (-496)) (-5 *1 (-1160 *3 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-862 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757)) @@ -2230,15 +2230,15 @@ ((*1 *1 *1) (-4 *1 (-1135))) ((*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-1160 *3 *2)) - (-4 *2 (-13 (-1156 *3) (-496) (-10 -8 (-15 -3145 ($ $ $)))))))) + (-4 *2 (-13 (-1156 *3) (-496) (-10 -8 (-15 -3146 ($ $ $)))))))) (((*1 *2 *1) (-12 (-4 *1 (-274 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-104)) - (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3944 *4)))))) + (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3945 *4)))))) ((*1 *2 *1) (-12 (-4 *1 (-450 *3 *4)) (-4 *3 (-72)) (-4 *4 (-760)) (-5 *2 (-584 (-454 *3 *4))))) ((*1 *2 *1) - (-12 (-5 *2 (-584 (-2 (|:| -3955 *3) (|:| -3939 *4)))) (-5 *1 (-675 *3 *4)) + (-12 (-5 *2 (-584 (-2 (|:| -3956 *3) (|:| -3940 *4)))) (-5 *1 (-675 *3 *4)) (-4 *3 (-962)) (-4 *4 (-664)))) ((*1 *2 *1) (-12 (-4 *1 (-1159 *3 *4)) (-4 *3 (-962)) (-4 *4 (-717)) @@ -2307,7 +2307,7 @@ (-12 (-4 *1 (-981 *2 *3)) (-4 *2 (-13 (-756) (-312))) (-4 *3 (-1156 *2)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-1159 *2 *3)) (-4 *3 (-717)) (|has| *2 (-15 ** (*2 *2 *3))) - (|has| *2 (-15 -3947 (*2 (-1091)))) (-4 *2 (-962))))) + (|has| *2 (-15 -3948 (*2 (-1091)))) (-4 *2 (-962))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-5 *1 (-148 *3)) (-4 *3 (-258)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-617 *3)) (-4 *3 (-1130)))) ((*1 *1 *1 *2) @@ -2420,12 +2420,12 @@ (|partial| -12 (-5 *2 (-695)) (-4 *1 (-1156 *3)) (-4 *3 (-962))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757)) - (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) (-4 *1 (-862 *4 *5 *3)))) + (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-862 *4 *5 *3)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-1156 *3))))) (((*1 *2 *1 *3) - (-12 (-5 *3 (-695)) (-4 *4 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-5 *3 (-695)) (-4 *4 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-1156 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1156 *3)) (-4 *3 (-962))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1156 *3)) (-4 *3 (-962))))) @@ -2486,14 +2486,14 @@ (|partial| -12 (-4 *1 (-1156 *2)) (-4 *2 (-962)) (-4 *2 (-496))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-1156 *2)) (-4 *2 (-962)) (-4 *2 (-496))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -3955 *4) (|:| -1973 *3) (|:| -2903 *3))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -3956 *4) (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) (-4 *1 (-978 *3 *4 *5)))) + (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-978 *3 *4 *5)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-496)) (-4 *3 (-962)) - (-5 *2 (-2 (|:| -3955 *3) (|:| -1973 *1) (|:| -2903 *1))) + (-5 *2 (-2 (|:| -3956 *3) (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-1156 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-312)) (-4 *4 (-496)) (-4 *5 (-1156 *4)) @@ -2510,14 +2510,14 @@ (((*1 *2 *2 *2) (-12 (-4 *3 (-962)) (-5 *1 (-1154 *3 *2)) (-4 *2 (-1156 *3))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-962)) (-5 *1 (-1154 *3 *2)) (-4 *2 (-1156 *3))))) (((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) + (|partial| -12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-1153 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-496) (-120))) (-5 *2 (-584 *3)) (-5 *1 (-1152 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-496) (-120))) - (-5 *2 (-2 (|:| -3139 *3) (|:| -3138 *3))) (-5 *1 (-1152 *4 *3)) + (-5 *2 (-2 (|:| -3140 *3) (|:| -3139 *3))) (-5 *1 (-1152 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *2 *2) (|partial| -12 (-4 *3 (-13 (-496) (-120))) (-5 *1 (-1152 *3 *2)) @@ -2541,7 +2541,7 @@ (-5 *2 (-2 (|:| |num| (-631 *4)) (|:| |den| *4))) (-5 *1 (-634 *4 *5)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *6 (-1156 *5)) - (-5 *2 (-2 (|:| -3267 *7) (|:| |rh| (-584 (-350 *6))))) + (-5 *2 (-2 (|:| -3268 *7) (|:| |rh| (-584 (-350 *6))))) (-5 *1 (-729 *5 *6 *7 *3)) (-5 *4 (-584 (-350 *6))) (-4 *7 (-601 *6)) (-4 *3 (-601 (-350 *6))))) ((*1 *2 *3) @@ -2666,7 +2666,7 @@ (-12 (-4 *4 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) (-15 -3832 ((-3 $ "failed") (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) (-15 -3833 ((-3 $ "failed") (-1091)))))) (-4 *5 (-718)) (-4 *7 (-496)) (-5 *2 (-348 *3)) (-5 *1 (-396 *4 *5 *6 *7 *3)) (-4 *6 (-496)) (-4 *3 (-862 *7 *5 *4)))) ((*1 *2 *3) @@ -2710,11 +2710,11 @@ (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) (-15 -3832 ((-3 $ "failed") (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) (-15 -3833 ((-3 $ "failed") (-1091)))))) (-4 *6 (-258)) (-5 *2 (-348 *3)) (-5 *1 (-670 *4 *5 *6 *3)) (-4 *3 (-862 (-858 *6) *4 *5)))) ((*1 *2 *3) - (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $))))) + (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $))))) (-4 *6 (-496)) (-5 *2 (-348 *3)) (-5 *1 (-672 *4 *5 *6 *3)) (-4 *3 (-862 (-350 (-858 *6)) *4 *5)))) ((*1 *2 *3) @@ -2829,7 +2829,7 @@ ((*1 *2 *1) (-12 (-4 *1 (-1135)) (-5 *2 (-85))))) (((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1133))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3229 (-584 (-1091))) (|:| -3230 (-584 (-1091))))) + (-12 (-5 *2 (-2 (|:| -3230 (-584 (-1091))) (|:| -3231 (-584 (-1091))))) (-5 *1 (-1133))))) (((*1 *2 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))) @@ -2851,7 +2851,7 @@ (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1014)) (-5 *2 (-85)) (-5 *1 (-1132 *3))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3230 (-584 *3)) (|:| -3229 (-584 *3)))) + (-12 (-5 *2 (-2 (|:| -3231 (-584 *3)) (|:| -3230 (-584 *3)))) (-5 *1 (-1132 *3)) (-4 *3 (-1014))))) (((*1 *2 *3) (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1186)) (-5 *1 (-1132 *4)))) @@ -2867,7 +2867,7 @@ (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4)) (-5 *3 (-1086 (-1086 *4)))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *3)) + (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3997)) (-4 *1 (-124 *3)) (-4 *3 (-1130)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1130)) (-5 *1 (-537 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1130)))) @@ -2882,7 +2882,7 @@ (((*1 *1 *2) (-12 (-5 *2 (-831)) (-4 *1 (-196 *3 *4)) (-4 *4 (-962)) (-4 *4 (-1130)))) ((*1 *1 *2) - (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-695))) + (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3959 *3) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5)) (-2 (|:| -2401 *2) (|:| -2402 *5)))) @@ -2929,12 +2929,12 @@ (((*1 *2 *3 *4 *5) (|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9)) (-4 *9 (-978 *6 *7 *8)) (-4 *6 (-496)) (-4 *7 (-718)) (-4 *8 (-757)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-584 *9)))) (-5 *3 (-584 *9)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *9)))) (-5 *3 (-584 *9)) (-4 *1 (-1125 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-978 *5 *6 *7)) (-4 *5 (-496)) (-4 *6 (-718)) (-4 *7 (-757)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-584 *8)))) (-5 *3 (-584 *8)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *8)))) (-5 *3 (-584 *8)) (-4 *1 (-1125 *5 *6 *7 *8))))) (((*1 *2 *1) (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757)) @@ -2942,7 +2942,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5)) - (-5 *2 (-2 (|:| -3862 (-584 *6)) (|:| -1703 (-584 *6))))))) + (-5 *2 (-2 (|:| -3863 (-584 *6)) (|:| -1703 (-584 *6))))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-584 *1)) (-4 *1 (-978 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)))) @@ -3064,7 +3064,7 @@ (-4 *6 (-757)) (-5 *2 (-584 *1)) (-4 *1 (-1125 *4 *5 *6 *7))))) (((*1 *2 *3) (-12 (-4 *4 (-496)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6)) - (-5 *2 (-584 (-2 (|:| -3862 *1) (|:| -1703 (-584 *7))))) (-5 *3 (-584 *7)) + (-5 *2 (-584 (-2 (|:| -3863 *1) (|:| -1703 (-584 *7))))) (-5 *3 (-584 *7)) (-4 *1 (-1125 *4 *5 *6 *7))))) (((*1 *2 *1) (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757)) @@ -3380,7 +3380,7 @@ (-12 (-5 *2 (-1186)) (-5 *1 (-167 *3)) (-4 *3 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 (*2 $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 (*2 $)) (-15 -1964 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-442)))) ((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-648)))) @@ -3436,7 +3436,7 @@ (((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1109 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))) (((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| -3861 *3) (|:| |entry| *4)))) (-4 *3 (-1014)) + (-12 (-5 *2 (-584 (-2 (|:| -3862 *3) (|:| |entry| *4)))) (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *1 (-1108 *3 *4)))) ((*1 *1) (-12 (-4 *1 (-1108 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-1106 *2)) (-4 *2 (-312))))) @@ -3567,13 +3567,13 @@ (-4 *6 (-13 (-258) (-951 (-485)) (-581 (-485)) (-120))) (-5 *1 (-596 *6 *2 *3)) (-4 *3 (-601 *2)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3997)))) - (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3997)))) + (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3998)))) + (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3998)))) (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2013 (-584 *4)))) (-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3997)))) - (-4 *7 (-13 (-324 *5) (-10 -7 (-6 -3997)))) + (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3998)))) + (-4 *7 (-13 (-324 *5) (-10 -7 (-6 -3998)))) (-5 *2 (-584 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2013 (-584 *7))))) (-5 *1 (-610 *5 *6 *7 *3)) (-5 *4 (-584 *7)) (-4 *3 (-628 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -3763,9 +3763,9 @@ (((*1 *2 *1) (|partial| -12 (-5 *2 (-584 (-234))) (-5 *1 (-234)))) ((*1 *2 *1) (-12 (-5 *2 (-584 (-1096))) (-5 *1 (-1096))))) (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1096))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2856)) (-5 *2 (-85)) (-5 *1 (-557)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2857)) (-5 *2 (-85)) (-5 *1 (-557)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2241)) (-5 *2 (-85)) (-5 *1 (-557)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2855)) (-5 *2 (-85)) (-5 *1 (-557)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2856)) (-5 *2 (-85)) (-5 *1 (-557)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2366)) (-5 *2 (-85)) (-5 *1 (-633 *4)) (-4 *4 (-553 (-773))))) @@ -3833,8 +3833,8 @@ (-12 (-5 *3 (-377)) (-5 *2 (-584 - (-3 (|:| -3543 (-1091)) - (|:| -3226 (-584 (-3 (|:| S (-1091)) (|:| P (-858 (-485))))))))) + (-3 (|:| -3544 (-1091)) + (|:| -3227 (-584 (-3 (|:| S (-1091)) (|:| P (-858 (-485))))))))) (-5 *1 (-1095))))) (((*1 *2 *1) (-12 (-5 *2 (-584 (-1091))) (-5 *1 (-1095))))) (((*1 *2 *1) @@ -3842,14 +3842,14 @@ (-5 *2 (-584 (-584 - (-3 (|:| -3543 (-1091)) - (|:| -3226 (-584 (-3 (|:| S (-1091)) (|:| P (-858 (-485)))))))))) + (-3 (|:| -3544 (-1091)) + (|:| -3227 (-584 (-3 (|:| S (-1091)) (|:| P (-858 (-485)))))))))) (-5 *1 (-1095))))) (((*1 *2 *1) (-12 (-5 *2 (-1016)) (-5 *1 (-1095))))) (((*1 *2 *3) (-12 (-5 *3 (-1091)) (-5 *2 (-1186)) (-5 *1 (-1094)))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1095))))) (((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| -3861 (-1091)) (|:| |entry| (-379))))) + (-12 (-5 *2 (-584 (-2 (|:| -3862 (-1091)) (|:| |entry| (-379))))) (-5 *1 (-1095))))) (((*1 *1) (-5 *1 (-1094)))) (((*1 *2 *3) (-12 (-5 *3 (-1091)) (-5 *2 (-1186)) (-5 *1 (-1094)))) @@ -3863,19 +3863,19 @@ ((*1 *2 *3 *4 *1) (-12 (-5 *4 (-584 (-1091))) (-5 *3 (-1091)) (-5 *2 (-1186)) (-5 *1 (-1094))))) (((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-377)) (|:| -3911 #1="void"))) (-5 *2 (-1186)) + (-12 (-5 *3 (-3 (|:| |fst| (-377)) (|:| -3912 #1="void"))) (-5 *2 (-1186)) (-5 *1 (-1094)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1091)) (-5 *4 (-3 (|:| |fst| (-377)) (|:| -3911 #1#))) + (-12 (-5 *3 (-1091)) (-5 *4 (-3 (|:| |fst| (-377)) (|:| -3912 #1#))) (-5 *2 (-1186)) (-5 *1 (-1094)))) ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1091)) (-5 *4 (-3 (|:| |fst| (-377)) (|:| -3911 #1#))) + (-12 (-5 *3 (-1091)) (-5 *4 (-3 (|:| |fst| (-377)) (|:| -3912 #1#))) (-5 *2 (-1186)) (-5 *1 (-1094))))) (((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1094)))) ((*1 *2 *3) (-12 (-5 *3 (-1091)) (-5 *2 (-1186)) (-5 *1 (-1094)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-1091)) (-5 *2 (-1186)) (-5 *1 (-1094))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1091)) (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3911 "void"))) + (-12 (-5 *3 (-1091)) (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3912 "void"))) (-5 *1 (-1094))))) (((*1 *2 *3 *1) (-12 (-5 *2 (-584 (-1091))) (-5 *1 (-1094)) (-5 *3 (-1091))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1091)) (-5 *2 (-1095)) (-5 *1 (-1094))))) @@ -3900,15 +3900,15 @@ ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -2585 (-584 (-773))) (|:| -2484 (-584 (-773))) - (|:| |presup| (-584 (-773))) (|:| -2583 (-584 (-773))) + (-2 (|:| -2586 (-584 (-773))) (|:| -2485 (-584 (-773))) + (|:| |presup| (-584 (-773))) (|:| -2584 (-584 (-773))) (|:| |args| (-584 (-773))))) (-5 *1 (-1091))))) (((*1 *1 *1 *2) (-12 (-5 *2 - (-2 (|:| -2585 (-584 (-773))) (|:| -2484 (-584 (-773))) - (|:| |presup| (-584 (-773))) (|:| -2583 (-584 (-773))) + (-2 (|:| -2586 (-584 (-773))) (|:| -2485 (-584 (-773))) + (|:| |presup| (-584 (-773))) (|:| -2584 (-584 (-773))) (|:| |args| (-584 (-773))))) (-5 *1 (-1091)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-584 (-773)))) (-5 *1 (-1091))))) @@ -3972,13 +3972,13 @@ ((*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-1082))))) (((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1130)) (-4 *1 (-124 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| -2402 (-695)) (|:| -3774 *4) (|:| |num| *4)))) + (-12 (-5 *2 (-584 (-2 (|:| -2402 (-695)) (|:| -3775 *4) (|:| |num| *4)))) (-4 *4 (-1156 *3)) (-4 *3 (-13 (-312) (-120))) (-5 *1 (-342 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3911 #1="void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3912 #1="void"))) (-5 *3 (-584 (-858 (-485)))) (-5 *4 (-85)) (-5 *1 (-379)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3911 #1#))) (-5 *3 (-584 (-1091))) + (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3912 #1#))) (-5 *3 (-584 (-1091))) (-5 *4 (-85)) (-5 *1 (-379)))) ((*1 *2 *1) (-12 (-5 *2 (-1070 *3)) (-5 *1 (-537 *3)) (-4 *3 (-1130)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-575 *2)) (-4 *2 (-146)))) @@ -3996,7 +3996,7 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-447)) (-5 *3 (-1029)) (-5 *1 (-750)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-783 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-1130)))) ((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| -3861 (-1091)) (|:| |entry| *4)))) (-4 *4 (-1014)) + (-12 (-5 *2 (-584 (-2 (|:| -3862 (-1091)) (|:| |entry| *4)))) (-4 *4 (-1014)) (-5 *1 (-799 *3 *4)) (-4 *3 (-1014)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-584 *5)) (-4 *5 (-13 (-1014) (-34))) @@ -4377,11 +4377,11 @@ (-12 (-5 *2 (-1070 *3)) (-4 *3 (-38 (-350 (-485)))) (-5 *1 (-1078 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-350 (-485)))) - (-5 *2 (-2 (|:| -3491 (-1070 *4)) (|:| -3492 (-1070 *4)))) + (-5 *2 (-2 (|:| -3492 (-1070 *4)) (|:| -3493 (-1070 *4)))) (-5 *1 (-1077 *4)) (-5 *3 (-1070 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-350 (-485)))) - (-5 *2 (-2 (|:| -3639 (-1070 *4)) (|:| -3635 (-1070 *4)))) + (-5 *2 (-2 (|:| -3640 (-1070 *4)) (|:| -3636 (-1070 *4)))) (-5 *1 (-1077 *4)) (-5 *3 (-1070 *4))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-1070 *3)) (-4 *3 (-312)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))) @@ -4473,7 +4473,7 @@ (-5 *1 (-1070 *4))))) (((*1 *2 *3 *1) (-12 - (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2596 (-695)) (|:| |period| (-695)))) + (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2597 (-695)) (|:| |period| (-695)))) (-5 *1 (-1070 *4)) (-4 *4 (-1130)) (-5 *3 (-695))))) (((*1 *1 *2) (-12 (-5 *2 (-1 (-1070 *3))) (-5 *1 (-1070 *3)) (-4 *3 (-1130))))) (((*1 *1 *2 *1) (-12 (-5 *1 (-584 *2)) (-4 *2 (-1130)))) @@ -4622,14 +4622,14 @@ (-2 (|:| -2337 (-356 *4 (-350 *4) *5 *6)) (|:| |principalPart| *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1156 *5)) (-4 *5 (-312)) - (-5 *2 (-2 (|:| |poly| *6) (|:| -3090 (-350 *6)) (|:| |special| (-350 *6)))) + (-5 *2 (-2 (|:| |poly| *6) (|:| -3091 (-350 *6)) (|:| |special| (-350 *6)))) (-5 *1 (-667 *5 *6)) (-5 *3 (-350 *6)))) ((*1 *2 *3) (-12 (-4 *4 (-312)) (-5 *2 (-584 *3)) (-5 *1 (-808 *3 *4)) (-4 *3 (-1156 *4)))) ((*1 *2 *3 *4 *4) (|partial| -12 (-5 *4 (-695)) (-4 *5 (-312)) - (-5 *2 (-2 (|:| -3139 *3) (|:| -3138 *3))) (-5 *1 (-808 *3 *5)) + (-5 *2 (-2 (|:| -3140 *3) (|:| -3139 *3))) (-5 *1 (-808 *3 *5)) (-4 *3 (-1156 *5)))) ((*1 *2 *3 *2 *4 *4) (-12 (-5 *2 (-584 *9)) (-5 *3 (-584 *8)) (-5 *4 (-85)) @@ -4794,7 +4794,7 @@ (-4 *3 (-13 (-392) (-951 (-485)) (-581 (-485)))) (-5 *1 (-526 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1156 *5)) (-4 *5 (-312)) - (-5 *2 (-2 (|:| -3090 *3) (|:| |special| *3))) (-5 *1 (-667 *5 *3)))) + (-5 *2 (-2 (|:| -3091 *3) (|:| |special| *3))) (-5 *1 (-667 *5 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1180 *5)) (-4 *5 (-312)) (-4 *5 (-962)) (-5 *2 (-584 (-584 (-631 *5)))) (-5 *1 (-944 *5)) (-5 *3 (-584 (-631 *5))))) @@ -4843,10 +4843,10 @@ (-4 *5 (-13 (-1014) (-34))) (-4 *6 (-13 (-1014) (-34))) (-5 *2 (-85)) (-5 *1 (-1056 *5 *6))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-124 *2)) (-4 *2 (-1130)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-124 *2)) (-4 *2 (-1130)) (-4 *2 (-1014)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3996)) (-4 *1 (-124 *3)) + (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3997)) (-4 *1 (-124 *3)) (-4 *3 (-1130)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1130)))) ((*1 *1 *2 *1 *3) @@ -4856,9 +4856,9 @@ (-12 (-5 *2 (-1055 *3 *4)) (-4 *3 (-13 (-1014) (-34))) (-4 *4 (-13 (-1014) (-34))) (-5 *1 (-1056 *3 *4))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3996)) (-4 *1 (-193 *3)) + (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3997)) (-4 *1 (-193 *3)) (-4 *3 (-1014)))) - ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -3996)) (-4 *1 (-193 *2)) (-4 *2 (-1014)))) + ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-193 *2)) (-4 *2 (-1014)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)) (-4 *2 (-1014)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1130)))) ((*1 *2 *3 *1) @@ -5051,25 +5051,25 @@ (((*1 *2 *1) (-12 (-4 *1 (-1049 *3)) (-4 *3 (-962)) (-5 *2 - (-2 (|:| -3851 (-695)) (|:| |curves| (-695)) (|:| |polygons| (-695)) + (-2 (|:| -3852 (-695)) (|:| |curves| (-695)) (|:| |polygons| (-695)) (|:| |constructs| (-695))))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3733 (-1086 *6)) (|:| -2402 (-485))))) + (-12 (-5 *3 (-584 (-2 (|:| -3734 (-1086 *6)) (|:| -2402 (-485))))) (-4 *6 (-258)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *2 (-85)) (-5 *1 (-682 *4 *5 *6 *7)) (-4 *7 (-862 *6 *4 *5)))) ((*1 *1 *1) (-12 (-4 *1 (-1049 *2)) (-4 *2 (-962))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1130)) (-5 *1 (-1047 *4 *2)) - (-4 *2 (-13 (-539 (-485) *4) (-318 *4) (-10 -7 (-6 -3997)))))) + (-4 *2 (-13 (-539 (-485) *4) (-318 *4) (-10 -7 (-6 -3998)))))) ((*1 *2 *2) (-12 (-4 *3 (-757)) (-4 *3 (-1130)) (-5 *1 (-1047 *3 *2)) - (-4 *2 (-13 (-539 (-485) *3) (-318 *3) (-10 -7 (-6 -3997))))))) + (-4 *2 (-13 (-539 (-485) *3) (-318 *3) (-10 -7 (-6 -3998))))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1130)) (-5 *1 (-1047 *4 *2)) - (-4 *2 (-13 (-539 (-485) *4) (-318 *4) (-10 -7 (-6 -3997)))))) + (-4 *2 (-13 (-539 (-485) *4) (-318 *4) (-10 -7 (-6 -3998)))))) ((*1 *2 *2) (-12 (-4 *3 (-757)) (-4 *3 (-1130)) (-5 *1 (-1047 *3 *2)) - (-4 *2 (-13 (-539 (-485) *3) (-318 *3) (-10 -7 (-6 -3997))))))) + (-4 *2 (-13 (-539 (-485) *3) (-318 *3) (-10 -7 (-6 -3998))))))) (((*1 *2 *3) (-12 (-5 *3 (-1180 *4)) (-4 *4 (-962)) (-4 *2 (-1156 *4)) (-5 *1 (-384 *4 *2)))) @@ -5165,8 +5165,8 @@ (|:| |maps| (-584 (-2 (|:| |arg| *5) (|:| |res| *5)))))) (-5 *1 (-1043 *3 *5)) (-4 *3 (-1156 *5))))) (((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-312)) (-4 *5 (-13 (-324 *4) (-10 -7 (-6 -3997)))) - (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3997)))) (-5 *1 (-610 *4 *5 *2 *3)) + (|partial| -12 (-4 *4 (-312)) (-4 *5 (-13 (-324 *4) (-10 -7 (-6 -3998)))) + (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3998)))) (-5 *1 (-610 *4 *5 *2 *3)) (-4 *3 (-628 *4 *5 *2)))) ((*1 *2 *3 *2) (|partial| -12 (-5 *2 (-1180 *4)) (-5 *3 (-631 *4)) (-4 *4 (-312)) @@ -5230,7 +5230,7 @@ (-4 *2 (-962))))) (((*1 *2 *3) (-12 (-5 *3 (-631 *2)) (-4 *4 (-1156 *2)) - (-4 *2 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-4 *2 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-5 *1 (-439 *2 *4 *5)) (-4 *5 (-353 *2 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1038 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2)) @@ -5240,27 +5240,27 @@ (-5 *1 (-461 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *3 (-324 *2)) (-4 *4 (-324 *2)) - (|has| *2 (-6 (-3998 "*"))) (-4 *2 (-962)))) + (|has| *2 (-6 (-3999 "*"))) (-4 *2 (-962)))) ((*1 *2 *3) (-12 (-4 *4 (-324 *2)) (-4 *5 (-324 *2)) (-4 *2 (-146)) (-5 *1 (-630 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1038 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2)) - (|has| *2 (-6 (-3998 "*"))) (-4 *2 (-962))))) + (|has| *2 (-6 (-3999 "*"))) (-4 *2 (-962))))) (((*1 *2 *1) (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *3 (-324 *2)) (-4 *4 (-324 *2)) - (|has| *2 (-6 (-3998 "*"))) (-4 *2 (-962)))) + (|has| *2 (-6 (-3999 "*"))) (-4 *2 (-962)))) ((*1 *2 *3) (-12 (-4 *4 (-324 *2)) (-4 *5 (-324 *2)) (-4 *2 (-146)) (-5 *1 (-630 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1038 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2)) - (|has| *2 (-6 (-3998 "*"))) (-4 *2 (-962))))) + (|has| *2 (-6 (-3999 "*"))) (-4 *2 (-962))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1130)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3997)) (-4 *1 (-429 *3)) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3998)) (-4 *1 (-429 *3)) (-4 *3 (-1130)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1036 *3)) (-4 *3 (-1130))))) (((*1 *2 *2 *1) (-12 (-4 *1 (-1035 *2)) (-4 *2 (-1130))))) @@ -5411,25 +5411,25 @@ (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8)) - (-5 *2 (-2 (|:| -3267 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9)))) + (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9)))) (-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9)))) ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8)) - (-5 *2 (-2 (|:| -3267 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9)))) + (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9)))) (-5 *1 (-1019 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8)) (-5 *2 - (-584 (-2 (|:| -3267 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9))))) + (-584 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9))))) (-5 *1 (-902 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9)))) ((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8)) (-5 *2 - (-584 (-2 (|:| -3267 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9))))) + (-584 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9))))) (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))) (((*1 *2 *2) (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7)))) @@ -5573,7 +5573,7 @@ (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) (((*1 *2 *1) - (-12 (-5 *2 (-584 (-2 (|:| -3861 (-1091)) (|:| |entry| *4)))) + (-12 (-5 *2 (-584 (-2 (|:| -3862 (-1091)) (|:| |entry| *4)))) (-5 *1 (-799 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014)))) ((*1 *2 *1) (-12 (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014)) @@ -5616,7 +5616,7 @@ (((*1 *2 *3 *1) (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-85)))) ((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-85)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-814 *4)) (-4 *4 (-1014)) (-5 *2 (-85)) (-5 *1 (-817 *4)))) @@ -5757,15 +5757,15 @@ (-4 *3 (-1021 *5 *6 *7 *8)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3225 (-584 (-858 *5)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-991 *5 *6)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-258) (-120))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3225 (-584 (-858 *4)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *4)) (|:| -3226 (-584 (-858 *4)))))) (-5 *1 (-991 *4 *5)) (-5 *3 (-584 (-858 *4))) (-14 *5 (-584 (-1091))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) - (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3225 (-584 (-858 *5)))))) + (-5 *2 (-584 (-2 (|:| -1748 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-991 *5 *6)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091)))))) (((*1 *1 *2) (-12 (-5 *2 (-584 (-988 *3 *4 *5))) (-4 *3 (-1014)) @@ -6003,7 +6003,7 @@ (-14 *4 (-584 (-1091))))) ((*1 *2 *1) (-12 (-4 *1 (-335 *2 *3)) (-4 *3 (-1014)) (-4 *2 (-962)))) ((*1 *2 *1) - (-12 (-14 *3 (-584 (-1091))) (-4 *5 (-196 (-3958 *3) (-695))) + (-12 (-14 *3 (-584 (-1091))) (-4 *5 (-196 (-3959 *3) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *4) (|:| -2402 *5)) (-2 (|:| -2401 *4) (|:| -2402 *5)))) @@ -6061,36 +6061,36 @@ (-12 (-4 *1 (-978 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757)) - (-5 *2 (-2 (|:| -3955 *1) (|:| |gap| (-695)) (|:| -2903 *1))) + (-5 *2 (-2 (|:| -3956 *1) (|:| |gap| (-695)) (|:| -2904 *1))) (-4 *1 (-978 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -3955 *1) (|:| |gap| (-695)) (|:| -2903 *1))) + (-5 *2 (-2 (|:| -3956 *1) (|:| |gap| (-695)) (|:| -2904 *1))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -3955 *3) (|:| |gap| (-695)) (|:| -1973 (-705 *3)) - (|:| -2903 (-705 *3)))) + (-2 (|:| -3956 *3) (|:| |gap| (-695)) (|:| -1973 (-705 *3)) + (|:| -2904 (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-962)))) ((*1 *2 *1 *1 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757)) - (-5 *2 (-2 (|:| -3955 *1) (|:| |gap| (-695)) (|:| -1973 *1) (|:| -2903 *1))) + (-5 *2 (-2 (|:| -3956 *1) (|:| |gap| (-695)) (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-978 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -3955 *1) (|:| |gap| (-695)) (|:| -1973 *1) (|:| -2903 *1))) + (-5 *2 (-2 (|:| -3956 *1) (|:| |gap| (-695)) (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-705 *2)) (-4 *2 (-962)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-978 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| |polnum| (-705 *3)) (|:| |polden| *3) (|:| -3482 (-695)))) + (-5 *2 (-2 (|:| |polnum| (-705 *3)) (|:| |polden| *3) (|:| -3483 (-695)))) (-5 *1 (-705 *3)) (-4 *3 (-962)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3482 (-695)))) + (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3483 (-695)))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-51)) (-5 *1 (-52 *2)) (-4 *2 (-1130)))) ((*1 *2 *3) @@ -6104,21 +6104,21 @@ ((*1 *1 *2) (|partial| OR (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-38 (-350 (-485))))) (-2561 (-4 *3 (-38 (-485)))) + (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-2562 (-4 *3 (-38 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-484))) (-2561 (-4 *3 (-38 (-350 (-485))))) + (-12 (-2562 (-4 *3 (-484))) (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-905 (-485)))) (-4 *3 (-38 (-350 (-485)))) + (-12 (-2562 (-4 *3 (-905 (-485)))) (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))))) ((*1 *1 *2) (|partial| OR (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) - (-12 (-2561 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) + (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) @@ -6136,21 +6136,21 @@ ((*1 *1 *2) (OR (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-38 (-350 (-485))))) (-2561 (-4 *3 (-38 (-485)))) + (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-2562 (-4 *3 (-38 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-484))) (-2561 (-4 *3 (-38 (-350 (-485))))) + (-12 (-2562 (-4 *3 (-484))) (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 *3)) - (-12 (-2561 (-4 *3 (-905 (-485)))) (-4 *3 (-38 (-350 (-485)))) + (-12 (-2562 (-4 *3 (-905 (-485)))) (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))))) ((*1 *1 *2) (OR (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) - (-12 (-2561 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) + (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))) (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5)) @@ -6181,24 +6181,24 @@ (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -3145 (-705 *3)) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3)))) + (-2 (|:| -3146 (-705 *3)) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -3145 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-5 *2 (-2 (|:| -3146 *1) (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3145 (-705 *3)) (|:| |coef1| (-705 *3)))) + (-12 (-5 *2 (-2 (|:| -3146 (-705 *3)) (|:| |coef1| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -3145 *1) (|:| |coef1| *1))) (-4 *1 (-978 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3146 *1) (|:| |coef1| *1))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3145 (-705 *3)) (|:| |coef2| (-705 *3)))) + (-12 (-5 *2 (-2 (|:| -3146 (-705 *3)) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) - (-5 *2 (-2 (|:| -3145 *1) (|:| |coef2| *1))) (-4 *1 (-978 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3146 *1) (|:| |coef2| *1))) (-4 *1 (-978 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *2 (-584 *1)) (-4 *1 (-978 *3 *4 *5))))) @@ -6294,18 +6294,18 @@ ((*1 *1 *1) (-5 *1 (-839))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1002 (-179))) (-5 *1 (-839)))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))) + (-12 (-5 *2 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))) (-5 *4 (-350 (-485))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))) + (-5 *2 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))) + (-12 (-5 *2 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))) (-5 *4 (-350 (-485))) (-5 *1 (-936 *3)) (-4 *3 (-1156 *4)))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))) + (-5 *2 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))) (-5 *1 (-936 *3)) (-4 *3 (-1156 (-350 (-485)))))) ((*1 *1 *1) (-12 (-4 *2 (-13 (-756) (-312))) (-5 *1 (-975 *2 *3)) (-4 *3 (-1156 *2))))) @@ -6509,8 +6509,8 @@ (-12 (-4 *4 (-312)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-5 *2 (-695)) (-5 *1 (-461 *4 *5 *6 *3)) (-4 *3 (-628 *4 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3997)))) - (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3997)))) (-5 *2 (-695)) + (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3998)))) + (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3998)))) (-5 *2 (-695)) (-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-631 *5)) (-5 *4 (-1180 *5)) (-4 *5 (-312)) (-5 *2 (-695)) @@ -6537,10 +6537,10 @@ (-12 (-4 *1 (-966 *3 *4 *5 *6 *7)) (-4 *5 (-962)) (-4 *6 (-196 *4 *5)) (-4 *7 (-196 *3 *5)) (-4 *5 (-496)) (-5 *2 (-695))))) (((*1 *2 *3) - (-12 (|has| *6 (-6 -3997)) (-4 *4 (-312)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) + (-12 (|has| *6 (-6 -3998)) (-4 *4 (-312)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-5 *2 (-584 *6)) (-5 *1 (-461 *4 *5 *6 *3)) (-4 *3 (-628 *4 *5 *6)))) ((*1 *2 *3) - (-12 (|has| *9 (-6 -3997)) (-4 *4 (-496)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) + (-12 (|has| *9 (-6 -3998)) (-4 *4 (-496)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-4 *7 (-905 *4)) (-4 *8 (-324 *7)) (-4 *9 (-324 *7)) (-5 *2 (-584 *6)) (-5 *1 (-462 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-628 *4 *5 *6)) (-4 *10 (-628 *7 *8 *9)))) @@ -6611,7 +6611,7 @@ (-12 (-5 *3 (-350 (-1086 *2))) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962)) (-4 *2 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $))))) (-5 *1 (-863 *5 *4 *6 *7 *2)) (-4 *7 (-862 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-350 (-1086 (-350 (-858 *5))))) (-5 *4 (-1091)) @@ -6638,12 +6638,12 @@ (-5 *2 (-350 (-1086 *3))) (-5 *1 (-863 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1086 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $))))) (-4 *7 (-862 *6 *5 *4)) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962)) (-5 *1 (-863 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) @@ -6657,7 +6657,7 @@ (-4 *2 (-757)) (-5 *1 (-863 *4 *2 *5 *6 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *6)) (-15 -2999 (*6 $)) (-15 -2998 (*6 $))))))) + (-10 -8 (-15 -3948 ($ *6)) (-15 -3000 (*6 $)) (-15 -2999 (*6 $))))))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-350 (-858 *4))) (-4 *4 (-496)) (-5 *2 (-1091)) (-5 *1 (-953 *4))))) @@ -6674,7 +6674,7 @@ (-5 *2 (-584 *5)) (-5 *1 (-863 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-887 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-717)) (-4 *5 (-757)) (-5 *2 (-584 *5)))) @@ -6708,7 +6708,7 @@ (-4 *2 (-13 (-1014) (-10 -8 (-15 * ($ $ $)))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-831)) (-5 *1 (-945 *2)) - (-4 *2 (-13 (-1014) (-10 -8 (-15 -3840 ($ $ $)))))))) + (-4 *2 (-13 (-1014) (-10 -8 (-15 -3841 ($ $ $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-584 (-1180 *5))) (-5 *4 (-485)) (-5 *2 (-1180 *5)) (-5 *1 (-944 *5)) (-4 *5 (-312)) (-4 *5 (-320)) (-4 *5 (-962))))) @@ -6778,10 +6778,10 @@ (-12 (-5 *3 (-695)) (-5 *2 (-631 (-858 *4))) (-5 *1 (-943 *4)) (-4 *4 (-962))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-631 *4)) (-5 *3 (-831)) (|has| *4 (-6 (-3998 "*"))) + (-12 (-5 *2 (-631 *4)) (-5 *3 (-831)) (|has| *4 (-6 (-3999 "*"))) (-4 *4 (-962)) (-5 *1 (-943 *4)))) ((*1 *2 *2 *3) - (-12 (-5 *2 (-584 (-631 *4))) (-5 *3 (-831)) (|has| *4 (-6 (-3998 "*"))) + (-12 (-5 *2 (-584 (-631 *4))) (-5 *3 (-831)) (|has| *4 (-6 (-3999 "*"))) (-4 *4 (-962)) (-5 *1 (-943 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-631 (-350 (-858 (-485))))) (-5 *2 (-584 (-631 (-265 (-485))))) @@ -6814,7 +6814,7 @@ (((*1 *2 *1 *2) (-12 (-5 *1 (-940 *2)) (-4 *2 (-1130))))) (((*1 *2 *2 *3) (-12 (-4 *3 (-312)) (-5 *1 (-939 *3 *2)) (-4 *2 (-601 *3)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-312)) (-5 *2 (-2 (|:| -3267 *3) (|:| -2514 (-584 *5)))) + (-12 (-4 *5 (-312)) (-5 *2 (-2 (|:| -3268 *3) (|:| -2515 (-584 *5)))) (-5 *1 (-939 *5 *3)) (-5 *4 (-584 *5)) (-4 *3 (-601 *5))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-975 (-938 *4) (-1086 (-938 *4)))) (-5 *3 (-773)) @@ -6823,44 +6823,44 @@ (|partial| -12 (-5 *2 (-975 (-938 *3) (-1086 (-938 *3)))) (-5 *1 (-938 *3)) (-4 *3 (-13 (-756) (-312) (-934)))))) (((*1 *2 *3) - (-12 (-5 *2 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *2 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *2 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))) - (-5 *4 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))))) + (-5 *4 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *2 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))) (-5 *4 (-350 (-485))))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3139 *5) (|:| -3138 *5)))) + (-12 (-5 *5 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3140 *5) (|:| -3139 *5)))) (-5 *1 (-935 *3)) (-4 *3 (-1156 (-485))) - (-5 *4 (-2 (|:| -3139 *5) (|:| -3138 *5))))) + (-5 *4 (-2 (|:| -3140 *5) (|:| -3139 *5))))) ((*1 *2 *3) - (-12 (-5 *2 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *2 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *1 (-936 *3)) (-4 *3 (-1156 (-350 (-485)))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *2 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *1 (-936 *3)) (-4 *3 (-1156 (-350 (-485)))) - (-5 *4 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))))) + (-5 *4 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3139 *4) (|:| -3138 *4)))) + (-12 (-5 *4 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3140 *4) (|:| -3139 *4)))) (-5 *1 (-936 *3)) (-4 *3 (-1156 *4)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3139 *5) (|:| -3138 *5)))) + (-12 (-5 *5 (-350 (-485))) (-5 *2 (-584 (-2 (|:| -3140 *5) (|:| -3139 *5)))) (-5 *1 (-936 *3)) (-4 *3 (-1156 *5)) - (-5 *4 (-2 (|:| -3139 *5) (|:| -3138 *5)))))) + (-5 *4 (-2 (|:| -3140 *5) (|:| -3139 *5)))))) (((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485)))))) + (-12 (-5 *3 (-584 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485)))))) (-5 *2 (-584 (-350 (-485)))) (-5 *1 (-935 *4)) (-4 *4 (-1156 (-485)))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3139 (-350 (-485))) (|:| -3138 (-350 (-485))))) + (-12 (-5 *3 (-2 (|:| -3140 (-350 (-485))) (|:| -3139 (-350 (-485))))) (-5 *2 (-350 (-485))) (-5 *1 (-935 *4)) (-4 *4 (-1156 (-485)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1180 *6)) (-5 *4 (-1180 (-485))) (-5 *5 (-485)) (-4 *6 (-1014)) (-5 *2 (-1 *6)) (-5 *1 (-931 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3403 *4) (|:| -1523 (-485))))) (-4 *4 (-1014)) + (-12 (-5 *3 (-584 (-2 (|:| -3404 *4) (|:| -1523 (-485))))) (-4 *4 (-1014)) (-5 *2 (-1 *4)) (-5 *1 (-931 *4))))) (((*1 *2 *3 *3 *3) (|partial| -12 (-4 *4 (-13 (-312) (-120) (-951 (-485)))) (-4 *5 (-1156 *4)) @@ -6870,14 +6870,14 @@ (-4 *5 (-13 (-312) (-120) (-951 (-485)))) (-5 *2 (-2 (|:| |a| *6) (|:| |b| (-350 *6)) (|:| |h| *6) (|:| |c1| (-350 *6)) - (|:| |c2| (-350 *6)) (|:| -3094 *6))) + (|:| |c2| (-350 *6)) (|:| -3095 *6))) (-5 *1 (-930 *5 *6)) (-5 *3 (-350 *6))))) (((*1 *2 *3 *3 *3 *4 *5) (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1156 *6)) (-4 *6 (-13 (-312) (-120) (-951 *4))) (-5 *4 (-485)) (-5 *2 (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-85)))) - (|:| -3267 + (|:| -3268 (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) (|:| |beta| *3))))) (-5 *1 (-929 *6 *3))))) @@ -6889,7 +6889,7 @@ (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1156 *5)) (-4 *5 (-13 (-312) (-120) (-951 (-485)))) (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-350 *6)) (|:| |c| (-350 *6)) (|:| -3094 *6))) + (-2 (|:| |a| *6) (|:| |b| (-350 *6)) (|:| |c| (-350 *6)) (|:| -3095 *6))) (-5 *1 (-929 *5 *6)) (-5 *3 (-350 *6))))) (((*1 *2 *3 *4 *4 *4 *5 *6 *7) (|partial| -12 (-5 *5 (-1091)) @@ -6916,7 +6916,7 @@ (-5 *7 (-1 (-3 (-2 (|:| -2137 *4) (|:| |coeff| *4)) "failed") *4 *4)) (-4 *4 (-13 (-1116) (-27) (-364 *8))) (-4 *8 (-13 (-392) (-120) (-951 *3) (-581 *3))) (-5 *3 (-485)) - (-5 *2 (-2 (|:| |ans| *4) (|:| -3138 *4) (|:| |sol?| (-85)))) + (-5 *2 (-2 (|:| |ans| *4) (|:| -3139 *4) (|:| |sol?| (-85)))) (-5 *1 (-927 *8 *4))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-780 *3)) (-5 *2 (-485)))) ((*1 *1 *1) (-4 *1 (-916))) ((*1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-926)))) @@ -6936,9 +6936,9 @@ (((*1 *2 *1 *1) (-12 (-4 *1 (-924 *3)) (-4 *3 (-1130)) (-4 *3 (-1014)) (-5 *2 (-85))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-584 *1)) (|has| *1 (-6 -3997)) (-4 *1 (-924 *3)) + (-12 (-5 *2 (-584 *1)) (|has| *1 (-6 -3998)) (-4 *1 (-924 *3)) (-4 *3 (-1130))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-924 *2)) (-4 *2 (-1130))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-924 *2)) (-4 *2 (-1130))))) (((*1 *2 *1) (|partial| -12 (-4 *1 (-139 *3)) (-4 *3 (-146)) (-4 *3 (-484)) (-5 *2 (-350 (-485))))) @@ -7003,7 +7003,7 @@ (((*1 *1 *2 *2) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-918 *3)) (-14 *3 (-485))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-348 *5)) (-4 *5 (-496)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *5) (|:| |radicand| (-584 *5)))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *5) (|:| |radicand| (-584 *5)))) (-5 *1 (-271 *5)) (-5 *4 (-695)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-916)) (-5 *2 (-485))))) (((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1014)) (-5 *1 (-914 *3))))) @@ -7099,39 +7099,39 @@ (-12 (-4 *3 (-1156 *2)) (-4 *2 (-1156 *4)) (-5 *1 (-899 *4 *2 *3 *5)) (-4 *4 (-299)) (-4 *5 (-662 *2 *3))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $))))) + (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $))))) (-4 *5 (-496)) (-5 *1 (-672 *4 *3 *5 *2)) (-4 *2 (-862 (-350 (-858 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) - (-15 -3832 ((-3 $ #1="failed") (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) + (-15 -3833 ((-3 $ #1="failed") (-1091)))))) (-5 *1 (-898 *4 *5 *3 *2)) (-4 *2 (-862 (-858 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-584 *6)) (-4 *6 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) (-15 -3832 ((-3 $ #1#) (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) (-15 -3833 ((-3 $ #1#) (-1091)))))) (-4 *4 (-962)) (-4 *5 (-718)) (-5 *1 (-898 *4 *5 *6 *2)) (-4 *2 (-862 (-858 *4) *5 *6))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $))))) + (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $))))) (-4 *5 (-496)) (-5 *1 (-672 *4 *3 *5 *2)) (-4 *2 (-862 (-350 (-858 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) - (-15 -3832 ((-3 $ #1="failed") (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) + (-15 -3833 ((-3 $ #1="failed") (-1091)))))) (-5 *1 (-898 *4 *5 *3 *2)) (-4 *2 (-862 (-858 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-584 *6)) (-4 *6 (-13 (-757) - (-10 -8 (-15 -3973 ((-1091) $)) (-15 -3832 ((-3 $ #1#) (-1091)))))) + (-10 -8 (-15 -3974 ((-1091) $)) (-15 -3833 ((-3 $ #1#) (-1091)))))) (-4 *4 (-962)) (-4 *5 (-718)) (-5 *1 (-898 *4 *5 *6 *2)) (-4 *2 (-862 (-858 *4) *5 *6))))) (((*1 *2 *2) (|partial| -12 (-4 *1 (-897 *2)) (-4 *2 (-1116))))) @@ -7230,7 +7230,7 @@ (((*1 *2 *3) (|partial| -12 (-4 *4 (-496)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6)) - (-5 *2 (-2 (|:| |bas| (-416 *4 *5 *6 *7)) (|:| -3324 (-584 *7)))) + (-5 *2 (-2 (|:| |bas| (-416 *4 *5 *6 *7)) (|:| -3325 (-584 *7)))) (-5 *1 (-891 *4 *5 *6 *7)) (-5 *3 (-584 *7))))) (((*1 *2 *2) (-12 (-5 *2 (-584 *6)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-496)) (-4 *4 (-718)) @@ -7337,7 +7337,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-584 (-814 *3))) (-5 *1 (-814 *3)) (-4 *3 (-1014)))) ((*1 *2 *1 *3) (-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757)) (-4 *6 (-978 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -3131 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3132 *1) (|:| |upper| *1))) (-4 *1 (-890 *4 *5 *3 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-890 *3 *4 *5 *6)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)) @@ -7381,7 +7381,7 @@ (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-962)) (-4 *3 (-717)))) ((*1 *2 *1) (-12 (-4 *1 (-335 *3 *2)) (-4 *3 (-962)) (-4 *2 (-1014)))) ((*1 *2 *1) - (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *6 (-196 (-3958 *3) (-695))) + (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *6 (-196 (-3959 *3) (-695))) (-14 *7 (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *6)) (-2 (|:| -2401 *5) (|:| -2402 *6)))) @@ -7396,7 +7396,7 @@ (-12 (-5 *3 (-584 (-831))) (-5 *1 (-125 *4 *2 *5)) (-14 *4 (-831)) (-4 *2 (-312)) (-14 *5 (-907 *4 *2)))) ((*1 *1 *2 *3) - (-12 (-5 *3 (-651 *5 *6 *7)) (-4 *5 (-757)) (-4 *6 (-196 (-3958 *4) (-695))) + (-12 (-5 *3 (-651 *5 *6 *7)) (-4 *5 (-757)) (-4 *6 (-196 (-3959 *4) (-695))) (-14 *7 (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *6)) (-2 (|:| -2401 *5) (|:| -2402 *6)))) @@ -7437,18 +7437,18 @@ (((*1 *2 *2) (-12 (-5 *1 (-132 *2)) (-4 *2 (-484)))) ((*1 *1 *2) (-12 (-5 *2 (-584 (-831))) (-5 *1 (-885))))) (((*1 *2 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-5 *2 (-584 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-584 (-831))) (-5 *1 (-885))))) (((*1 *2 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1070 (-885))) (-5 *1 (-885))))) (((*1 *2 *1) (-12 (-5 *2 (-584 (-783 (-831) (-831)))) (-5 *1 (-885))))) (((*1 *2 *1) (-12 (-5 *2 (-831)) (-5 *1 (-885))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3757 *4))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3758 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3757 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3758 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-496)) (-5 *1 (-883 *2 *3)) (-4 *3 (-1156 *2))))) (((*1 *2 *2 *2 *2 *3) @@ -7458,22 +7458,22 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-695)) (-4 *2 (-496)) (-5 *1 (-883 *2 *4)) (-4 *4 (-1156 *2))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) (-4 *1 (-258)))) + (-12 (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-258)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *3 (-1014)) (-5 *2 (-2 (|:| |lm| *1) (|:| |rm| *1))) (-4 *1 (-336 *3)))) ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -1973 (-695)) (|:| -2903 (-695)))) (-5 *1 (-695)))) + (-12 (-5 *2 (-2 (|:| -1973 (-695)) (|:| -2904 (-695)))) (-5 *1 (-695)))) ((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-392)) (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| -2877 *4))) (-5 *1 (-883 *4 *3)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -2878 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-392)) (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2877 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2878 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-496)) (-4 *2 (-392)) (-5 *1 (-883 *2 *3)) (-4 *3 (-1156 *2))))) @@ -7484,21 +7484,21 @@ (-12 (-4 *4 (-496)) (-5 *2 (-584 *3)) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3758 *4))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3759 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3758 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3759 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3145 *3))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3146 *3))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3145 *3))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3146 *3))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3145 *3))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3146 *3))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) @@ -7528,18 +7528,18 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-695)) (-4 *4 (-496)) (-5 *1 (-883 *4 *2)) (-4 *2 (-1156 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3757 *4))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3758 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3757 *4))) + (-12 (-4 *4 (-496)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3758 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-496)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3757 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3758 *4))) (-5 *1 (-883 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *1) - (-12 (-4 *1 (-347)) (-2561 (|has| *1 (-6 -3987))) - (-2561 (|has| *1 (-6 -3979))))) + (-12 (-4 *1 (-347)) (-2562 (|has| *1 (-6 -3988))) + (-2562 (|has| *1 (-6 -3980))))) ((*1 *2 *1) (-12 (-4 *1 (-369 *2)) (-4 *2 (-1014)) (-4 *2 (-757)))) ((*1 *1) (-4 *1 (-753))) ((*1 *1 *1 *1) (-4 *1 (-760))) ((*1 *2 *1) (-12 (-4 *1 (-882 *2)) (-4 *2 (-757))))) @@ -7608,14 +7608,14 @@ (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-584 (-1091))) (-4 *5 (-13 (-312) (-120))) (-5 *2 - (-2 (|:| -3955 (-584 (-485))) (|:| |poly| (-584 (-1086 *5))) + (-2 (|:| -3956 (-584 (-485))) (|:| |poly| (-584 (-1086 *5))) (|:| |prim| (-1086 *5)))) (-5 *1 (-873 *5)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-584 (-858 *6))) (-5 *4 (-584 (-1091))) (-5 *5 (-1091)) (-4 *6 (-13 (-312) (-120))) (-5 *2 - (-2 (|:| -3955 (-584 (-485))) (|:| |poly| (-584 (-1086 *6))) + (-2 (|:| -3956 (-584 (-485))) (|:| |poly| (-584 (-1086 *6))) (|:| |prim| (-1086 *6)))) (-5 *1 (-873 *6))))) (((*1 *1 *2 *3) @@ -7635,34 +7635,34 @@ (((*1 *1 *2) (-12 (-5 *2 (-1034)) (-5 *1 (-866))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-496)) (-4 *3 (-862 *7 *5 *6)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *3) (|:| |radicand| (-584 *3)))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *3) (|:| |radicand| (-584 *3)))) (-5 *1 (-865 *5 *6 *7 *3 *8)) (-5 *4 (-695)) (-4 *8 (-13 (-312) - (-10 -8 (-15 -3947 ($ *3)) (-15 -2999 (*3 $)) (-15 -2998 (*3 $)))))))) + (-10 -8 (-15 -3948 ($ *3)) (-15 -3000 (*3 $)) (-15 -2999 (*3 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *7 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-496)) (-4 *8 (-862 *7 *5 *6)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *3) (|:| |radicand| *3))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *3) (|:| |radicand| *3))) (-5 *1 (-865 *5 *6 *7 *8 *3)) (-5 *4 (-695)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *8)) (-15 -2999 (*8 $)) (-15 -2998 (*8 $)))))))) + (-10 -8 (-15 -3948 ($ *8)) (-15 -3000 (*8 $)) (-15 -2999 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-350 (-485))) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-496)) (-4 *8 (-862 *7 *5 *6)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *9) (|:| |radicand| *9))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *9) (|:| |radicand| *9))) (-5 *1 (-865 *5 *6 *7 *8 *9)) (-5 *4 (-695)) (-4 *9 (-13 (-312) - (-10 -8 (-15 -3947 ($ *8)) (-15 -2999 (*8 $)) (-15 -2998 (*8 $)))))))) + (-10 -8 (-15 -3948 ($ *8)) (-15 -3000 (*8 $)) (-15 -2999 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-718)) (-4 *6 (-757)) (-4 *3 (-496)) (-4 *7 (-862 *3 *5 *6)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *8) (|:| |radicand| *8))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *8) (|:| |radicand| *8))) (-5 *1 (-865 *5 *6 *3 *7 *8)) (-5 *4 (-695)) (-4 *8 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-962)) (-4 *3 (-1014)) (-5 *2 (-2 (|:| |val| *1) (|:| -2402 (-485)))) (-4 *1 (-364 *3)))) @@ -7675,7 +7675,7 @@ (-5 *1 (-863 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-1091)) (-4 *4 (-962)) (-4 *4 (-1014)) (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2402 (-485)))) (-4 *1 (-364 *4)))) @@ -7697,7 +7697,7 @@ (-5 *1 (-863 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-1026)) (-4 *3 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-364 *3)))) @@ -7711,7 +7711,7 @@ (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-584 *3)) (-5 *1 (-863 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-364 *3)))) @@ -7725,7 +7725,7 @@ (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-584 *3)) (-5 *1 (-863 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1) (-12 (-4 *3 (-962)) (-4 *4 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-335 *3 *4)))) ((*1 *2 *1) @@ -8005,7 +8005,7 @@ (-12 (-5 *3 (-584 - (-2 (|:| -3109 (-695)) + (-2 (|:| -3110 (-695)) (|:| |eqns| (-584 (-2 (|:| |det| *7) (|:| |rows| (-584 (-485))) @@ -8018,7 +8018,7 @@ (-12 (-5 *3 (-584 - (-2 (|:| -3109 (-695)) + (-2 (|:| -3110 (-695)) (|:| |eqns| (-584 (-2 (|:| |det| *7) (|:| |rows| (-584 (-485))) @@ -8035,7 +8035,7 @@ (-12 (-5 *3 (-2 (|:| |mat| (-631 (-350 (-858 *4)))) (|:| |vec| (-584 (-350 (-858 *4)))) - (|:| -3109 (-695)) (|:| |rows| (-584 (-485))) (|:| |cols| (-584 (-485))))) + (|:| -3110 (-695)) (|:| |rows| (-584 (-485))) (|:| |cols| (-584 (-485))))) (-4 *4 (-13 (-258) (-120))) (-4 *5 (-13 (-757) (-554 (-1091)))) (-4 *6 (-718)) (-5 *2 @@ -8055,7 +8055,7 @@ (-4 *6 (-13 (-757) (-554 (-1091)))) (-4 *7 (-718)) (-5 *2 (-584 - (-2 (|:| -3109 (-695)) + (-2 (|:| -3110 (-695)) (|:| |eqns| (-584 (-2 (|:| |det| *8) (|:| |rows| (-584 (-485))) @@ -8228,7 +8228,7 @@ (-12 (-5 *3 (-584 *4)) (-4 *4 (-312)) (-4 *2 (-1156 *4)) (-5 *1 (-835 *4 *2))))) (((*1 *2 *3) - (-12 (-4 *1 (-833)) (-5 *2 (-2 (|:| -3955 (-584 *1)) (|:| -2410 *1))) + (-12 (-4 *1 (-833)) (-5 *2 (-2 (|:| -3956 (-584 *1)) (|:| -2410 *1))) (-5 *3 (-584 *1))))) (((*1 *2 *3 *1) (-12 (-4 *1 (-833)) (-5 *2 (-633 (-584 *1))) (-5 *3 (-584 *1))))) @@ -8309,13 +8309,13 @@ (|partial| -12 (-5 *3 (-283 *5 *6 *7 *8)) (-4 *5 (-364 *4)) (-4 *6 (-1156 *5)) (-4 *7 (-1156 (-350 *6))) (-4 *8 (-291 *5 *6 *7)) (-4 *4 (-13 (-496) (-951 (-485)))) - (-5 *2 (-2 (|:| -3773 (-695)) (|:| -2384 *8))) + (-5 *2 (-2 (|:| -3774 (-695)) (|:| -2384 *8))) (-5 *1 (-823 *4 *5 *6 *7 *8)))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-283 (-350 (-485)) *4 *5 *6)) (-4 *4 (-1156 (-350 (-485)))) (-4 *5 (-1156 (-350 *4))) (-4 *6 (-291 (-350 (-485)) *4 *5)) - (-5 *2 (-2 (|:| -3773 (-695)) (|:| -2384 *6))) (-5 *1 (-824 *4 *5 *6))))) + (-5 *2 (-2 (|:| -3774 (-695)) (|:| -2384 *6))) (-5 *1 (-824 *4 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-283 *5 *6 *7 *8)) (-4 *5 (-364 *4)) (-4 *6 (-1156 *5)) (-4 *7 (-1156 (-350 *6))) (-4 *8 (-291 *5 *6 *7)) @@ -8438,7 +8438,7 @@ (((*1 *1 *2) (-12 (-5 *2 (-584 (-584 *3))) (-4 *3 (-1014)) (-4 *1 (-816 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-1057 *4 *2)) (-14 *4 (-831)) - (-4 *2 (-13 (-962) (-10 -7 (-6 (-3998 "*"))))) (-5 *1 (-815 *4 *2))))) + (-4 *2 (-13 (-962) (-10 -7 (-6 (-3999 "*"))))) (-5 *1 (-815 *4 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |preimage| (-584 *3)) (|:| |image| (-584 *3)))) (-5 *1 (-814 *3)) (-4 *3 (-1014))))) @@ -8515,7 +8515,7 @@ ((*1 *1) (-12 (-4 *1 (-410 *2 *3)) (-4 *2 (-146)) (-4 *3 (-23)))) ((*1 *1) (-5 *1 (-474))) ((*1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1014))))) (((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| -2514 (-86)) (|:| |arg| (-584 (-801 *3))))) + (|partial| -12 (-5 *2 (-2 (|:| -2515 (-86)) (|:| |arg| (-584 (-801 *3))))) (-5 *1 (-801 *3)) (-4 *3 (-1014)))) ((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-86)) (-5 *2 (-584 (-801 *4))) (-5 *1 (-801 *4)) @@ -8572,11 +8572,11 @@ (-4 *3 (-951 (-1091))) (-4 *3 (-797 *5)) (-4 *4 (-554 (-801 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1014)) (-5 *2 (-584 (-249 (-858 *3)))) (-5 *1 (-798 *5 *3 *4)) - (-4 *3 (-962)) (-2561 (-4 *3 (-951 (-1091)))) (-4 *3 (-797 *5)) + (-4 *3 (-962)) (-2562 (-4 *3 (-951 (-1091)))) (-4 *3 (-797 *5)) (-4 *4 (-554 (-801 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1014)) (-5 *2 (-799 *5 *3)) (-5 *1 (-798 *5 *3 *4)) - (-2561 (-4 *3 (-951 (-1091)))) (-2561 (-4 *3 (-962))) (-4 *3 (-797 *5)) + (-2562 (-4 *3 (-951 (-1091)))) (-2562 (-4 *3 (-962))) (-4 *3 (-797 *5)) (-4 *4 (-554 (-801 *5)))))) (((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-1091)) (-5 *2 (-85)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-86)) (-5 *2 (-85)))) @@ -8632,7 +8632,7 @@ (-4 *4 (-780 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-831)) (-5 *1 (-346 *3)) (-4 *3 (-347)))) ((*1 *2) (-12 (-5 *2 (-831)) (-5 *1 (-346 *3)) (-4 *3 (-347)))) - ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3987)) (-4 *1 (-347)))) + ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3988)) (-4 *1 (-347)))) ((*1 *2) (-12 (-4 *1 (-347)) (-5 *2 (-831)))) ((*1 *2 *1) (-12 (-4 *1 (-780 *3)) (-5 *2 (-1070 (-485)))))) (((*1 *2 *1) @@ -8670,9 +8670,8 @@ (-5 *1 (-777 *5 *4 *6)) (-4 *4 (-1173 *5)) (-4 *6 (-1156 *5))))) (((*1 *2 *1) (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-5 *2 (-584 *3)))) ((*1 *2 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-5 *2 (-584 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-584 *3)) (-5 *1 (-676 *3)) (-4 *3 (-1014)))) ((*1 *2 *1) (-12 (-5 *2 (-584 (-381))) (-5 *1 (-775))))) (((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-773))))) (((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-773))))) @@ -8766,35 +8765,35 @@ ((*1 *2 *3 *3 *2) (-12 (-5 *3 (-695)) (-5 *1 (-766 *2)) (-4 *2 (-146))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-695)) (-5 *1 (-766 *2)) (-4 *2 (-146))))) (((*1 *2 *1 *1) - (-12 (-4 *3 (-312)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-4 *3 (-312)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-762 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-69 *5)) (-4 *5 (-312)) (-4 *5 (-962)) - (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-763 *5 *3)) + (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-763 *5 *3)) (-4 *3 (-762 *5))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-312)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) + (-12 (-4 *4 (-312)) (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-691 *3 *4)) (-4 *3 (-646 *4)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-312)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-4 *3 (-312)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-762 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-69 *5)) (-4 *5 (-312)) (-4 *5 (-962)) - (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-763 *5 *3)) + (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-763 *5 *3)) (-4 *3 (-762 *5))))) (((*1 *2 *1 *1) - (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-762 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-69 *5)) (-4 *5 (-496)) (-4 *5 (-962)) - (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-763 *5 *3)) + (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-763 *5 *3)) (-4 *3 (-762 *5))))) (((*1 *2 *1 *1) - (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2903 *1))) + (-12 (-4 *3 (-496)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1973 *1) (|:| -2904 *1))) (-4 *1 (-762 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-69 *5)) (-4 *5 (-496)) (-4 *5 (-962)) - (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-763 *5 *3)) + (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-763 *5 *3)) (-4 *3 (-762 *5))))) (((*1 *2 *3 *4 *2) (-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-591 *5)) (-4 *5 (-962)) @@ -8834,8 +8833,8 @@ (((*1 *2 *2 *2) (-12 (-4 *3 (-312)) (-5 *1 (-691 *2 *3)) (-4 *2 (-646 *3)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-312))))) (((*1 *1) - (-12 (-4 *1 (-347)) (-2561 (|has| *1 (-6 -3987))) - (-2561 (|has| *1 (-6 -3979))))) + (-12 (-4 *1 (-347)) (-2562 (|has| *1 (-6 -3988))) + (-2562 (|has| *1 (-6 -3980))))) ((*1 *2 *1) (-12 (-4 *1 (-369 *2)) (-4 *2 (-1014)) (-4 *2 (-757)))) ((*1 *2 *1) (-12 (-4 *1 (-743 *2)) (-4 *2 (-757)))) ((*1 *1) (-4 *1 (-753))) ((*1 *1 *1 *1) (-4 *1 (-760)))) @@ -8937,7 +8936,7 @@ (-2 (|:| A (-631 *5)) (|:| |eqs| (-584 - (-2 (|:| C (-631 *5)) (|:| |g| (-1180 *5)) (|:| -3267 *6) + (-2 (|:| C (-631 *5)) (|:| |g| (-1180 *5)) (|:| -3268 *6) (|:| |rh| *5)))))) (-5 *1 (-734 *5 *6)) (-5 *3 (-631 *5)) (-5 *4 (-1180 *5)) (-4 *6 (-601 *5)))) @@ -8982,23 +8981,23 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-584 *5) *6)) (-4 *5 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *6 (-1156 *5)) - (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3267 *3)))) + (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3268 *3)))) (-5 *1 (-730 *5 *6 *3 *7)) (-4 *3 (-601 *6)) (-4 *7 (-601 (-350 *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-584 *5) *6)) (-4 *5 (-13 (-312) (-120) (-951 (-485)) (-951 (-350 (-485))))) (-4 *6 (-1156 *5)) - (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3267 (-599 *6 (-350 *6)))))) + (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3268 (-599 *6 (-350 *6)))))) (-5 *1 (-733 *5 *6)) (-5 *3 (-599 *6 (-350 *6)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 (-584 *7) *7 (-1086 *7))) (-5 *5 (-1 (-348 *7) *7)) (-4 *7 (-1156 *6)) (-4 *6 (-13 (-312) (-120) (-951 (-350 (-485))))) - (-5 *2 (-584 (-2 (|:| |frac| (-350 *7)) (|:| -3267 *3)))) + (-5 *2 (-584 (-2 (|:| |frac| (-350 *7)) (|:| -3268 *3)))) (-5 *1 (-730 *6 *7 *3 *8)) (-4 *3 (-601 *7)) (-4 *8 (-601 (-350 *7))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-348 *6) *6)) (-4 *6 (-1156 *5)) (-4 *5 (-13 (-312) (-120) (-951 (-485)) (-951 (-350 (-485))))) - (-5 *2 (-584 (-2 (|:| |frac| (-350 *6)) (|:| -3267 (-599 *6 (-350 *6)))))) + (-5 *2 (-584 (-2 (|:| |frac| (-350 *6)) (|:| -3268 (-599 *6 (-350 *6)))))) (-5 *1 (-733 *5 *6)) (-5 *3 (-599 *6 (-350 *6)))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-312)) (-4 *7 (-1156 *5)) (-4 *4 (-662 *5 *7)) @@ -9040,11 +9039,11 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-584 *5) *6)) (-4 *5 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *6 (-1156 *5)) - (-5 *2 (-584 (-2 (|:| -3953 *5) (|:| -3267 *3)))) (-5 *1 (-730 *5 *6 *3 *7)) + (-5 *2 (-584 (-2 (|:| -3954 *5) (|:| -3268 *3)))) (-5 *1 (-730 *5 *6 *3 *7)) (-4 *3 (-601 *6)) (-4 *7 (-601 (-350 *6)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *5 (-1156 *4)) - (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -3267 *5)))) + (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -3268 *5)))) (-5 *1 (-730 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-601 (-350 *5)))))) (((*1 *2 *3) (-12 (-4 *2 (-1156 *4)) (-5 *1 (-730 *4 *2 *3 *5)) @@ -9060,19 +9059,19 @@ (-4 *3 (-601 (-350 *2)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *5 (-1156 *4)) - (-5 *2 (-584 (-2 (|:| -3774 *5) (|:| -3227 *5)))) (-5 *1 (-729 *4 *5 *3 *6)) + (-5 *2 (-584 (-2 (|:| -3775 *5) (|:| -3228 *5)))) (-5 *1 (-729 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-601 (-350 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *4 (-1156 *5)) - (-5 *2 (-584 (-2 (|:| -3774 *4) (|:| -3227 *4)))) (-5 *1 (-729 *5 *4 *3 *6)) + (-5 *2 (-584 (-2 (|:| -3775 *4) (|:| -3228 *4)))) (-5 *1 (-729 *5 *4 *3 *6)) (-4 *3 (-601 *4)) (-4 *6 (-601 (-350 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *5 (-1156 *4)) - (-5 *2 (-584 (-2 (|:| -3774 *5) (|:| -3227 *5)))) (-5 *1 (-729 *4 *5 *6 *3)) + (-5 *2 (-584 (-2 (|:| -3775 *5) (|:| -3228 *5)))) (-5 *1 (-729 *4 *5 *6 *3)) (-4 *6 (-601 *5)) (-4 *3 (-601 (-350 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-312) (-120) (-951 (-350 (-485))))) (-4 *4 (-1156 *5)) - (-5 *2 (-584 (-2 (|:| -3774 *4) (|:| -3227 *4)))) (-5 *1 (-729 *5 *4 *6 *3)) + (-5 *2 (-584 (-2 (|:| -3775 *4) (|:| -3228 *4)))) (-5 *1 (-729 *5 *4 *6 *3)) (-4 *6 (-601 *4)) (-4 *3 (-601 (-350 *4)))))) (((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-350 *2)) (-4 *2 (-1156 *5)) @@ -9126,55 +9125,55 @@ (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-330) (-330))) (-5 *4 (-330)) (-5 *2 - (-2 (|:| -3403 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) + (-2 (|:| -3404 *4) (|:| -1597 *4) (|:| |totalpts| (-485)) (|:| |success| (-85)))) (-5 *1 (-712)) (-5 *5 (-485))))) (((*1 *2 *3 *4 *5 *5 *4 *6) @@ -9341,13 +9340,13 @@ (-4 *3 (-962))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| -3757 *3) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3)))) + (-5 *2 (-2 (|:| -3758 *3) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3757 *3) (|:| |coef1| (-705 *3)))) (-5 *1 (-705 *3)) + (-12 (-5 *2 (-2 (|:| -3758 *3) (|:| |coef1| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3757 *3) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3)) + (-12 (-5 *2 (-2 (|:| -3758 *3) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3)) (-4 *3 (-496)) (-4 *3 (-962))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-631 (-350 (-485)))) @@ -9391,7 +9390,7 @@ (-4 *10 (-862 *9 *7 *8)) (-5 *2 (-2 (|:| |deter| (-584 (-1086 *10))) - (|:| |dterm| (-584 (-584 (-2 (|:| -3079 (-695)) (|:| |pcoef| *10))))) + (|:| |dterm| (-584 (-584 (-2 (|:| -3080 (-695)) (|:| |pcoef| *10))))) (|:| |nfacts| (-584 *6)) (|:| |nlead| (-584 *10)))) (-5 *1 (-702 *6 *7 *8 *9 *10)) (-5 *3 (-1086 *10)) (-5 *4 (-584 *6)) (-5 *5 (-584 *10))))) @@ -9459,7 +9458,7 @@ (-4 *7 (-757)) (-4 *8 (-258)) (-4 *9 (-862 *8 *6 *7)) (-4 *6 (-718)) (-5 *2 (-2 (|:| |upol| (-1086 *8)) (|:| |Lval| (-584 *8)) - (|:| |Lfact| (-584 (-2 (|:| -3733 (-1086 *8)) (|:| -2402 (-485))))) + (|:| |Lfact| (-584 (-2 (|:| -3734 (-1086 *8)) (|:| -2402 (-485))))) (|:| |ctpol| *8))) (-5 *1 (-682 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5) @@ -9467,7 +9466,7 @@ (-4 *6 (-718)) (-4 *9 (-862 *8 *6 *7)) (-5 *2 (-2 (|:| |unitPart| *9) - (|:| |suPart| (-584 (-2 (|:| -3733 (-1086 *9)) (|:| -2402 (-485))))))) + (|:| |suPart| (-584 (-2 (|:| -3734 (-1086 *9)) (|:| -2402 (-485))))))) (-5 *1 (-682 *6 *7 *8 *9)) (-5 *3 (-1086 *9))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-485)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-258)) @@ -9478,7 +9477,7 @@ (-12 (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-258)) (-5 *2 (-348 *3)) (-5 *1 (-682 *5 *4 *6 *3)) (-4 *3 (-862 *6 *5 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3733 (-1086 *6)) (|:| -2402 (-485))))) + (-12 (-5 *3 (-584 (-2 (|:| -3734 (-1086 *6)) (|:| -2402 (-485))))) (-4 *6 (-258)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *2 (-485)) (-5 *1 (-682 *4 *5 *6 *7)) (-4 *7 (-862 *6 *4 *5))))) (((*1 *2 *3) @@ -9489,6 +9488,7 @@ (((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1014)) (-5 *1 (-676 *3)))) ((*1 *1 *2) (-12 (-5 *1 (-676 *2)) (-4 *2 (-1014)))) ((*1 *1) (-12 (-5 *1 (-676 *2)) (-4 *2 (-1014))))) +(((*1 *2 *1) (-12 (-5 *2 (-584 *3)) (-5 *1 (-676 *3)) (-4 *3 (-1014))))) (((*1 *2 *1) (-12 (-4 *1 (-277 *3 *4)) (-4 *3 (-962)) (-4 *4 (-717)) (-5 *2 (-695)))) ((*1 *2 *1) @@ -9498,18 +9498,18 @@ (((*1 *2 *3 *4) (-12 (-4 *6 (-496)) (-4 *2 (-862 *3 *5 *4)) (-5 *1 (-672 *5 *4 *6 *2)) (-5 *3 (-350 (-858 *6))) (-4 *5 (-718)) - (-4 *4 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $)))))))) + (-4 *4 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1086 (-858 *6))) (-4 *6 (-496)) (-4 *2 (-862 (-350 (-858 *6)) *5 *4)) (-5 *1 (-672 *5 *4 *6 *2)) - (-4 *5 (-718)) (-4 *4 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $)))))))) + (-4 *5 (-718)) (-4 *4 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1086 *2)) (-4 *2 (-862 (-350 (-858 *6)) *5 *4)) (-5 *1 (-672 *5 *4 *6 *2)) (-4 *5 (-718)) - (-4 *4 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $))))) (-4 *6 (-496))))) + (-4 *4 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $))))) (-4 *6 (-496))))) (((*1 *2 *3) - (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3973 ((-1091) $))))) - (-4 *6 (-496)) (-5 *2 (-2 (|:| -2484 (-858 *6)) (|:| -2059 (-858 *6)))) + (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3974 ((-1091) $))))) + (-4 *6 (-496)) (-5 *2 (-2 (|:| -2485 (-858 *6)) (|:| -2059 (-858 *6)))) (-5 *1 (-672 *4 *5 *6 *3)) (-4 *3 (-862 (-350 (-858 *6)) *4 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-584 *8)) (-5 *4 (-108 *5 *6 *7)) (-14 *5 (-485)) @@ -9524,7 +9524,7 @@ (-5 *1 (-667 *5 *2)) (-4 *5 (-312))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1156 *5)) (-4 *5 (-312)) - (-5 *2 (-2 (|:| -3090 (-348 *3)) (|:| |special| (-348 *3)))) + (-5 *2 (-2 (|:| -3091 (-348 *3)) (|:| |special| (-348 *3)))) (-5 *1 (-667 *5 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-666 *2)) (-4 *2 (-72))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-665 *3))))) @@ -9616,7 +9616,7 @@ (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| -12 (-5 *2 (-584 (-1086 *13))) (-5 *3 (-1086 *13)) (-5 *4 (-584 *12)) (-5 *5 (-584 *10)) (-5 *6 (-584 *13)) - (-5 *7 (-584 (-584 (-2 (|:| -3079 (-695)) (|:| |pcoef| *13))))) + (-5 *7 (-584 (-584 (-2 (|:| -3080 (-695)) (|:| |pcoef| *13))))) (-5 *8 (-584 (-695))) (-5 *9 (-1180 (-584 (-1086 *10)))) (-4 *12 (-757)) (-4 *10 (-258)) (-4 *13 (-862 *10 *11 *12)) (-4 *11 (-718)) (-5 *1 (-645 *11 *12 *10 *13))))) @@ -9662,10 +9662,10 @@ (-4 *4 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))) (((*1 *2 *3 *3) (-12 (-4 *3 (-258)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3)) - (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-630 *3 *4 *5 *6)) + (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-630 *3 *4 *5 *6)) (-4 *6 (-628 *3 *4 *5)))) ((*1 *2 *3 *3) - (-12 (-5 *2 (-2 (|:| -1973 *3) (|:| -2903 *3))) (-5 *1 (-639 *3)) + (-12 (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-639 *3)) (-4 *3 (-258))))) (((*1 *2 *2 *3 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) @@ -9698,13 +9698,13 @@ ((*1 *2 *2 *3 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2576 *5)))) (-4 *5 (-1156 *4)) + (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2577 *5)))) (-4 *5 (-1156 *4)) (-4 *4 (-299)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-584 (-2 (|:| -3733 *5) (|:| -3949 (-485))))) (-5 *4 (-485)) + (-12 (-5 *3 (-584 (-2 (|:| -3734 *5) (|:| -3950 (-485))))) (-5 *4 (-485)) (-4 *5 (-1156 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-485)) (-5 *2 (-584 (-2 (|:| -3733 *3) (|:| -3949 *4)))) + (-12 (-5 *4 (-485)) (-5 *2 (-584 (-2 (|:| -3734 *3) (|:| -3950 *4)))) (-5 *1 (-636 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)) (-4 *2 (-1014)))) @@ -9827,8 +9827,8 @@ (|:| -2013 (-584 (-1180 (-350 *8)))))) (-5 *1 (-612 *5 *6 *7 *8))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3997)))) - (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3997)))) (-5 *2 (-85)) + (-12 (-4 *5 (-312)) (-4 *6 (-13 (-324 *5) (-10 -7 (-6 -3998)))) + (-4 *4 (-13 (-324 *5) (-10 -7 (-6 -3998)))) (-5 *2 (-85)) (-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-631 *5)) (-5 *4 (-1180 *5)) (-4 *5 (-312)) (-5 *2 (-85)) @@ -9863,12 +9863,12 @@ (((*1 *1 *1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-594 *3)) (-4 *3 (-1130)))) ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-485)) (-4 *1 (-594 *2)) (-4 *2 (-1130))))) (((*1 *2 *1) - (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3944 *4)))) + (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3945 *4)))) (-5 *1 (-592 *3 *4 *5)) (-4 *3 (-1014)) (-4 *4 (-23)) (-14 *5 *4)))) (((*1 *1 *2 *3) (-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1014)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *2) - (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3944 *4)))) (-4 *3 (-1014)) + (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3945 *4)))) (-4 *3 (-1014)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-592 *3 *4 *5))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-485)) (-5 *1 (-310 *3)) (-4 *3 (-1014)))) ((*1 *2 *1 *3) @@ -9889,7 +9889,7 @@ ((*1 *1 *1) (-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1014)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *1) (-12 (-4 *1 (-214 *2)) (-4 *2 (-1130)))) - ((*1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-324 *2)) (-4 *2 (-1130)))) + ((*1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-324 *2)) (-4 *2 (-1130)))) ((*1 *1 *1) (-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1014)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1) @@ -9948,7 +9948,7 @@ (-4 *5 (-312)) (-4 *5 (-496)) (-5 *2 (-1180 *5)) (-5 *1 (-579 *5 *4)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 *5))) - (-2561 (-4 *5 (-312))) (-4 *5 (-496)) (-5 *2 (-1180 (-350 *5))) + (-2562 (-4 *5 (-312))) (-4 *5 (-496)) (-5 *2 (-1180 (-350 *5))) (-5 *1 (-579 *5 *4))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-1180 *5)) (-4 *5 (-13 (-962) (-581 *4))) @@ -10222,7 +10222,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-539 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1130)) (-5 *2 (-584 *3))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-539 *4 *3)) (-4 *4 (-1014)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-539 *4 *3)) (-4 *4 (-1014)) (-4 *3 (-1130)) (-4 *3 (-1014)) (-5 *2 (-85))))) (((*1 *2 *1) (-12 (-4 *1 (-539 *2 *3)) (-4 *3 (-1130)) (-4 *2 (-1014)) (-4 *2 (-757))))) @@ -10232,10 +10232,10 @@ (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1130)) (-4 *3 (-324 *2)) (-4 *4 (-324 *2)))) ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -3997)) (-4 *1 (-539 *3 *2)) (-4 *3 (-1014)) + (-12 (|has| *1 (-6 -3998)) (-4 *1 (-539 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1130))))) (((*1 *2 *1 *3 *3) - (-12 (|has| *1 (-6 -3997)) (-4 *1 (-539 *3 *4)) (-4 *3 (-1014)) + (-12 (|has| *1 (-6 -3998)) (-4 *1 (-539 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1130)) (-5 *2 (-1186))))) (((*1 *2 *2 *3 *4) (-12 (-5 *3 (-584 (-551 *2))) (-5 *4 (-584 (-1091))) @@ -10369,7 +10369,7 @@ (((*1 *2 *2 *3) (|partial| -12 (-5 *3 (-695)) (-5 *1 (-524 *2)) (-4 *2 (-484)))) ((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -2695 *3) (|:| -2402 (-695)))) (-5 *1 (-524 *3)) + (-12 (-5 *2 (-2 (|:| -2696 *3) (|:| -2402 (-695)))) (-5 *1 (-524 *3)) (-4 *3 (-484))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-695)) (-5 *2 (-85)) (-5 *1 (-524 *3)) (-4 *3 (-484))))) @@ -10422,7 +10422,7 @@ (-5 *1 (-511 *5 *6)) (-5 *3 (-350 *6))))) (((*1 *2 *2 *3) (|partial| -12 (-5 *2 (-563 *4 *5)) - (-5 *3 (-1 (-2 (|:| |ans| *4) (|:| -3138 *4) (|:| |sol?| (-85))) (-485) *4)) + (-5 *3 (-1 (-2 (|:| |ans| *4) (|:| -3139 *4) (|:| |sol?| (-85))) (-485) *4)) (-4 *4 (-312)) (-4 *5 (-1156 *4)) (-5 *1 (-511 *4 *5))))) (((*1 *2 *2 *3 *4) (|partial| -12 @@ -10441,7 +10441,7 @@ (-5 *1 (-511 *5 *6)) (-5 *3 (-350 *6))))) (((*1 *2 *3 *4 *5 *6) (|partial| -12 (-5 *4 (-1 *8 *8)) - (-5 *5 (-1 (-2 (|:| |ans| *7) (|:| -3138 *7) (|:| |sol?| (-85))) (-485) *7)) + (-5 *5 (-1 (-2 (|:| |ans| *7) (|:| -3139 *7) (|:| |sol?| (-85))) (-485) *7)) (-5 *6 (-584 (-350 *8))) (-4 *7 (-312)) (-4 *8 (-1156 *7)) (-5 *3 (-350 *8)) (-5 *2 (-2 @@ -10463,7 +10463,7 @@ (-5 *1 (-511 *7 *8))))) (((*1 *2 *3 *4 *5 *3) (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3138 *6) (|:| |sol?| (-85))) (-485) *6)) + (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3139 *6) (|:| |sol?| (-85))) (-485) *6)) (-4 *6 (-312)) (-4 *7 (-1156 *6)) (-5 *2 (-3 (-2 (|:| |answer| (-350 *7)) (|:| |a0| *6)) @@ -10484,7 +10484,7 @@ (-5 *1 (-511 *6 *7)) (-5 *3 (-350 *7))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3138 *6) (|:| |sol?| (-85))) (-485) *6)) + (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3139 *6) (|:| |sol?| (-85))) (-485) *6)) (-4 *6 (-312)) (-4 *7 (-1156 *6)) (-5 *2 (-2 (|:| |answer| (-520 (-350 *7))) (|:| |a0| *6))) (-5 *1 (-511 *6 *7)) (-5 *3 (-350 *7))))) @@ -10726,7 +10726,7 @@ (-5 *2 (-2 (|:| -2137 *3) (|:| |coeff| *3))) (-5 *1 (-497 *5 *3)) (-4 *3 (-13 (-27) (-1116) (-364 *5)))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1773 *1) (|:| -3983 *1) (|:| |associate| *1))) + (-12 (-5 *2 (-2 (|:| -1773 *1) (|:| -3984 *1) (|:| |associate| *1))) (-4 *1 (-496))))) (((*1 *1 *1) (-4 *1 (-496)))) (((*1 *2 *1 *1) (-12 (-4 *1 (-496)) (-5 *2 (-85))))) @@ -10891,7 +10891,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-1180 *4)) (-4 *4 (-299)) (-5 *2 (-1086 *4)) (-5 *1 (-467 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034)))))) + (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034)))))) (-4 *4 (-299)) (-5 *2 (-1186)) (-5 *1 (-467 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-466)) (-5 *2 (-633 (-101)))))) (((*1 *2 *1) (-12 (-4 *1 (-466)) (-5 *2 (-633 (-489)))))) @@ -11030,13 +11030,13 @@ (-12 (-5 *3 (-831)) (-5 *2 (-1186)) (-5 *1 (-167 *4)) (-4 *4 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 (*2 $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 (*2 $)) (-15 -1964 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-167 *3)) (-4 *3 (-13 (-757) - (-10 -8 (-15 -3801 ((-1074) $ (-1091))) (-15 -3618 (*2 $)) + (-10 -8 (-15 -3802 ((-1074) $ (-1091))) (-15 -3619 (*2 $)) (-15 -1964 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-442))))) (((*1 *2 *3 *4) @@ -11060,27 +11060,27 @@ (-12 (-5 *2 (-2 (|:| -2013 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3)))) - (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) (-4 *4 (-1156 *3)) + (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4)))) ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-695)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) + (-12 (-5 *2 (-695)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) (((*1 *2 *3 *3 *2 *4) (-12 (-5 *3 (-631 *2)) (-5 *4 (-485)) - (-4 *2 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) (-4 *5 (-1156 *2)) + (-4 *2 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *5 (-1156 *2)) (-5 *1 (-439 *2 *5 *6)) (-4 *6 (-353 *2 *5))))) (((*1 *2 *3 *2 *4) (-12 (-5 *3 (-631 *2)) (-5 *4 (-695)) - (-4 *2 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) (-4 *5 (-1156 *2)) + (-4 *2 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *5 (-1156 *2)) (-5 *1 (-439 *2 *5 *6)) (-4 *6 (-353 *2 *5))))) (((*1 *2 *3 *4 *4) (-12 (-5 *4 (-695)) (-4 *5 (-299)) (-4 *6 (-1156 *5)) @@ -11107,22 +11107,22 @@ (((*1 *2 *3 *1) (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-429 *4)) + (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3997)) (-4 *1 (-429 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-429 *4)) + (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3997)) (-4 *1 (-429 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) (((*1 *2 *3 *1) (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-695)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-695)))) ((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-429 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-695)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3996)) (-4 *1 (-429 *4)) + (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3997)) (-4 *1 (-429 *4)) (-4 *4 (-1130)) (-5 *2 (-695))))) (((*1 *1 *2) (-12 (-5 *2 (-350 (-485))) (-5 *1 (-427))))) (((*1 *2 *3) @@ -11140,7 +11140,7 @@ (-4 *4 (-962)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-485))) (-14 *3 (-584 (-1091))) (-5 *1 (-394 *3 *4 *5)) - (-4 *4 (-962)) (-4 *5 (-196 (-3958 *3) (-695))))) + (-4 *4 (-962)) (-4 *5 (-196 (-3959 *3) (-695))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-421 *3 *4)) (-14 *3 (-584 (-1091))) (-4 *4 (-962))))) @@ -11204,30 +11204,30 @@ (-4 *7 (-862 *6 *5 *3)) (-5 *1 (-402 *5 *3 *6 *7 *2)) (-4 *2 (-13 (-951 (-350 (-485))) (-312) - (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) + (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) (((*1 *2 *1) (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-14 *6 (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *2)) (-2 (|:| -2401 *5) (|:| -2402 *2)))) - (-4 *2 (-196 (-3958 *3) (-695))) (-5 *1 (-401 *3 *4 *5 *2 *6 *7)) + (-4 *2 (-196 (-3959 *3) (-695))) (-5 *1 (-401 *3 *4 *5 *2 *6 *7)) (-4 *5 (-757)) (-4 *7 (-862 *4 *2 (-774 *3)))))) (((*1 *2 *1) - (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-695))) + (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3959 *3) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5)) (-2 (|:| -2401 *2) (|:| -2402 *5)))) (-4 *2 (-757)) (-5 *1 (-401 *3 *4 *2 *5 *6 *7)) (-4 *7 (-862 *4 *5 (-774 *3)))))) (((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-584 (-1091))) (-4 *2 (-146)) (-4 *4 (-196 (-3958 *5) (-695))) + (-12 (-14 *5 (-584 (-1091))) (-4 *2 (-146)) (-4 *4 (-196 (-3959 *5) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *3) (|:| -2402 *4)) (-2 (|:| -2401 *3) (|:| -2402 *4)))) (-5 *1 (-401 *5 *2 *3 *4 *6 *7)) (-4 *3 (-757)) (-4 *7 (-862 *2 *4 (-774 *5)))))) (((*1 *1 *2 *3 *1) - (-12 (-14 *4 (-584 (-1091))) (-4 *2 (-146)) (-4 *3 (-196 (-3958 *4) (-695))) + (-12 (-14 *4 (-584 (-1091))) (-4 *2 (-146)) (-4 *3 (-196 (-3959 *4) (-695))) (-14 *6 (-1 (-85) (-2 (|:| -2401 *5) (|:| -2402 *3)) (-2 (|:| -2401 *5) (|:| -2402 *3)))) @@ -11558,7 +11558,7 @@ (-12 (-5 *3 (-831)) (-5 *4 (-348 *2)) (-4 *2 (-1156 *5)) (-5 *1 (-384 *5 *2)) (-4 *5 (-962))))) (((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3733 *4) (|:| -3949 (-485))))) + (-12 (-5 *3 (-584 (-2 (|:| -3734 *4) (|:| -3950 (-485))))) (-4 *4 (-1156 (-485))) (-5 *2 (-676 (-695))) (-5 *1 (-382 *4)))) ((*1 *2 *3) (-12 (-5 *3 (-348 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-962)) @@ -11604,11 +11604,11 @@ (((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-382 *3)) (-4 *3 (-1156 (-485)))))) (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-382 *3)) (-4 *3 (-1156 (-485)))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -2579 (-485)) (|:| -1780 (-584 *3)))) (-5 *1 (-382 *3)) + (-12 (-5 *2 (-2 (|:| -2580 (-485)) (|:| -1780 (-584 *3)))) (-5 *1 (-382 *3)) (-4 *3 (-1156 (-485)))))) (((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-348 *3)) (-4 *3 (-496)))) ((*1 *2 *3) - (-12 (-5 *3 (-584 (-2 (|:| -3733 *4) (|:| -3949 (-485))))) + (-12 (-5 *3 (-584 (-2 (|:| -3734 *4) (|:| -3950 (-485))))) (-4 *4 (-1156 (-485))) (-5 *2 (-695)) (-5 *1 (-382 *4))))) (((*1 *2) (-12 (-5 *2 (-831)) (-5 *1 (-382 *3)) (-4 *3 (-1156 (-485))))) ((*1 *2 *2) (-12 (-5 *2 (-831)) (-5 *1 (-382 *3)) (-4 *3 (-1156 (-485)))))) @@ -11628,7 +11628,7 @@ (|:| -1780 (-584 (-2 (|:| |irr| *4) (|:| -2396 (-485))))))) (-4 *4 (-1156 (-485))) (-5 *2 (-348 *4)) (-5 *1 (-382 *4))))) (((*1 *2 *1) - (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3911 "void"))) (-5 *1 (-379))))) + (-12 (-5 *2 (-3 (|:| |fst| (-377)) (|:| -3912 "void"))) (-5 *1 (-379))))) (((*1 *2 *1) (-12 (-5 *2 (-584 (-858 (-485)))) (-5 *1 (-379))))) (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-379))))) (((*1 *1) (-5 *1 (-379)))) @@ -11646,7 +11646,7 @@ (-12 (-4 *4 (-13 (-496) (-951 (-485)))) (-4 *5 (-364 *4)) (-5 *2 (-3 (|:| |overq| (-1086 (-350 (-485)))) (|:| |overan| (-1086 (-48))) - (|:| -2640 (-85)))) + (|:| -2641 (-85)))) (-5 *1 (-378 *4 *5 *3)) (-4 *3 (-1156 *5))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-496) (-951 (-485)))) (-4 *5 (-364 *4)) @@ -11689,19 +11689,19 @@ (-14 *4 (-1091)) (-14 *5 *2))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-392) (-951 (-485)) (-581 (-485)))) - (-4 *2 (-13 (-27) (-1116) (-364 *3) (-10 -8 (-15 -3947 ($ *4))))) + (-4 *2 (-13 (-27) (-1116) (-364 *3) (-10 -8 (-15 -3948 ($ *4))))) (-4 *4 (-756)) (-4 *5 (-13 (-1159 *2 *4) (-312) (-1116) - (-10 -8 (-15 -3759 ($ $)) (-15 -3813 ($ $))))) + (-10 -8 (-15 -3760 ($ $)) (-15 -3814 ($ $))))) (-5 *1 (-367 *3 *2 *4 *5 *6 *7)) (-4 *6 (-897 *5)) (-14 *7 (-1091))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-85)) (-4 *6 (-13 (-392) (-951 (-485)) (-581 (-485)))) - (-4 *3 (-13 (-27) (-1116) (-364 *6) (-10 -8 (-15 -3947 ($ *7))))) + (-4 *3 (-13 (-27) (-1116) (-364 *6) (-10 -8 (-15 -3948 ($ *7))))) (-4 *7 (-756)) (-4 *8 (-13 (-1159 *3 *7) (-312) (-1116) - (-10 -8 (-15 -3759 ($ $)) (-15 -3813 ($ $))))) + (-10 -8 (-15 -3760 ($ $)) (-15 -3814 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1074)) (|:| |prob| (-1074)))))) @@ -11709,11 +11709,11 @@ (-14 *10 (-1091))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-85)) (-4 *6 (-13 (-392) (-951 (-485)) (-581 (-485)))) - (-4 *3 (-13 (-27) (-1116) (-364 *6) (-10 -8 (-15 -3947 ($ *7))))) + (-4 *3 (-13 (-27) (-1116) (-364 *6) (-10 -8 (-15 -3948 ($ *7))))) (-4 *7 (-756)) (-4 *8 (-13 (-1159 *3 *7) (-312) (-1116) - (-10 -8 (-15 -3759 ($ $)) (-15 -3813 ($ $))))) + (-10 -8 (-15 -3760 ($ $)) (-15 -3814 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1074)) (|:| |prob| (-1074)))))) @@ -11740,7 +11740,7 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1091)) (-4 *1 (-364 *3)) (-4 *3 (-1014))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1014)) - (-5 *2 (-2 (|:| -3955 (-485)) (|:| |var| (-551 *1)))) (-4 *1 (-364 *3))))) + (-5 *2 (-2 (|:| -3956 (-485)) (|:| |var| (-551 *1)))) (-4 *1 (-364 *3))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-348 *3)) (-4 *3 (-496)) (-5 *1 (-362 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1180 *3)) (-4 *3 (-312)) (-4 *1 (-280 *3)))) ((*1 *1 *2 *3) @@ -11811,13 +11811,13 @@ (-5 *2 (-631 *3))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-348 *2)) (-4 *2 (-496))))) (((*1 *2 *1) - (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3944 (-485))))) (-5 *1 (-310 *3)) + (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3945 (-485))))) (-5 *1 (-310 *3)) (-4 *3 (-1014)))) ((*1 *2 *1) (-12 (-4 *1 (-336 *3)) (-4 *3 (-1014)) - (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3944 (-695))))))) + (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3945 (-695))))))) ((*1 *2 *1) - (-12 (-5 *2 (-584 (-2 (|:| -3733 *3) (|:| -2402 (-485))))) (-5 *1 (-348 *3)) + (-12 (-5 *2 (-584 (-2 (|:| -3734 *3) (|:| -2402 (-485))))) (-5 *1 (-348 *3)) (-4 *3 (-496))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-348 *2)) (-4 *2 (-496))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-485)) (-5 *1 (-348 *3)) (-4 *3 (-496))))) @@ -11835,14 +11835,14 @@ (((*1 *1 *1) (-12 (-5 *1 (-348 *2)) (-4 *2 (-496))))) (((*1 *2 *1) (-12 (-4 *1 (-347)) (-5 *2 (-485))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-695)) (-5 *3 (-85)) (-5 *1 (-81)))) - ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3987)) (-4 *1 (-347)))) + ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3988)) (-4 *1 (-347)))) ((*1 *2) (-12 (-4 *1 (-347)) (-5 *2 (-831))))) -(((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3987)) (-4 *1 (-347)))) +(((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3988)) (-4 *1 (-347)))) ((*1 *2) (-12 (-4 *1 (-347)) (-5 *2 (-831))))) (((*1 *2 *3) - (-12 (-5 *3 (-485)) (|has| *1 (-6 -3987)) (-4 *1 (-347)) (-5 *2 (-831))))) + (-12 (-5 *3 (-485)) (|has| *1 (-6 -3988)) (-4 *1 (-347)) (-5 *2 (-831))))) (((*1 *2 *3) - (-12 (-5 *3 (-485)) (|has| *1 (-6 -3987)) (-4 *1 (-347)) (-5 *2 (-831))))) + (-12 (-5 *3 (-485)) (|has| *1 (-6 -3988)) (-4 *1 (-347)) (-5 *2 (-831))))) (((*1 *2 *1) (-12 (-4 *1 (-299)) (-5 *2 (-695)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-345)) (-5 *2 (-695))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-345)) (-5 *2 (-695)))) @@ -11854,7 +11854,7 @@ (-12 (-4 *2 (-1156 *3)) (-5 *1 (-342 *3 *2)) (-4 *3 (-13 (-312) (-120)))))) (((*1 *2 *1) (-12 (-4 *3 (-13 (-312) (-120))) - (-5 *2 (-584 (-2 (|:| -2402 (-695)) (|:| -3774 *4) (|:| |num| *4)))) + (-5 *2 (-584 (-2 (|:| -2402 (-695)) (|:| -3775 *4) (|:| |num| *4)))) (-5 *1 (-342 *3 *4)) (-4 *4 (-1156 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-773)) (-5 *1 (-340 *3 *4 *5)) (-14 *3 (-695)) (-14 *4 (-695)) @@ -11924,13 +11924,13 @@ (((*1 *2 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1186)) (-5 *1 (-330))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1130)) (-5 *1 (-327 *4 *2)) - (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3997))))))) + (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3998))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1130)) (-5 *1 (-327 *4 *2)) - (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3997))))))) + (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3998))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1130)) (-5 *1 (-327 *4 *2)) - (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3997))))))) + (-4 *2 (-13 (-324 *4) (-10 -7 (-6 -3998))))))) (((*1 *1 *2) (-12 (-5 *2 (-615 *3)) (-4 *3 (-757)) (-4 *1 (-326 *3 *4)) (-4 *4 (-146))))) (((*1 *2 *1) @@ -11939,11 +11939,11 @@ (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-324 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) (((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-485)) (|has| *1 (-6 -3997)) (-4 *1 (-324 *3)) (-4 *3 (-1130))))) + (-12 (-5 *2 (-485)) (|has| *1 (-6 -3998)) (-4 *1 (-324 *3)) (-4 *3 (-1130))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -3997)) (-4 *1 (-324 *2)) (-4 *2 (-1130)) (-4 *2 (-757)))) + (-12 (|has| *1 (-6 -3998)) (-4 *1 (-324 *2)) (-4 *2 (-1130)) (-4 *2 (-757)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-85) *3 *3)) (|has| *1 (-6 -3997)) (-4 *1 (-324 *3)) + (-12 (-5 *2 (-1 (-85) *3 *3)) (|has| *1 (-6 -3998)) (-4 *1 (-324 *3)) (-4 *3 (-1130))))) (((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1180 *1)) (-4 *1 (-316 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) @@ -12022,8 +12022,8 @@ (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299)) (-4 *2 (-13 (-345) - (-10 -7 (-15 -3947 (*2 *4)) (-15 -2011 ((-831) *2)) - (-15 -2013 ((-1180 *2) (-831))) (-15 -3929 (*2 *2))))) + (-10 -7 (-15 -3948 (*2 *4)) (-15 -2011 ((-831) *2)) + (-15 -2013 ((-1180 *2) (-831))) (-15 -3930 (*2 *2))))) (-5 *1 (-306 *2 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-299)) (-5 *2 (-870 (-1086 *4))) (-5 *1 (-305 *4)) @@ -12056,13 +12056,13 @@ ((*1 *2 *3) (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299)) (-5 *2 (-85)) (-5 *1 (-305 *4))))) (((*1 *2) - (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3403 (-818 *3)) (|:| -2401 (-1034)))))) + (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3404 (-818 *3)) (|:| -2401 (-1034)))))) (-5 *1 (-301 *3 *4)) (-14 *3 (-831)) (-14 *4 (-831)))) ((*1 *2) - (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3403 *3) (|:| -2401 (-1034)))))) + (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3404 *3) (|:| -2401 (-1034)))))) (-5 *1 (-302 *3 *4)) (-4 *3 (-299)) (-14 *4 (-3 (-1086 *3) *2)))) ((*1 *2) - (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3403 *3) (|:| -2401 (-1034)))))) + (-12 (-5 *2 (-1180 (-584 (-2 (|:| -3404 *3) (|:| -2401 (-1034)))))) (-5 *1 (-303 *3 *4)) (-4 *3 (-299)) (-14 *4 (-831))))) (((*1 *2) (-12 (-5 *2 (-631 (-818 *3))) (-5 *1 (-301 *3 *4)) (-14 *3 (-831)) @@ -12070,23 +12070,23 @@ ((*1 *2) (-12 (-5 *2 (-631 *3)) (-5 *1 (-302 *3 *4)) (-4 *3 (-299)) (-14 *4 - (-3 (-1086 *3) (-1180 (-584 (-2 (|:| -3403 *3) (|:| -2401 (-1034))))))))) + (-3 (-1086 *3) (-1180 (-584 (-2 (|:| -3404 *3) (|:| -2401 (-1034))))))))) ((*1 *2) (-12 (-5 *2 (-631 *3)) (-5 *1 (-303 *3 *4)) (-4 *3 (-299)) (-14 *4 (-831))))) (((*1 *2 *3) - (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034)))))) + (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034)))))) (-4 *4 (-299)) (-5 *2 (-695)) (-5 *1 (-296 *4)))) ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-301 *3 *4)) (-14 *3 (-831)) (-14 *4 (-831)))) ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-302 *3 *4)) (-4 *3 (-299)) (-14 *4 - (-3 (-1086 *3) (-1180 (-584 (-2 (|:| -3403 *3) (|:| -2401 (-1034))))))))) + (-3 (-1086 *3) (-1180 (-584 (-2 (|:| -3404 *3) (|:| -2401 (-1034))))))))) ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-303 *3 *4)) (-4 *3 (-299)) (-14 *4 (-831))))) (((*1 *2) (-12 (-4 *1 (-299)) - (-5 *2 (-584 (-2 (|:| -3733 (-485)) (|:| -2402 (-485)))))))) + (-5 *2 (-584 (-2 (|:| -3734 (-485)) (|:| -2402 (-485)))))))) (((*1 *2 *3) (-12 (-4 *1 (-299)) (-5 *3 (-485)) (-5 *2 (-1103 (-831) (-695)))))) (((*1 *1) (-4 *1 (-299)))) (((*1 *2) @@ -12094,18 +12094,18 @@ (((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 - (-3 (-1086 *4) (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034))))))) + (-3 (-1086 *4) (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034))))))) (-5 *1 (-296 *4)) (-4 *4 (-299))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-831)) - (-5 *2 (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034)))))) + (-5 *2 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034)))))) (-5 *1 (-296 *4)) (-4 *4 (-299))))) (((*1 *2 *3) - (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034)))))) + (-12 (-5 *3 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034)))))) (-4 *4 (-299)) (-5 *2 (-631 *4)) (-5 *1 (-296 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299)) - (-5 *2 (-1180 (-584 (-2 (|:| -3403 *4) (|:| -2401 (-1034)))))) + (-5 *2 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034)))))) (-5 *1 (-296 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299)) (-5 *2 (-870 (-1034))) @@ -12461,7 +12461,7 @@ (-12 (-5 *3 (-485)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1130)) (-4 *4 (-324 *2)) (-4 *5 (-324 *2)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -3997)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014)) + (-12 (|has| *1 (-6 -3998)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1130))))) (((*1 *2 *3 *4) (-12 (-4 *4 (-312)) (-5 *2 (-584 (-1070 *4))) (-5 *1 (-240 *4 *5)) @@ -12472,7 +12472,7 @@ (((*1 *1 *1 *2) (-12 (-5 *2 (-1147 (-485))) (-4 *1 (-237 *3)) (-4 *3 (-1130)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3996)) (-4 *1 (-193 *3)) + (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3997)) (-4 *1 (-193 *3)) (-4 *3 (-1014)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) (((*1 *1 *2 *3 *4) @@ -12843,8 +12843,8 @@ (((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-757)) (-5 *1 (-203 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-202 *2)) (-4 *2 (-1130))))) (((*1 *1 *1) (-12 (-4 *1 (-202 *2)) (-4 *2 (-1130))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-202 *2)) (-4 *2 (-1130))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-202 *2)) (-4 *2 (-1130))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-202 *2)) (-4 *2 (-1130))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-202 *2)) (-4 *2 (-1130))))) (((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-485)) (-5 *1 (-199)))) ((*1 *2 *3) (-12 (-5 *3 (-584 (-1074))) (-5 *2 (-485)) (-5 *1 (-199))))) (((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-199)))) @@ -12917,7 +12917,7 @@ (((*1 *2 *2 *3 *2) (-12 (-5 *3 (-695)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1156 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-299)) (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -2576 *3)))) + (-12 (-4 *4 (-299)) (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -2577 *3)))) (-5 *1 (-170 *4 *3)) (-4 *3 (-1156 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-85)) (-4 *5 (-299)) @@ -13140,7 +13140,7 @@ (((*1 *2 *3 *1) (|partial| -12 (-5 *3 (-1 (-85) *2)) (-4 *1 (-124 *2)) (-4 *2 (-1130))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -3996)) (-4 *1 (-124 *2)) (-4 *2 (-1130)) + (-12 (|has| *1 (-6 -3997)) (-4 *1 (-124 *2)) (-4 *2 (-1130)) (-4 *2 (-1014))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-1135)) (-4 *5 (-1156 *4)) @@ -13153,7 +13153,7 @@ (-4 *3 (-1156 (-350 *4)))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-350 *6)) (-4 *5 (-1135)) (-4 *6 (-1156 *5)) - (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3955 *3) (|:| |radicand| *6))) + (-5 *2 (-2 (|:| -2402 (-695)) (|:| -3956 *3) (|:| |radicand| *6))) (-5 *1 (-121 *5 *6 *7)) (-5 *4 (-695)) (-4 *7 (-1156 *3))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-1135)) (-4 *5 (-1156 *4)) @@ -13161,7 +13161,7 @@ (-5 *1 (-121 *4 *5 *3)) (-4 *3 (-1156 (-350 *5)))))) (((*1 *2 *3) (-12 (-4 *4 (-1135)) (-4 *5 (-1156 *4)) - (-5 *2 (-2 (|:| -3955 (-350 *5)) (|:| |poly| *3))) (-5 *1 (-121 *4 *5 *3)) + (-5 *2 (-2 (|:| -3956 (-350 *5)) (|:| |poly| *3))) (-5 *1 (-121 *4 *5 *3)) (-4 *3 (-1156 (-350 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-117))))) (((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-117)))) @@ -13229,8 +13229,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-695)) (-5 *1 (-93 *3)) (-4 *3 (-1156 (-485)))))) (((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-93 *3)) (-4 *3 (-1156 (-485))))) ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *1 (-93 *3)) (-4 *3 (-1156 (-485)))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-92 *2)) (-4 *2 (-1130))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3997)) (-4 *1 (-92 *2)) (-4 *2 (-1130))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-92 *2)) (-4 *2 (-1130))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3998)) (-4 *1 (-92 *2)) (-4 *2 (-1130))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-312) (-951 (-350 *2)))) (-5 *2 (-485)) (-5 *1 (-88 *4 *3)) (-4 *3 (-1156 *4))))) @@ -13263,11 +13263,11 @@ (((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1130))))) (((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1130))))) (((*1 *2 *3) - (-12 (|has| *2 (-6 (-3998 "*"))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) + (-12 (|has| *2 (-6 (-3999 "*"))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) (-4 *2 (-962)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1156 *2)) (-4 *4 (-628 *2 *5 *6))))) (((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-3998 "*"))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) + (-12 (|has| *2 (-6 (-3999 "*"))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) (-4 *2 (-962)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1156 *2)) (-4 *4 (-628 *2 *5 *6))))) (((*1 *2 *3 *3) @@ -13299,7 +13299,7 @@ (((*1 *2 *3 *4) (-12 (-4 *5 (-312)) (-4 *5 (-496)) (-5 *2 - (-2 (|:| |minor| (-584 (-831))) (|:| -3267 *3) + (-2 (|:| |minor| (-584 (-831))) (|:| -3268 *3) (|:| |minors| (-584 (-584 (-831)))) (|:| |ops| (-584 *3)))) (-5 *1 (-61 *5 *3)) (-5 *4 (-831)) (-4 *3 (-601 *5))))) (((*1 *2 *3) @@ -13375,84 +13375,84 @@ (-4 *5 (-496)) (-5 *1 (-41 *5 *2)) (-4 *2 (-364 *5)) (-4 *2 (-13 (-312) (-254) - (-10 -8 (-15 -2999 ((-1040 *5 (-551 $)) $)) - (-15 -2998 ((-1040 *5 (-551 $)) $)) - (-15 -3947 ($ (-1040 *5 (-551 $)))))))))) + (-10 -8 (-15 -3000 ((-1040 *5 (-551 $)) $)) + (-15 -2999 ((-1040 *5 (-551 $)) $)) + (-15 -3948 ($ (-1040 *5 (-551 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-392) (-951 (-485)))) (-4 *3 (-496)) (-5 *1 (-41 *3 *2)) (-4 *2 (-364 *3)) (-4 *2 (-13 (-312) (-254) - 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58577) (-3900 . 58476) + (-3901 . 58375) (-3902 . 58274) (-3903 . 58159) (-3904 . 58044) + (-3905 . 57993) (-3906 . 57876) (-3907 . 57818) (-3908 . 57717) + (-3909 . 57616) (-3910 . 57515) (-3911 . 57399) (-3912 . 57370) + (-3913 . 56639) (-3914 . 56514) (-3915 . 56389) (-3916 . 56249) + (-3917 . 56131) (-3918 . 56006) (-3919 . 55851) (-3920 . 54868) + (-3921 . 54009) (-3922 . 53955) (-3923 . 53901) (-3924 . 53693) + (-3925 . 53321) (-3926 . 52910) (-3927 . 52552) (-3928 . 52194) + (-3929 . 52042) (-3930 . 51740) (-3931 . 51584) (-3932 . 51258) + (-3933 . 51188) (-3934 . 51118) (-3935 . 50909) (-3936 . 50300) + (-3937 . 50096) (-3938 . 49723) (-3939 . 49214) (-3940 . 48949) + (-3941 . 48468) (-3942 . 47987) (-3943 . 47862) (-3944 . 46762) + (-3945 . 45686) (-3946 . 45113) (-3947 . 44895) (-3948 . 36569) + (-3949 . 36384) (-3950 . 34301) (-3951 . 32133) (-3952 . 31987) + (-3953 . 31809) (-3954 . 31402) (-3955 . 31107) (-3956 . 30759) + (-3957 . 30593) (-3958 . 30427) (-3959 . 29945) 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