diff options
| -rw-r--r-- | src/ChangeLog | 6 | ||||
| -rw-r--r-- | src/algebra/compiler.spad.pamphlet | 88 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1282 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1408 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 36 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8286 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 2720 |
7 files changed, 6954 insertions, 6872 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 4b020b69..b519d5b3 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,11 @@ 2010-03-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/compiler.spad.pamphlet (InternalRepresentationForm): Tidy. + (InternalTypeForm): Likewise. + (CompilerPackage): Expand. + +2010-03-12 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/compiler.spad.pamphlet: New. (InternalTypeForm): New. (Elaboration): New. diff --git a/src/algebra/compiler.spad.pamphlet b/src/algebra/compiler.spad.pamphlet index 24d0b6d8..2a0df829 100644 --- a/src/algebra/compiler.spad.pamphlet +++ b/src/algebra/compiler.spad.pamphlet @@ -23,12 +23,10 @@ ++ This domain provides representations for the intermediate ++ form data structure used by the Spad elaborator. InternalRepresentationForm(): Public == Private where - Public == Join(CoercibleTo OutputForm, HomotopicTo Syntax) - Private == add - coerce(x: %): Syntax == x : Syntax - coerce(x: Syntax): % == x : % - coerce(x: %): OutputForm == - (x : Syntax)::OutputForm + Public == Join(SetCategory, HomotopicTo Syntax) + Private == Syntax add + coerce(x: %): Syntax == rep x + coerce(x: Syntax): % == per x @ @@ -39,7 +37,20 @@ InternalRepresentationForm(): Public == Private where ++ Date Last Modified: March 12, 2010 ++ Description: ++ This domain provides representations for internal type form. -InternalTypeForm() == InternalRepresentationForm +InternalTypeForm(): Public == Private where + Public == Join(SetCategory, HomotopicTo Syntax) with + jokerMode: % + ++ \spad{jokerMode} is a constant that stands for any mode + ++ in a type inference context + noValueMode: % + ++ \spad{noValueMode} is a constant mode that indicates that + ++ the value of an expression is to be ignored. + voidMode: % + ++ \spad{voidMode} is a constant mode denoting Void. + Private == InternalRepresentationForm add + jokerMode == _$EmptyMode$Foreign(Builtin) + noValueMode == _$NoValueMode$Foreign(Builtin) + voidMode == _$Void$Foreign(Builtin) @ @@ -82,18 +93,77 @@ Elaboration(): Public == Private where ++ This package implements a Spad compiler. CompilerPackage(): Public == Private where Public == Type with - macroExpand: (Syntax, Environment) -> Syntax + macroExpand: (SpadAst, Environment) -> SpadAst ++ \spad{macroExpand(s,e)} traverses the syntax object \spad{s} ++ replacing all (niladic) macro invokations with the ++ corresponding substitution. - elaborate: Syntax -> Elaboration + elaborate: SpadAst -> Maybe Elaboration ++ \spad{elaborate(s)} returns the elaboration of the syntax ++ object \spad{s} in the empty environement. Private == add + macro IR == InternalRepresentationForm + macro TFORM == InternalTypeForm + macro RESULT == Maybe Elaboration + macro ENV == Environment + import ENV + import IR + import RESULT + inline RESULT + macroExpand(s,e) == -- FIXME: this is a short-term stopgap. macroExpand(s,e)$Foreign(Builtin) + -- fecth the active definition of 'x', if any from environment `e'. + getValue(x: Identifier, e: ENV): RESULT == + case getProperty(x,'value,e) is + val@SExpression => + T := destruct(val)$SExpression + just elaboration(first(T) : IR, second(T) : TFORM, e) + otherwise => nothing -- not defined + + -- fetch the active declaration of 'x', if any from environment `e'. + getMode(x: Identifier, e: ENV): Maybe TFORM == + val := getValue(x,e) + val case nothing => -- symbol is not defined + decl := getProperty(x,'mode,e) + decl case nothing => nothing -- nor declared + T := destruct(decl)$SExpression + just(second(T) : TFORM) + typeForm val + + -- simply coerce the elaboration `T' to mode `m'. + coerceSimply(T: RESULT, m: TFORM): RESULT == + T case nothing => T + t := typeForm(T@Elaboration) + m = jokerMode or t = m => T + m = noValueMode or m = voidMode or t = jokerMode => + just elaboration(irForm T, m, environment T) + nothing + + -- implicitly coerce the eloboration `T' to one that is + -- valid in a mode context `m'. + coerceTo(T: RESULT, m:TFORM): RESULT == + coerceSimply(T,m) + + -- elaborate an identifier in the current environment. + elaborateIdentifier(x: Identifier, t: TFORM, e: ENV): RESULT == + r := + case getValue(x,e) is + val@Elaboration => just val + otherwise => case getMode(x,e) is + decl@Elaboration => + coerceTo(getValue(x,e), t) + + -- elaborate a syntax `s' under context `m', in the envionment `e'. + doElaborate(s: SpadAst, t: TFORM, e: ENV): RESULT == + case s is + id@Identifier => elaborateIdentifier(id,t,e) + otherwise => nothing + + elaborate s == + doElaborate(s,jokerMode,empty()$ENV) + @ diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 8e837cdc..a8f3a706 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2264819 . 3477425184) +(2265141 . 3477435921) (-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."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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},{}...,{}\\spad{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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4431 . T) (-4429 . T) (-4428 . T) ((-4436 "*") . T) (-4427 . T) (-4432 . T) (-4426 . T)) +((-4434 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4430 . T) (-4435 . T) (-4429 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3505) +(-32 R -3508) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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 -4434))) +((|HasAttribute| |#1| (QUOTE -4437))) (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . 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"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . 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 a1,{}...,{}an."))) NIL NIL -(-40 -3505 UP UPUP -3023) +(-40 -3508 UP UPUP -3026) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4427 |has| (-412 |#2|) (-367)) (-4432 |has| (-412 |#2|) (-367)) (-4426 |has| (-412 |#2|) (-367)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3969 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3969 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3969 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3969 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) -(-41 R -3505) +((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3972 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +(-41 R -3508) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -426) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-310)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4431 |has| |#1| (-562)) (-4429 . T) (-4428 . T)) +((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-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."))) -((-4434 . T) (-4435 . T)) -((-3969 (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-855)))) (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) +((-4437 . T) (-4438 . T)) +((-3972 (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855)))) (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4431 . T)) +((-4434 . 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 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 -3505) +(-54 |Base| R -3508) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,77 +158,77 @@ 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")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|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}\\spad{'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}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . 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}"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-61 -3982) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +(-61 -3985) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-62 -3982) +(-62 -3985) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -3982) +(-63 -3985) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-64 -3982) +(-64 -3985) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -3982) +(-65 -3985) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -3982) +(-66 -3985) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -3982) +(-67 -3985) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -3982) +(-68 -3985) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -3982) +(-69 -3985) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -3982) +(-70 -3985) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -3982) +(-71 -3985) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -3982) +(-72 -3985) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -3982) +(-73 -3985) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -3982) +(-74 -3985) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -3982) +(-75 -3985) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -240,51 +240,51 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3982) +(-78 -3985) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3982) +(-79 -3985) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3982) +(-80 -3985) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3982) +(-81 -3985) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -3982) +(-82 -3985) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3982) +(-83 -3985) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3982) +(-84 -3985) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3982) +(-85 -3985) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3982) +(-86 -3985) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3982) +(-87 -3985) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -3982) +(-88 -3985) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-89 -3982) +(-89 -3985) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4434 . T)) +((-4437 . T)) NIL (-98) ((|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.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|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."))) -((-4434 . T) ((-4436 "*") . T) (-4435 . T) (-4431 . T) (-4429 . T) (-4428 . T) (-4427 . T) (-4432 . T) (-4426 . T) (-4425 . T) (-4424 . T) (-4423 . T) (-4422 . T) (-4430 . T) (-4433 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4421 . T)) +((-4437 . T) ((-4439 "*") . T) (-4438 . T) (-4434 . T) (-4432 . T) (-4431 . T) (-4430 . T) (-4435 . T) (-4429 . T) (-4428 . T) (-4427 . T) (-4426 . T) (-4425 . T) (-4433 . T) (-4436 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4424 . T)) NIL (-99 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}."))) -((-4431 . T)) +((-4434 . T)) NIL (-100 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}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4436 "*")))) +((|HasAttribute| |#1| (QUOTE (-4439 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4434 . T)) +((-4437 . T)) NIL (-106 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}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 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}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4435 . T)) +((-4438 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3969 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-868))))) (-111 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}"))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -388,22 +388,22 @@ 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 [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 -(-115 -3505 UP) +(-115 -3508 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 (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{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}."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-916))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-116 |#1|) (QUOTE (-1026))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-3969 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-1157))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-916))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-116 |#1|) (QUOTE (-1026))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-3972 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-1157))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-916)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4435))) +((|HasAttribute| |#1| (QUOTE -4438))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,15 +414,15 @@ NIL NIL (-121 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"))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,24 +430,24 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-127 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."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-128) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-3969 (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-128) (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107)))) (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-3972 (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-128) (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107)))) (|HasCategory| (-128) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-128) (QUOTE (-1107))) (|HasCategory| (-128) (LIST (QUOTE -312) (QUOTE (-128)))))) (-130) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -466,13 +466,13 @@ NIL NIL (-134) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4436 "*") . T)) +(((-4439 "*") . T)) NIL -(-135 |minix| -3030 R) +(-135 |minix| -3033 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-136 |minix| -3030 S T$) +(-136 |minix| -3033 S T$) ((|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 @@ -494,8 +494,8 @@ NIL NIL (-141) ((|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}."))) -((-4434 . T) (-4424 . T) (-4435 . T)) -((-3969 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4437 . T) (-4427 . T) (-4438 . T)) +((-3972 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -510,7 +510,7 @@ NIL NIL (-145) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4431 . T)) +((-4434 . T)) NIL (-146 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 \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4431 . T)) +((-4434 . T)) NIL -(-148 -3505 UP UPUP) +(-148 -3508 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 @@ -531,14 +531,14 @@ NIL (-150 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasAttribute| |#1| (QUOTE -4434))) +((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasAttribute| |#1| (QUOTE -4437))) (-151 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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 (-152 |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."))) -((-4429 . T) (-4428 . T) (-4431 . T)) +((-4432 . T) (-4431 . T) (-4434 . T)) NIL (-153) ((|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."))) @@ -560,7 +560,7 @@ 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 -(-158 R -3505) +(-158 R -3508) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -591,23 +591,23 @@ NIL (-165 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 (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4430)) (|HasAttribute| |#2| (QUOTE -4433)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4433)) (|HasAttribute| |#2| (QUOTE -4436)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562)))) (-166 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})"))) -((-4427 -3969 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4430 |has| |#1| (-6 -4430)) (-4433 |has| |#1| (-6 -4433)) (-1466 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 -3972 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4433 |has| |#1| (-6 -4433)) (-4436 |has| |#1| (-6 -4436)) (-1466 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-167 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."))) NIL NIL (-168) -((|constructor| (NIL "This package implements a Spad compiler.")) (|elaborate| ((|Elaboration| (|Syntax|)) "\\spad{elaborate(s)} returns the elaboration of the syntax object \\spad{s} in the empty environement.")) (|macroExpand| (((|Syntax|) (|Syntax|) (|Environment|)) "\\spad{macroExpand(s,e)} traverses the syntax object \\spad{s} replacing all (niladic) macro invokations with the corresponding substitution."))) +((|constructor| (NIL "This package implements a Spad compiler.")) (|elaborate| (((|Maybe| (|Elaboration|)) (|SpadAst|)) "\\spad{elaborate(s)} returns the elaboration of the syntax object \\spad{s} in the empty environement.")) (|macroExpand| (((|SpadAst|) (|SpadAst|) (|Environment|)) "\\spad{macroExpand(s,e)} traverses the syntax object \\spad{s} replacing all (niladic) macro invokations with the corresponding substitution."))) NIL NIL (-169 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}."))) -((-4427 -3969 (|has| |#1| (-562)) (-12 (|has| |#1| (-310)) (|has| |#1| (-916)))) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4430 |has| |#1| (-6 -4430)) (-4433 |has| |#1| (-6 -4433)) (-1466 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1208)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) 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T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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(|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-234))) (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4433)) (|HasAttribute| |#1| (QUOTE -4436)) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-354))))) (-170 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -622,7 +622,7 @@ NIL NIL (-173) ((|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."))) -(((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-174) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -630,7 +630,7 @@ NIL NIL (-175 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4436 "*") . T) (-4427 . T) (-4432 . T) (-4426 . T) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") . T) (-4430 . T) (-4435 . T) (-4429 . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-176) ((|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|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -684,7 +684,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -(-189 R -3505) +(-189 R -3508) ((|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 @@ -792,23 +792,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-216 -3505 UP UPUP R) +(-216 -3508 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 -(-217 -3505 FP) +(-217 -3508 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-218) ((|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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3969 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-219) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-220 R -3505) +(-220 R -3508) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -822,19 +822,19 @@ NIL NIL (-223 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-224 |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}."))) -((-4431 . T)) +((-4434 . T)) NIL -(-225 R -3505) +(-225 R -3508) ((|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 (-226) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4210 . T) (-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-227) ((|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)}.}"))) @@ -842,15 +842,15 @@ NIL NIL (-228 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}"))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4436 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-229 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 (-230 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."))) -((-4435 . T)) +((-4438 . T)) NIL (-231 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -858,7 +858,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4431 . T)) +((-4434 . T)) NIL (-233 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -866,33 +866,33 @@ NIL NIL (-234) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4431 . T)) +((-4434 . T)) NIL (-235 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4434))) +((|HasAttribute| |#1| (QUOTE -4437))) (-236 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}."))) -((-4435 . T)) +((-4438 . T)) NIL (-237) ((|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 -(-238 S -3030 R) +(-238 S -3033 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4431)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1107)))) -(-239 -3030 R) +((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4434)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1107)))) +(-239 -3033 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4428 |has| |#2| (-1055)) (-4429 |has| |#2| (-1055)) (-4431 |has| |#2| (-6 -4431)) ((-4436 "*") |has| |#2| (-173)) (-4434 . T)) +((-4431 |has| |#2| (-1055)) (-4432 |has| |#2| (-1055)) (-4434 |has| |#2| (-6 -4434)) ((-4439 "*") |has| |#2| (-173)) (-4437 . T)) NIL -(-240 -3030 R) +(-240 -3033 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."))) -((-4428 |has| |#2| (-1055)) (-4429 |has| |#2| (-1055)) (-4431 |has| |#2| (-6 -4431)) ((-4436 "*") |has| |#2| (-173)) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-367))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1055)))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-798))) (-3969 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (QUOTE (-731))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1055)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3969 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (QUOTE (-234))) (-3969 (|HasCategory| |#2| (QUOTE (-25))) 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(|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#2| (QUOTE -4434)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) +(-241 -3033 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL @@ -906,7 +906,7 @@ NIL NIL (-244) ((|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}."))) -((-4427 . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-245 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."))) @@ -914,16 +914,16 @@ NIL NIL (-246 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}"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-247 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-248 |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"))) -(((-4436 "*") |has| |#2| (-173)) (-4427 |has| |#2| (-562)) (-4432 |has| |#2| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4432)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-249) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#3| (QUOTE (-1055)))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551)))))) (|HasCategory| (-551) (QUOTE (-855))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055)))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055)))) (|HasCategory| |#3| (QUOTE (-731)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasAttribute| |#3| (QUOTE -4434)) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-254 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-234)))) (-255 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-256 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}."))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-257 |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."))) @@ -994,8 +994,8 @@ NIL NIL (-266 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"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-267 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1040,11 +1040,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-278 R -3505) +(-278 R -3508) ((|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 -(-279 R -3505) +(-279 R -3508) ((|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 @@ -1070,7 +1070,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) (-285 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}."))) -((-4435 . T)) +((-4438 . T)) NIL (-286 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}."))) @@ -1091,18 +1091,18 @@ NIL (-290 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 -4435))) +((|HasAttribute| |#1| (QUOTE -4438))) (-291 |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 -(-292 S R |Mod| -2224 -3950 |exactQuo|) +(-292 S R |Mod| -2224 -3953 |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}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-293) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4427 . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-294) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Identifier|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{setProperty!(n,p,v,e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `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 `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1114,16 +1114,16 @@ NIL NIL (-296 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4431 -3969 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4428 |has| |#1| (-1055)) (-4429 |has| |#1| (-1055))) -((|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3969 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3969 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3969 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-301))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-3969 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) +((-4434 -3972 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4431 |has| |#1| (-1055)) (-4432 |has| |#1| (-1055))) +((|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3972 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731)))) (|HasCategory| |#1| (QUOTE (-478))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1118)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-301))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-478)))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-731)))) (-297 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL (-298 |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."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-299) ((|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 @@ -1136,11 +1136,11 @@ 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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|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 -(-302 -3505 S) +(-302 -3508 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 -(-303 E -3505) +(-303 E -3508) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1170,7 +1170,7 @@ NIL NIL (-310) ((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-311 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#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}."))) @@ -1180,7 +1180,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-313 -3505) +(-313 -3508) ((|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 @@ -1194,12 +1194,12 @@ NIL NIL (-316 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))}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1026))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-3969 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1157))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-234))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -312) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -289) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-310))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-916)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . 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(|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."))) -((-4431 -3969 (-3265 (|has| |#1| (-1055)) (|has| |#1| (-644 (-551)))) (-12 (|has| |#1| (-562)) (-3969 (-3265 (|has| |#1| (-1055)) (|has| |#1| (-644 (-551)))) (|has| |#1| (-1055)) (|has| |#1| (-478)))) (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) ((-4436 "*") |has| |#1| (-562)) (-4427 |has| |#1| (-562)) (-4432 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(LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) 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(QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1118)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-21)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-25)))) (-3972 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1055)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1118))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-318 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1208,7 +1208,7 @@ 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 -(-320 R -3505) +(-320 R -3508) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1218,8 +1218,8 @@ NIL NIL (-322 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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-323 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1230,7 +1230,7 @@ NIL NIL (-325 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-797)))) (-326 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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}\\spad{'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1246,19 +1246,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173)))) (-329 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 \\spad{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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-330 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."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-331 S -3505) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-331 S -3508) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-372)))) -(-332 -3505) +(-332 -3508) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-333) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1276,7 +1276,7 @@ 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 -(-337 -3505 UP UPUP R) +(-337 -3508 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1284,11 +1284,11 @@ 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 -(-339 S -3505 UP UPUP R) +(-339 S -3508 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-340 -3505 UP UPUP R) +(-340 -3508 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1302,19 +1302,19 @@ NIL NIL (-343 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-382)))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-344 |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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) -(-345 S -3505 UP UPUP) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +(-345 S -3508 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-367)))) -(-346 -3505 UP UPUP) +(-346 -3508 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4427 |has| (-412 |#2|) (-367)) (-4432 |has| (-412 |#2|) (-367)) (-4426 |has| (-412 |#2|) (-367)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-347 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}."))) @@ -1322,16 +1322,16 @@ NIL NIL (-348 |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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-349 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-350 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-351 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1346,51 +1346,51 @@ NIL NIL (-354) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL -(-355 R UP -3505) +(-355 R UP -3508) ((|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 (-356 |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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-372)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-372))) (|HasCategory| (-912 |#1|) (QUOTE (-145)))) (-357 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-358 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-359 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 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(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-361 -3505 GF) +(-361 -3508 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-362 -3505 FP FPP) +(-362 -3508 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-363 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-364 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-365 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4431 . T)) +((-4434 . T)) NIL (-366 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1398,7 +1398,7 @@ NIL NIL (-367) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-368 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."))) @@ -1414,7 +1414,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-371 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\\spad{'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\\spad{'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\\spad{'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(\\spad{\"*\"})} 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\\spad{'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\\spad{'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\\spad{'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\\spad{'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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4431 |has| |#1| (-562)) (-4429 . T) (-4428 . T)) +((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) NIL (-372) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1426,15 +1426,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-367)))) (-374 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 ( \\spad{Tr}(\\spad{vi} * \\spad{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}\\spad{'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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-375 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{>=} \\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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107)))) (-376 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{>=} \\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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4434 . T)) +((-4437 . T)) NIL (-377 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378 |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.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#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) (-4429 . T) (-4428 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4432 . T) (-4431 . T)) NIL (-379 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."))) @@ -1454,11 +1454,11 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-381 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4431 . T)) +((-4434 . T)) NIL (-382) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4417 . T) (-4425 . T) (-4210 . T) (-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4420 . T) (-4428 . T) (-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-383 |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 \\spad{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}."))) @@ -1470,11 +1470,11 @@ NIL NIL (-385 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."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-386 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.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-387) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1482,7 +1482,7 @@ NIL NIL (-388 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.\\spad{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}."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-389) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) @@ -1498,7 +1498,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-392) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-393) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1510,13 +1510,13 @@ NIL NIL (-395 |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"))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-396) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-397 -3505 UP UPUP R) +(-397 -3508 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 @@ -1540,11 +1540,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-403 -3982 |returnType| -1512 |symbols|) +(-403 -3985 |returnType| -1512 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-404 -3505 UP) +(-404 -3508 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1558,28 +1558,28 @@ NIL NIL (-407) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-408 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4417)) (|HasAttribute| |#1| (QUOTE -4425))) +((|HasAttribute| |#1| (QUOTE -4420)) (|HasAttribute| |#1| (QUOTE -4428))) (-409) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-4210 . T) (-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-410 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #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."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1227))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1227))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) (-411 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL (-412 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4421 -12 (|has| |#1| (-6 -4432)) (|has| |#1| (-457)) (|has| |#1| (-6 -4421))) (-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-825))) (-3969 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4421)) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4424 -12 (|has| |#1| (-6 -4435)) (|has| |#1| (-457)) (|has| |#1| (-6 -4424))) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-825))) (-3972 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4424)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-413 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 @@ -1590,7 +1590,7 @@ NIL NIL (-415 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{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},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-416 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1600,15 +1600,15 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-418 R -3505 UP A) +(-418 R -3508 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4431 . T)) +((-4434 . T)) NIL (-419 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 -(-420 R -3505 UP A |ibasis|) +(-420 R -3508 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1044) (|devaluate| |#2|)))) @@ -1622,7 +1622,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-423 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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\\spad{'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.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to 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."))) -((-4431 |has| |#1| (-562)) (-4429 . T) (-4428 . T)) +((-4434 |has| |#1| (-562)) (-4432 . T) (-4431 . T)) NIL (-424 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)}."))) @@ -1634,7 +1634,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1118))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (-426 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4431 -3969 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) ((-4436 "*") |has| |#1| (-562)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-562)) (-4426 |has| |#1| (-562))) +((-4434 -3972 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) ((-4439 "*") |has| |#1| (-562)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-562)) (-4429 |has| |#1| (-562))) NIL (-427 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\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}."))) @@ -1654,33 +1654,33 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-431 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4434 . T) (-4424 . T) (-4435 . T)) +((-4437 . T) (-4427 . T) (-4438 . T)) NIL (-432 S A R B) ((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-433 R -3505) +(-433 R -3508) ((|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 (-434 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"))) -((-4421 -12 (|has| |#1| (-6 -4421)) (|has| |#2| (-6 -4421))) (-4428 . T) (-4429 . T) (-4431 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4421)) (|HasAttribute| |#2| (QUOTE -4421)))) -(-435 R -3505) +((-4424 -12 (|has| |#1| (-6 -4424)) (|has| |#2| (-6 -4424))) (-4431 . T) (-4432 . T) (-4434 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4424)) (|HasAttribute| |#2| (QUOTE -4424)))) +(-435 R -3508) ((|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 -(-436 R -3505) +(-436 R -3508) ((|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 -(-437 R -3505) +(-437 R -3508) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-438 R -3505) +(-438 R -3508) ((|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 @@ -1688,7 +1688,7 @@ 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 -(-440 R -3505 UP) +(-440 R -3508 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-48))))) @@ -1720,7 +1720,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-448 R UP -3505) +(-448 R UP -3508) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1758,16 +1758,16 @@ NIL NIL (-457) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-458 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"))) -((-4431 |has| (-412 (-952 |#1|)) (-562)) (-4429 . T) (-4428 . T)) +((-4434 |has| (-412 (-952 |#1|)) (-562)) (-4432 . T) (-4431 . T)) ((|HasCategory| (-412 (-952 |#1|)) (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-412 (-952 |#1|)) (QUOTE (-562)))) (-459 |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"))) -(((-4436 "*") |has| |#2| (-173)) (-4427 |has| |#2| (-562)) (-4432 |has| |#2| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4432)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-460 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1794,7 +1794,7 @@ NIL NIL (-466 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-467 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1802,7 +1802,7 @@ NIL NIL (-468 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-469 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} 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}."))) @@ -1832,7 +1832,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-476 |lv| -3505 R) +(-476 |lv| -3508 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1842,23 +1842,23 @@ NIL NIL (-478) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4431 . T)) +((-4434 . T)) NIL (-479 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-480 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) +((-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-481 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)}"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-482) ((|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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-483) ((|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'."))) @@ -1866,29 +1866,29 @@ NIL NIL (-484 |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."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-485) ((|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\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-486 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))))) (|HasCategory| (-551) (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#2| (QUOTE -4434)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-488) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-489 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-490 -3505 UP UPUP R) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +(-490 -3508 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1898,12 +1898,12 @@ NIL NIL (-492) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3969 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-493 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 -4434)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) +((|HasAttribute| |#1| (QUOTE -4437)) (|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-494 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1924,33 +1924,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-499 -3505 UP |AlExt| |AlPol|) +(-499 -3508 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-500) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-551))))) (-501 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-502 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-503 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 -(-504 R UP -3505) +(-504 R UP -3508) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-505 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1107))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-868))))) (-506 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)}."))) @@ -1964,7 +1964,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-509 -3505 |Expon| |VarSet| |DPoly|) +(-509 -3508 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-1183))))) @@ -2014,36 +2014,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-797)))) (-521 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-522) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-523 |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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((-3969 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((-3972 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) (-524 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-525 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-526 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4435))) +((|HasAttribute| |#3| (QUOTE -4438))) (-527 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 -4435))) +((|HasAttribute| |#7| (QUOTE -4438))) (-528 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4436 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-529) ((|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 @@ -2076,7 +2076,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-537 K -3505 |Par|) +(-537 K -3508 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2100,7 +2100,7 @@ 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 -(-543 K -3505 |Par|) +(-543 K -3508 |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 @@ -2130,11 +2130,11 @@ NIL NIL (-550) ((|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."))) -((-4432 . T) (-4433 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-551) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4416 . T) (-4422 . T) (-4426 . T) (-4421 . T) (-4432 . T) (-4433 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4419 . T) (-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-552) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2154,13 +2154,13 @@ NIL NIL (-556 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) -(-557 R -3505) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +(-557 R -3508) ((|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 -(-558 R0 -3505 UP UPUP R) +(-558 R0 -3508 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 @@ -2170,7 +2170,7 @@ NIL NIL (-560 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-4210 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4213 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-561 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."))) @@ -2178,9 +2178,9 @@ NIL NIL (-562) ((|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."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL -(-563 R -3505) +(-563 R -3508) ((|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},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #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 @@ -2192,7 +2192,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-566 R -3505 L) +(-566 R -3508 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}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #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}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #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 -663) (|devaluate| |#2|)))) @@ -2200,11 +2200,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-568 -3505 UP UPUP R) +(-568 -3508 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 -(-569 -3505 UP) +(-569 -3508 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 @@ -2212,15 +2212,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-571 R -3505 L) +(-571 R -3508 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}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -663) (|devaluate| |#2|)))) -(-572 R -3505) +(-572 R -3508) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-573 -3505 UP) +(-573 -3508 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2228,27 +2228,27 @@ 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 -(-575 -3505) +(-575 -3508) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-576 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."))) -((-4210 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4213 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-577) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-578 R -3505) +(-578 R -3508) ((|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 (-457))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-287))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-287)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-579 -3505 UP) +(-579 -3508 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 -(-580 R -3505) +(-580 R -3508) ((|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 @@ -2270,25 +2270,25 @@ NIL NIL (-585 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-586 |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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-587) ((|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 -(-588 -3505) +(-588 -3508) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183))))) -(-589 E -3505) +(-589 E -3508) ((|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 -(-590 R -3505) +(-590 R -3508) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL @@ -2322,22 +2322,22 @@ NIL NIL (-598 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-3969 (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-3972 (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-599 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-600 |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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|)))) (|HasCategory| (-551) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551)))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-551)) (|devaluate| |#1|)))) (|HasCategory| (-551) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-551)))))) (-601 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4436 "*") |has| |#1| (-562)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-562)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-562)))) (-602) -((|constructor| (NIL "This domain provides representations for internal type form."))) +((|constructor| (NIL "This domain provides representations for internal type form.")) (|voidMode| (($) "\\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"))) NIL NIL (-603 A B) @@ -2348,7 +2348,7 @@ 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 -(-605 R -3505 FG) +(-605 R -3508 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2358,12 +2358,12 @@ NIL NIL (-607 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-608 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 -4435)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4434)) (|HasCategory| |#3| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4437)) (|HasCategory| |#3| (QUOTE (-1107)))) (-609 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2378,19 +2378,19 @@ NIL NIL (-612 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4431 -3969 (-3265 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4429 . T) (-4428 . T)) -((-3969 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4434 -3972 (-3268 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4432 . T) (-4431 . T)) +((-3972 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-613 |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."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-614 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 (-615 |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}."))) -((-4435 . T)) +((-4438 . T)) NIL (-616 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."))) @@ -2408,7 +2408,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-620 -3505 UP) +(-620 -3508 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2426,7 +2426,7 @@ NIL NIL (-624 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}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-853)))) (-625 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."))) @@ -2434,15 +2434,15 @@ NIL NIL (-626 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."))) -((-4431 . T)) +((-4434 . T)) NIL -(-627 R -3505) +(-627 R -3508) ((|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 (-628 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"))) -((-4429 . T) (-4428 . T) ((-4436 "*") . T) (-4427 . T) (-4431 . T)) +((-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4430 . T) (-4434 . T)) ((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (-629 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(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2458,13 +2458,13 @@ NIL NIL (-632 |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.\\spad{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(\\spad{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}}."))) -((-4431 . T)) +((-4434 . T)) NIL (-633 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(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{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{\\spad{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(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{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{\\spad{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) NIL NIL -(-634 R -3505) +(-634 R -3508) ((|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 @@ -2472,25 +2472,25 @@ 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 -(-636 |lv| -3505) +(-636 |lv| -3508) ((|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 (-637) ((|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}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|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."))) -((-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-1165) (QUOTE (-855))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) +((-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-1165) (QUOTE (-855))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-638 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)."))) -((-4431 -3969 (-3265 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4429 . T) (-4428 . T)) -((-3969 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4434 -3972 (-3268 (|has| |#2| (-371 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4432 . T) (-4431 . T)) +((-3972 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-639 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-640 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4429 . T) (-4428 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4432 . T) (-4431 . T)) NIL (-641 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))}."))) @@ -2503,10 +2503,10 @@ NIL (-643 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-3755 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) +((-3758 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) (-644 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4431 . T)) +((-4434 . T)) NIL (-645 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2514,8 +2514,8 @@ NIL NIL (-646 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-647 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2538,8 +2538,8 @@ NIL NIL (-652 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-653 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2551,30 +2551,30 @@ NIL (-655 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{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#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}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4435))) +((|HasAttribute| |#1| (QUOTE -4438))) (-656 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{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL (-657 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}."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) ((|HasCategory| |#1| (QUOTE (-796)))) -(-658 R -3505 L) +(-658 R -3508 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 -(-659 A -2829) +(-659 A -2832) ((|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}}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-660 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}}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-661 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-662 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2582,9 +2582,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-663 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}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL -(-664 -3505 UP) +(-664 -3508 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)))) @@ -2606,7 +2606,7 @@ NIL NIL (-669 |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.\\spad{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) (-4429 . T) (-4428 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4432 . T) (-4431 . T)) ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-173)))) (-670 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}."))) @@ -2614,13 +2614,13 @@ NIL NIL (-671 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}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL -(-672 -3505 |Row| |Col| M) +(-672 -3508 |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 -(-673 -3505) +(-673 -3508) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #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 @@ -2630,8 +2630,8 @@ NIL NIL (-675 |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."))) -((-4431 . T) (-4434 . T) (-4428 . T) (-4429 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4436 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562))) (-3969 (|HasAttribute| |#2| (QUOTE (-4436 #1#))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4434 . T) (-4437 . T) (-4431 . T) (-4432 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4439 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562))) (-3972 (|HasAttribute| |#2| (QUOTE (-4439 #1#))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-676) ((|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 @@ -2651,7 +2651,7 @@ NIL (-680 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-681) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2691,10 +2691,10 @@ NIL (-690 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4436 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-562)))) (-691 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-692 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}."))) @@ -2706,8 +2706,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562)))) (-694 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."))) -((-4434 . T) (-4435 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4436 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4437 . T) (-4438 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4439 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-695 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2716,7 +2716,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-697 S -3505 FLAF FLAS) +(-697 S -3508 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2726,11 +2726,11 @@ NIL NIL (-699) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4427 . T) (-4432 |has| (-704) (-367)) (-4426 |has| (-704) (-367)) (-1466 . T) (-4433 |has| (-704) (-6 -4433)) (-4430 |has| (-704) (-6 -4430)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-3969 (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-234))) (-3969 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-354)))) (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3969 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-354)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-704) (QUOTE (-1026))) (|HasCategory| (-704) (QUOTE (-1208))) (-12 (|HasCategory| (-704) (QUOTE (-1008))) (|HasCategory| (-704) (QUOTE (-1208)))) (-3969 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-367)))) (-3969 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (QUOTE (-916))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-1208)))) (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916))) (-3969 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-367)))) (-3969 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-562)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| (-704) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-704) (QUOTE (-562))) (|HasAttribute| (-704) (QUOTE -4433)) (|HasAttribute| (-704) (QUOTE -4430)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-145)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-354))))) +((-4430 . T) (-4435 |has| (-704) (-367)) (-4429 |has| (-704) (-367)) (-1466 . T) (-4436 |has| (-704) (-6 -4436)) (-4433 |has| (-704) (-6 -4433)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-3972 (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-234))) (-3972 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-354)))) (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (-3972 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-354)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-704) (QUOTE (-1026))) (|HasCategory| (-704) (QUOTE (-1208))) (-12 (|HasCategory| (-704) (QUOTE (-1008))) (|HasCategory| (-704) (QUOTE (-1208)))) (-3972 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-367)))) (-3972 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-916)))) (-12 (|HasCategory| (-704) (QUOTE (-354))) (|HasCategory| (-704) (QUOTE (-916))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-1208)))) (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916))) (-3972 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-367)))) (-3972 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-562)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| (-704) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-704) (QUOTE (-562))) (|HasAttribute| (-704) (QUOTE -4436)) (|HasAttribute| (-704) (QUOTE -4433)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-145)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-916)))) (|HasCategory| (-704) (QUOTE (-354))))) (-700 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}."))) -((-4435 . T)) +((-4438 . T)) NIL (-701 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 \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2740,13 +2740,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #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 -(-703 OV E -3505 PG) +(-703 OV E -3508 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 (-704) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-4210 . T) (-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4213 . T) (-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-705 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2754,7 +2754,7 @@ NIL NIL (-706) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4433 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4436 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-707 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-711 S -3081 I) +(-711 S -3084 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 @@ -2782,7 +2782,7 @@ NIL NIL (-713 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)}.}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-714 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}."))) @@ -2792,25 +2792,25 @@ 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 -(-716 R |Mod| -2224 -3950 |exactQuo|) +(-716 R |Mod| -2224 -3953 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-717 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4430 |has| |#1| (-367)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4433 |has| |#1| (-367)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-718 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-719 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) (-4431 . T)) +((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-720 R |Mod| -2224 -3950 |exactQuo|) +(-720 R |Mod| -2224 -3953 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4431 . T)) +((-4434 . T)) NIL (-721 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2818,11 +2818,11 @@ NIL NIL (-722 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL -(-723 -3505) +(-723 -3508) ((|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]]}."))) -((-4431 . T)) +((-4434 . T)) NIL (-724 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."))) @@ -2846,7 +2846,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-372)))) (-729 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."))) -((-4427 |has| |#1| (-367)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-730 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."))) @@ -2856,7 +2856,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-732 -3505 UP) +(-732 -3508 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 @@ -2874,8 +2874,8 @@ NIL NIL (-736 |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."))) -(((-4436 "*") |has| |#2| (-173)) (-4427 |has| |#2| (-562)) (-4432 |has| |#2| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3969 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3969 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4432)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4439 "*") |has| |#2| (-173)) (-4430 |has| |#2| (-562)) (-4435 |has| |#2| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . 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It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2890,15 +2890,15 @@ NIL NIL (-740 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) (-4431 . T)) +((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-855)))) (-741 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}."))) -((-4434 . T) (-4424 . T) (-4435 . T)) +((-4437 . T) (-4427 . T) (-4438 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-742 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4424 . T) (-4435 . T)) +((-4427 . T) (-4438 . T)) NIL (-743) ((|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."))) @@ -2910,7 +2910,7 @@ NIL NIL (-745 |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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4429 . T) (-4428 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-746 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"))) @@ -2926,7 +2926,7 @@ NIL NIL (-749 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{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}."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-750) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3008,11 +3008,11 @@ 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 -(-770 -3505) +(-770 -3508) ((|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 -(-771 P -3505) +(-771 P -3508) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3020,7 +3020,7 @@ NIL NIL NIL NIL -(-773 UP -3505) +(-773 UP -3508) ((|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 @@ -3034,9 +3034,9 @@ NIL NIL (-776) ((|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."))) -(((-4436 "*") . T)) +(((-4439 "*") . T)) NIL -(-777 R -3505) +(-777 R -3508) ((|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 @@ -3056,7 +3056,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-782 -3505 |ExtF| |SUEx| |ExtP| |n|) +(-782 -3508 |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 @@ -3070,12 +3070,12 @@ NIL NIL (-785 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . 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T) (-4431 . T) (-4434 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4430 |has| |#1| (-367)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4433 |has| |#1| (-367)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-787 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 @@ -3086,7 +3086,7 @@ NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) (-789 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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.}"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-790 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}."))) @@ -3134,7 +3134,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-801 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-802) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) @@ -3142,9 +3142,9 @@ NIL NIL (-803 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-3969 (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) -(-804 -3969 R OS S) +((-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-3972 (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1002 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) +(-804 -3972 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL @@ -3152,11 +3152,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-806 R -3505 L) +(-806 R -3508 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-807 R -3505) +(-807 R -3508) ((|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 @@ -3164,7 +3164,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-809 R -3505) +(-809 R -3508) ((|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 @@ -3172,11 +3172,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-811 -3505 UP UPUP R) +(-811 -3508 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 -(-812 -3505 UP L LQ) +(-812 -3508 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3184,41 +3184,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-814 -3505 UP L LQ) +(-814 -3508 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-815 -3505 UP) +(-815 -3508 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}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #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}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-816 -3505 L UP A LO) +(-816 -3508 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 -(-817 -3505 UP) +(-817 -3508 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-818 -3505 LO) +(-818 -3508 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 -(-819 -3505 LODO) +(-819 -3508 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-820 -3030 S |f|) +(-820 -3033 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4428 |has| |#2| (-1055)) (-4429 |has| |#2| (-1055)) (-4431 |has| |#2| (-6 -4431)) ((-4436 "*") |has| |#2| (-173)) (-4434 . 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(|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))))) (|HasCategory| (-551) (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#2| (QUOTE -4434)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-821 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"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-823 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-822 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4436 "*") |has| |#2| (-367)) (-4427 |has| |#2| (-367)) (-4432 |has| |#2| (-367)) (-4426 |has| |#2| (-367)) (-4431 . T) (-4429 . T) (-4428 . T)) +(((-4439 "*") |has| |#2| (-367)) (-4430 |has| |#2| (-367)) (-4435 |has| |#2| (-367)) (-4429 |has| |#2| (-367)) (-4434 . T) (-4432 . T) (-4431 . T)) ((|HasCategory| |#2| (QUOTE (-367)))) (-823 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}))."))) @@ -3230,7 +3230,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-825) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-826) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3262,7 +3262,7 @@ NIL NIL (-833 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-234)))) (-834) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) @@ -3270,7 +3270,7 @@ NIL NIL (-835 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4434 . T) (-4424 . T) (-4435 . T)) +((-4437 . T) (-4427 . T) (-4438 . T)) NIL (-836) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3278,15 +3278,15 @@ NIL NIL (-837 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."))) -((-4431 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4434 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) (-838 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL (-839 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) (-4431 . T)) +((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-840 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}."))) @@ -3318,8 +3318,8 @@ NIL NIL (-847 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4431 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3969 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3969 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4434 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-3972 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-550)))) (-848 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3328,7 +3328,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-850 -3030 S) +(-850 -3033 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3342,7 +3342,7 @@ NIL NIL (-853) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4431 . T)) +((-4434 . T)) NIL (-854 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3358,19 +3358,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173)))) (-857 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\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 \\spad{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\\spad{''}.")) (|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\\spad{''}.")) (|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)}.}"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-858 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{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) -(-859 R |sigma| -3674) +(-859 R |sigma| -3677) ((|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."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) -(-860 |x| R |sigma| -3674) +(-860 |x| R |sigma| -3677) ((|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}."))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-367)))) (-861 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..)}."))) @@ -3414,7 +3414,7 @@ NIL NIL (-871 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: \\spad{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)"))) -((-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) (-4431 . T)) +((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-872 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)."))) @@ -3426,24 +3426,24 @@ NIL NIL (-874 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{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)."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-875 |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}."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-876 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-874 |#1|) (QUOTE (-916))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-147))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-874 |#1|) (QUOTE (-1026))) (|HasCategory| (-874 |#1|) (QUOTE (-825))) (-3969 (|HasCategory| (-874 |#1|) (QUOTE (-825))) (|HasCategory| (-874 |#1|) (QUOTE (-855)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-1157))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-234))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -874) (|devaluate| |#1|)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (QUOTE (-310))) (|HasCategory| (-874 |#1|) (QUOTE (-550))) (|HasCategory| (-874 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-874 |#1|) (QUOTE (-916))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-147))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-874 |#1|) (QUOTE (-1026))) (|HasCategory| (-874 |#1|) (QUOTE (-825))) (-3972 (|HasCategory| (-874 |#1|) (QUOTE (-825))) (|HasCategory| (-874 |#1|) (QUOTE (-855)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-1157))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| (-874 |#1|) (QUOTE (-234))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -874) (|devaluate| |#1|)) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| (-874 |#1|) (QUOTE (-310))) (|HasCategory| (-874 |#1|) (QUOTE (-550))) (|HasCategory| (-874 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-874 |#1|) (QUOTE (-916)))) (|HasCategory| (-874 |#1|) (QUOTE (-145))))) (-877 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (-3969 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (-3972 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-878 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107)))) (-3969 (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107)))) (-3972 (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-1107))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))))) (-879) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3503,7 +3503,7 @@ NIL (-893 |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 (-3755 (|HasCategory| |#2| (QUOTE (-1055)))) (-3755 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-3755 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) +((-12 (-3758 (|HasCategory| |#2| (QUOTE (-1055)))) (-3758 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-3758 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-894 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\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL @@ -3516,7 +3516,7 @@ 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 \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and \\spad{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 \\spad{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 \\spad{'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 -(-897 R -3081) +(-897 R -3084) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3536,7 +3536,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-902 UP -3505) +(-902 UP -3508) ((|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 @@ -3554,23 +3554,23 @@ NIL NIL (-906 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4431 . T)) +((-4434 . T)) NIL (-907 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-908 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.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4431 . T)) -((-3969 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) +((-4434 . T)) +((-3972 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (-909 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-910 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}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p, el)} returns the image of {\\em el} under 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."))) -((-4431 . T)) +((-4434 . T)) NIL (-911 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}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(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}."))) @@ -3578,7 +3578,7 @@ NIL NIL (-912 |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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-913 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."))) @@ -3594,9 +3594,9 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-916) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{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}."))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL -(-917 R0 -3505 UP UPUP R) +(-917 R0 -3508 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 @@ -3610,7 +3610,7 @@ NIL NIL (-920 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\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} 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} \\spad{``p}-adically\\spad{''} 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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-921 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."))) @@ -3624,13 +3624,13 @@ 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\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-924 -3505) +(-924 -3508) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL (-925) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4436 "*") . T)) +(((-4439 "*") . T)) NIL (-926 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})."))) @@ -3638,13 +3638,13 @@ NIL NIL (-927) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL -(-928 |xx| -3505) +(-928 |xx| -3508) ((|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 -(-929 -3505 P) +(-929 -3508 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3672,7 +3672,7 @@ 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 \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-936 R -3505) +(-936 R -3508) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3680,7 +3680,7 @@ 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 -(-938 S R -3505) +(-938 S R -3508) ((|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 @@ -3700,11 +3700,11 @@ 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 -892) (|devaluate| |#1|)))) -(-943 -3081) +(-943 -3084) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-944 R -3505 -3081) +(-944 R -3508 -3084) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3726,8 +3726,8 @@ NIL NIL (-949 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-950 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3738,8 +3738,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-853)))) (-952 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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-953 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 @@ -3751,12 +3751,12 @@ NIL (-955 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 \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#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 \\spad{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 \\spad{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 (-916))) (|HasAttribute| |#2| (QUOTE -4432)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (-956 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 \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL -(-957 E V R P -3505) +(-957 E V R P -3508) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3764,7 +3764,7 @@ 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 -(-959 E V R P -3505) +(-959 E V R P -3508) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-457)))) @@ -3778,16 +3778,16 @@ NIL NIL (-962 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4432))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4435))) (-963 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 (-964 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-965 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3796,7 +3796,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-967 -3505) +(-967 -3508) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3810,8 +3810,8 @@ NIL NIL (-970 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"))) -((-4431 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) +((-4434 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-971) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3826,7 +3826,7 @@ NIL NIL (-974 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-975 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{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{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.\\spad{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{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\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{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{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} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + 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{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} 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{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} 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}) \\spad{>=} 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 = \\spad{+/-} 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 \\spad{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}) \\spad{>=} 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}) \\spad{>=} 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}) \\spad{>=} 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{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} 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}}"))) @@ -3846,7 +3846,7 @@ NIL NIL (-979 |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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-980) ((|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 \\spad{x-},{} \\spad{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}."))) @@ -3858,7 +3858,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-982 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?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{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,{}\\spad{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{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{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{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{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?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4434 . T)) +((-4437 . T)) NIL (-983 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(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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 \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{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(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{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},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{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(\\spad{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(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{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?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{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 \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3874,7 +3874,7 @@ NIL NIL (-986 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}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-987 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3892,7 +3892,7 @@ 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 -(-991 K R UP -3505) +(-991 K R UP -3508) ((|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 @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-1157)))) (-997 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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-998 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}."))) @@ -3934,19 +3934,19 @@ NIL NIL (-1001 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\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."))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-1002 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.}"))) -((-4427 |has| |#1| (-293)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4430 |has| |#1| (-293)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) (-1003 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL ((|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-293)))) (-1004 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4427 |has| |#1| (-293)) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4430 |has| |#1| (-293)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1005 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3954,8 +3954,8 @@ NIL NIL (-1006 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1007 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3964,14 +3964,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1009 -3505 UP UPUP |radicnd| |n|) +(-1009 -3508 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4427 |has| (-412 |#2|) (-367)) (-4432 |has| (-412 |#2|) (-367)) (-4426 |has| (-412 |#2|) (-367)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3969 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3969 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3969 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3969 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +((-4430 |has| (-412 |#2|) (-367)) (-4435 |has| (-412 |#2|) (-367)) (-4429 |has| (-412 |#2|) (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-354))) (-3972 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-354)))) (-3972 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-354))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) (-1010 |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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3969 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3969 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-551) (QUOTE (-916))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-551) (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-147))) (|HasCategory| (-551) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-1026))) (|HasCategory| (-551) (QUOTE (-825))) (-3972 (|HasCategory| (-551) (QUOTE (-825))) (|HasCategory| (-551) (QUOTE (-855)))) (|HasCategory| (-551) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-1157))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-551) (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-551) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-551) (QUOTE (-234))) (|HasCategory| (-551) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-551) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -312) (QUOTE (-551)))) (|HasCategory| (-551) (LIST (QUOTE -289) (QUOTE (-551)) (QUOTE (-551)))) (|HasCategory| (-551) (QUOTE (-310))) (|HasCategory| (-551) (QUOTE (-550))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-551) (LIST (QUOTE -644) (QUOTE (-551)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (-3972 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-551) (QUOTE (-916)))) (|HasCategory| (-551) (QUOTE (-145))))) (-1011) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3991,7 +3991,7 @@ NIL (-1015 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{:=} \\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 -4435)) (|HasCategory| |#2| (QUOTE (-1107)))) +((|HasAttribute| |#1| (QUOTE -4438)) (|HasCategory| |#2| (QUOTE (-1107)))) (-1016 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{:=} \\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 @@ -4002,21 +4002,21 @@ NIL NIL (-1018) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4427 . T) (-4432 . T) (-4426 . T) (-4429 . T) (-4428 . T) ((-4436 "*") . T) (-4431 . T)) +((-4430 . T) (-4435 . T) (-4429 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4434 . T)) NIL -(-1019 R -3505) +(-1019 R -3508) ((|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 -(-1020 R -3505) +(-1020 R -3508) ((|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 -(-1021 -3505 UP) +(-1021 -3508 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 -(-1022 -3505 UP) +(-1022 -3508 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 @@ -4050,9 +4050,9 @@ NIL NIL (-1030 |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"))) -((-4427 . T) (-4432 . T) (-4426 . T) (-4429 . T) (-4428 . T) ((-4436 "*") . T) (-4431 . T)) -((-3969 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) -(-1031 -3505 L) +((-4430 . T) (-4435 . T) (-4429 . T) (-4432 . T) (-4431 . T) ((-4439 "*") . T) (-4434 . T)) +((-3972 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-412 (-551)) (LIST (QUOTE -1044) (QUOTE (-551))))) +(-1031 -3508 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 @@ -4062,7 +4062,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1107)))) (-1033 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1034) ((|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."))) @@ -4071,7 +4071,7 @@ NIL (-1035 R) ((|constructor| (NIL "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{<=} \\spad{i} \\spad{<=} \\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{<=} \\spad{i} \\spad{<=} \\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 (-4436 "*")))) +((|HasAttribute| |#1| (QUOTE (-4439 "*")))) (-1036 R) ((|constructor| (NIL "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\\spad{'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\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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 @@ -4088,14 +4088,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1040 -3505 |Expon| |VarSet| |FPol| |LFPol|) +(-1040 -3508 |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"))) -(((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1041) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) (-1042) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4138,7 +4138,7 @@ NIL NIL (-1052 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{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}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1107))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -785) (|devaluate| |#1|) (LIST (QUOTE -869) (|devaluate| |#2|)))))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-869 |#2|) (QUOTE (-372))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1053) ((|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"))) @@ -4150,9 +4150,9 @@ NIL NIL (-1055) ((|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."))) -((-4431 . T)) +((-4434 . T)) NIL -(-1056 |xx| -3505) +(-1056 |xx| -3508) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4166,12 +4166,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-310))) (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (QUOTE (-562))) (|HasCategory| |#4| (QUOTE (-173)))) (-1059 |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.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4434 . T) (-4429 . T) (-4428 . T)) +((-4437 . T) (-4432 . T) (-4431 . T)) NIL (-1060 |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}."))) -((-4434 . T) (-4429 . T) (-4428 . T)) -((|HasCategory| |#3| (QUOTE (-173))) (-3969 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4432 . T) (-4431 . T)) +((|HasCategory| |#3| (QUOTE (-173))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868))))) (-1061 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4194,7 +4194,7 @@ NIL NIL (-1066) ((|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.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1067 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4202,19 +4202,19 @@ NIL NIL (-1068) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4422 . T) (-4426 . T) (-4421 . T) (-4432 . T) (-4433 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1069) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2263) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| (-51) (QUOTE (-1107))) (|HasCategory| (-51) (LIST (QUOTE -312) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (QUOTE (-1107))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-51) (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-51) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1183)) (|:| -2263 (-51))) (LIST (QUOTE -618) (QUOTE (-868))))) (-1070 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -997) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-1183))))) (-1071 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#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}}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-1072) ((|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'."))) @@ -4238,7 +4238,7 @@ NIL NIL (-1077 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}{\\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1078 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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."))) @@ -4252,7 +4252,7 @@ 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 -(-1081 |Base| R -3505) +(-1081 |Base| R -3508) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4260,7 +4260,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1083 |Base| R -3505) +(-1083 |Base| R -3508) ((|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 @@ -4270,8 +4270,8 @@ NIL NIL (-1085 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."))) -((-4427 |has| |#1| (-367)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) +((-4430 |has| |#1| (-367)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-354))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-354)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) (-1086 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4302,8 +4302,8 @@ NIL NIL (-1093 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"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1094 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 @@ -4342,15 +4342,15 @@ NIL NIL (-1103 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)}}"))) -((-4434 . T) (-4424 . T) (-4435 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4437 . T) (-4427 . T) (-4438 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1104 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL (-1105 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4424 . T)) +((-4427 . T)) NIL (-1106 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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}."))) @@ -4390,7 +4390,7 @@ NIL NIL (-1115 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 \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{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.}"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1116) ((|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| (|Integer|)) (|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| (|Integer|)) (|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| (|Integer|))) "\\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."))) @@ -4406,8 +4406,8 @@ NIL NIL (-1119 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4428 |has| |#3| (-1055)) (-4429 |has| |#3| (-1055)) (-4431 |has| |#3| (-6 -4431)) ((-4436 "*") |has| |#3| (-173)) (-4434 . 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(|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551)))))) (|HasCategory| (-551) (QUOTE (-855))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1183))))) (-3972 (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (|HasCategory| |#3| (QUOTE (-1055)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-551))))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasAttribute| |#3| (QUOTE -4434)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1107))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-1120 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4420,7 +4420,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1123 R -3505) +(-1123 R -3508) ((|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 @@ -4434,19 +4434,19 @@ NIL NIL (-1126) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|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."))) -((-4422 . T) (-4426 . T) (-4421 . T) (-4432 . T) (-4433 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4425 . T) (-4429 . T) (-4424 . T) (-4435 . T) (-4436 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1127 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}) = \\spad{#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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4434 . T) (-4435 . T)) +((-4437 . T) (-4438 . T)) NIL (-1128 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4436 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) +((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4439 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) (-1129 |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}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4434 . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4437 . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1130 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}."))) @@ -4454,17 +4454,17 @@ NIL NIL (-1131 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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3969 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4432)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-3972 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4435)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1132 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) (-1133 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}"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL -(-1134 UP -3505) +(-1134 UP -3508) ((|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 @@ -4518,19 +4518,19 @@ NIL NIL (-1147 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107))) (-3969 (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107))) (-3972 (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1107)))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-868))))) (-1148 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4431 . T) (-4423 |has| |#2| (-6 (-4436 "*"))) (-4434 . T) (-4428 . T) (-4429 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4436 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3969 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (-3969 (|HasAttribute| |#2| (QUOTE (-4436 "*"))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4434 . T) (-4426 |has| |#2| (-6 (-4439 "*"))) (-4437 . T) (-4431 . T) (-4432 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (QUOTE (-367))) (-3972 (|HasAttribute| |#2| (QUOTE (-4439 "*"))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-1149 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1150) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1151 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\\spad{'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{\\spad{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.}"))) @@ -4538,12 +4538,12 @@ NIL NIL (-1152 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1153 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}."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1154 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4554,8 +4554,8 @@ NIL NIL (-1156 |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."))) -((-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) +((-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-1157) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4570,8 +4570,8 @@ NIL NIL (-1160 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."))) -((-4435 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4438 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1161 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4586,16 +4586,16 @@ NIL NIL (-1164) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1165) NIL -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| (-144) (QUOTE (-1107))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-1166 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (QUOTE (-1107))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 (-1165)) (|:| -2263 |#1|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1167 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 \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4626,9 +4626,9 @@ NIL NIL (-1174 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4638,8 +4638,8 @@ NIL NIL (-1177 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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 @@ -4650,12 +4650,12 @@ NIL NIL (-1180 |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.")) 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1182) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4670,8 +4670,8 @@ NIL NIL (-1185 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-6 -4432)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3969 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-977) (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4432))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-6 -4435)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-3972 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-977) (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4435))) (-1186) ((|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 @@ -4710,8 +4710,8 @@ NIL NIL (-1195 |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}"))) -((-4434 . T) (-4435 . T)) -((-12 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4301) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3969 (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) +((-4437 . T) (-4438 . T)) +((-12 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4304) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2263) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -619) (QUOTE (-540)))) (-12 (|HasCategory| |#2| (QUOTE (-1107))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1107))) (-3972 (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (LIST (QUOTE -618) (QUOTE (-868))))) (-1196 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 @@ -4726,7 +4726,7 @@ NIL NIL (-1199 |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}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4435 . T)) +((-4438 . T)) NIL (-1200 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} 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."))) @@ -4766,8 +4766,8 @@ NIL NIL (-1209 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4435 . T) (-4434 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) +((-4438 . T) (-4437 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1107))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (-1210 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4776,7 +4776,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1212 R -3505) +(-1212 R -3508) ((|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 @@ -4784,21 +4784,21 @@ 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 -(-1214 R -3505) +(-1214 R -3508) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -896) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -892) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -892) (|devaluate| |#1|))))) (-1215 |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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-367)))) (-1216 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-372)))) (-1217 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1218 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}."))) @@ -4812,7 +4812,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) -(-1221 -3505) +(-1221 -3508) ((|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}."))) 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((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL (-1234 |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{<=} \\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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1235 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)}."))) @@ -4874,12 +4874,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-1236 |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)}.")) 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(|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-145)))))) (-1238 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4894,8 +4894,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-853)))) (-1241 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4436 "*") |has| |#2| (-173)) (-4427 |has| |#2| (-562)) (-4430 |has| |#2| (-367)) (-4432 |has| |#2| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . 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T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-382)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-382))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-551)))) (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-551))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-382)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551))))) (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -896) (QUOTE (-551)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-540))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-551)))) (-3972 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (-3972 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-3972 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE -4435)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (-3972 (-12 (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| $ (QUOTE (-145)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1242 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4922,7 +4922,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1157)))) (-1248 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 \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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\\spad{'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}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4430 |has| |#1| (-367)) (-4432 |has| |#1| (-6 -4432)) (-4429 . T) (-4428 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4433 |has| |#1| (-367)) (-4435 |has| |#1| (-6 -4435)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-1249 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."))) @@ -4931,10 +4931,10 @@ NIL (-1250 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4387) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4390) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) (-1251 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1252 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4942,15 +4942,15 @@ NIL NIL (-1253 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1254 |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 (-1255 |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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1256 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)}."))) @@ -4958,28 +4958,28 @@ NIL NIL (-1257 |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)}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1258 |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)}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4432 |has| |#1| (-367)) (-4426 |has| |#1| (-367)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3969 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4435 |has| |#1| (-367)) (-4429 |has| |#1| (-367)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-173))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-551)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-3972 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-551)))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551)))))) (-1259 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))}."))) -(((-4436 "*") |has| (-1253 |#2| |#3| |#4|) (-173)) (-4427 |has| (-1253 |#2| |#3| |#4|) (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-173))) (-3969 (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-562)))) +(((-4439 "*") |has| (-1253 |#2| |#3| |#4|) (-173)) (-4430 |has| (-1253 |#2| |#3| |#4|) (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-173))) (-3972 (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551)))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-551)))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-562)))) (-1260 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4435))) +((|HasAttribute| |#1| (QUOTE -4438))) (-1261 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\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} \\spad{>=} 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} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#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} \\spad{>=} 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL (-1262 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3969 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4387) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4253) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (QUOTE (-562))) (-3972 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -4390) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-551))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasSignature| |#1| (LIST (QUOTE -4256) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#1|))))))) (-1263 |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 @@ -4987,16 +4987,16 @@ NIL (-1264 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -3494) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4253) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-551)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -3497) (LIST (LIST (QUOTE -646) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4256) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasCategory| |#2| (QUOTE (-367)))) (-1265 |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."))) -(((-4436 "*") |has| |#1| (-173)) (-4427 |has| |#1| (-562)) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") |has| |#1| (-173)) (-4430 |has| |#1| (-562)) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1266 |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 -(-1267 -3505 UP L UTS) +(-1267 -3508 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 (-562)))) @@ -5014,12 +5014,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1271 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})\\spad{*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) NIL (-1272 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4435 . T) (-4434 . T)) -((-3969 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3969 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3969 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4438 . T) (-4437 . T)) +((-3972 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-3972 (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-540)))) (-3972 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-551) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1107))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-1273 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -5050,13 +5050,13 @@ NIL NIL (-1280 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}."))) -((-4429 . T) (-4428 . T)) +((-4432 . T) (-4431 . T)) NIL (-1281 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]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1282 K R UP -3505) +(-1282 K R UP -3508) ((|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 @@ -5070,56 +5070,56 @@ NIL NIL (-1285 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: \\spad{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)"))) -((-4429 |has| |#1| (-173)) (-4428 |has| |#1| (-173)) (-4431 . T)) +((-4432 |has| |#1| (-173)) (-4431 |has| |#1| (-173)) (-4434 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-1286 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}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{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{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4435 . T) (-4434 . T)) +((-4438 . T) (-4437 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-540)))) (|HasCategory| |#4| (QUOTE (-1107))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-868))))) (-1287 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.\\spad{fr})"))) -((-4428 . T) (-4429 . T) (-4431 . T)) +((-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1288 |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."))) -((-4431 . T) (-4427 |has| |#2| (-6 -4427)) (-4429 . T) (-4428 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4427))) +((-4434 . T) (-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4430))) (-1289 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.\\spad{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 -(-1290 S -3505) +(-1290 S -3508) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1291 -3505) +(-1291 -3508) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) -((-4426 . T) (-4432 . T) (-4427 . T) ((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +((-4429 . T) (-4435 . T) (-4430 . T) ((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL (-1292 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4427 |has| |#2| (-6 -4427)) (-4429 . T) (-4428 . T) (-4431 . T)) +((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-1293 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4427 |has| |#2| (-6 -4427)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasAttribute| |#2| (QUOTE -4427))) +((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-551))))) (|HasAttribute| |#2| (QUOTE -4430))) (-1294 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."))) -((-4427 |has| |#1| (-6 -4427)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4427))) +((-4430 |has| |#1| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4430))) (-1295 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4427 |has| |#2| (-6 -4427)) (-4429 . T) (-4428 . T) (-4431 . T)) +((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) NIL (-1296 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4431 . T) (-4432 |has| |#1| (-6 -4432)) (-4427 |has| |#1| (-6 -4427)) (-4429 . T) (-4428 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4431)) (|HasAttribute| |#1| (QUOTE -4432)) (|HasAttribute| |#1| (QUOTE -4427))) +((-4434 . T) (-4435 |has| |#1| (-6 -4435)) (-4430 |has| |#1| (-6 -4430)) (-4432 . T) (-4431 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4434)) (|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4430))) (-1297 |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."))) -((-4427 |has| |#2| (-6 -4427)) (-4429 . T) (-4428 . T) (-4431 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4427))) +((-4430 |has| |#2| (-6 -4430)) (-4432 . T) (-4431 . T) (-4434 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4430))) (-1298 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL @@ -5134,7 +5134,7 @@ NIL NIL (-1301 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4436 "*") . T) (-4428 . T) (-4429 . T) (-4431 . T)) +(((-4439 "*") . T) (-4431 . T) (-4432 . T) (-4434 . T)) NIL NIL NIL @@ -5152,4 +5152,4 @@ NIL NIL NIL NIL -((-3 NIL 2264799 2264804 2264809 2264814) (-2 NIL 2264779 2264784 2264789 2264794) (-1 NIL 2264759 2264764 2264769 2264774) (0 NIL 2264739 2264744 2264749 2264754) (-1301 "ZMOD.spad" 2264548 2264561 2264677 2264734) (-1300 "ZLINDEP.spad" 2263614 2263625 2264538 2264543) (-1299 "ZDSOLVE.spad" 2253559 2253581 2263604 2263609) (-1298 "YSTREAM.spad" 2253054 2253065 2253549 2253554) (-1297 "XRPOLY.spad" 2252274 2252294 2252910 2252979) (-1296 "XPR.spad" 2250069 2250082 2251992 2252091) (-1295 "XPOLYC.spad" 2249388 2249404 2249995 2250064) (-1294 "XPOLY.spad" 2248943 2248954 2249244 2249313) (-1293 "XPBWPOLY.spad" 2247380 2247400 2248723 2248792) (-1292 "XFALG.spad" 2244428 2244444 2247306 2247375) (-1291 "XF.spad" 2242891 2242906 2244330 2244423) (-1290 "XF.spad" 2241334 2241351 2242775 2242780) (-1289 "XEXPPKG.spad" 2240585 2240611 2241324 2241329) (-1288 "XDPOLY.spad" 2240199 2240215 2240441 2240510) (-1287 "XALG.spad" 2239859 2239870 2240155 2240194) (-1286 "WUTSET.spad" 2235698 2235715 2239505 2239532) (-1285 "WP.spad" 2234897 2234941 2235556 2235623) (-1284 "WHILEAST.spad" 2234695 2234704 2234887 2234892) (-1283 "WHEREAST.spad" 2234366 2234375 2234685 2234690) (-1282 "WFFINTBS.spad" 2232029 2232051 2234356 2234361) (-1281 "WEIER.spad" 2230251 2230262 2232019 2232024) (-1280 "VSPACE.spad" 2229924 2229935 2230219 2230246) (-1279 "VSPACE.spad" 2229617 2229630 2229914 2229919) (-1278 "VOID.spad" 2229294 2229303 2229607 2229612) (-1277 "VIEWDEF.spad" 2224495 2224504 2229284 2229289) (-1276 "VIEW3D.spad" 2208456 2208465 2224485 2224490) (-1275 "VIEW2D.spad" 2196347 2196356 2208446 2208451) (-1274 "VIEW.spad" 2194027 2194036 2196337 2196342) (-1273 "VECTOR2.spad" 2192666 2192679 2194017 2194022) (-1272 "VECTOR.spad" 2191340 2191351 2191591 2191618) (-1271 "VECTCAT.spad" 2189244 2189255 2191308 2191335) (-1270 "VECTCAT.spad" 2186955 2186968 2189021 2189026) (-1269 "VARIABLE.spad" 2186735 2186750 2186945 2186950) (-1268 "UTYPE.spad" 2186379 2186388 2186725 2186730) (-1267 "UTSODETL.spad" 2185674 2185698 2186335 2186340) (-1266 "UTSODE.spad" 2183890 2183910 2185664 2185669) (-1265 "UTSCAT.spad" 2181369 2181385 2183788 2183885) (-1264 "UTSCAT.spad" 2178492 2178510 2180913 2180918) (-1263 "UTS2.spad" 2178087 2178122 2178482 2178487) (-1262 "UTS.spad" 2172891 2172919 2176554 2176651) (-1261 "URAGG.spad" 2167564 2167575 2172881 2172886) (-1260 "URAGG.spad" 2162201 2162214 2167520 2167525) (-1259 "UPXSSING.spad" 2159846 2159872 2161282 2161415) (-1258 "UPXSCONS.spad" 2157605 2157625 2157978 2158127) (-1257 "UPXSCCA.spad" 2156176 2156196 2157451 2157600) (-1256 "UPXSCCA.spad" 2154889 2154911 2156166 2156171) (-1255 "UPXSCAT.spad" 2153478 2153494 2154735 2154884) (-1254 "UPXS2.spad" 2153021 2153074 2153468 2153473) (-1253 "UPXS.spad" 2150175 2150203 2151153 2151302) (-1252 "UPSQFREE.spad" 2148590 2148604 2150165 2150170) (-1251 "UPSCAT.spad" 2146201 2146225 2148488 2148585) (-1250 "UPSCAT.spad" 2143518 2143544 2145807 2145812) (-1249 "UPOLYC2.spad" 2142989 2143008 2143508 2143513) (-1248 "UPOLYC.spad" 2138029 2138040 2142831 2142984) (-1247 "UPOLYC.spad" 2132961 2132974 2137765 2137770) (-1246 "UPMP.spad" 2131861 2131874 2132951 2132956) (-1245 "UPDIVP.spad" 2131426 2131440 2131851 2131856) (-1244 "UPDECOMP.spad" 2129671 2129685 2131416 2131421) (-1243 "UPCDEN.spad" 2128880 2128896 2129661 2129666) (-1242 "UP2.spad" 2128244 2128265 2128870 2128875) (-1241 "UP.spad" 2125443 2125458 2125830 2125983) (-1240 "UNISEG2.spad" 2124940 2124953 2125399 2125404) (-1239 "UNISEG.spad" 2124293 2124304 2124859 2124864) (-1238 "UNIFACT.spad" 2123396 2123408 2124283 2124288) (-1237 "ULSCONS.spad" 2115792 2115812 2116162 2116311) (-1236 "ULSCCAT.spad" 2113529 2113549 2115638 2115787) (-1235 "ULSCCAT.spad" 2111374 2111396 2113485 2113490) (-1234 "ULSCAT.spad" 2109606 2109622 2111220 2111369) (-1233 "ULS2.spad" 2109120 2109173 2109596 2109601) (-1232 "ULS.spad" 2099678 2099706 2100765 2101194) (-1231 "UINT8.spad" 2099555 2099564 2099668 2099673) (-1230 "UINT64.spad" 2099431 2099440 2099545 2099550) (-1229 "UINT32.spad" 2099307 2099316 2099421 2099426) (-1228 "UINT16.spad" 2099183 2099192 2099297 2099302) (-1227 "UFD.spad" 2098248 2098257 2099109 2099178) (-1226 "UFD.spad" 2097375 2097386 2098238 2098243) (-1225 "UDVO.spad" 2096256 2096265 2097365 2097370) (-1224 "UDPO.spad" 2093749 2093760 2096212 2096217) (-1223 "TYPEAST.spad" 2093668 2093677 2093739 2093744) (-1222 "TYPE.spad" 2093600 2093609 2093658 2093663) (-1221 "TWOFACT.spad" 2092252 2092267 2093590 2093595) (-1220 "TUPLE.spad" 2091738 2091749 2092151 2092156) (-1219 "TUBETOOL.spad" 2088605 2088614 2091728 2091733) (-1218 "TUBE.spad" 2087252 2087269 2088595 2088600) (-1217 "TSETCAT.spad" 2074379 2074396 2087220 2087247) (-1216 "TSETCAT.spad" 2061492 2061511 2074335 2074340) (-1215 "TS.spad" 2060091 2060107 2061057 2061154) (-1214 "TRMANIP.spad" 2054457 2054474 2059797 2059802) (-1213 "TRIMAT.spad" 2053420 2053445 2054447 2054452) (-1212 "TRIGMNIP.spad" 2051947 2051964 2053410 2053415) (-1211 "TRIGCAT.spad" 2051459 2051468 2051937 2051942) (-1210 "TRIGCAT.spad" 2050969 2050980 2051449 2051454) (-1209 "TREE.spad" 2049544 2049555 2050576 2050603) (-1208 "TRANFUN.spad" 2049383 2049392 2049534 2049539) (-1207 "TRANFUN.spad" 2049220 2049231 2049373 2049378) (-1206 "TOPSP.spad" 2048894 2048903 2049210 2049215) (-1205 "TOOLSIGN.spad" 2048557 2048568 2048884 2048889) (-1204 "TEXTFILE.spad" 2047118 2047127 2048547 2048552) (-1203 "TEX1.spad" 2046674 2046685 2047108 2047113) (-1202 "TEX.spad" 2043820 2043829 2046664 2046669) (-1201 "TEMUTL.spad" 2043375 2043384 2043810 2043815) (-1200 "TBCMPPK.spad" 2041468 2041491 2043365 2043370) (-1199 "TBAGG.spad" 2040518 2040541 2041448 2041463) (-1198 "TBAGG.spad" 2039576 2039601 2040508 2040513) (-1197 "TANEXP.spad" 2038984 2038995 2039566 2039571) (-1196 "TABLEAU.spad" 2038465 2038476 2038974 2038979) (-1195 "TABLE.spad" 2036876 2036899 2037146 2037173) (-1194 "TABLBUMP.spad" 2033679 2033690 2036866 2036871) (-1193 "SYSTEM.spad" 2032907 2032916 2033669 2033674) (-1192 "SYSSOLP.spad" 2030390 2030401 2032897 2032902) (-1191 "SYSPTR.spad" 2030289 2030298 2030380 2030385) (-1190 "SYSNNI.spad" 2029471 2029482 2030279 2030284) (-1189 "SYSINT.spad" 2028875 2028886 2029461 2029466) (-1188 "SYNTAX.spad" 2025081 2025090 2028865 2028870) (-1187 "SYMTAB.spad" 2023149 2023158 2025071 2025076) (-1186 "SYMS.spad" 2019178 2019187 2023139 2023144) (-1185 "SYMPOLY.spad" 2018185 2018196 2018267 2018394) (-1184 "SYMFUNC.spad" 2017686 2017697 2018175 2018180) (-1183 "SYMBOL.spad" 2015189 2015198 2017676 2017681) (-1182 "SWITCH.spad" 2011960 2011969 2015179 2015184) (-1181 "SUTS.spad" 2008865 2008893 2010427 2010524) (-1180 "SUPXS.spad" 2006006 2006034 2006997 2007146) (-1179 "SUPFRACF.spad" 2005111 2005129 2005996 2006001) (-1178 "SUP2.spad" 2004503 2004516 2005101 2005106) (-1177 "SUP.spad" 2001316 2001327 2002089 2002242) (-1176 "SUMRF.spad" 2000290 2000301 2001306 2001311) (-1175 "SUMFS.spad" 1999927 1999944 2000280 2000285) (-1174 "SULS.spad" 1990472 1990500 1991572 1992001) (-1173 "SUCHTAST.spad" 1990241 1990250 1990462 1990467) (-1172 "SUCH.spad" 1989923 1989938 1990231 1990236) (-1171 "SUBSPACE.spad" 1982038 1982053 1989913 1989918) (-1170 "SUBRESP.spad" 1981208 1981222 1981994 1981999) (-1169 "STTFNC.spad" 1977676 1977692 1981198 1981203) (-1168 "STTF.spad" 1973775 1973791 1977666 1977671) (-1167 "STTAYLOR.spad" 1966410 1966421 1973656 1973661) (-1166 "STRTBL.spad" 1964915 1964932 1965064 1965091) (-1165 "STRING.spad" 1964324 1964333 1964338 1964365) (-1164 "STRICAT.spad" 1964112 1964121 1964292 1964319) (-1163 "STREAM3.spad" 1963685 1963700 1964102 1964107) (-1162 "STREAM2.spad" 1962813 1962826 1963675 1963680) (-1161 "STREAM1.spad" 1962519 1962530 1962803 1962808) (-1160 "STREAM.spad" 1959437 1959448 1962044 1962059) (-1159 "STINPROD.spad" 1958373 1958389 1959427 1959432) (-1158 "STEPAST.spad" 1957607 1957616 1958363 1958368) (-1157 "STEP.spad" 1956808 1956817 1957597 1957602) (-1156 "STBL.spad" 1955334 1955362 1955501 1955516) (-1155 "STAGG.spad" 1954409 1954420 1955324 1955329) (-1154 "STAGG.spad" 1953482 1953495 1954399 1954404) (-1153 "STACK.spad" 1952839 1952850 1953089 1953116) (-1152 "SREGSET.spad" 1950543 1950560 1952485 1952512) (-1151 "SRDCMPK.spad" 1949104 1949124 1950533 1950538) (-1150 "SRAGG.spad" 1944247 1944256 1949072 1949099) (-1149 "SRAGG.spad" 1939410 1939421 1944237 1944242) (-1148 "SQMATRIX.spad" 1937026 1937044 1937942 1938029) (-1147 "SPLTREE.spad" 1931578 1931591 1936462 1936489) (-1146 "SPLNODE.spad" 1928166 1928179 1931568 1931573) (-1145 "SPFCAT.spad" 1926975 1926984 1928156 1928161) (-1144 "SPECOUT.spad" 1925527 1925536 1926965 1926970) (-1143 "SPADXPT.spad" 1917122 1917131 1925517 1925522) (-1142 "spad-parser.spad" 1916587 1916596 1917112 1917117) (-1141 "SPADAST.spad" 1916288 1916297 1916577 1916582) (-1140 "SPACEC.spad" 1900487 1900498 1916278 1916283) (-1139 "SPACE3.spad" 1900263 1900274 1900477 1900482) (-1138 "SORTPAK.spad" 1899812 1899825 1900219 1900224) (-1137 "SOLVETRA.spad" 1897575 1897586 1899802 1899807) (-1136 "SOLVESER.spad" 1896103 1896114 1897565 1897570) (-1135 "SOLVERAD.spad" 1892129 1892140 1896093 1896098) (-1134 "SOLVEFOR.spad" 1890591 1890609 1892119 1892124) (-1133 "SNTSCAT.spad" 1890191 1890208 1890559 1890586) (-1132 "SMTS.spad" 1888463 1888489 1889756 1889853) (-1131 "SMP.spad" 1885938 1885958 1886328 1886455) (-1130 "SMITH.spad" 1884783 1884808 1885928 1885933) (-1129 "SMATCAT.spad" 1882893 1882923 1884727 1884778) (-1128 "SMATCAT.spad" 1880935 1880967 1882771 1882776) (-1127 "SKAGG.spad" 1879898 1879909 1880903 1880930) (-1126 "SINT.spad" 1878730 1878739 1879764 1879893) (-1125 "SIMPAN.spad" 1878458 1878467 1878720 1878725) (-1124 "SIGNRF.spad" 1877583 1877594 1878448 1878453) (-1123 "SIGNEF.spad" 1876869 1876886 1877573 1877578) (-1122 "SIGAST.spad" 1876254 1876263 1876859 1876864) (-1121 "SIG.spad" 1875584 1875593 1876244 1876249) (-1120 "SHP.spad" 1873512 1873527 1875540 1875545) (-1119 "SHDP.spad" 1863223 1863250 1863732 1863863) (-1118 "SGROUP.spad" 1862831 1862840 1863213 1863218) (-1117 "SGROUP.spad" 1862437 1862448 1862821 1862826) (-1116 "SGCF.spad" 1855600 1855609 1862427 1862432) (-1115 "SFRTCAT.spad" 1854530 1854547 1855568 1855595) (-1114 "SFRGCD.spad" 1853593 1853613 1854520 1854525) (-1113 "SFQCMPK.spad" 1848230 1848250 1853583 1853588) (-1112 "SFORT.spad" 1847669 1847683 1848220 1848225) (-1111 "SEXOF.spad" 1847512 1847552 1847659 1847664) (-1110 "SEXCAT.spad" 1845113 1845153 1847502 1847507) (-1109 "SEX.spad" 1845005 1845014 1845103 1845108) (-1108 "SETMN.spad" 1843457 1843474 1844995 1845000) (-1107 "SETCAT.spad" 1842779 1842788 1843447 1843452) (-1106 "SETCAT.spad" 1842099 1842110 1842769 1842774) (-1105 "SETAGG.spad" 1838648 1838659 1842079 1842094) (-1104 "SETAGG.spad" 1835205 1835218 1838638 1838643) (-1103 "SET.spad" 1833529 1833540 1834626 1834665) (-1102 "SEQAST.spad" 1833232 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1428261) (-878 "PAIR.spad" 1426223 1426236 1426824 1426829) (-877 "PADICRC.spad" 1423557 1423575 1424728 1424821) (-876 "PADICRAT.spad" 1421572 1421584 1421793 1421886) (-875 "PADICCT.spad" 1420121 1420133 1421498 1421567) (-874 "PADIC.spad" 1419816 1419828 1420047 1420116) (-873 "PADEPAC.spad" 1418505 1418524 1419806 1419811) (-872 "PADE.spad" 1417257 1417273 1418495 1418500) (-871 "OWP.spad" 1416497 1416527 1417115 1417182) (-870 "OVERSET.spad" 1416070 1416078 1416487 1416492) (-869 "OVAR.spad" 1415851 1415874 1416060 1416065) (-868 "OUTFORM.spad" 1405243 1405251 1415841 1415846) (-867 "OUTBFILE.spad" 1404661 1404669 1405233 1405238) (-866 "OUTBCON.spad" 1403667 1403675 1404651 1404656) (-865 "OUTBCON.spad" 1402671 1402681 1403657 1403662) (-864 "OUT.spad" 1401757 1401765 1402661 1402666) (-863 "OSI.spad" 1401232 1401240 1401747 1401752) (-862 "OSGROUP.spad" 1401150 1401158 1401222 1401227) (-861 "ORTHPOL.spad" 1399635 1399645 1401067 1401072) (-860 "OREUP.spad" 1399088 1399116 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(-822 "ODR.spad" 1346969 1346995 1347137 1347286) (-821 "ODPOL.spad" 1344351 1344361 1344691 1344818) (-820 "ODP.spad" 1334198 1334218 1334571 1334702) (-819 "ODETOOLS.spad" 1332847 1332866 1334188 1334193) (-818 "ODESYS.spad" 1330541 1330558 1332837 1332842) (-817 "ODERTRIC.spad" 1326550 1326567 1330498 1330503) (-816 "ODERED.spad" 1325949 1325973 1326540 1326545) (-815 "ODERAT.spad" 1323566 1323583 1325939 1325944) (-814 "ODEPRRIC.spad" 1320603 1320625 1323556 1323561) (-813 "ODEPROB.spad" 1319860 1319868 1320593 1320598) (-812 "ODEPRIM.spad" 1317194 1317216 1319850 1319855) (-811 "ODEPAL.spad" 1316580 1316604 1317184 1317189) (-810 "ODEPACK.spad" 1303246 1303254 1316570 1316575) (-809 "ODEINT.spad" 1302681 1302697 1303236 1303241) (-808 "ODEIFTBL.spad" 1300076 1300084 1302671 1302676) (-807 "ODEEF.spad" 1295571 1295587 1300066 1300071) (-806 "ODECONST.spad" 1295108 1295126 1295561 1295566) (-805 "ODECAT.spad" 1293706 1293714 1295098 1295103) (-804 "OCTCT2.spad" 1293352 1293373 1293696 1293701) (-803 "OCT.spad" 1291488 1291498 1292202 1292241) (-802 "OCAMON.spad" 1291336 1291344 1291478 1291483) (-801 "OC.spad" 1289132 1289142 1291292 1291331) (-800 "OC.spad" 1286653 1286665 1288815 1288820) (-799 "OASGP.spad" 1286468 1286476 1286643 1286648) (-798 "OAMONS.spad" 1285990 1285998 1286458 1286463) (-797 "OAMON.spad" 1285851 1285859 1285980 1285985) (-796 "OAGROUP.spad" 1285713 1285721 1285841 1285846) (-795 "NUMTUBE.spad" 1285304 1285320 1285703 1285708) (-794 "NUMQUAD.spad" 1273280 1273288 1285294 1285299) (-793 "NUMODE.spad" 1264634 1264642 1273270 1273275) (-792 "NUMINT.spad" 1262200 1262208 1264624 1264629) (-791 "NUMFMT.spad" 1261040 1261048 1262190 1262195) (-790 "NUMERIC.spad" 1253154 1253164 1260845 1260850) (-789 "NTSCAT.spad" 1251662 1251678 1253122 1253149) (-788 "NTPOLFN.spad" 1251213 1251223 1251579 1251584) (-787 "NSUP2.spad" 1250605 1250617 1251203 1251208) (-786 "NSUP.spad" 1243651 1243661 1248191 1248344) (-785 "NSMP.spad" 1239882 1239901 1240190 1240317) (-784 "NREP.spad" 1238260 1238274 1239872 1239877) (-783 "NPCOEF.spad" 1237506 1237526 1238250 1238255) (-782 "NORMRETR.spad" 1237104 1237143 1237496 1237501) (-781 "NORMPK.spad" 1235006 1235025 1237094 1237099) (-780 "NORMMA.spad" 1234694 1234720 1234996 1235001) (-779 "NONE1.spad" 1234370 1234380 1234684 1234689) (-778 "NONE.spad" 1234111 1234119 1234360 1234365) (-777 "NODE1.spad" 1233598 1233614 1234101 1234106) (-776 "NNI.spad" 1232493 1232501 1233572 1233593) (-775 "NLINSOL.spad" 1231119 1231129 1232483 1232488) (-774 "NIPROB.spad" 1229660 1229668 1231109 1231114) (-773 "NFINTBAS.spad" 1227220 1227237 1229650 1229655) (-772 "NETCLT.spad" 1227194 1227205 1227210 1227215) (-771 "NCODIV.spad" 1225410 1225426 1227184 1227189) (-770 "NCNTFRAC.spad" 1225052 1225066 1225400 1225405) (-769 "NCEP.spad" 1223218 1223232 1225042 1225047) (-768 "NASRING.spad" 1222814 1222822 1223208 1223213) (-767 "NASRING.spad" 1222408 1222418 1222804 1222809) (-766 "NARNG.spad" 1221760 1221768 1222398 1222403) (-765 "NARNG.spad" 1221110 1221120 1221750 1221755) (-764 "NAGSP.spad" 1220187 1220195 1221100 1221105) (-763 "NAGS.spad" 1209848 1209856 1220177 1220182) (-762 "NAGF07.spad" 1208279 1208287 1209838 1209843) (-761 "NAGF04.spad" 1202681 1202689 1208269 1208274) (-760 "NAGF02.spad" 1196750 1196758 1202671 1202676) (-759 "NAGF01.spad" 1192511 1192519 1196740 1196745) (-758 "NAGE04.spad" 1186211 1186219 1192501 1192506) (-757 "NAGE02.spad" 1176871 1176879 1186201 1186206) (-756 "NAGE01.spad" 1172873 1172881 1176861 1176866) (-755 "NAGD03.spad" 1170877 1170885 1172863 1172868) (-754 "NAGD02.spad" 1163624 1163632 1170867 1170872) (-753 "NAGD01.spad" 1157917 1157925 1163614 1163619) (-752 "NAGC06.spad" 1153792 1153800 1157907 1157912) (-751 "NAGC05.spad" 1152293 1152301 1153782 1153787) (-750 "NAGC02.spad" 1151560 1151568 1152283 1152288) (-749 "NAALG.spad" 1151101 1151111 1151528 1151555) (-748 "NAALG.spad" 1150662 1150674 1151091 1151096) (-747 "MULTSQFR.spad" 1147620 1147637 1150652 1150657) (-746 "MULTFACT.spad" 1147003 1147020 1147610 1147615) (-745 "MTSCAT.spad" 1145097 1145118 1146901 1146998) (-744 "MTHING.spad" 1144756 1144766 1145087 1145092) (-743 "MSYSCMD.spad" 1144190 1144198 1144746 1144751) (-742 "MSETAGG.spad" 1144035 1144045 1144158 1144185) (-741 "MSET.spad" 1141993 1142003 1143741 1143780) (-740 "MRING.spad" 1138970 1138982 1141701 1141768) (-739 "MRF2.spad" 1138540 1138554 1138960 1138965) (-738 "MRATFAC.spad" 1138086 1138103 1138530 1138535) (-737 "MPRFF.spad" 1136126 1136145 1138076 1138081) (-736 "MPOLY.spad" 1133597 1133612 1133956 1134083) (-735 "MPCPF.spad" 1132861 1132880 1133587 1133592) (-734 "MPC3.spad" 1132678 1132718 1132851 1132856) (-733 "MPC2.spad" 1132324 1132357 1132668 1132673) (-732 "MONOTOOL.spad" 1130675 1130692 1132314 1132319) (-731 "MONOID.spad" 1129994 1130002 1130665 1130670) (-730 "MONOID.spad" 1129311 1129321 1129984 1129989) (-729 "MONOGEN.spad" 1128059 1128072 1129171 1129306) (-728 "MONOGEN.spad" 1126829 1126844 1127943 1127948) (-727 "MONADWU.spad" 1124859 1124867 1126819 1126824) (-726 "MONADWU.spad" 1122887 1122897 1124849 1124854) (-725 "MONAD.spad" 1122047 1122055 1122877 1122882) (-724 "MONAD.spad" 1121205 1121215 1122037 1122042) (-723 "MOEBIUS.spad" 1119941 1119955 1121185 1121200) (-722 "MODULE.spad" 1119811 1119821 1119909 1119936) (-721 "MODULE.spad" 1119701 1119713 1119801 1119806) (-720 "MODRING.spad" 1119036 1119075 1119681 1119696) (-719 "MODOP.spad" 1117701 1117713 1118858 1118925) (-718 "MODMONOM.spad" 1117432 1117450 1117691 1117696) (-717 "MODMON.spad" 1114227 1114243 1114946 1115099) (-716 "MODFIELD.spad" 1113589 1113628 1114129 1114222) (-715 "MMLFORM.spad" 1112449 1112457 1113579 1113584) (-714 "MMAP.spad" 1112191 1112225 1112439 1112444) (-713 "MLO.spad" 1110650 1110660 1112147 1112186) (-712 "MLIFT.spad" 1109262 1109279 1110640 1110645) (-711 "MKUCFUNC.spad" 1108797 1108815 1109252 1109257) (-710 "MKRECORD.spad" 1108401 1108414 1108787 1108792) (-709 "MKFUNC.spad" 1107808 1107818 1108391 1108396) (-708 "MKFLCFN.spad" 1106776 1106786 1107798 1107803) (-707 "MKBCFUNC.spad" 1106271 1106289 1106766 1106771) (-706 "MINT.spad" 1105710 1105718 1106173 1106266) (-705 "MHROWRED.spad" 1104221 1104231 1105700 1105705) (-704 "MFLOAT.spad" 1102741 1102749 1104111 1104216) (-703 "MFINFACT.spad" 1102141 1102163 1102731 1102736) (-702 "MESH.spad" 1099928 1099936 1102131 1102136) (-701 "MDDFACT.spad" 1098139 1098149 1099918 1099923) (-700 "MDAGG.spad" 1097430 1097440 1098119 1098134) (-699 "MCMPLX.spad" 1093441 1093449 1094055 1094256) (-698 "MCDEN.spad" 1092651 1092663 1093431 1093436) (-697 "MCALCFN.spad" 1089773 1089799 1092641 1092646) (-696 "MAYBE.spad" 1089057 1089068 1089763 1089768) (-695 "MATSTOR.spad" 1086365 1086375 1089047 1089052) (-694 "MATRIX.spad" 1085069 1085079 1085553 1085580) (-693 "MATLIN.spad" 1082413 1082437 1084953 1084958) (-692 "MATCAT2.spad" 1081695 1081743 1082403 1082408) (-691 "MATCAT.spad" 1073424 1073446 1081663 1081690) (-690 "MATCAT.spad" 1065025 1065049 1073266 1073271) (-689 "MAPPKG3.spad" 1063940 1063954 1065015 1065020) (-688 "MAPPKG2.spad" 1063278 1063290 1063930 1063935) (-687 "MAPPKG1.spad" 1062106 1062116 1063268 1063273) (-686 "MAPPAST.spad" 1061421 1061429 1062096 1062101) (-685 "MAPHACK3.spad" 1061233 1061247 1061411 1061416) (-684 "MAPHACK2.spad" 1061002 1061014 1061223 1061228) (-683 "MAPHACK1.spad" 1060646 1060656 1060992 1060997) (-682 "MAGMA.spad" 1058436 1058453 1060636 1060641) (-681 "MACROAST.spad" 1058015 1058023 1058426 1058431) (-680 "M3D.spad" 1055735 1055745 1057393 1057398) (-679 "LZSTAGG.spad" 1052973 1052983 1055725 1055730) (-678 "LZSTAGG.spad" 1050209 1050221 1052963 1052968) (-677 "LWORD.spad" 1046914 1046931 1050199 1050204) (-676 "LSTAST.spad" 1046698 1046706 1046904 1046909) (-675 "LSQM.spad" 1044925 1044939 1045319 1045370) (-674 "LSPP.spad" 1044460 1044477 1044915 1044920) (-673 "LSMP1.spad" 1042295 1042309 1044450 1044455) (-672 "LSMP.spad" 1041152 1041180 1042285 1042290) (-671 "LSAGG.spad" 1040821 1040831 1041120 1041147) (-670 "LSAGG.spad" 1040510 1040522 1040811 1040816) (-669 "LPOLY.spad" 1039464 1039483 1040366 1040435) (-668 "LPEFRAC.spad" 1038735 1038745 1039454 1039459) (-667 "LOGIC.spad" 1038337 1038345 1038725 1038730) (-666 "LOGIC.spad" 1037937 1037947 1038327 1038332) (-665 "LODOOPS.spad" 1036867 1036879 1037927 1037932) (-664 "LODOF.spad" 1035913 1035930 1036824 1036829) (-663 "LODOCAT.spad" 1034579 1034589 1035869 1035908) (-662 "LODOCAT.spad" 1033243 1033255 1034535 1034540) (-661 "LODO2.spad" 1032516 1032528 1032923 1032962) (-660 "LODO1.spad" 1031916 1031926 1032196 1032235) (-659 "LODO.spad" 1031300 1031316 1031596 1031635) (-658 "LODEEF.spad" 1030102 1030120 1031290 1031295) (-657 "LO.spad" 1029503 1029517 1030036 1030063) (-656 "LNAGG.spad" 1025335 1025345 1029493 1029498) (-655 "LNAGG.spad" 1021131 1021143 1025291 1025296) (-654 "LMOPS.spad" 1017899 1017916 1021121 1021126) (-653 "LMODULE.spad" 1017667 1017677 1017889 1017894) (-652 "LMDICT.spad" 1016954 1016964 1017218 1017245) (-651 "LLINSET.spad" 1016351 1016361 1016944 1016949) (-650 "LITERAL.spad" 1016257 1016268 1016341 1016346) (-649 "LIST3.spad" 1015568 1015582 1016247 1016252) (-648 "LIST2MAP.spad" 1012471 1012483 1015558 1015563) (-647 "LIST2.spad" 1011173 1011185 1012461 1012466) (-646 "LIST.spad" 1008908 1008918 1010320 1010347) (-645 "LINSET.spad" 1008530 1008540 1008898 1008903) (-644 "LINEXP.spad" 1007964 1007974 1008510 1008525) (-643 "LINDEP.spad" 1006773 1006785 1007876 1007881) (-642 "LIMITRF.spad" 1004720 1004730 1006763 1006768) (-641 "LIMITPS.spad" 1003630 1003643 1004710 1004715) (-640 "LIECAT.spad" 1003106 1003116 1003556 1003625) (-639 "LIECAT.spad" 1002610 1002622 1003062 1003067) (-638 "LIE.spad" 1000626 1000638 1001900 1002045) (-637 "LIB.spad" 998676 998684 999285 999300) (-636 "LGROBP.spad" 996029 996048 998666 998671) (-635 "LFCAT.spad" 995088 995096 996019 996024) (-634 "LF.spad" 994043 994059 995078 995083) (-633 "LEXTRIPK.spad" 989546 989561 994033 994038) (-632 "LEXP.spad" 987549 987576 989526 989541) (-631 "LETAST.spad" 987248 987256 987539 987544) (-630 "LEADCDET.spad" 985646 985663 987238 987243) (-629 "LAZM3PK.spad" 984350 984372 985636 985641) (-628 "LAUPOL.spad" 983043 983056 983943 984012) (-627 "LAPLACE.spad" 982626 982642 983033 983038) (-626 "LALG.spad" 982402 982412 982606 982621) (-625 "LALG.spad" 982186 982198 982392 982397) (-624 "LA.spad" 981626 981640 982108 982147) (-623 "KVTFROM.spad" 981361 981371 981616 981621) (-622 "KTVLOGIC.spad" 980873 980881 981351 981356) (-621 "KRCFROM.spad" 980611 980621 980863 980868) (-620 "KOVACIC.spad" 979334 979351 980601 980606) (-619 "KONVERT.spad" 979056 979066 979324 979329) (-618 "KOERCE.spad" 978793 978803 979046 979051) (-617 "KERNEL2.spad" 978496 978508 978783 978788) (-616 "KERNEL.spad" 977151 977161 978280 978285) (-615 "KDAGG.spad" 976260 976282 977131 977146) (-614 "KDAGG.spad" 975377 975401 976250 976255) (-613 "KAFILE.spad" 974340 974356 974575 974602) (-612 "JORDAN.spad" 972169 972181 973630 973775) (-611 "JOINAST.spad" 971863 971871 972159 972164) (-610 "JAVACODE.spad" 971729 971737 971853 971858) (-609 "IXAGG.spad" 969862 969886 971719 971724) (-608 "IXAGG.spad" 967850 967876 969709 969714) (-607 "IVECTOR.spad" 966620 966635 966775 966802) (-606 "ITUPLE.spad" 965781 965791 966610 966615) (-605 "ITRIGMNP.spad" 964620 964639 965771 965776) (-604 "ITFUN3.spad" 964126 964140 964610 964615) (-603 "ITFUN2.spad" 963870 963882 964116 964121) (-602 "ITFORM.spad" 963764 963772 963860 963865) (-601 "ITAYLOR.spad" 961758 961773 963628 963725) (-600 "ISUPS.spad" 954195 954210 960732 960829) (-599 "ISUMP.spad" 953696 953712 954185 954190) (-598 "ISTRING.spad" 952784 952797 952865 952892) (-597 "ISAST.spad" 952503 952511 952774 952779) (-596 "IRURPK.spad" 951220 951239 952493 952498) (-595 "IRSN.spad" 949224 949232 951210 951215) (-594 "IRRF2F.spad" 947709 947719 949180 949185) (-593 "IRREDFFX.spad" 947310 947321 947699 947704) (-592 "IROOT.spad" 945649 945659 947300 947305) (-591 "IRFORM.spad" 945497 945505 945639 945644) (-590 "IR2F.spad" 944703 944719 945487 945492) (-589 "IR2.spad" 943731 943747 944693 944698) (-588 "IR.spad" 941532 941546 943586 943613) (-587 "IPRNTPK.spad" 941292 941300 941522 941527) (-586 "IPF.spad" 940857 940869 941097 941190) (-585 "IPADIC.spad" 940618 940644 940783 940852) (-584 "IP4ADDR.spad" 940175 940183 940608 940613) (-583 "IOMODE.spad" 939796 939804 940165 940170) (-582 "IOBFILE.spad" 939157 939165 939786 939791) (-581 "IOBCON.spad" 939022 939030 939147 939152) (-580 "INVLAPLA.spad" 938671 938687 939012 939017) (-579 "INTTR.spad" 932065 932082 938661 938666) (-578 "INTTOOLS.spad" 929820 929836 931639 931644) (-577 "INTSLPE.spad" 929140 929148 929810 929815) (-576 "INTRVL.spad" 928706 928716 929054 929135) (-575 "INTRF.spad" 927130 927144 928696 928701) (-574 "INTRET.spad" 926562 926572 927120 927125) (-573 "INTRAT.spad" 925289 925306 926552 926557) (-572 "INTPM.spad" 923674 923690 924932 924937) (-571 "INTPAF.spad" 921545 921563 923606 923611) (-570 "INTPACK.spad" 911919 911927 921535 921540) (-569 "INTHERTR.spad" 911193 911210 911909 911914) (-568 "INTHERAL.spad" 910863 910887 911183 911188) (-567 "INTHEORY.spad" 907302 907310 910853 910858) (-566 "INTG0.spad" 901053 901071 907234 907239) (-565 "INTFTBL.spad" 896507 896515 901043 901048) (-564 "INTFACT.spad" 895566 895576 896497 896502) (-563 "INTEF.spad" 893953 893969 895556 895561) (-562 "INTDOM.spad" 892576 892584 893879 893948) (-561 "INTDOM.spad" 891261 891271 892566 892571) (-560 "INTCAT.spad" 889520 889530 891175 891256) (-559 "INTBIT.spad" 889027 889035 889510 889515) (-558 "INTALG.spad" 888215 888242 889017 889022) (-557 "INTAF.spad" 887715 887731 888205 888210) (-556 "INTABL.spad" 886233 886264 886396 886423) (-555 "INT8.spad" 886113 886121 886223 886228) (-554 "INT64.spad" 885992 886000 886103 886108) (-553 "INT32.spad" 885871 885879 885982 885987) (-552 "INT16.spad" 885750 885758 885861 885866) (-551 "INT.spad" 885198 885206 885604 885745) (-550 "INS.spad" 882701 882709 885100 885193) (-549 "INS.spad" 880290 880300 882691 882696) (-548 "INPSIGN.spad" 879760 879773 880280 880285) (-547 "INPRODPF.spad" 878856 878875 879750 879755) (-546 "INPRODFF.spad" 877944 877968 878846 878851) (-545 "INNMFACT.spad" 876919 876936 877934 877939) (-544 "INMODGCD.spad" 876407 876437 876909 876914) (-543 "INFSP.spad" 874704 874726 876397 876402) (-542 "INFPROD0.spad" 873784 873803 874694 874699) (-541 "INFORM1.spad" 873409 873419 873774 873779) (-540 "INFORM.spad" 870608 870616 873399 873404) (-539 "INFINITY.spad" 870160 870168 870598 870603) (-538 "INETCLTS.spad" 870137 870145 870150 870155) (-537 "INEP.spad" 868675 868697 870127 870132) (-536 "INDE.spad" 868404 868421 868665 868670) (-535 "INCRMAPS.spad" 867825 867835 868394 868399) (-534 "INBFILE.spad" 866897 866905 867815 867820) (-533 "INBFF.spad" 862691 862702 866887 866892) (-532 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"CTORCALL.spad" 215585 215595 215986 215991) (-184 "CTOR.spad" 215276 215284 215575 215580) (-183 "CSTTOOLS.spad" 214521 214534 215266 215271) (-182 "CRFP.spad" 208245 208258 214511 214516) (-181 "CRCEAST.spad" 207965 207973 208235 208240) (-180 "CRAPACK.spad" 207016 207026 207955 207960) (-179 "CPMATCH.spad" 206520 206535 206941 206946) (-178 "CPIMA.spad" 206225 206244 206510 206515) (-177 "COORDSYS.spad" 201234 201244 206215 206220) (-176 "CONTOUR.spad" 200645 200653 201224 201229) (-175 "CONTFRAC.spad" 196395 196405 200547 200640) (-174 "CONDUIT.spad" 196153 196161 196385 196390) (-173 "COMRING.spad" 195827 195835 196091 196148) (-172 "COMPPROP.spad" 195345 195353 195817 195822) (-171 "COMPLPAT.spad" 195112 195127 195335 195340) (-170 "COMPLEX2.spad" 194827 194839 195102 195107) (-169 "COMPLEX.spad" 188964 188974 189208 189469) (-168 "COMPILER.spad" 188528 188536 188954 188959) (-167 "COMPFACT.spad" 188130 188144 188518 188523) (-166 "COMPCAT.spad" 186202 186212 187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMMAAST.spad" 183046 183054 183273 183278) (-161 "COMM.spad" 182857 182865 183036 183041) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN2.spad" 152290 152317 152890 152895) (-135 "CARTEN.spad" 147577 147601 152280 152285) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTEBUF.spad" 141359 141367 142669 142696) (-128 "BYTE.spad" 140786 140794 141349 141354) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP1.spad" 125493 125503 128017 128022) (-113 "BOP.spad" 120675 120683 125483 125488) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP80.spad" 96764 96777 97432 97437) (-87 "ASP8.spad" 95807 95820 96754 96759) (-86 "ASP78.spad" 95258 95271 95797 95802) (-85 "ASP77.spad" 94627 94640 95248 95253) (-84 "ASP74.spad" 93719 93732 94617 94622) (-83 "ASP73.spad" 92990 93003 93709 93714) (-82 "ASP7.spad" 92150 92163 92980 92985) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP49.spad" 86342 86355 87333 87338) (-77 "ASP42.spad" 84749 84788 86332 86337) (-76 "ASP41.spad" 83328 83367 84739 84744) (-75 "ASP4.spad" 82623 82636 83318 83323) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP19.spad" 61377 61390 66681 66686) (-63 "ASP12.spad" 60791 60804 61367 61372) (-62 "ASP10.spad" 60062 60075 60781 60786) (-61 "ASP1.spad" 59443 59456 60052 60057) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY12.spad" 57516 57527 58793 58798) (-58 "ARRAY1.spad" 56353 56362 56699 56726) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY1.spad" 45243 45252 46162 46167) (-51 "ANY.spad" 44102 44109 45233 45238) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2265121 2265126 2265131 2265136) (-2 NIL 2265101 2265106 2265111 2265116) (-1 NIL 2265081 2265086 2265091 2265096) (0 NIL 2265061 2265066 2265071 2265076) (-1301 "ZMOD.spad" 2264870 2264883 2264999 2265056) (-1300 "ZLINDEP.spad" 2263936 2263947 2264860 2264865) (-1299 "ZDSOLVE.spad" 2253881 2253903 2263926 2263931) (-1298 "YSTREAM.spad" 2253376 2253387 2253871 2253876) (-1297 "XRPOLY.spad" 2252596 2252616 2253232 2253301) (-1296 "XPR.spad" 2250391 2250404 2252314 2252413) (-1295 "XPOLYC.spad" 2249710 2249726 2250317 2250386) (-1294 "XPOLY.spad" 2249265 2249276 2249566 2249635) (-1293 "XPBWPOLY.spad" 2247702 2247722 2249045 2249114) (-1292 "XFALG.spad" 2244750 2244766 2247628 2247697) (-1291 "XF.spad" 2243213 2243228 2244652 2244745) (-1290 "XF.spad" 2241656 2241673 2243097 2243102) (-1289 "XEXPPKG.spad" 2240907 2240933 2241646 2241651) (-1288 "XDPOLY.spad" 2240521 2240537 2240763 2240832) (-1287 "XALG.spad" 2240181 2240192 2240477 2240516) (-1286 "WUTSET.spad" 2236020 2236037 2239827 2239854) (-1285 "WP.spad" 2235219 2235263 2235878 2235945) (-1284 "WHILEAST.spad" 2235017 2235026 2235209 2235214) (-1283 "WHEREAST.spad" 2234688 2234697 2235007 2235012) (-1282 "WFFINTBS.spad" 2232351 2232373 2234678 2234683) (-1281 "WEIER.spad" 2230573 2230584 2232341 2232346) (-1280 "VSPACE.spad" 2230246 2230257 2230541 2230568) (-1279 "VSPACE.spad" 2229939 2229952 2230236 2230241) (-1278 "VOID.spad" 2229616 2229625 2229929 2229934) (-1277 "VIEWDEF.spad" 2224817 2224826 2229606 2229611) (-1276 "VIEW3D.spad" 2208778 2208787 2224807 2224812) (-1275 "VIEW2D.spad" 2196669 2196678 2208768 2208773) (-1274 "VIEW.spad" 2194349 2194358 2196659 2196664) (-1273 "VECTOR2.spad" 2192988 2193001 2194339 2194344) (-1272 "VECTOR.spad" 2191662 2191673 2191913 2191940) (-1271 "VECTCAT.spad" 2189566 2189577 2191630 2191657) (-1270 "VECTCAT.spad" 2187277 2187290 2189343 2189348) (-1269 "VARIABLE.spad" 2187057 2187072 2187267 2187272) (-1268 "UTYPE.spad" 2186701 2186710 2187047 2187052) (-1267 "UTSODETL.spad" 2185996 2186020 2186657 2186662) (-1266 "UTSODE.spad" 2184212 2184232 2185986 2185991) (-1265 "UTSCAT.spad" 2181691 2181707 2184110 2184207) (-1264 "UTSCAT.spad" 2178814 2178832 2181235 2181240) (-1263 "UTS2.spad" 2178409 2178444 2178804 2178809) (-1262 "UTS.spad" 2173213 2173241 2176876 2176973) (-1261 "URAGG.spad" 2167886 2167897 2173203 2173208) (-1260 "URAGG.spad" 2162523 2162536 2167842 2167847) (-1259 "UPXSSING.spad" 2160168 2160194 2161604 2161737) (-1258 "UPXSCONS.spad" 2157927 2157947 2158300 2158449) (-1257 "UPXSCCA.spad" 2156498 2156518 2157773 2157922) (-1256 "UPXSCCA.spad" 2155211 2155233 2156488 2156493) (-1255 "UPXSCAT.spad" 2153800 2153816 2155057 2155206) (-1254 "UPXS2.spad" 2153343 2153396 2153790 2153795) (-1253 "UPXS.spad" 2150497 2150525 2151475 2151624) (-1252 "UPSQFREE.spad" 2148912 2148926 2150487 2150492) (-1251 "UPSCAT.spad" 2146523 2146547 2148810 2148907) (-1250 "UPSCAT.spad" 2143840 2143866 2146129 2146134) (-1249 "UPOLYC2.spad" 2143311 2143330 2143830 2143835) (-1248 "UPOLYC.spad" 2138351 2138362 2143153 2143306) (-1247 "UPOLYC.spad" 2133283 2133296 2138087 2138092) (-1246 "UPMP.spad" 2132183 2132196 2133273 2133278) (-1245 "UPDIVP.spad" 2131748 2131762 2132173 2132178) (-1244 "UPDECOMP.spad" 2129993 2130007 2131738 2131743) (-1243 "UPCDEN.spad" 2129202 2129218 2129983 2129988) (-1242 "UP2.spad" 2128566 2128587 2129192 2129197) (-1241 "UP.spad" 2125765 2125780 2126152 2126305) (-1240 "UNISEG2.spad" 2125262 2125275 2125721 2125726) (-1239 "UNISEG.spad" 2124615 2124626 2125181 2125186) (-1238 "UNIFACT.spad" 2123718 2123730 2124605 2124610) (-1237 "ULSCONS.spad" 2116114 2116134 2116484 2116633) (-1236 "ULSCCAT.spad" 2113851 2113871 2115960 2116109) (-1235 "ULSCCAT.spad" 2111696 2111718 2113807 2113812) (-1234 "ULSCAT.spad" 2109928 2109944 2111542 2111691) (-1233 "ULS2.spad" 2109442 2109495 2109918 2109923) (-1232 "ULS.spad" 2100000 2100028 2101087 2101516) (-1231 "UINT8.spad" 2099877 2099886 2099990 2099995) (-1230 "UINT64.spad" 2099753 2099762 2099867 2099872) (-1229 "UINT32.spad" 2099629 2099638 2099743 2099748) (-1228 "UINT16.spad" 2099505 2099514 2099619 2099624) (-1227 "UFD.spad" 2098570 2098579 2099431 2099500) (-1226 "UFD.spad" 2097697 2097708 2098560 2098565) (-1225 "UDVO.spad" 2096578 2096587 2097687 2097692) (-1224 "UDPO.spad" 2094071 2094082 2096534 2096539) (-1223 "TYPEAST.spad" 2093990 2093999 2094061 2094066) (-1222 "TYPE.spad" 2093922 2093931 2093980 2093985) (-1221 "TWOFACT.spad" 2092574 2092589 2093912 2093917) (-1220 "TUPLE.spad" 2092060 2092071 2092473 2092478) (-1219 "TUBETOOL.spad" 2088927 2088936 2092050 2092055) (-1218 "TUBE.spad" 2087574 2087591 2088917 2088922) (-1217 "TSETCAT.spad" 2074701 2074718 2087542 2087569) (-1216 "TSETCAT.spad" 2061814 2061833 2074657 2074662) (-1215 "TS.spad" 2060413 2060429 2061379 2061476) (-1214 "TRMANIP.spad" 2054779 2054796 2060119 2060124) (-1213 "TRIMAT.spad" 2053742 2053767 2054769 2054774) (-1212 "TRIGMNIP.spad" 2052269 2052286 2053732 2053737) (-1211 "TRIGCAT.spad" 2051781 2051790 2052259 2052264) (-1210 "TRIGCAT.spad" 2051291 2051302 2051771 2051776) (-1209 "TREE.spad" 2049866 2049877 2050898 2050925) (-1208 "TRANFUN.spad" 2049705 2049714 2049856 2049861) (-1207 "TRANFUN.spad" 2049542 2049553 2049695 2049700) (-1206 "TOPSP.spad" 2049216 2049225 2049532 2049537) (-1205 "TOOLSIGN.spad" 2048879 2048890 2049206 2049211) (-1204 "TEXTFILE.spad" 2047440 2047449 2048869 2048874) (-1203 "TEX1.spad" 2046996 2047007 2047430 2047435) (-1202 "TEX.spad" 2044142 2044151 2046986 2046991) (-1201 "TEMUTL.spad" 2043697 2043706 2044132 2044137) (-1200 "TBCMPPK.spad" 2041790 2041813 2043687 2043692) (-1199 "TBAGG.spad" 2040840 2040863 2041770 2041785) (-1198 "TBAGG.spad" 2039898 2039923 2040830 2040835) (-1197 "TANEXP.spad" 2039306 2039317 2039888 2039893) (-1196 "TABLEAU.spad" 2038787 2038798 2039296 2039301) (-1195 "TABLE.spad" 2037198 2037221 2037468 2037495) (-1194 "TABLBUMP.spad" 2034001 2034012 2037188 2037193) (-1193 "SYSTEM.spad" 2033229 2033238 2033991 2033996) (-1192 "SYSSOLP.spad" 2030712 2030723 2033219 2033224) (-1191 "SYSPTR.spad" 2030611 2030620 2030702 2030707) (-1190 "SYSNNI.spad" 2029793 2029804 2030601 2030606) (-1189 "SYSINT.spad" 2029197 2029208 2029783 2029788) (-1188 "SYNTAX.spad" 2025403 2025412 2029187 2029192) (-1187 "SYMTAB.spad" 2023471 2023480 2025393 2025398) (-1186 "SYMS.spad" 2019500 2019509 2023461 2023466) (-1185 "SYMPOLY.spad" 2018507 2018518 2018589 2018716) (-1184 "SYMFUNC.spad" 2018008 2018019 2018497 2018502) (-1183 "SYMBOL.spad" 2015511 2015520 2017998 2018003) (-1182 "SWITCH.spad" 2012282 2012291 2015501 2015506) (-1181 "SUTS.spad" 2009187 2009215 2010749 2010846) (-1180 "SUPXS.spad" 2006328 2006356 2007319 2007468) (-1179 "SUPFRACF.spad" 2005433 2005451 2006318 2006323) (-1178 "SUP2.spad" 2004825 2004838 2005423 2005428) (-1177 "SUP.spad" 2001638 2001649 2002411 2002564) (-1176 "SUMRF.spad" 2000612 2000623 2001628 2001633) (-1175 "SUMFS.spad" 2000249 2000266 2000602 2000607) (-1174 "SULS.spad" 1990794 1990822 1991894 1992323) (-1173 "SUCHTAST.spad" 1990563 1990572 1990784 1990789) (-1172 "SUCH.spad" 1990245 1990260 1990553 1990558) (-1171 "SUBSPACE.spad" 1982360 1982375 1990235 1990240) (-1170 "SUBRESP.spad" 1981530 1981544 1982316 1982321) (-1169 "STTFNC.spad" 1977998 1978014 1981520 1981525) (-1168 "STTF.spad" 1974097 1974113 1977988 1977993) (-1167 "STTAYLOR.spad" 1966732 1966743 1973978 1973983) (-1166 "STRTBL.spad" 1965237 1965254 1965386 1965413) (-1165 "STRING.spad" 1964646 1964655 1964660 1964687) (-1164 "STRICAT.spad" 1964434 1964443 1964614 1964641) (-1163 "STREAM3.spad" 1964007 1964022 1964424 1964429) (-1162 "STREAM2.spad" 1963135 1963148 1963997 1964002) (-1161 "STREAM1.spad" 1962841 1962852 1963125 1963130) (-1160 "STREAM.spad" 1959759 1959770 1962366 1962381) (-1159 "STINPROD.spad" 1958695 1958711 1959749 1959754) (-1158 "STEPAST.spad" 1957929 1957938 1958685 1958690) (-1157 "STEP.spad" 1957130 1957139 1957919 1957924) (-1156 "STBL.spad" 1955656 1955684 1955823 1955838) (-1155 "STAGG.spad" 1954731 1954742 1955646 1955651) (-1154 "STAGG.spad" 1953804 1953817 1954721 1954726) (-1153 "STACK.spad" 1953161 1953172 1953411 1953438) (-1152 "SREGSET.spad" 1950865 1950882 1952807 1952834) (-1151 "SRDCMPK.spad" 1949426 1949446 1950855 1950860) (-1150 "SRAGG.spad" 1944569 1944578 1949394 1949421) (-1149 "SRAGG.spad" 1939732 1939743 1944559 1944564) (-1148 "SQMATRIX.spad" 1937348 1937366 1938264 1938351) (-1147 "SPLTREE.spad" 1931900 1931913 1936784 1936811) (-1146 "SPLNODE.spad" 1928488 1928501 1931890 1931895) (-1145 "SPFCAT.spad" 1927297 1927306 1928478 1928483) (-1144 "SPECOUT.spad" 1925849 1925858 1927287 1927292) (-1143 "SPADXPT.spad" 1917444 1917453 1925839 1925844) (-1142 "spad-parser.spad" 1916909 1916918 1917434 1917439) (-1141 "SPADAST.spad" 1916610 1916619 1916899 1916904) (-1140 "SPACEC.spad" 1900809 1900820 1916600 1916605) (-1139 "SPACE3.spad" 1900585 1900596 1900799 1900804) (-1138 "SORTPAK.spad" 1900134 1900147 1900541 1900546) (-1137 "SOLVETRA.spad" 1897897 1897908 1900124 1900129) (-1136 "SOLVESER.spad" 1896425 1896436 1897887 1897892) (-1135 "SOLVERAD.spad" 1892451 1892462 1896415 1896420) (-1134 "SOLVEFOR.spad" 1890913 1890931 1892441 1892446) (-1133 "SNTSCAT.spad" 1890513 1890530 1890881 1890908) (-1132 "SMTS.spad" 1888785 1888811 1890078 1890175) (-1131 "SMP.spad" 1886260 1886280 1886650 1886777) (-1130 "SMITH.spad" 1885105 1885130 1886250 1886255) (-1129 "SMATCAT.spad" 1883215 1883245 1885049 1885100) (-1128 "SMATCAT.spad" 1881257 1881289 1883093 1883098) (-1127 "SKAGG.spad" 1880220 1880231 1881225 1881252) (-1126 "SINT.spad" 1879052 1879061 1880086 1880215) (-1125 "SIMPAN.spad" 1878780 1878789 1879042 1879047) (-1124 "SIGNRF.spad" 1877905 1877916 1878770 1878775) (-1123 "SIGNEF.spad" 1877191 1877208 1877895 1877900) (-1122 "SIGAST.spad" 1876576 1876585 1877181 1877186) (-1121 "SIG.spad" 1875906 1875915 1876566 1876571) (-1120 "SHP.spad" 1873834 1873849 1875862 1875867) (-1119 "SHDP.spad" 1863545 1863572 1864054 1864185) (-1118 "SGROUP.spad" 1863153 1863162 1863535 1863540) (-1117 "SGROUP.spad" 1862759 1862770 1863143 1863148) (-1116 "SGCF.spad" 1855922 1855931 1862749 1862754) (-1115 "SFRTCAT.spad" 1854852 1854869 1855890 1855917) (-1114 "SFRGCD.spad" 1853915 1853935 1854842 1854847) (-1113 "SFQCMPK.spad" 1848552 1848572 1853905 1853910) (-1112 "SFORT.spad" 1847991 1848005 1848542 1848547) (-1111 "SEXOF.spad" 1847834 1847874 1847981 1847986) (-1110 "SEXCAT.spad" 1845435 1845475 1847824 1847829) (-1109 "SEX.spad" 1845327 1845336 1845425 1845430) (-1108 "SETMN.spad" 1843779 1843796 1845317 1845322) (-1107 "SETCAT.spad" 1843101 1843110 1843769 1843774) (-1106 "SETCAT.spad" 1842421 1842432 1843091 1843096) (-1105 "SETAGG.spad" 1838970 1838981 1842401 1842416) (-1104 "SETAGG.spad" 1835527 1835540 1838960 1838965) (-1103 "SET.spad" 1833851 1833862 1834948 1834987) (-1102 "SEQAST.spad" 1833554 1833563 1833841 1833846) (-1101 "SEGXCAT.spad" 1832710 1832723 1833544 1833549) (-1100 "SEGCAT.spad" 1831635 1831646 1832700 1832705) (-1099 "SEGBIND2.spad" 1831333 1831346 1831625 1831630) (-1098 "SEGBIND.spad" 1831091 1831102 1831280 1831285) (-1097 "SEGAST.spad" 1830805 1830814 1831081 1831086) (-1096 "SEG2.spad" 1830240 1830253 1830761 1830766) (-1095 "SEG.spad" 1830053 1830064 1830159 1830164) (-1094 "SDVAR.spad" 1829329 1829340 1830043 1830048) (-1093 "SDPOL.spad" 1826755 1826766 1827046 1827173) (-1092 "SCPKG.spad" 1824844 1824855 1826745 1826750) (-1091 "SCOPE.spad" 1823997 1824006 1824834 1824839) (-1090 "SCACHE.spad" 1822693 1822704 1823987 1823992) (-1089 "SASTCAT.spad" 1822602 1822611 1822683 1822688) (-1088 "SAOS.spad" 1822474 1822483 1822592 1822597) (-1087 "SAERFFC.spad" 1822187 1822207 1822464 1822469) (-1086 "SAEFACT.spad" 1821888 1821908 1822177 1822182) (-1085 "SAE.spad" 1820063 1820079 1820674 1820809) (-1084 "RURPK.spad" 1817722 1817738 1820053 1820058) (-1083 "RULESET.spad" 1817175 1817199 1817712 1817717) (-1082 "RULECOLD.spad" 1817027 1817040 1817165 1817170) (-1081 "RULE.spad" 1815267 1815291 1817017 1817022) (-1080 "RTVALUE.spad" 1815002 1815011 1815257 1815262) (-1079 "RSTRCAST.spad" 1814719 1814728 1814992 1814997) (-1078 "RSETGCD.spad" 1811097 1811117 1814709 1814714) (-1077 "RSETCAT.spad" 1801033 1801050 1811065 1811092) (-1076 "RSETCAT.spad" 1790989 1791008 1801023 1801028) (-1075 "RSDCMPK.spad" 1789441 1789461 1790979 1790984) (-1074 "RRCC.spad" 1787825 1787855 1789431 1789436) (-1073 "RRCC.spad" 1786207 1786239 1787815 1787820) (-1072 "RPTAST.spad" 1785909 1785918 1786197 1786202) (-1071 "RPOLCAT.spad" 1765269 1765284 1785777 1785904) (-1070 "RPOLCAT.spad" 1744343 1744360 1764853 1764858) (-1069 "ROUTINE.spad" 1740226 1740235 1742990 1743017) (-1068 "ROMAN.spad" 1739554 1739563 1740092 1740221) (-1067 "ROIRC.spad" 1738634 1738666 1739544 1739549) (-1066 "RNS.spad" 1737537 1737546 1738536 1738629) (-1065 "RNS.spad" 1736526 1736537 1737527 1737532) (-1064 "RNGBIND.spad" 1735686 1735700 1736481 1736486) (-1063 "RNG.spad" 1735421 1735430 1735676 1735681) (-1062 "RMODULE.spad" 1735186 1735197 1735411 1735416) (-1061 "RMCAT2.spad" 1734606 1734663 1735176 1735181) (-1060 "RMATRIX.spad" 1733430 1733449 1733773 1733812) (-1059 "RMATCAT.spad" 1729009 1729040 1733386 1733425) (-1058 "RMATCAT.spad" 1724478 1724511 1728857 1728862) (-1057 "RLINSET.spad" 1723872 1723883 1724468 1724473) (-1056 "RINTERP.spad" 1723760 1723780 1723862 1723867) (-1055 "RING.spad" 1723230 1723239 1723740 1723755) (-1054 "RING.spad" 1722708 1722719 1723220 1723225) (-1053 "RIDIST.spad" 1722100 1722109 1722698 1722703) (-1052 "RGCHAIN.spad" 1720683 1720699 1721585 1721612) (-1051 "RGBCSPC.spad" 1720464 1720476 1720673 1720678) (-1050 "RGBCMDL.spad" 1719994 1720006 1720454 1720459) (-1049 "RFFACTOR.spad" 1719456 1719467 1719984 1719989) (-1048 "RFFACT.spad" 1719191 1719203 1719446 1719451) (-1047 "RFDIST.spad" 1718187 1718196 1719181 1719186) (-1046 "RF.spad" 1715829 1715840 1718177 1718182) (-1045 "RETSOL.spad" 1715248 1715261 1715819 1715824) (-1044 "RETRACT.spad" 1714676 1714687 1715238 1715243) (-1043 "RETRACT.spad" 1714102 1714115 1714666 1714671) (-1042 "RETAST.spad" 1713914 1713923 1714092 1714097) (-1041 "RESULT.spad" 1711974 1711983 1712561 1712588) (-1040 "RESRING.spad" 1711321 1711368 1711912 1711969) (-1039 "RESLATC.spad" 1710645 1710656 1711311 1711316) (-1038 "REPSQ.spad" 1710376 1710387 1710635 1710640) (-1037 "REPDB.spad" 1710083 1710094 1710366 1710371) (-1036 "REP2.spad" 1699741 1699752 1709925 1709930) (-1035 "REP1.spad" 1693937 1693948 1699691 1699696) (-1034 "REP.spad" 1691491 1691500 1693927 1693932) (-1033 "REGSET.spad" 1689288 1689305 1691137 1691164) (-1032 "REF.spad" 1688623 1688634 1689243 1689248) (-1031 "REDORDER.spad" 1687829 1687846 1688613 1688618) (-1030 "RECLOS.spad" 1686612 1686632 1687316 1687409) (-1029 "REALSOLV.spad" 1685752 1685761 1686602 1686607) (-1028 "REAL0Q.spad" 1683050 1683065 1685742 1685747) (-1027 "REAL0.spad" 1679894 1679909 1683040 1683045) (-1026 "REAL.spad" 1679766 1679775 1679884 1679889) (-1025 "RDUCEAST.spad" 1679487 1679496 1679756 1679761) (-1024 "RDIV.spad" 1679142 1679167 1679477 1679482) (-1023 "RDIST.spad" 1678709 1678720 1679132 1679137) (-1022 "RDETRS.spad" 1677573 1677591 1678699 1678704) (-1021 "RDETR.spad" 1675712 1675730 1677563 1677568) (-1020 "RDEEFS.spad" 1674811 1674828 1675702 1675707) (-1019 "RDEEF.spad" 1673821 1673838 1674801 1674806) (-1018 "RCFIELD.spad" 1671007 1671016 1673723 1673816) (-1017 "RCFIELD.spad" 1668279 1668290 1670997 1671002) (-1016 "RCAGG.spad" 1666207 1666218 1668269 1668274) (-1015 "RCAGG.spad" 1664062 1664075 1666126 1666131) (-1014 "RATRET.spad" 1663422 1663433 1664052 1664057) (-1013 "RATFACT.spad" 1663114 1663126 1663412 1663417) (-1012 "RANDSRC.spad" 1662433 1662442 1663104 1663109) (-1011 "RADUTIL.spad" 1662189 1662198 1662423 1662428) (-1010 "RADIX.spad" 1659110 1659124 1660656 1660749) (-1009 "RADFF.spad" 1657523 1657560 1657642 1657798) (-1008 "RADCAT.spad" 1657118 1657127 1657513 1657518) (-1007 "RADCAT.spad" 1656711 1656722 1657108 1657113) (-1006 "QUEUE.spad" 1656059 1656070 1656318 1656345) (-1005 "QUATCT2.spad" 1655679 1655698 1656049 1656054) (-1004 "QUATCAT.spad" 1653849 1653860 1655609 1655674) (-1003 "QUATCAT.spad" 1651770 1651783 1653532 1653537) (-1002 "QUAT.spad" 1650351 1650362 1650694 1650759) (-1001 "QUAGG.spad" 1649178 1649189 1650319 1650346) (-1000 "QQUTAST.spad" 1648946 1648955 1649168 1649173) (-999 "QFORM.spad" 1648411 1648425 1648936 1648941) (-998 "QFCAT2.spad" 1648104 1648120 1648401 1648406) (-997 "QFCAT.spad" 1646807 1646817 1648006 1648099) (-996 "QFCAT.spad" 1645101 1645113 1646302 1646307) (-995 "QEQUAT.spad" 1644660 1644668 1645091 1645096) (-994 "QCMPACK.spad" 1639407 1639426 1644650 1644655) (-993 "QALGSET2.spad" 1637403 1637421 1639397 1639402) (-992 "QALGSET.spad" 1633484 1633516 1637317 1637322) (-991 "PWFFINTB.spad" 1630900 1630921 1633474 1633479) (-990 "PUSHVAR.spad" 1630239 1630258 1630890 1630895) (-989 "PTRANFN.spad" 1626367 1626377 1630229 1630234) (-988 "PTPACK.spad" 1623455 1623465 1626357 1626362) (-987 "PTFUNC2.spad" 1623278 1623292 1623445 1623450) (-986 "PTCAT.spad" 1622533 1622543 1623246 1623273) (-985 "PSQFR.spad" 1621840 1621864 1622523 1622528) (-984 "PSEUDLIN.spad" 1620726 1620736 1621830 1621835) (-983 "PSETPK.spad" 1606159 1606175 1620604 1620609) (-982 "PSETCAT.spad" 1600079 1600102 1606139 1606154) (-981 "PSETCAT.spad" 1593973 1593998 1600035 1600040) (-980 "PSCURVE.spad" 1592956 1592964 1593963 1593968) (-979 "PSCAT.spad" 1591739 1591768 1592854 1592951) (-978 "PSCAT.spad" 1590612 1590643 1591729 1591734) (-977 "PRTITION.spad" 1589573 1589581 1590602 1590607) (-976 "PRTDAST.spad" 1589292 1589300 1589563 1589568) (-975 "PRS.spad" 1578854 1578871 1589248 1589253) (-974 "PRQAGG.spad" 1578289 1578299 1578822 1578849) (-973 "PROPLOG.spad" 1577588 1577596 1578279 1578284) (-972 "PROPFRML.spad" 1576156 1576167 1577578 1577583) (-971 "PROPERTY.spad" 1575644 1575652 1576146 1576151) (-970 "PRODUCT.spad" 1573326 1573338 1573610 1573665) (-969 "PRINT.spad" 1573078 1573086 1573316 1573321) (-968 "PRIMES.spad" 1571331 1571341 1573068 1573073) (-967 "PRIMELT.spad" 1569412 1569426 1571321 1571326) (-966 "PRIMCAT.spad" 1569039 1569047 1569402 1569407) (-965 "PRIMARR2.spad" 1567806 1567818 1569029 1569034) (-964 "PRIMARR.spad" 1566811 1566821 1566989 1567016) (-963 "PREASSOC.spad" 1566193 1566205 1566801 1566806) (-962 "PR.spad" 1564585 1564597 1565284 1565411) (-961 "PPCURVE.spad" 1563722 1563730 1564575 1564580) (-960 "PORTNUM.spad" 1563497 1563505 1563712 1563717) (-959 "POLYROOT.spad" 1562346 1562368 1563453 1563458) (-958 "POLYLIFT.spad" 1561611 1561634 1562336 1562341) (-957 "POLYCATQ.spad" 1559729 1559751 1561601 1561606) (-956 "POLYCAT.spad" 1553199 1553220 1559597 1559724) (-955 "POLYCAT.spad" 1546007 1546030 1552407 1552412) (-954 "POLY2UP.spad" 1545459 1545473 1545997 1546002) (-953 "POLY2.spad" 1545056 1545068 1545449 1545454) (-952 "POLY.spad" 1542391 1542401 1542906 1543033) (-951 "POLUTIL.spad" 1541332 1541361 1542347 1542352) (-950 "POLTOPOL.spad" 1540080 1540095 1541322 1541327) (-949 "POINT.spad" 1538918 1538928 1539005 1539032) (-948 "PNTHEORY.spad" 1535620 1535628 1538908 1538913) (-947 "PMTOOLS.spad" 1534395 1534409 1535610 1535615) (-946 "PMSYM.spad" 1533944 1533954 1534385 1534390) (-945 "PMQFCAT.spad" 1533535 1533549 1533934 1533939) (-944 "PMPREDFS.spad" 1532989 1533011 1533525 1533530) (-943 "PMPRED.spad" 1532468 1532482 1532979 1532984) (-942 "PMPLCAT.spad" 1531548 1531566 1532400 1532405) (-941 "PMLSAGG.spad" 1531133 1531147 1531538 1531543) (-940 "PMKERNEL.spad" 1530712 1530724 1531123 1531128) (-939 "PMINS.spad" 1530292 1530302 1530702 1530707) (-938 "PMFS.spad" 1529869 1529887 1530282 1530287) (-937 "PMDOWN.spad" 1529159 1529173 1529859 1529864) (-936 "PMASSFS.spad" 1528126 1528142 1529149 1529154) (-935 "PMASS.spad" 1527136 1527144 1528116 1528121) (-934 "PLOTTOOL.spad" 1526916 1526924 1527126 1527131) (-933 "PLOT3D.spad" 1523380 1523388 1526906 1526911) (-932 "PLOT1.spad" 1522537 1522547 1523370 1523375) (-931 "PLOT.spad" 1517460 1517468 1522527 1522532) (-930 "PLEQN.spad" 1504750 1504777 1517450 1517455) (-929 "PINTERPA.spad" 1504534 1504550 1504740 1504745) (-928 "PINTERP.spad" 1504156 1504175 1504524 1504529) (-927 "PID.spad" 1503126 1503134 1504082 1504151) (-926 "PICOERCE.spad" 1502783 1502793 1503116 1503121) (-925 "PI.spad" 1502392 1502400 1502757 1502778) (-924 "PGROEB.spad" 1500993 1501007 1502382 1502387) (-923 "PGE.spad" 1492610 1492618 1500983 1500988) (-922 "PGCD.spad" 1491500 1491517 1492600 1492605) (-921 "PFRPAC.spad" 1490649 1490659 1491490 1491495) (-920 "PFR.spad" 1487312 1487322 1490551 1490644) (-919 "PFOTOOLS.spad" 1486570 1486586 1487302 1487307) (-918 "PFOQ.spad" 1485940 1485958 1486560 1486565) (-917 "PFO.spad" 1485359 1485386 1485930 1485935) (-916 "PFECAT.spad" 1483041 1483049 1485285 1485354) (-915 "PFECAT.spad" 1480751 1480761 1482997 1483002) (-914 "PFBRU.spad" 1478639 1478651 1480741 1480746) (-913 "PFBR.spad" 1476199 1476222 1478629 1478634) (-912 "PF.spad" 1475773 1475785 1476004 1476097) (-911 "PERMGRP.spad" 1470535 1470545 1475763 1475768) (-910 "PERMCAT.spad" 1469093 1469103 1470515 1470530) (-909 "PERMAN.spad" 1467625 1467639 1469083 1469088) (-908 "PERM.spad" 1463310 1463320 1467455 1467470) (-907 "PENDTREE.spad" 1462651 1462661 1462939 1462944) (-906 "PDRING.spad" 1461202 1461212 1462631 1462646) (-905 "PDRING.spad" 1459761 1459773 1461192 1461197) (-904 "PDEPROB.spad" 1458776 1458784 1459751 1459756) (-903 "PDEPACK.spad" 1452816 1452824 1458766 1458771) (-902 "PDECOMP.spad" 1452286 1452303 1452806 1452811) (-901 "PDECAT.spad" 1450642 1450650 1452276 1452281) (-900 "PCOMP.spad" 1450495 1450508 1450632 1450637) (-899 "PBWLB.spad" 1449083 1449100 1450485 1450490) (-898 "PATTERN2.spad" 1448821 1448833 1449073 1449078) (-897 "PATTERN1.spad" 1447157 1447173 1448811 1448816) (-896 "PATTERN.spad" 1441696 1441706 1447147 1447152) (-895 "PATRES2.spad" 1441368 1441382 1441686 1441691) (-894 "PATRES.spad" 1438943 1438955 1441358 1441363) (-893 "PATMATCH.spad" 1437140 1437171 1438651 1438656) (-892 "PATMAB.spad" 1436569 1436579 1437130 1437135) (-891 "PATLRES.spad" 1435655 1435669 1436559 1436564) (-890 "PATAB.spad" 1435419 1435429 1435645 1435650) (-889 "PARTPERM.spad" 1432819 1432827 1435409 1435414) (-888 "PARSURF.spad" 1432253 1432281 1432809 1432814) (-887 "PARSU2.spad" 1432050 1432066 1432243 1432248) (-886 "script-parser.spad" 1431570 1431578 1432040 1432045) (-885 "PARSCURV.spad" 1431004 1431032 1431560 1431565) (-884 "PARSC2.spad" 1430795 1430811 1430994 1430999) (-883 "PARPCURV.spad" 1430257 1430285 1430785 1430790) (-882 "PARPC2.spad" 1430048 1430064 1430247 1430252) (-881 "PARAMAST.spad" 1429176 1429184 1430038 1430043) (-880 "PAN2EXPR.spad" 1428588 1428596 1429166 1429171) (-879 "PALETTE.spad" 1427558 1427566 1428578 1428583) (-878 "PAIR.spad" 1426545 1426558 1427146 1427151) (-877 "PADICRC.spad" 1423879 1423897 1425050 1425143) (-876 "PADICRAT.spad" 1421894 1421906 1422115 1422208) (-875 "PADICCT.spad" 1420443 1420455 1421820 1421889) (-874 "PADIC.spad" 1420138 1420150 1420369 1420438) (-873 "PADEPAC.spad" 1418827 1418846 1420128 1420133) (-872 "PADE.spad" 1417579 1417595 1418817 1418822) (-871 "OWP.spad" 1416819 1416849 1417437 1417504) (-870 "OVERSET.spad" 1416392 1416400 1416809 1416814) (-869 "OVAR.spad" 1416173 1416196 1416382 1416387) (-868 "OUTFORM.spad" 1405565 1405573 1416163 1416168) (-867 "OUTBFILE.spad" 1404983 1404991 1405555 1405560) (-866 "OUTBCON.spad" 1403989 1403997 1404973 1404978) (-865 "OUTBCON.spad" 1402993 1403003 1403979 1403984) (-864 "OUT.spad" 1402079 1402087 1402983 1402988) (-863 "OSI.spad" 1401554 1401562 1402069 1402074) (-862 "OSGROUP.spad" 1401472 1401480 1401544 1401549) (-861 "ORTHPOL.spad" 1399957 1399967 1401389 1401394) (-860 "OREUP.spad" 1399410 1399438 1399637 1399676) (-859 "ORESUP.spad" 1398711 1398735 1399090 1399129) (-858 "OREPCTO.spad" 1396568 1396580 1398631 1398636) (-857 "OREPCAT.spad" 1390715 1390725 1396524 1396563) (-856 "OREPCAT.spad" 1384752 1384764 1390563 1390568) (-855 "ORDSET.spad" 1383924 1383932 1384742 1384747) (-854 "ORDSET.spad" 1383094 1383104 1383914 1383919) (-853 "ORDRING.spad" 1382484 1382492 1383074 1383089) (-852 "ORDRING.spad" 1381882 1381892 1382474 1382479) (-851 "ORDMON.spad" 1381737 1381745 1381872 1381877) (-850 "ORDFUNS.spad" 1380869 1380885 1381727 1381732) (-849 "ORDFIN.spad" 1380689 1380697 1380859 1380864) (-848 "ORDCOMP2.spad" 1379982 1379994 1380679 1380684) (-847 "ORDCOMP.spad" 1378447 1378457 1379529 1379558) (-846 "OPTPROB.spad" 1377085 1377093 1378437 1378442) (-845 "OPTPACK.spad" 1369494 1369502 1377075 1377080) (-844 "OPTCAT.spad" 1367173 1367181 1369484 1369489) (-843 "OPSIG.spad" 1366827 1366835 1367163 1367168) (-842 "OPQUERY.spad" 1366376 1366384 1366817 1366822) (-841 "OPERCAT.spad" 1365842 1365852 1366366 1366371) (-840 "OPERCAT.spad" 1365306 1365318 1365832 1365837) (-839 "OP.spad" 1365048 1365058 1365128 1365195) (-838 "ONECOMP2.spad" 1364472 1364484 1365038 1365043) (-837 "ONECOMP.spad" 1363217 1363227 1364019 1364048) (-836 "OMSERVER.spad" 1362223 1362231 1363207 1363212) (-835 "OMSAGG.spad" 1362011 1362021 1362179 1362218) (-834 "OMPKG.spad" 1360627 1360635 1362001 1362006) (-833 "OMLO.spad" 1360052 1360064 1360513 1360552) (-832 "OMEXPR.spad" 1359886 1359896 1360042 1360047) (-831 "OMERRK.spad" 1358920 1358928 1359876 1359881) (-830 "OMERR.spad" 1358465 1358473 1358910 1358915) (-829 "OMENC.spad" 1357809 1357817 1358455 1358460) (-828 "OMDEV.spad" 1352118 1352126 1357799 1357804) (-827 "OMCONN.spad" 1351527 1351535 1352108 1352113) (-826 "OM.spad" 1350500 1350508 1351517 1351522) (-825 "OINTDOM.spad" 1350263 1350271 1350426 1350495) (-824 "OFMONOID.spad" 1348386 1348396 1350219 1350224) (-823 "ODVAR.spad" 1347647 1347657 1348376 1348381) (-822 "ODR.spad" 1347291 1347317 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(-746 "MULTFACT.spad" 1147325 1147342 1147932 1147937) (-745 "MTSCAT.spad" 1145419 1145440 1147223 1147320) (-744 "MTHING.spad" 1145078 1145088 1145409 1145414) (-743 "MSYSCMD.spad" 1144512 1144520 1145068 1145073) (-742 "MSETAGG.spad" 1144357 1144367 1144480 1144507) (-741 "MSET.spad" 1142315 1142325 1144063 1144102) (-740 "MRING.spad" 1139292 1139304 1142023 1142090) (-739 "MRF2.spad" 1138862 1138876 1139282 1139287) (-738 "MRATFAC.spad" 1138408 1138425 1138852 1138857) (-737 "MPRFF.spad" 1136448 1136467 1138398 1138403) (-736 "MPOLY.spad" 1133919 1133934 1134278 1134405) (-735 "MPCPF.spad" 1133183 1133202 1133909 1133914) (-734 "MPC3.spad" 1133000 1133040 1133173 1133178) (-733 "MPC2.spad" 1132646 1132679 1132990 1132995) (-732 "MONOTOOL.spad" 1130997 1131014 1132636 1132641) (-731 "MONOID.spad" 1130316 1130324 1130987 1130992) (-730 "MONOID.spad" 1129633 1129643 1130306 1130311) (-729 "MONOGEN.spad" 1128381 1128394 1129493 1129628) (-728 "MONOGEN.spad" 1127151 1127166 1128265 1128270) (-727 "MONADWU.spad" 1125181 1125189 1127141 1127146) (-726 "MONADWU.spad" 1123209 1123219 1125171 1125176) (-725 "MONAD.spad" 1122369 1122377 1123199 1123204) (-724 "MONAD.spad" 1121527 1121537 1122359 1122364) (-723 "MOEBIUS.spad" 1120263 1120277 1121507 1121522) (-722 "MODULE.spad" 1120133 1120143 1120231 1120258) (-721 "MODULE.spad" 1120023 1120035 1120123 1120128) (-720 "MODRING.spad" 1119358 1119397 1120003 1120018) (-719 "MODOP.spad" 1118023 1118035 1119180 1119247) (-718 "MODMONOM.spad" 1117754 1117772 1118013 1118018) (-717 "MODMON.spad" 1114549 1114565 1115268 1115421) (-716 "MODFIELD.spad" 1113911 1113950 1114451 1114544) (-715 "MMLFORM.spad" 1112771 1112779 1113901 1113906) (-714 "MMAP.spad" 1112513 1112547 1112761 1112766) (-713 "MLO.spad" 1110972 1110982 1112469 1112508) (-712 "MLIFT.spad" 1109584 1109601 1110962 1110967) (-711 "MKUCFUNC.spad" 1109119 1109137 1109574 1109579) (-710 "MKRECORD.spad" 1108723 1108736 1109109 1109114) (-709 "MKFUNC.spad" 1108130 1108140 1108713 1108718) (-708 "MKFLCFN.spad" 1107098 1107108 1108120 1108125) (-707 "MKBCFUNC.spad" 1106593 1106611 1107088 1107093) (-706 "MINT.spad" 1106032 1106040 1106495 1106588) (-705 "MHROWRED.spad" 1104543 1104553 1106022 1106027) (-704 "MFLOAT.spad" 1103063 1103071 1104433 1104538) (-703 "MFINFACT.spad" 1102463 1102485 1103053 1103058) (-702 "MESH.spad" 1100250 1100258 1102453 1102458) (-701 "MDDFACT.spad" 1098461 1098471 1100240 1100245) (-700 "MDAGG.spad" 1097752 1097762 1098441 1098456) (-699 "MCMPLX.spad" 1093763 1093771 1094377 1094578) (-698 "MCDEN.spad" 1092973 1092985 1093753 1093758) (-697 "MCALCFN.spad" 1090095 1090121 1092963 1092968) (-696 "MAYBE.spad" 1089379 1089390 1090085 1090090) (-695 "MATSTOR.spad" 1086687 1086697 1089369 1089374) (-694 "MATRIX.spad" 1085391 1085401 1085875 1085902) (-693 "MATLIN.spad" 1082735 1082759 1085275 1085280) (-692 "MATCAT2.spad" 1082017 1082065 1082725 1082730) (-691 "MATCAT.spad" 1073746 1073768 1081985 1082012) (-690 "MATCAT.spad" 1065347 1065371 1073588 1073593) (-689 "MAPPKG3.spad" 1064262 1064276 1065337 1065342) (-688 "MAPPKG2.spad" 1063600 1063612 1064252 1064257) (-687 "MAPPKG1.spad" 1062428 1062438 1063590 1063595) (-686 "MAPPAST.spad" 1061743 1061751 1062418 1062423) (-685 "MAPHACK3.spad" 1061555 1061569 1061733 1061738) (-684 "MAPHACK2.spad" 1061324 1061336 1061545 1061550) (-683 "MAPHACK1.spad" 1060968 1060978 1061314 1061319) (-682 "MAGMA.spad" 1058758 1058775 1060958 1060963) (-681 "MACROAST.spad" 1058337 1058345 1058748 1058753) (-680 "M3D.spad" 1056057 1056067 1057715 1057720) (-679 "LZSTAGG.spad" 1053295 1053305 1056047 1056052) (-678 "LZSTAGG.spad" 1050531 1050543 1053285 1053290) (-677 "LWORD.spad" 1047236 1047253 1050521 1050526) (-676 "LSTAST.spad" 1047020 1047028 1047226 1047231) (-675 "LSQM.spad" 1045247 1045261 1045641 1045692) (-674 "LSPP.spad" 1044782 1044799 1045237 1045242) (-673 "LSMP1.spad" 1042617 1042631 1044772 1044777) (-672 "LSMP.spad" 1041474 1041502 1042607 1042612) (-671 "LSAGG.spad" 1041143 1041153 1041442 1041469) (-670 "LSAGG.spad" 1040832 1040844 1041133 1041138) (-669 "LPOLY.spad" 1039786 1039805 1040688 1040757) (-668 "LPEFRAC.spad" 1039057 1039067 1039776 1039781) (-667 "LOGIC.spad" 1038659 1038667 1039047 1039052) (-666 "LOGIC.spad" 1038259 1038269 1038649 1038654) (-665 "LODOOPS.spad" 1037189 1037201 1038249 1038254) (-664 "LODOF.spad" 1036235 1036252 1037146 1037151) (-663 "LODOCAT.spad" 1034901 1034911 1036191 1036230) (-662 "LODOCAT.spad" 1033565 1033577 1034857 1034862) (-661 "LODO2.spad" 1032838 1032850 1033245 1033284) (-660 "LODO1.spad" 1032238 1032248 1032518 1032557) (-659 "LODO.spad" 1031622 1031638 1031918 1031957) (-658 "LODEEF.spad" 1030424 1030442 1031612 1031617) (-657 "LO.spad" 1029825 1029839 1030358 1030385) (-656 "LNAGG.spad" 1025657 1025667 1029815 1029820) (-655 "LNAGG.spad" 1021453 1021465 1025613 1025618) (-654 "LMOPS.spad" 1018221 1018238 1021443 1021448) (-653 "LMODULE.spad" 1017989 1017999 1018211 1018216) (-652 "LMDICT.spad" 1017276 1017286 1017540 1017567) (-651 "LLINSET.spad" 1016673 1016683 1017266 1017271) (-650 "LITERAL.spad" 1016579 1016590 1016663 1016668) (-649 "LIST3.spad" 1015890 1015904 1016569 1016574) (-648 "LIST2MAP.spad" 1012793 1012805 1015880 1015885) (-647 "LIST2.spad" 1011495 1011507 1012783 1012788) (-646 "LIST.spad" 1009230 1009240 1010642 1010669) (-645 "LINSET.spad" 1008852 1008862 1009220 1009225) (-644 "LINEXP.spad" 1008286 1008296 1008832 1008847) (-643 "LINDEP.spad" 1007095 1007107 1008198 1008203) (-642 "LIMITRF.spad" 1005042 1005052 1007085 1007090) (-641 "LIMITPS.spad" 1003952 1003965 1005032 1005037) (-640 "LIECAT.spad" 1003428 1003438 1003878 1003947) (-639 "LIECAT.spad" 1002932 1002944 1003384 1003389) (-638 "LIE.spad" 1000948 1000960 1002222 1002367) (-637 "LIB.spad" 998998 999006 999607 999622) (-636 "LGROBP.spad" 996351 996370 998988 998993) (-635 "LFCAT.spad" 995410 995418 996341 996346) (-634 "LF.spad" 994365 994381 995400 995405) (-633 "LEXTRIPK.spad" 989868 989883 994355 994360) (-632 "LEXP.spad" 987871 987898 989848 989863) (-631 "LETAST.spad" 987570 987578 987861 987866) (-630 "LEADCDET.spad" 985968 985985 987560 987565) (-629 "LAZM3PK.spad" 984672 984694 985958 985963) (-628 "LAUPOL.spad" 983365 983378 984265 984334) (-627 "LAPLACE.spad" 982948 982964 983355 983360) (-626 "LALG.spad" 982724 982734 982928 982943) (-625 "LALG.spad" 982508 982520 982714 982719) (-624 "LA.spad" 981948 981962 982430 982469) (-623 "KVTFROM.spad" 981683 981693 981938 981943) (-622 "KTVLOGIC.spad" 981195 981203 981673 981678) (-621 "KRCFROM.spad" 980933 980943 981185 981190) (-620 "KOVACIC.spad" 979656 979673 980923 980928) (-619 "KONVERT.spad" 979378 979388 979646 979651) (-618 "KOERCE.spad" 979115 979125 979368 979373) (-617 "KERNEL2.spad" 978818 978830 979105 979110) (-616 "KERNEL.spad" 977473 977483 978602 978607) (-615 "KDAGG.spad" 976582 976604 977453 977468) (-614 "KDAGG.spad" 975699 975723 976572 976577) (-613 "KAFILE.spad" 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 742345ac..dad40acb 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,5 +1,5 @@ -(188527 . 3477425190) +(188581 . 3477435927) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -43,26 +43,26 @@ (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) ((((-868)) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) (((|#1| |#2|) . T)) -((((-551) (-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) -((((-551) (-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T) ((|#2|) . T)) -(((#1=(-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) #1#) |has| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)))) ((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) -((((-551) (-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) +((((-551) (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) +((((-551) (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#2|) . T)) +(((#1=(-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) #1#) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)))) ((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) +((((-551) (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1| |#2|) . T)) ((((-169 (-382))) . T) (((-226)) . T) (((-382)) . T)) ((((-412 (-551))) . T) (((-551)) . T)) @@ -93,11 +93,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -110,13 +110,13 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| (-58 |#1|) (-58 |#1|)) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-694 (-343 (-3962) (-3962 (QUOTE X) (QUOTE HESS)) (-704)))) . T)) +((((-694 (-343 (-3965) (-3965 (QUOTE X) (QUOTE HESS)) (-704)))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -133,7 +133,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) -((((-1272 (-343 (-3962) (-3962 (QUOTE X)) (-704)))) . T)) +((((-1272 (-343 (-3965) (-3965 (QUOTE X)) (-704)))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -144,7 +144,7 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -163,7 +163,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) ((((-868)) . T)) @@ -240,7 +240,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -249,7 +249,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -258,7 +258,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) @@ -327,20 +327,20 @@ ((((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) (|has| |#1| (-826)) -(-3969 (|has| |#1| (-145)) (|has| |#1| (-354))) +(-3972 (|has| |#1| (-145)) (|has| |#1| (-354))) ((((-868)) . T)) (|has| |#1| (-147)) (((|#1|) . 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T)) (((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107)))) @@ -1430,10 +1430,10 @@ ((((-551) |#2|) . T)) ((((-551) |#2|) . T)) (|has| |#2| (-798)) -(-3969 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3969 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3969 (|has| |#2| (-798)) (|has| |#2| (-853))) -(-3969 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) +(-3972 (|has| |#2| (-798)) (|has| |#2| (-853))) (|has| |#2| (-853)) (|has| |#2| (-853)) (((|#2|) |has| |#2| (-367))) @@ -1442,7 +1442,7 @@ ((((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -1491,11 +1491,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1508,7 +1508,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| (-501 |#1| |#3|) (-501 |#1| |#2|)) . T)) ((((-112)) . T)) ((((-112)) . T)) @@ -1542,11 +1542,11 @@ (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1577,15 +1577,15 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1| |#4| |#5|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1599,7 +1599,7 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1| (-607 |#1| |#3|) (-607 |#1| |#2|)) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -1644,13 +1644,13 @@ (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -(((|#2|) . T) (((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((#1=(-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) #1#) |has| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4301 |#1|) (|:| -2263 |#2|))))) -(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) (((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) |has| (-2 (|:| -4301 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4301 |#1|) (|:| -2263 |#2|))))) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) -((((-2 (|:| -4301 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +(((|#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((#1=(-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) #1#) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))))) +(((|#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) (((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) |has| (-2 (|:| -4304 |#1|) (|:| -2263 |#2|)) (-312 (-2 (|:| -4304 |#1|) (|:| -2263 |#2|))))) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) +((((-2 (|:| -4304 |#1|) (|:| -2263 |#2|))) . T)) (((|#1| |#2|) . T)) ((($) . T)) ((($ $) . T)) @@ -1728,10 +1728,10 @@ ((($) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-3969 (|has| |#1| (-173)) (|has| |#1| (-562))) -((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3969 (|has| |#1| (-173)) (|has| |#1| (-562)))) -((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3969 (|has| |#1| (-173)) (|has| |#1| (-562)))) -(((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551)))) ((|#1| |#1|) . T) (($ $) -3969 (|has| |#1| (-173)) (|has| |#1| (-562)))) +(-3972 (|has| |#1| (-173)) (|has| |#1| (-562))) +((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) +((((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) . T) (($) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) +(((#1=(-412 (-551)) #1#) |has| |#1| (-38 (-412 (-551)))) ((|#1| |#1|) . T) (($ $) -3972 (|has| |#1| (-173)) (|has| |#1| (-562)))) (|has| |#1| (-562)) (|has| |#1| (-562)) ((((-551)) . T) (((-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((|#1|) |has| |#1| (-173)) (($) |has| |#1| (-562))) @@ -1753,7 +1753,9 @@ (((|#1|) . T) (($) . T)) ((((-868)) . T)) (((|#1|) . T) (($) . T) (((-551)) . T)) -((((-868)) . T)) +((((-1188)) . T)) +((((-1188)) . T)) +((((-1188)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -1762,11 +1764,11 @@ ((((-551) |#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) (((|#1|) . T)) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) . T)) (|has| |#1| (-855)) (((|#1|) . T)) @@ -1777,7 +1779,7 @@ ((((-1188)) . T)) ((((-1223)) . T) (((-868)) . T) (((-1188)) . T)) ((((-1188)) . T)) -(((|#1|) -3969 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3972 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#1|) |has| |#2| (-423 |#1|))) (((|#1|) . T)) (((|#1|) . T)) @@ -1792,16 +1794,16 @@ ((((-1165) |#1|) . T)) ((((-1165) |#1|) . T)) ((((-1165) |#1|) . T)) -((((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) . T)) -((((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) . T)) -(((|#1|) . T) (((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((#1=(-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) #1#) |has| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (-312 (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))))) -(((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) (((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) |has| (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|)) (-312 (-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))))) -((((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) . T)) -((((-2 (|:| -4301 (-1165)) (|:| -2263 |#1|))) . T)) +((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) +((((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . T)) +(((|#1|) . T) (((-2 (|:| -4304 (-1165)) (|:| -2263 |#1|))) . 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T)) +(((#1=(-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) #1#) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))))) +((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) |has| (-2 (|:| -4304 (-1165)) (|:| -2263 (-51))) (-312 (-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))))) +((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) +((((-2 (|:| -4304 (-1165)) (|:| -2263 (-51)))) . T)) ((((-1165) (-51)) . T)) -(((|#1|) -3969 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -3972 (|has| |#2| (-371 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#1|) |has| |#2| (-423 |#1|))) (((|#1|) . T)) (((|#1|) . T)) @@ -1874,11 +1876,11 @@ (|has| |#1| (-826)) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-855)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) -(-3969 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) +(-3972 (|has| |#1| (-855)) (|has| |#1| (-1107))) (((|#1|) . T)) ((((-540)) |has| |#1| (-619 (-540)))) ((((-551) |#1|) . T)) @@ -1902,7 +1904,7 @@ (|has| |#1| (-1107)) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -1982,7 +1984,7 @@ (((|#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) -(((|#2|) |has| |#2| (-6 (-4436 "*")))) +(((|#2|) |has| |#2| (-6 (-4439 "*")))) (((|#2| |#2|) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2010,7 +2012,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-868)) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -2027,7 +2029,7 @@ ((((-1188)) . T)) ((((-540)) |has| |#1| (-619 (-540)))) (((|#1| (-1272 |#1|) (-1272 |#1|)) . T)) -((((-868)) -3969 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) +((((-868)) -3972 (|has| |#1| (-618 (-868))) (|has| |#1| (-1107)))) (((|#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (|has| |#1| (-1107)) @@ -2104,10 +2106,10 @@ ((((-868)) . T)) ((((-412 $) (-412 $)) |has| |#1| (-562)) (($ $) . T) ((|#1| |#1|) . 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T) ((#1=(-412 (-551)) #1#) |has| |#2| (-38 (-412 (-551))))) +((($) -3972 (|has| |#2| (-367)) (|has| |#2| (-457)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) |has| |#2| (-173)) (((-412 (-551))) |has| |#2| (-38 (-412 (-551))))) (((|#2|) . T)) ((((-1088)) . T) ((|#2|) . T) (((-551)) |has| |#2| (-1044 (-551))) (((-412 (-551))) |has| |#2| (-1044 (-412 (-551))))) (((|#2| (-776)) . T)) @@ -3707,21 +3709,21 @@ (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)) -(-3969 (|has| |#1| (-367)) (|has| |#1| (-562))) +(-3972 (|has| |#1| (-367)) (|has| |#1| (-562))) ((((-868)) . T)) -(((|#1|) . T) (($) -3969 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3969 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) -(((|#1|) . T) (($) -3969 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-562))) (((-412 (-551))) -3969 (|has| |#1| (-38 (-412 (-551)))) (|has| |#1| (-367)))) -(((|#1| |#1|) . 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((-1296 . -1063) T) ((-1296 . -1118) T) ((-1296 . -731) T) ((-1296 . -21) T) ((-1296 . -651) 187990) ((-1296 . -23) T) ((-1296 . -1107) T) ((-1296 . -618) 187972) ((-1296 . -102) T) ((-1296 . -25) T) ((-1296 . -131) T) ((-1296 . -653) 187946) ((-1296 . -621) 187902) ((-1296 . -1287) 187886) ((-1296 . -722) 187856) ((-1296 . -645) 187826) ((-1296 . -1062) 187810) ((-1296 . -1057) 187794) ((-1296 . -111) 187773) ((-1296 . -38) 187743) ((-1296 . -388) 187722) ((-1296 . -1044) 187706) ((-1294 . -1295) 187682) ((-1294 . -1044) 187656) ((-1294 . -621) 187602) ((-1294 . -1055) T) ((-1294 . -1063) T) ((-1294 . -1118) T) ((-1294 . -731) T) ((-1294 . -21) T) ((-1294 . -651) 187561) ((-1294 . -23) T) ((-1294 . -1107) T) ((-1294 . -618) 187543) ((-1294 . -102) T) ((-1294 . -25) T) ((-1294 . -131) T) ((-1294 . -653) 187517) ((-1294 . -1287) 187501) ((-1294 . -722) 187471) ((-1294 . -645) 187441) ((-1294 . -1062) 187425) ((-1294 . -1057) 187409) ((-1294 . -111) 187388) ((-1294 . -38) 187358) ((-1294 . -1292) 187334) ((-1293 . -1295) 187313) ((-1293 . -1044) 187270) ((-1293 . -621) 187199) ((-1293 . -1055) T) ((-1293 . -1063) T) ((-1293 . -1118) T) ((-1293 . -731) T) ((-1293 . -21) T) ((-1293 . -651) 187158) ((-1293 . -23) T) ((-1293 . -1107) T) ((-1293 . -618) 187140) ((-1293 . -102) T) ((-1293 . -25) T) ((-1293 . -131) T) ((-1293 . -653) 187114) ((-1293 . -1287) 187098) ((-1293 . -722) 187068) ((-1293 . -645) 187038) ((-1293 . -1062) 187022) ((-1293 . -1057) 187006) ((-1293 . -111) 186985) ((-1293 . -38) 186955) ((-1293 . -1292) 186934) ((-1293 . -388) 186906) ((-1288 . -388) 186878) ((-1288 . -621) 186827) ((-1288 . -1044) 186804) ((-1288 . -645) 186774) ((-1288 . -722) 186744) ((-1288 . -653) 186718) ((-1288 . -651) 186677) ((-1288 . -131) T) ((-1288 . -25) T) ((-1288 . -102) T) ((-1288 . -618) 186659) ((-1288 . -1107) T) ((-1288 . -23) T) ((-1288 . -21) T) ((-1288 . -1062) 186643) ((-1288 . -1057) 186627) ((-1288 . -111) 186606) ((-1288 . -1295) 186585) ((-1288 . -1055) T) ((-1288 . -1063) T) ((-1288 . -1118) T) ((-1288 . -731) T) ((-1288 . -1287) 186569) ((-1288 . -38) 186539) ((-1288 . -1292) 186518) ((-1286 . -1217) 186487) ((-1286 . -618) 186449) ((-1286 . -151) 186433) ((-1286 . -34) T) ((-1286 . -1222) T) ((-1286 . -312) 186371) ((-1286 . -519) 186304) ((-1286 . -1107) T) ((-1286 . -102) T) ((-1286 . -494) 186288) ((-1286 . -619) 186249) ((-1286 . -982) 186218) ((-1285 . -1055) T) ((-1285 . -1063) T) ((-1285 . -1118) T) ((-1285 . -731) T) ((-1285 . -21) T) ((-1285 . -651) 186163) ((-1285 . -23) T) ((-1285 . -1107) T) ((-1285 . -618) 186132) ((-1285 . -102) T) ((-1285 . -25) T) ((-1285 . -131) T) ((-1285 . -653) 186092) ((-1285 . -621) 186034) ((-1285 . -495) 186018) ((-1285 . -38) 185988) ((-1285 . -111) 185953) ((-1285 . -1057) 185923) ((-1285 . -1062) 185893) ((-1285 . -645) 185863) ((-1285 . -722) 185833) ((-1284 . -1089) T) ((-1284 . -495) 185814) ((-1284 . -618) 185780) ((-1284 . -621) 185761) ((-1284 . -1107) T) ((-1284 . -102) T) ((-1284 . -93) T) ((-1283 . -1089) T) ((-1283 . -495) 185742) ((-1283 . -618) 185708) ((-1283 . -621) 185689) ((-1283 . -1107) T) ((-1283 . -102) T) ((-1283 . -93) T) ((-1278 . -618) 185671) ((-1276 . -1107) T) ((-1276 . -618) 185653) ((-1276 . -102) T) ((-1275 . -1107) T) ((-1275 . -618) 185635) ((-1275 . -102) T) ((-1272 . -1271) 185619) ((-1272 . -376) 185603) ((-1272 . -855) 185582) ((-1272 . -151) 185566) ((-1272 . -34) T) ((-1272 . -1222) T) ((-1272 . -618) 185478) ((-1272 . -312) 185416) ((-1272 . -519) 185349) ((-1272 . -1107) 185299) ((-1272 . -102) 185249) ((-1272 . -494) 185233) ((-1272 . -619) 185194) ((-1272 . -609) 185171) ((-1272 . -289) 185148) ((-1272 . -291) 185125) ((-1272 . -656) 185109) ((-1272 . -19) 185093) ((-1269 . -1107) T) ((-1269 . -618) 185059) ((-1269 . -102) T) ((-1262 . -1265) 185043) ((-1262 . -234) 185002) ((-1262 . -621) 184884) ((-1262 . -653) 184809) ((-1262 . -651) 184719) ((-1262 . -131) T) ((-1262 . -25) T) ((-1262 . -102) T) ((-1262 . -618) 184701) ((-1262 . -1107) T) ((-1262 . -23) T) ((-1262 . -21) T) ((-1262 . -731) T) ((-1262 . -1118) T) ((-1262 . -1063) T) ((-1262 . -1055) T) ((-1262 . -289) 184686) ((-1262 . -906) 184599) ((-1262 . -979) 184568) ((-1262 . -38) 184465) ((-1262 . -111) 184334) ((-1262 . -1057) 184217) ((-1262 . -1062) 184100) ((-1262 . -645) 183997) ((-1262 . -722) 183894) ((-1262 . -145) 183873) ((-1262 . -147) 183852) ((-1262 . -173) 183803) ((-1262 . -562) 183782) ((-1262 . -293) 183761) ((-1262 . -47) 183738) ((-1262 . -1251) 183715) ((-1262 . -35) 183681) ((-1262 . -95) 183647) ((-1262 . -287) 183613) ((-1262 . -498) 183579) ((-1262 . -1211) 183545) ((-1262 . -1208) 183511) ((-1262 . -1008) 183477) ((-1259 . -329) 183421) ((-1259 . -1044) 183387) ((-1259 . -417) 183353) ((-1259 . -38) 183245) ((-1259 . -621) 183119) ((-1259 . -653) 183024) ((-1259 . -651) 182914) ((-1259 . -731) T) ((-1259 . -1118) T) ((-1259 . -1063) T) ((-1259 . -1055) T) ((-1259 . -111) 182806) ((-1259 . -1057) 182711) ((-1259 . -1062) 182616) ((-1259 . -21) T) ((-1259 . -23) T) ((-1259 . -1107) T) ((-1259 . -618) 182598) ((-1259 . -102) T) ((-1259 . -25) T) ((-1259 . -131) T) ((-1259 . -645) 182490) ((-1259 . -722) 182382) ((-1259 . -145) 182343) ((-1259 . -147) 182304) ((-1259 . -173) T) ((-1259 . -562) T) ((-1259 . -293) T) ((-1259 . -47) 182248) ((-1258 . -1257) 182227) ((-1258 . -367) 182206) ((-1258 . -1227) 182185) ((-1258 . -927) 182164) ((-1258 . -562) 182115) ((-1258 . -173) 182046) ((-1258 . -621) 181859) ((-1258 . -722) 181700) ((-1258 . -645) 181541) ((-1258 . -38) 181382) ((-1258 . -457) 181361) ((-1258 . -310) 181340) ((-1258 . -653) 181237) ((-1258 . -651) 181119) ((-1258 . -731) T) ((-1258 . -1118) T) ((-1258 . -1063) T) ((-1258 . -1055) T) ((-1258 . -111) 180940) ((-1258 . -1057) 180775) ((-1258 . -1062) 180610) ((-1258 . -21) T) ((-1258 . -23) T) ((-1258 . -1107) T) ((-1258 . -618) 180592) ((-1258 . -102) T) ((-1258 . -25) T) ((-1258 . -131) T) ((-1258 . -293) 180543) ((-1258 . -244) 180522) ((-1258 . -1008) 180488) ((-1258 . -1208) 180454) ((-1258 . -1211) 180420) ((-1258 . -498) 180386) ((-1258 . -287) 180352) ((-1258 . -95) 180318) ((-1258 . -35) 180284) ((-1258 . -1251) 180254) ((-1258 . -47) 180224) ((-1258 . -147) 180203) ((-1258 . -145) 180182) ((-1258 . -979) 180144) ((-1258 . -906) 180050) ((-1258 . -289) 180035) ((-1258 . -234) 179987) ((-1258 . -1255) 179971) ((-1258 . -1044) 179955) ((-1253 . -1257) 179916) ((-1253 . -367) 179895) ((-1253 . -1227) 179874) ((-1253 . -927) 179853) ((-1253 . -562) 179804) ((-1253 . -173) 179735) ((-1253 . -621) 179478) ((-1253 . -722) 179319) ((-1253 . -645) 179160) ((-1253 . -38) 179001) ((-1253 . -457) 178980) ((-1253 . -310) 178959) ((-1253 . -653) 178856) ((-1253 . -651) 178738) ((-1253 . -731) T) ((-1253 . -1118) T) ((-1253 . -1063) T) ((-1253 . -1055) T) ((-1253 . -111) 178559) ((-1253 . -1057) 178394) ((-1253 . -1062) 178229) ((-1253 . -21) T) ((-1253 . -23) T) ((-1253 . -1107) T) ((-1253 . -618) 178211) ((-1253 . -102) T) ((-1253 . -25) T) ((-1253 . -131) T) ((-1253 . -293) 178162) ((-1253 . -244) 178141) ((-1253 . -1008) 178107) ((-1253 . -1208) 178073) ((-1253 . -1211) 178039) ((-1253 . -498) 178005) ((-1253 . -287) 177971) ((-1253 . -95) 177937) ((-1253 . -35) 177903) ((-1253 . -1251) 177873) ((-1253 . -47) 177843) ((-1253 . -147) 177822) ((-1253 . -145) 177801) ((-1253 . -979) 177763) ((-1253 . -906) 177669) ((-1253 . -289) 177654) ((-1253 . -234) 177606) ((-1253 . -1255) 177590) ((-1253 . -1044) 177525) ((-1241 . -1248) 177509) ((-1241 . -1157) 177487) ((-1241 . -619) NIL) ((-1241 . -312) 177474) ((-1241 . -519) 177421) ((-1241 . -329) 177398) ((-1241 . -1044) 177278) ((-1241 . -417) 177262) ((-1241 . -38) 177091) ((-1241 . -111) 176900) ((-1241 . -1057) 176723) ((-1241 . -1062) 176546) ((-1241 . -651) 176456) ((-1241 . -653) 176381) ((-1241 . -645) 176210) ((-1241 . -722) 176039) ((-1241 . -621) 175787) ((-1241 . -145) 175766) ((-1241 . -147) 175745) ((-1241 . -47) 175722) ((-1241 . -381) 175706) ((-1241 . -644) 175654) ((-1241 . -906) 175597) ((-1241 . -892) NIL) ((-1241 . -916) 175576) ((-1241 . -1227) 175555) ((-1241 . -956) 175524) ((-1241 . -927) 175503) ((-1241 . -562) 175414) ((-1241 . -293) 175325) ((-1241 . -173) 175216) ((-1241 . -457) 175147) ((-1241 . -310) 175126) ((-1241 . -289) 175053) ((-1241 . -234) T) ((-1241 . -131) T) ((-1241 . -25) T) ((-1241 . -102) T) ((-1241 . -618) 175035) ((-1241 . -1107) T) ((-1241 . -23) T) ((-1241 . -21) T) ((-1241 . -731) T) ((-1241 . -1118) T) ((-1241 . -1063) T) ((-1241 . -1055) T) ((-1241 . -232) 175019) ((-1239 . -1100) 175003) ((-1239 . -623) 174987) ((-1239 . -1107) 174965) ((-1239 . -618) 174932) ((-1239 . -102) 174910) ((-1239 . -1101) 174867) ((-1237 . -1236) 174846) ((-1237 . -1008) 174812) ((-1237 . -1208) 174778) ((-1237 . -1211) 174744) ((-1237 . -498) 174710) ((-1237 . -287) 174676) ((-1237 . -95) 174642) ((-1237 . -35) 174608) ((-1237 . -1251) 174585) ((-1237 . -47) 174562) ((-1237 . -621) 174310) ((-1237 . -722) 174124) ((-1237 . -645) 173938) ((-1237 . -653) 173808) ((-1237 . -651) 173663) ((-1237 . -1062) 173471) ((-1237 . -1057) 173279) ((-1237 . -111) 173068) ((-1237 . -38) 172882) ((-1237 . -979) 172851) ((-1237 . -289) 172771) ((-1237 . -1234) 172755) ((-1237 . -731) T) ((-1237 . -1118) T) ((-1237 . -1063) T) ((-1237 . -1055) T) ((-1237 . -21) T) ((-1237 . -23) T) ((-1237 . -1107) T) ((-1237 . -618) 172737) ((-1237 . -102) T) ((-1237 . -25) T) ((-1237 . -131) T) ((-1237 . -145) 172662) ((-1237 . -147) 172587) ((-1237 . -619) 172258) ((-1237 . -232) 172228) ((-1237 . -906) 172079) ((-1237 . -234) 171984) ((-1237 . -367) 171963) ((-1237 . -1227) 171942) ((-1237 . -927) 171921) ((-1237 . -562) 171872) ((-1237 . -173) 171803) ((-1237 . -457) 171782) ((-1237 . -310) 171761) ((-1237 . -293) 171712) ((-1237 . -244) 171691) ((-1237 . -342) 171661) ((-1237 . -519) 171521) ((-1237 . -312) 171460) ((-1237 . -381) 171430) ((-1237 . -644) 171338) ((-1237 . -405) 171308) ((-1237 . -1222) 171287) ((-1237 . -892) 171160) ((-1237 . -825) 171113) ((-1237 . -796) 171066) ((-1237 . -797) 171019) ((-1237 . -855) 170918) ((-1237 . -799) 170871) ((-1237 . -802) 170824) ((-1237 . -853) 170777) ((-1237 . -890) 170747) ((-1237 . -916) 170700) ((-1237 . -1026) 170652) ((-1237 . -1044) 170438) ((-1237 . -1157) 170390) ((-1237 . -997) 170360) ((-1232 . -1236) 170321) ((-1232 . -1008) 170287) ((-1232 . -1208) 170253) ((-1232 . -1211) 170219) ((-1232 . -498) 170185) ((-1232 . -287) 170151) ((-1232 . -95) 170117) ((-1232 . -35) 170083) ((-1232 . -1251) 170060) ((-1232 . -47) 170037) ((-1232 . -621) 169832) ((-1232 . -722) 169628) ((-1232 . -645) 169424) ((-1232 . -653) 169276) ((-1232 . -651) 169113) ((-1232 . -1062) 168903) ((-1232 . -1057) 168693) ((-1232 . -111) 168462) ((-1232 . -38) 168258) ((-1232 . -979) 168227) ((-1232 . -289) 168075) ((-1232 . -1234) 168059) ((-1232 . -731) T) ((-1232 . -1118) T) ((-1232 . -1063) T) ((-1232 . -1055) T) ((-1232 . -21) T) ((-1232 . -23) T) ((-1232 . -1107) T) ((-1232 . -618) 168041) ((-1232 . -102) T) ((-1232 . -25) T) ((-1232 . -131) T) ((-1232 . -145) 167948) ((-1232 . -147) 167855) ((-1232 . -619) NIL) ((-1232 . -232) 167807) ((-1232 . -906) 167640) ((-1232 . -234) 167527) ((-1232 . -367) 167506) ((-1232 . -1227) 167485) ((-1232 . -927) 167464) ((-1232 . -562) 167415) ((-1232 . -173) 167346) ((-1232 . -457) 167325) ((-1232 . -310) 167304) ((-1232 . -293) 167255) ((-1232 . -244) 167234) ((-1232 . -342) 167186) ((-1232 . -519) 166955) ((-1232 . -312) 166840) ((-1232 . -381) 166792) ((-1232 . -644) 166744) ((-1232 . -405) 166696) ((-1232 . -1222) 166675) ((-1232 . -892) NIL) ((-1232 . -825) NIL) ((-1232 . -796) NIL) ((-1232 . -797) NIL) ((-1232 . -855) NIL) ((-1232 . -799) NIL) ((-1232 . -802) NIL) ((-1232 . -853) NIL) ((-1232 . -890) 166627) ((-1232 . -916) NIL) ((-1232 . -1026) NIL) ((-1232 . -1044) 166593) ((-1232 . -1157) NIL) ((-1232 . -997) 166545) ((-1231 . -849) T) ((-1231 . -855) T) ((-1231 . -1107) T) ((-1231 . -618) 166527) ((-1231 . -102) T) ((-1231 . -372) T) ((-1230 . -849) T) ((-1230 . -855) T) ((-1230 . -1107) T) ((-1230 . -618) 166509) ((-1230 . -102) T) ((-1230 . -372) T) ((-1229 . -849) T) ((-1229 . -855) T) ((-1229 . -1107) T) ((-1229 . -618) 166491) ((-1229 . -102) T) ((-1229 . -372) T) ((-1228 . -849) T) ((-1228 . -855) T) ((-1228 . -1107) T) ((-1228 . -618) 166473) ((-1228 . -102) T) ((-1228 . -372) T) ((-1223 . -1089) T) ((-1223 . -495) 166454) ((-1223 . -618) 166420) ((-1223 . -621) 166401) ((-1223 . -1107) T) ((-1223 . -102) T) ((-1223 . -93) T) ((-1220 . -495) 166378) ((-1220 . -618) 166290) ((-1220 . -621) 166267) ((-1220 . -1107) 166245) ((-1220 . -102) 166223) ((-1215 . -745) 166199) ((-1215 . -35) 166165) ((-1215 . -95) 166131) ((-1215 . -287) 166097) ((-1215 . -498) 166063) ((-1215 . -1211) 166029) ((-1215 . -1208) 165995) ((-1215 . -1008) 165961) ((-1215 . -47) 165930) ((-1215 . -38) 165827) ((-1215 . -645) 165724) ((-1215 . -722) 165621) ((-1215 . -621) 165503) ((-1215 . -293) 165482) ((-1215 . -562) 165461) ((-1215 . -111) 165330) ((-1215 . -1057) 165213) ((-1215 . -1062) 165096) ((-1215 . -173) 165047) ((-1215 . -147) 165026) ((-1215 . -145) 165005) ((-1215 . -653) 164930) ((-1215 . -651) 164840) ((-1215 . -979) 164802) ((-1215 . -1055) T) ((-1215 . -1063) T) ((-1215 . -1118) T) ((-1215 . -731) T) ((-1215 . -21) T) ((-1215 . -23) T) ((-1215 . -1107) T) ((-1215 . -618) 164784) ((-1215 . -102) T) ((-1215 . -25) T) ((-1215 . -131) T) ((-1215 . -906) 164765) ((-1215 . -519) 164732) ((-1215 . -312) 164719) ((-1209 . -1016) 164703) ((-1209 . -34) T) ((-1209 . -1222) T) ((-1209 . -618) 164635) ((-1209 . -312) 164573) ((-1209 . -519) 164506) ((-1209 . -1107) 164484) ((-1209 . -102) 164462) ((-1209 . -494) 164446) ((-1204 . -369) 164420) ((-1204 . -102) T) ((-1204 . -618) 164402) ((-1204 . -1107) T) ((-1202 . -1107) T) ((-1202 . -618) 164384) ((-1202 . -102) T) ((-1202 . -621) 164366) ((-1195 . -1199) 164345) ((-1195 . -230) 164295) ((-1195 . -107) 164245) ((-1195 . -312) 164049) ((-1195 . -519) 163841) ((-1195 . -494) 163778) ((-1195 . -151) 163728) ((-1195 . -619) NIL) ((-1195 . -236) 163678) ((-1195 . -615) 163657) ((-1195 . -291) 163636) ((-1195 . -289) 163615) ((-1195 . -102) T) ((-1195 . -1107) T) ((-1195 . -618) 163597) ((-1195 . -1222) T) ((-1195 . -34) T) ((-1195 . -609) 163576) ((-1193 . -1222) T) ((-1191 . -1107) T) ((-1191 . -618) 163558) ((-1191 . -102) T) ((-1190 . -849) T) ((-1190 . -855) T) ((-1190 . -1107) T) ((-1190 . -618) 163540) ((-1190 . -102) T) ((-1190 . -372) T) ((-1189 . -849) T) ((-1189 . -855) T) ((-1189 . -1107) T) ((-1189 . -618) 163522) ((-1189 . -102) T) ((-1189 . -372) T) ((-1188 . -1268) T) ((-1188 . -1107) T) ((-1188 . -618) 163489) ((-1188 . -102) T) ((-1188 . -1044) 163425) ((-1188 . -621) 163361) ((-1187 . -618) 163343) ((-1186 . -618) 163325) ((-1185 . -329) 163302) ((-1185 . -1044) 163198) ((-1185 . -417) 163182) ((-1185 . -38) 163079) ((-1185 . -621) 162932) ((-1185 . -653) 162857) ((-1185 . -651) 162767) ((-1185 . -731) T) ((-1185 . -1118) T) ((-1185 . -1063) T) ((-1185 . -1055) T) ((-1185 . -111) 162636) ((-1185 . -1057) 162519) ((-1185 . -1062) 162402) ((-1185 . -21) T) ((-1185 . -23) T) ((-1185 . -1107) T) ((-1185 . -618) 162384) ((-1185 . -102) T) ((-1185 . -25) T) ((-1185 . -131) T) ((-1185 . -645) 162281) ((-1185 . -722) 162178) ((-1185 . -145) 162157) ((-1185 . -147) 162136) ((-1185 . -173) 162087) ((-1185 . -562) 162066) ((-1185 . -293) 162045) ((-1185 . -47) 162022) ((-1183 . -855) T) ((-1183 . -102) T) ((-1183 . -618) 162004) ((-1183 . -1107) T) ((-1183 . -619) 161926) ((-1183 . -826) T) ((-1183 . -621) 161907) ((-1183 . -892) 161874) ((-1182 . -618) 161856) ((-1181 . -1265) 161840) ((-1181 . -234) 161799) ((-1181 . -621) 161681) ((-1181 . -653) 161606) ((-1181 . -651) 161516) ((-1181 . -131) T) ((-1181 . -25) T) ((-1181 . -102) T) ((-1181 . -618) 161498) ((-1181 . -1107) T) ((-1181 . -23) T) ((-1181 . -21) T) ((-1181 . -731) T) ((-1181 . -1118) T) ((-1181 . -1063) T) ((-1181 . -1055) T) ((-1181 . -289) 161483) ((-1181 . -906) 161396) ((-1181 . -979) 161365) ((-1181 . -38) 161262) ((-1181 . -111) 161131) ((-1181 . -1057) 161014) ((-1181 . -1062) 160897) ((-1181 . -645) 160794) ((-1181 . -722) 160691) ((-1181 . -145) 160670) ((-1181 . -147) 160649) ((-1181 . -173) 160600) ((-1181 . -562) 160579) ((-1181 . -293) 160558) ((-1181 . -47) 160535) ((-1181 . -1251) 160512) ((-1181 . -35) 160478) ((-1181 . -95) 160444) ((-1181 . -287) 160410) ((-1181 . -498) 160376) ((-1181 . -1211) 160342) ((-1181 . -1208) 160308) ((-1181 . -1008) 160274) ((-1180 . -1257) 160235) ((-1180 . -367) 160214) ((-1180 . -1227) 160193) ((-1180 . -927) 160172) ((-1180 . -562) 160123) ((-1180 . -173) 160054) ((-1180 . -621) 159797) ((-1180 . -722) 159638) ((-1180 . -645) 159479) ((-1180 . -38) 159320) ((-1180 . -457) 159299) ((-1180 . -310) 159278) ((-1180 . -653) 159175) ((-1180 . -651) 159057) ((-1180 . -731) T) ((-1180 . -1118) T) ((-1180 . -1063) T) ((-1180 . -1055) T) ((-1180 . -111) 158878) ((-1180 . -1057) 158713) ((-1180 . -1062) 158548) ((-1180 . -21) T) ((-1180 . -23) T) ((-1180 . -1107) T) ((-1180 . -618) 158530) ((-1180 . -102) T) ((-1180 . -25) T) ((-1180 . -131) T) ((-1180 . -293) 158481) ((-1180 . -244) 158460) ((-1180 . -1008) 158426) ((-1180 . -1208) 158392) ((-1180 . -1211) 158358) ((-1180 . -498) 158324) ((-1180 . -287) 158290) ((-1180 . -95) 158256) ((-1180 . -35) 158222) ((-1180 . -1251) 158192) ((-1180 . -47) 158162) ((-1180 . -147) 158141) ((-1180 . -145) 158120) ((-1180 . -979) 158082) ((-1180 . -906) 157988) ((-1180 . -289) 157973) ((-1180 . -234) 157925) ((-1180 . -1255) 157909) ((-1180 . -1044) 157844) ((-1177 . -1248) 157828) ((-1177 . -1157) 157806) ((-1177 . -619) NIL) ((-1177 . -312) 157793) ((-1177 . -519) 157740) ((-1177 . -329) 157717) ((-1177 . -1044) 157597) ((-1177 . -417) 157581) ((-1177 . -38) 157410) ((-1177 . -111) 157219) ((-1177 . -1057) 157042) ((-1177 . -1062) 156865) ((-1177 . -651) 156775) ((-1177 . -653) 156700) ((-1177 . -645) 156529) ((-1177 . -722) 156358) ((-1177 . -621) 156127) ((-1177 . -145) 156106) ((-1177 . -147) 156085) ((-1177 . -47) 156062) ((-1177 . -381) 156046) ((-1177 . -644) 155994) ((-1177 . -906) 155937) ((-1177 . -892) NIL) ((-1177 . -916) 155916) ((-1177 . -1227) 155895) ((-1177 . -956) 155864) ((-1177 . -927) 155843) ((-1177 . -562) 155754) ((-1177 . -293) 155665) ((-1177 . -173) 155556) ((-1177 . -457) 155487) ((-1177 . -310) 155466) ((-1177 . -289) 155393) ((-1177 . -234) T) ((-1177 . -131) T) ((-1177 . -25) T) ((-1177 . -102) T) ((-1177 . -618) 155375) ((-1177 . -1107) T) ((-1177 . -23) T) ((-1177 . -21) T) ((-1177 . -731) T) ((-1177 . -1118) T) ((-1177 . -1063) T) ((-1177 . -1055) T) ((-1177 . -232) 155359) ((-1174 . -1236) 155320) ((-1174 . -1008) 155286) ((-1174 . -1208) 155252) ((-1174 . -1211) 155218) ((-1174 . -498) 155184) ((-1174 . -287) 155150) ((-1174 . -95) 155116) ((-1174 . -35) 155082) ((-1174 . -1251) 155059) ((-1174 . -47) 155036) ((-1174 . -621) 154831) ((-1174 . -722) 154627) ((-1174 . -645) 154423) ((-1174 . -653) 154275) ((-1174 . -651) 154112) ((-1174 . -1062) 153902) ((-1174 . -1057) 153692) ((-1174 . -111) 153461) ((-1174 . -38) 153257) ((-1174 . -979) 153226) ((-1174 . -289) 153074) ((-1174 . -1234) 153058) ((-1174 . -731) T) ((-1174 . -1118) T) ((-1174 . -1063) T) ((-1174 . -1055) T) ((-1174 . -21) T) ((-1174 . -23) T) ((-1174 . -1107) T) ((-1174 . -618) 153040) ((-1174 . -102) T) ((-1174 . -25) T) ((-1174 . -131) T) ((-1174 . -145) 152947) ((-1174 . -147) 152854) ((-1174 . -619) NIL) ((-1174 . -232) 152806) ((-1174 . -906) 152639) ((-1174 . -234) 152526) ((-1174 . -367) 152505) ((-1174 . -1227) 152484) ((-1174 . -927) 152463) ((-1174 . -562) 152414) ((-1174 . -173) 152345) ((-1174 . -457) 152324) ((-1174 . -310) 152303) ((-1174 . -293) 152254) ((-1174 . -244) 152233) ((-1174 . -342) 152185) ((-1174 . -519) 151954) ((-1174 . -312) 151839) ((-1174 . -381) 151791) ((-1174 . -644) 151743) ((-1174 . -405) 151695) ((-1174 . -1222) 151674) ((-1174 . -892) NIL) ((-1174 . -825) NIL) ((-1174 . -796) NIL) ((-1174 . -797) NIL) ((-1174 . -855) NIL) ((-1174 . -799) NIL) ((-1174 . -802) NIL) ((-1174 . -853) NIL) ((-1174 . -890) 151626) ((-1174 . -916) NIL) ((-1174 . -1026) NIL) ((-1174 . -1044) 151592) ((-1174 . -1157) NIL) ((-1174 . -997) 151544) ((-1173 . -1089) T) ((-1173 . -495) 151525) ((-1173 . -618) 151491) ((-1173 . -621) 151472) ((-1173 . -1107) T) ((-1173 . -102) T) ((-1173 . -93) T) ((-1172 . -1107) T) ((-1172 . -618) 151454) ((-1172 . -102) T) ((-1171 . -1107) T) ((-1171 . -618) 151436) ((-1171 . -102) T) ((-1166 . -1199) 151412) ((-1166 . -230) 151359) ((-1166 . -107) 151306) ((-1166 . -312) 151101) ((-1166 . -519) 150884) ((-1166 . -494) 150818) ((-1166 . -151) 150765) ((-1166 . -619) NIL) ((-1166 . -236) 150712) ((-1166 . -615) 150688) ((-1166 . -291) 150664) ((-1166 . -289) 150640) ((-1166 . -102) T) ((-1166 . -1107) T) ((-1166 . -618) 150622) ((-1166 . -1222) T) ((-1166 . -34) T) ((-1166 . -609) 150598) ((-1165 . -1164) T) ((-1165 . -19) 150580) ((-1165 . -656) 150562) ((-1165 . -291) 150537) ((-1165 . -289) 150512) ((-1165 . -609) 150487) ((-1165 . -619) NIL) ((-1165 . -494) 150469) ((-1165 . -519) NIL) ((-1165 . -312) NIL) ((-1165 . -1222) T) ((-1165 . -34) T) ((-1165 . -151) 150451) ((-1165 . -855) T) ((-1165 . -376) 150433) ((-1165 . -1150) T) ((-1165 . -102) T) ((-1165 . -618) 150415) ((-1165 . -1107) T) ((-1165 . -826) T) ((-1160 . -679) 150399) ((-1160 . -656) 150383) ((-1160 . -291) 150360) ((-1160 . -289) 150337) ((-1160 . -609) 150314) ((-1160 . -619) 150275) ((-1160 . -494) 150259) ((-1160 . -102) 150237) ((-1160 . -1107) 150215) ((-1160 . -519) 150148) ((-1160 . -312) 150086) ((-1160 . -618) 150018) ((-1160 . -1222) T) ((-1160 . -34) T) ((-1160 . -151) 150002) ((-1160 . -1261) 149986) ((-1160 . -1016) 149970) ((-1160 . -1155) 149954) ((-1160 . -621) 149931) ((-1158 . -1089) T) ((-1158 . -495) 149912) ((-1158 . -618) 149878) ((-1158 . -621) 149859) ((-1158 . -1107) T) ((-1158 . -102) T) ((-1158 . -93) T) ((-1156 . -1199) 149838) ((-1156 . -230) 149788) ((-1156 . -107) 149738) ((-1156 . -312) 149542) ((-1156 . -519) 149334) ((-1156 . -494) 149271) ((-1156 . -151) 149221) ((-1156 . -619) NIL) ((-1156 . -236) 149171) ((-1156 . -615) 149150) ((-1156 . -291) 149129) ((-1156 . -289) 149108) ((-1156 . -102) T) ((-1156 . -1107) T) ((-1156 . -618) 149090) ((-1156 . -1222) T) ((-1156 . -34) T) ((-1156 . -609) 149069) ((-1153 . -1127) 149053) ((-1153 . -494) 149037) ((-1153 . -102) 149015) ((-1153 . -1107) 148993) ((-1153 . -519) 148926) ((-1153 . -312) 148864) ((-1153 . -618) 148796) ((-1153 . -1222) T) ((-1153 . -34) T) ((-1153 . -107) 148780) ((-1152 . -1115) 148749) ((-1152 . -1217) 148718) ((-1152 . -618) 148680) ((-1152 . -151) 148664) ((-1152 . -34) T) ((-1152 . -1222) T) ((-1152 . -312) 148602) ((-1152 . -519) 148535) ((-1152 . -1107) T) ((-1152 . -102) T) ((-1152 . -494) 148519) ((-1152 . -619) 148480) ((-1152 . -982) 148449) ((-1152 . -1077) 148418) ((-1148 . -1129) 148363) ((-1148 . -494) 148347) ((-1148 . -519) 148280) ((-1148 . -312) 148218) ((-1148 . -1222) T) ((-1148 . -34) T) ((-1148 . -1059) 148158) ((-1148 . -1044) 148054) ((-1148 . -621) 147972) ((-1148 . -417) 147956) ((-1148 . -644) 147904) ((-1148 . -381) 147888) ((-1148 . -234) 147867) ((-1148 . -906) 147826) ((-1148 . -232) 147810) ((-1148 . -722) 147742) ((-1148 . -645) 147674) ((-1148 . -653) 147648) ((-1148 . -651) 147607) ((-1148 . -131) T) ((-1148 . -25) T) ((-1148 . -102) T) ((-1148 . -618) 147569) ((-1148 . -1107) T) ((-1148 . -23) T) ((-1148 . -21) T) ((-1148 . -1062) 147553) ((-1148 . -1057) 147537) ((-1148 . -111) 147516) ((-1148 . -1055) T) ((-1148 . -1063) T) ((-1148 . -1118) T) ((-1148 . -731) T) ((-1148 . -38) 147476) ((-1148 . -619) 147437) ((-1147 . -1016) 147408) ((-1147 . -34) T) ((-1147 . -1222) T) ((-1147 . -618) 147390) ((-1147 . -312) 147316) ((-1147 . -519) 147235) ((-1147 . -1107) T) ((-1147 . -102) T) ((-1147 . -494) 147206) ((-1146 . -1107) T) ((-1146 . -618) 147188) ((-1146 . -102) T) ((-1141 . -1143) T) ((-1141 . -1268) T) ((-1141 . -93) T) ((-1141 . -102) T) ((-1141 . -618) 147154) ((-1141 . -1107) T) ((-1141 . -621) 147135) ((-1141 . -495) 147116) ((-1141 . -1089) T) ((-1139 . -1140) 147100) ((-1139 . -102) T) ((-1139 . -618) 147082) ((-1139 . -1107) T) ((-1132 . -745) 147061) ((-1132 . -35) 147027) ((-1132 . -95) 146993) ((-1132 . -287) 146959) ((-1132 . -498) 146925) ((-1132 . -1211) 146891) ((-1132 . -1208) 146857) ((-1132 . -1008) 146823) ((-1132 . -47) 146795) ((-1132 . -38) 146692) ((-1132 . -645) 146589) ((-1132 . -722) 146486) ((-1132 . -621) 146368) ((-1132 . -293) 146347) ((-1132 . -562) 146326) ((-1132 . -111) 146195) ((-1132 . -1057) 146078) ((-1132 . -1062) 145961) ((-1132 . -173) 145912) ((-1132 . -147) 145891) ((-1132 . -145) 145870) ((-1132 . -653) 145795) ((-1132 . -651) 145705) ((-1132 . -979) 145672) ((-1132 . -1055) T) ((-1132 . -1063) T) ((-1132 . -1118) T) ((-1132 . -731) T) ((-1132 . -21) T) ((-1132 . -23) T) ((-1132 . -1107) T) ((-1132 . -618) 145654) ((-1132 . -102) T) ((-1132 . -25) T) ((-1132 . -131) T) ((-1132 . -906) 145638) ((-1132 . -519) 145608) ((-1132 . -312) 145595) ((-1131 . -956) 145562) ((-1131 . -621) 145354) ((-1131 . -1044) 145237) ((-1131 . -1227) 145216) ((-1131 . -916) 145195) ((-1131 . -892) 145054) ((-1131 . -906) 145038) ((-1131 . -519) 144990) ((-1131 . -457) 144941) ((-1131 . -644) 144889) ((-1131 . -381) 144873) ((-1131 . -47) 144845) ((-1131 . -38) 144694) ((-1131 . -645) 144543) ((-1131 . -722) 144392) ((-1131 . -293) 144323) ((-1131 . -562) 144254) ((-1131 . -111) 144083) ((-1131 . -1057) 143926) ((-1131 . -1062) 143769) ((-1131 . -173) 143680) ((-1131 . -147) 143659) ((-1131 . -145) 143638) ((-1131 . -653) 143563) ((-1131 . -651) 143473) ((-1131 . -131) T) ((-1131 . -25) T) ((-1131 . -102) T) ((-1131 . -618) 143455) ((-1131 . -1107) T) ((-1131 . -23) T) ((-1131 . -21) T) ((-1131 . -1055) T) ((-1131 . -1063) T) ((-1131 . -1118) T) ((-1131 . -731) T) ((-1131 . -417) 143439) ((-1131 . -329) 143411) ((-1131 . -312) 143398) ((-1131 . -619) 143146) ((-1126 . -550) T) ((-1126 . -1227) T) ((-1126 . -1157) T) ((-1126 . -1044) 143128) ((-1126 . -619) 143043) ((-1126 . -1026) T) ((-1126 . -892) 143025) ((-1126 . -853) T) ((-1126 . -802) T) ((-1126 . -799) T) ((-1126 . -855) T) ((-1126 . -797) T) ((-1126 . -796) T) ((-1126 . -825) T) ((-1126 . -644) 143007) ((-1126 . -927) T) ((-1126 . -562) T) ((-1126 . -293) T) ((-1126 . -173) T) ((-1126 . -621) 142979) ((-1126 . -722) 142966) ((-1126 . -645) 142953) ((-1126 . -1062) 142940) ((-1126 . -1057) 142927) ((-1126 . -111) 142912) ((-1126 . -38) 142899) ((-1126 . -457) T) ((-1126 . -310) T) ((-1126 . -234) T) ((-1126 . -143) T) ((-1126 . -1055) T) ((-1126 . -1063) T) ((-1126 . -1118) T) ((-1126 . -731) T) ((-1126 . -21) T) ((-1126 . -651) 142871) ((-1126 . -23) T) ((-1126 . -1107) T) ((-1126 . -618) 142853) ((-1126 . -102) T) ((-1126 . -25) T) ((-1126 . -131) T) ((-1126 . -653) 142840) ((-1126 . -147) T) ((-1126 . -849) T) ((-1126 . -372) T) ((-1126 . -667) T) ((-1126 . -826) T) ((-1122 . -1089) T) ((-1122 . -495) 142821) ((-1122 . -618) 142787) ((-1122 . -621) 142768) ((-1122 . -1107) T) ((-1122 . -102) T) ((-1122 . -93) T) ((-1121 . -1107) T) ((-1121 . -618) 142750) ((-1121 . -102) T) ((-1119 . -239) 142729) ((-1119 . -1280) 142699) ((-1119 . -796) 142678) ((-1119 . -853) 142657) ((-1119 . -802) 142608) ((-1119 . -799) 142559) ((-1119 . -855) 142510) ((-1119 . -797) 142461) ((-1119 . -798) 142440) ((-1119 . -291) 142417) ((-1119 . -289) 142394) ((-1119 . -494) 142378) ((-1119 . -519) 142311) ((-1119 . -312) 142249) ((-1119 . -1222) T) ((-1119 . -34) T) ((-1119 . -609) 142226) ((-1119 . -1044) 142053) ((-1119 . -621) 141783) ((-1119 . -417) 141752) ((-1119 . -644) 141658) ((-1119 . -381) 141627) ((-1119 . -372) 141606) ((-1119 . -234) 141558) ((-1119 . -906) 141490) ((-1119 . -232) 141459) ((-1119 . -111) 141349) ((-1119 . -1057) 141246) ((-1119 . -1062) 141143) ((-1119 . -173) 141122) ((-1119 . -618) 140853) ((-1119 . -722) 140795) ((-1119 . -645) 140737) ((-1119 . -653) 140585) ((-1119 . -651) 140335) ((-1119 . -131) 140205) ((-1119 . -23) 140075) ((-1119 . -21) 139985) ((-1119 . -1055) 139915) ((-1119 . -1063) 139845) ((-1119 . -1118) 139755) ((-1119 . -731) 139665) ((-1119 . -38) 139635) ((-1119 . -1107) 139425) ((-1119 . -102) 139215) ((-1119 . -25) 139066) ((-1112 . -401) T) ((-1112 . -1222) T) ((-1112 . -618) 139048) ((-1111 . -1110) 139012) ((-1111 . -102) T) ((-1111 . -618) 138994) ((-1111 . -1107) T) ((-1111 . -623) 138909) ((-1109 . -1110) 138861) ((-1109 . -102) T) ((-1109 . -618) 138843) ((-1109 . -1107) T) ((-1109 . -623) 138746) ((-1108 . -372) T) ((-1108 . -102) T) ((-1108 . -618) 138728) ((-1108 . -1107) T) ((-1103 . -431) 138712) ((-1103 . -1105) 138696) ((-1103 . -372) 138675) ((-1103 . -236) 138659) ((-1103 . -619) 138620) ((-1103 . -151) 138604) ((-1103 . -494) 138588) ((-1103 . -102) T) ((-1103 . -1107) T) ((-1103 . -519) 138521) ((-1103 . -312) 138459) ((-1103 . -618) 138441) ((-1103 . -1222) T) ((-1103 . -34) T) ((-1103 . -107) 138425) ((-1103 . -230) 138409) ((-1102 . -1089) T) ((-1102 . -495) 138390) ((-1102 . -618) 138356) ((-1102 . -621) 138337) ((-1102 . -1107) T) ((-1102 . -102) T) ((-1102 . -93) T) ((-1098 . -1222) T) ((-1098 . -1107) 138307) ((-1098 . -618) 138266) ((-1098 . -102) 138236) ((-1097 . -1089) T) ((-1097 . -495) 138217) ((-1097 . -618) 138183) ((-1097 . -621) 138164) ((-1097 . -1107) T) ((-1097 . -102) T) ((-1097 . -93) T) ((-1095 . -1100) 138148) ((-1095 . -623) 138132) ((-1095 . -1107) 138110) ((-1095 . -618) 138077) ((-1095 . -102) 138055) ((-1095 . -1101) 138013) ((-1094 . -268) 137997) ((-1094 . -621) 137981) ((-1094 . -1044) 137965) ((-1094 . -1107) T) ((-1094 . -618) 137947) ((-1094 . -102) T) ((-1094 . -855) T) ((-1093 . -255) 137884) ((-1093 . -621) 137620) ((-1093 . -1044) 137447) ((-1093 . -619) NIL) ((-1093 . -329) 137408) ((-1093 . -417) 137392) ((-1093 . -38) 137241) ((-1093 . -111) 137070) ((-1093 . -1057) 136913) ((-1093 . -1062) 136756) ((-1093 . -651) 136666) ((-1093 . -653) 136591) ((-1093 . -645) 136440) ((-1093 . -722) 136289) ((-1093 . -145) 136268) ((-1093 . -147) 136247) ((-1093 . -173) 136158) ((-1093 . -562) 136089) ((-1093 . -293) 136020) ((-1093 . -47) 135981) ((-1093 . -381) 135965) ((-1093 . -644) 135913) ((-1093 . -457) 135864) ((-1093 . -519) 135731) ((-1093 . -906) 135666) ((-1093 . -892) NIL) ((-1093 . -916) 135645) ((-1093 . -1227) 135624) ((-1093 . -956) 135569) ((-1093 . -312) 135556) ((-1093 . -234) 135535) ((-1093 . -131) T) ((-1093 . -25) T) ((-1093 . -102) T) ((-1093 . -618) 135517) ((-1093 . -1107) T) ((-1093 . -23) T) ((-1093 . -21) T) ((-1093 . -731) T) ((-1093 . -1118) T) ((-1093 . -1063) T) ((-1093 . -1055) T) ((-1093 . -232) 135501) ((-1091 . -618) 135483) ((-1088 . -855) T) ((-1088 . -102) T) ((-1088 . -618) 135465) ((-1088 . -1107) T) ((-1088 . -619) 135446) ((-1085 . -729) 135425) ((-1085 . -1044) 135321) ((-1085 . -417) 135305) ((-1085 . -644) 135253) ((-1085 . -381) 135237) ((-1085 . -374) 135216) ((-1085 . -147) 135195) ((-1085 . -621) 135013) ((-1085 . -722) 134881) ((-1085 . -645) 134749) ((-1085 . -653) 134659) ((-1085 . -651) 134554) ((-1085 . -1062) 134464) ((-1085 . -1057) 134374) ((-1085 . -111) 134270) ((-1085 . -38) 134138) ((-1085 . -415) 134117) ((-1085 . -407) 134096) ((-1085 . -145) 134047) ((-1085 . -1157) 134026) ((-1085 . -354) 134005) ((-1085 . -372) 133956) ((-1085 . -244) 133907) ((-1085 . -293) 133858) ((-1085 . -310) 133809) ((-1085 . -457) 133760) ((-1085 . -562) 133711) ((-1085 . -927) 133662) ((-1085 . -1227) 133613) ((-1085 . -367) 133564) ((-1085 . -234) 133489) ((-1085 . -906) 133422) ((-1085 . -232) 133392) ((-1085 . -619) 133376) ((-1085 . -21) T) ((-1085 . -23) T) ((-1085 . -1107) T) ((-1085 . -618) 133358) ((-1085 . -102) T) ((-1085 . -25) T) ((-1085 . -131) T) ((-1085 . -1055) T) ((-1085 . -1063) T) ((-1085 . -1118) T) ((-1085 . -731) T) ((-1085 . -173) T) 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-609) 132339) ((-1068 . -550) T) ((-1068 . -1227) T) ((-1068 . -1157) T) ((-1068 . -1044) 132321) ((-1068 . -619) 132236) ((-1068 . -1026) T) ((-1068 . -892) 132218) ((-1068 . -853) T) ((-1068 . -802) T) ((-1068 . -799) T) ((-1068 . -855) T) ((-1068 . -797) T) ((-1068 . -796) T) ((-1068 . -825) T) ((-1068 . -644) 132200) ((-1068 . -927) T) ((-1068 . -562) T) ((-1068 . -293) T) ((-1068 . -173) T) ((-1068 . -621) 132172) ((-1068 . -722) 132159) ((-1068 . -645) 132146) ((-1068 . -1062) 132133) ((-1068 . -1057) 132120) ((-1068 . -111) 132105) ((-1068 . -38) 132092) ((-1068 . -457) T) ((-1068 . -310) T) ((-1068 . -234) T) ((-1068 . -143) T) ((-1068 . -1055) T) ((-1068 . -1063) T) ((-1068 . -1118) T) ((-1068 . -731) T) ((-1068 . -21) T) ((-1068 . -651) 132064) ((-1068 . -23) T) ((-1068 . -1107) T) ((-1068 . -618) 132046) ((-1068 . -102) T) ((-1068 . -25) T) ((-1068 . -131) T) ((-1068 . -653) 132033) ((-1068 . -147) T) ((-1068 . -623) 132014) ((-1067 . -1074) 131993) ((-1067 . -102) T) 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-621) 130709) ((-1042 . -1107) T) ((-1042 . -102) T) ((-1042 . -93) T) ((-1041 . -1199) 130684) ((-1041 . -230) 130630) ((-1041 . -107) 130576) ((-1041 . -312) 130427) ((-1041 . -519) 130271) ((-1041 . -494) 130202) ((-1041 . -151) 130148) ((-1041 . -619) NIL) ((-1041 . -236) 130094) ((-1041 . -615) 130069) ((-1041 . -291) 130044) ((-1041 . -289) 130019) ((-1041 . -102) T) ((-1041 . -1107) T) ((-1041 . -618) 130001) ((-1041 . -1222) T) ((-1041 . -34) T) ((-1041 . -609) 129976) ((-1040 . -173) T) ((-1040 . -621) 129945) ((-1040 . -731) T) ((-1040 . -1118) T) ((-1040 . -1063) T) ((-1040 . -1055) T) ((-1040 . -653) 129919) ((-1040 . -651) 129878) ((-1040 . -131) T) ((-1040 . -25) T) ((-1040 . -102) T) ((-1040 . -618) 129860) ((-1040 . -1107) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -1062) 129834) ((-1040 . -1057) 129808) ((-1040 . -111) 129775) ((-1040 . -38) 129759) ((-1040 . -645) 129743) ((-1040 . -722) 129727) ((-1033 . -1077) 129696) ((-1033 . -982) 129665) ((-1033 . -619) 129626) ((-1033 . -494) 129610) ((-1033 . -102) T) ((-1033 . -1107) T) ((-1033 . -519) 129543) ((-1033 . -312) 129481) ((-1033 . -618) 129443) ((-1033 . -1222) T) ((-1033 . -34) T) ((-1033 . -151) 129427) ((-1033 . -1217) 129396) ((-1032 . -1222) T) ((-1032 . -1107) 129374) ((-1032 . -618) 129341) ((-1032 . -102) 129319) ((-1030 . -1018) T) ((-1030 . -1008) T) ((-1030 . -796) T) ((-1030 . -797) T) ((-1030 . -855) T) ((-1030 . -799) T) ((-1030 . -802) T) ((-1030 . -853) T) ((-1030 . -1044) 129199) ((-1030 . -417) 129161) ((-1030 . -244) T) ((-1030 . -293) T) ((-1030 . -310) T) ((-1030 . -457) T) ((-1030 . -38) 129098) ((-1030 . -645) 129035) ((-1030 . -722) 128972) ((-1030 . -621) 128909) ((-1030 . -562) T) ((-1030 . -927) T) ((-1030 . -1227) T) ((-1030 . -367) T) ((-1030 . -111) 128825) ((-1030 . -1057) 128762) ((-1030 . -1062) 128699) ((-1030 . -173) T) ((-1030 . -147) T) ((-1030 . -653) 128636) ((-1030 . -651) 128573) ((-1030 . -131) T) ((-1030 . -25) T) ((-1030 . -102) T) ((-1030 . -618) 128555) ((-1030 . -1107) T) ((-1030 . -23) T) ((-1030 . -21) T) ((-1030 . -1055) T) ((-1030 . -1063) T) ((-1030 . -1118) T) ((-1030 . -731) T) ((-1025 . -1089) T) ((-1025 . -495) 128536) ((-1025 . -618) 128502) ((-1025 . -621) 128483) ((-1025 . -1107) T) ((-1025 . -102) T) ((-1025 . -93) T) ((-1010 . -997) 128465) ((-1010 . -1157) T) ((-1010 . -621) 128415) ((-1010 . -1044) 128375) ((-1010 . -619) 128305) ((-1010 . -1026) T) ((-1010 . -916) NIL) ((-1010 . -890) 128287) ((-1010 . -853) T) ((-1010 . -802) T) ((-1010 . -799) T) ((-1010 . -855) T) ((-1010 . -797) T) ((-1010 . -796) T) ((-1010 . -825) T) ((-1010 . -892) 128269) ((-1010 . -1222) T) ((-1010 . -405) 128251) ((-1010 . -644) 128233) ((-1010 . -381) 128215) ((-1010 . -289) NIL) ((-1010 . -312) NIL) ((-1010 . -519) NIL) ((-1010 . -342) 128197) ((-1010 . -244) T) ((-1010 . -111) 128131) ((-1010 . -1057) 128081) ((-1010 . -1062) 128031) ((-1010 . -293) T) ((-1010 . -722) 127981) ((-1010 . -645) 127931) ((-1010 . -653) 127881) ((-1010 . -651) 127831) ((-1010 . -38) 127781) ((-1010 . -310) T) ((-1010 . -457) T) ((-1010 . -173) T) ((-1010 . -562) T) ((-1010 . -927) T) ((-1010 . -1227) T) ((-1010 . -367) T) ((-1010 . -234) T) ((-1010 . -906) NIL) ((-1010 . -232) 127763) ((-1010 . -147) T) ((-1010 . -145) NIL) ((-1010 . -131) T) ((-1010 . -25) T) ((-1010 . -102) T) ((-1010 . -618) 127723) ((-1010 . -1107) T) ((-1010 . -23) T) ((-1010 . -21) T) ((-1010 . -1055) T) ((-1010 . -1063) T) ((-1010 . -1118) T) ((-1010 . -731) T) ((-1009 . -346) 127697) ((-1009 . -173) T) ((-1009 . -621) 127627) ((-1009 . -731) T) ((-1009 . -1118) T) ((-1009 . -1063) T) ((-1009 . -1055) T) ((-1009 . -653) 127572) ((-1009 . -651) 127502) ((-1009 . -131) T) ((-1009 . -25) T) ((-1009 . -102) T) ((-1009 . -618) 127484) ((-1009 . -1107) T) ((-1009 . -23) T) ((-1009 . -21) T) ((-1009 . -1062) 127429) ((-1009 . -1057) 127374) ((-1009 . -111) 127303) ((-1009 . -619) 127287) ((-1009 . -232) 127264) ((-1009 . -906) 127216) ((-1009 . -234) 127188) ((-1009 . -367) T) ((-1009 . -1227) T) ((-1009 . -927) T) ((-1009 . -562) T) ((-1009 . -722) 127133) ((-1009 . -645) 127078) ((-1009 . -38) 127023) ((-1009 . -457) T) ((-1009 . -310) T) ((-1009 . -293) T) ((-1009 . -244) T) ((-1009 . -372) NIL) ((-1009 . -354) NIL) ((-1009 . -1157) NIL) ((-1009 . -145) 126995) ((-1009 . -407) NIL) ((-1009 . -415) 126967) ((-1009 . -147) 126939) ((-1009 . -374) 126911) ((-1009 . -381) 126888) ((-1009 . -644) 126827) ((-1009 . -417) 126804) ((-1009 . -1044) 126692) ((-1009 . -729) 126664) ((-1006 . -1001) 126648) ((-1006 . -494) 126632) ((-1006 . -102) 126610) ((-1006 . -1107) 126588) ((-1006 . -519) 126521) ((-1006 . -312) 126459) ((-1006 . -618) 126391) ((-1006 . -1222) T) ((-1006 . -34) T) ((-1006 . -107) 126375) ((-1002 . -1004) 126359) ((-1002 . -855) 126338) ((-1002 . -1044) 126234) ((-1002 . -417) 126218) ((-1002 . -644) 126166) ((-1002 . -381) 126150) ((-1002 . -289) 126108) ((-1002 . -312) 126073) ((-1002 . -519) 125985) ((-1002 . -342) 125969) 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-102) T) ((-977 . -802) T) ((-977 . -799) T) ((-977 . -855) T) ((-977 . -797) T) ((-977 . -23) T) ((-977 . -1107) T) ((-977 . -618) 124807) ((-977 . -102) T) ((-977 . -25) T) ((-977 . -131) T) ((-977 . -619) 124782) ((-976 . -1089) T) ((-976 . -495) 124763) ((-976 . -618) 124729) ((-976 . -621) 124710) ((-976 . -1107) T) ((-976 . -102) T) ((-976 . -93) T) ((-972 . -973) T) ((-972 . -102) T) ((-972 . -618) 124692) ((-972 . -1107) T) ((-972 . -621) 124676) ((-971 . -618) 124658) ((-970 . -1107) T) ((-970 . -618) 124640) ((-970 . -102) T) ((-970 . -372) 124593) ((-970 . -731) 124492) ((-970 . -1118) 124391) ((-970 . -23) 124202) ((-970 . -25) 124013) ((-970 . -131) 123868) ((-970 . -478) 123821) ((-970 . -21) 123776) ((-970 . -651) 123720) ((-970 . -798) 123673) ((-970 . -797) 123626) ((-970 . -855) 123525) ((-970 . -799) 123478) ((-970 . -802) 123431) ((-964 . -19) 123415) ((-964 . -656) 123399) ((-964 . -291) 123376) ((-964 . -289) 123353) ((-964 . -609) 123330) ((-964 . -619) 123291) 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. -1227) 121181) ((-952 . -916) 121160) ((-952 . -892) 121085) ((-952 . -906) 121066) ((-952 . -519) 121013) ((-952 . -457) 120964) ((-952 . -644) 120912) ((-952 . -381) 120896) ((-952 . -47) 120865) ((-952 . -38) 120714) ((-952 . -645) 120563) ((-952 . -722) 120412) ((-952 . -293) 120343) ((-952 . -562) 120274) ((-952 . -111) 120103) ((-952 . -1057) 119946) ((-952 . -1062) 119789) ((-952 . -173) 119700) ((-952 . -147) 119679) ((-952 . -145) 119658) ((-952 . -653) 119583) ((-952 . -651) 119493) ((-952 . -131) T) ((-952 . -25) T) ((-952 . -102) T) ((-952 . -618) 119475) ((-952 . -1107) T) ((-952 . -23) T) ((-952 . -21) T) ((-952 . -1055) T) ((-952 . -1063) T) ((-952 . -1118) T) ((-952 . -731) T) ((-952 . -417) 119459) ((-952 . -329) 119428) ((-952 . -312) 119415) ((-952 . -619) 119276) ((-949 . -986) 119260) ((-949 . -19) 119244) ((-949 . -656) 119228) ((-949 . -291) 119205) ((-949 . -289) 119182) ((-949 . -609) 119159) ((-949 . -619) 119120) ((-949 . -494) 119104) ((-949 . -102) 119054) ((-949 . -1107) 119004) ((-949 . -519) 118937) ((-949 . -312) 118875) ((-949 . -618) 118787) ((-949 . -1222) T) ((-949 . -34) T) ((-949 . -151) 118771) ((-949 . -855) 118750) ((-949 . -376) 118734) ((-949 . -1271) 118718) ((-949 . -623) 118695) ((-933 . -980) T) ((-933 . -618) 118677) ((-931 . -961) T) ((-931 . -618) 118659) ((-925 . -799) T) ((-925 . -855) T) ((-925 . -1107) T) ((-925 . -618) 118641) ((-925 . -102) T) ((-925 . -25) T) ((-925 . -731) T) ((-925 . -1118) T) ((-920 . -367) T) ((-920 . -1227) T) ((-920 . -927) T) ((-920 . -562) T) ((-920 . -173) T) ((-920 . -621) 118578) ((-920 . -722) 118530) ((-920 . -645) 118482) ((-920 . -38) 118434) ((-920 . -457) T) ((-920 . -310) T) ((-920 . -653) 118386) ((-920 . -651) 118323) ((-920 . -731) T) ((-920 . -1118) T) ((-920 . -1063) T) ((-920 . -1055) T) ((-920 . -111) 118261) ((-920 . -1057) 118213) ((-920 . -1062) 118165) ((-920 . -21) T) ((-920 . -23) T) ((-920 . -1107) T) ((-920 . -618) 118147) ((-920 . -102) T) ((-920 . -25) T) ((-920 . -131) T) ((-920 . -293) T) ((-920 . -244) T) ((-912 . -354) T) ((-912 . -1157) T) ((-912 . -372) T) ((-912 . -145) T) ((-912 . -367) T) ((-912 . -1227) T) ((-912 . -927) T) ((-912 . -562) T) ((-912 . -173) T) ((-912 . -621) 118097) ((-912 . -722) 118062) ((-912 . -645) 118027) ((-912 . -38) 117992) ((-912 . -457) T) ((-912 . -310) T) ((-912 . -111) 117948) ((-912 . -1057) 117913) ((-912 . -1062) 117878) ((-912 . -651) 117828) ((-912 . -653) 117793) ((-912 . -293) T) ((-912 . -244) T) ((-912 . -407) T) ((-912 . -1055) T) ((-912 . -1063) T) ((-912 . -1118) T) ((-912 . -731) T) ((-912 . -21) T) ((-912 . -23) T) ((-912 . -1107) T) ((-912 . -618) 117775) ((-912 . -102) T) ((-912 . -25) T) ((-912 . -131) T) ((-912 . -234) T) ((-912 . -332) 117762) ((-912 . -147) 117744) ((-912 . -1044) 117731) ((-912 . -1280) 117718) ((-912 . -1291) 117705) ((-912 . -619) 117687) ((-911 . -1107) T) ((-911 . -618) 117669) ((-911 . -102) T) ((-908 . -910) 117653) ((-908 . -855) 117604) ((-908 . -731) T) ((-908 . -1107) T) ((-908 . -618) 117586) ((-908 . -102) T) ((-908 . -1118) T) ((-908 . -478) T) ((-907 . -119) 117570) ((-907 . -494) 117554) ((-907 . -102) 117532) ((-907 . -1107) 117510) ((-907 . -519) 117443) ((-907 . -312) 117381) ((-907 . -618) 117292) ((-907 . -1222) T) ((-907 . -34) T) ((-907 . -1016) 117276) ((-904 . -1107) T) ((-904 . -618) 117258) ((-904 . -102) T) ((-899 . -855) T) ((-899 . -102) T) ((-899 . -618) 117240) ((-899 . -1107) T) ((-899 . -1044) 117217) ((-899 . -621) 117194) ((-896 . -1107) T) ((-896 . -618) 117176) ((-896 . -102) T) ((-896 . -1044) 117144) ((-896 . -621) 117112) ((-894 . -1107) T) ((-894 . -618) 117094) ((-894 . -102) T) ((-891 . -1107) T) ((-891 . -618) 117076) ((-891 . -102) T) ((-881 . -1089) T) ((-881 . -495) 117057) ((-881 . -618) 117023) ((-881 . -621) 117004) ((-881 . -1107) T) ((-881 . -102) T) ((-881 . -93) T) ((-881 . -1268) T) ((-879 . -1107) T) ((-879 . -618) 116986) ((-879 . -102) T) ((-878 . -1222) T) ((-878 . -618) 116858) ((-878 . -1107) 116809) ((-878 . -102) 116760) ((-877 . -997) 116744) ((-877 . -1157) 116722) ((-877 . -1044) 116588) ((-877 . -621) 116486) ((-877 . -619) 116293) ((-877 . -1026) 116271) ((-877 . -916) 116250) ((-877 . -890) 116234) ((-877 . -853) 116213) ((-877 . -802) 116192) ((-877 . -799) 116171) ((-877 . -855) 116122) ((-877 . -797) 116101) ((-877 . -796) 116080) ((-877 . -825) 116059) ((-877 . -892) 115984) ((-877 . -1222) T) ((-877 . -405) 115968) ((-877 . -644) 115916) ((-877 . -381) 115900) ((-877 . -289) 115858) ((-877 . -312) 115823) ((-877 . -519) 115735) ((-877 . -342) 115719) ((-877 . -244) T) ((-877 . -111) 115657) ((-877 . -1057) 115609) ((-877 . -1062) 115561) ((-877 . -293) T) ((-877 . -722) 115513) ((-877 . -645) 115465) ((-877 . -653) 115417) ((-877 . -651) 115354) ((-877 . -38) 115306) ((-877 . -310) T) ((-877 . -457) T) ((-877 . -173) T) ((-877 . -562) T) ((-877 . -927) T) ((-877 . -1227) T) ((-877 . -367) T) ((-877 . -234) 115285) ((-877 . -906) 115244) 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114282) ((-876 . -310) T) ((-876 . -457) T) ((-876 . -173) T) ((-876 . -562) T) ((-876 . -927) T) ((-876 . -1227) T) ((-876 . -367) T) ((-876 . -234) NIL) ((-876 . -906) NIL) ((-876 . -232) 114259) ((-876 . -147) T) ((-876 . -145) NIL) ((-876 . -131) T) ((-876 . -25) T) ((-876 . -102) T) ((-876 . -618) 114241) ((-876 . -1107) T) ((-876 . -23) T) ((-876 . -21) T) ((-876 . -1055) T) ((-876 . -1063) T) ((-876 . -1118) T) ((-876 . -731) T) ((-874 . -875) 114225) ((-874 . -927) T) ((-874 . -562) T) ((-874 . -293) T) ((-874 . -173) T) ((-874 . -621) 114197) ((-874 . -722) 114184) ((-874 . -645) 114171) ((-874 . -1062) 114158) ((-874 . -1057) 114145) ((-874 . -111) 114130) ((-874 . -38) 114117) ((-874 . -457) T) ((-874 . -310) T) ((-874 . -1055) T) ((-874 . -1063) T) ((-874 . -1118) T) ((-874 . -731) T) ((-874 . -21) T) ((-874 . -651) 114089) ((-874 . -23) T) ((-874 . -1107) T) ((-874 . -618) 114071) ((-874 . -102) T) ((-874 . -25) T) ((-874 . -131) T) ((-874 . -653) 114058) ((-874 . -147) T) 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. -38) 109338) ((-822 . -457) 109317) ((-822 . -310) 109296) ((-822 . -293) 109275) ((-822 . -244) 109254) ((-821 . -255) 109193) ((-821 . -621) 108930) ((-821 . -1044) 108758) ((-821 . -619) NIL) ((-821 . -329) 108720) ((-821 . -417) 108704) ((-821 . -38) 108553) ((-821 . -111) 108382) ((-821 . -1057) 108225) ((-821 . -1062) 108068) ((-821 . -651) 107978) ((-821 . -653) 107903) ((-821 . -645) 107752) ((-821 . -722) 107601) ((-821 . -145) 107580) ((-821 . -147) 107559) ((-821 . -173) 107470) ((-821 . -562) 107401) ((-821 . -293) 107332) ((-821 . -47) 107294) ((-821 . -381) 107278) ((-821 . -644) 107226) ((-821 . -457) 107177) ((-821 . -519) 107045) ((-821 . -906) 106981) ((-821 . -892) NIL) ((-821 . -916) 106960) ((-821 . -1227) 106939) ((-821 . -956) 106886) ((-821 . -312) 106873) ((-821 . -234) 106852) ((-821 . -131) T) ((-821 . -25) T) ((-821 . -102) T) ((-821 . -618) 106834) ((-821 . -1107) T) ((-821 . -23) T) ((-821 . -21) T) ((-821 . -731) T) ((-821 . -1118) T) ((-821 . -1063) T) 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103733) ((-820 . -38) 103703) ((-820 . -1107) 103493) ((-820 . -102) 103283) ((-820 . -25) 103134) ((-813 . -1107) T) ((-813 . -618) 103116) ((-813 . -102) T) ((-803 . -801) 103100) ((-803 . -855) 103079) ((-803 . -1044) 102859) ((-803 . -621) 102705) ((-803 . -417) 102668) ((-803 . -289) 102626) ((-803 . -312) 102591) ((-803 . -519) 102503) ((-803 . -342) 102487) ((-803 . -372) 102466) ((-803 . -619) 102427) ((-803 . -147) 102406) ((-803 . -145) 102385) ((-803 . -722) 102369) ((-803 . -645) 102353) ((-803 . -653) 102327) ((-803 . -651) 102286) ((-803 . -131) T) ((-803 . -25) T) ((-803 . -102) T) ((-803 . -618) 102268) ((-803 . -1107) T) ((-803 . -23) T) ((-803 . -21) T) ((-803 . -1062) 102252) ((-803 . -1057) 102236) ((-803 . -111) 102215) ((-803 . -1055) T) ((-803 . -1063) T) ((-803 . -1118) T) ((-803 . -731) T) ((-803 . -38) 102199) ((-786 . -1248) 102183) ((-786 . -1157) 102161) ((-786 . -619) NIL) ((-786 . -312) 102148) ((-786 . -519) 102095) ((-786 . -329) 102072) ((-786 . -1044) 101931) ((-786 . -417) 101915) ((-786 . -38) 101744) ((-786 . -111) 101553) ((-786 . -1057) 101376) ((-786 . -1062) 101199) ((-786 . -651) 101109) ((-786 . -653) 101034) ((-786 . -645) 100863) ((-786 . -722) 100692) ((-786 . -621) 100440) ((-786 . -145) 100419) ((-786 . -147) 100398) ((-786 . -47) 100375) ((-786 . -381) 100359) ((-786 . -644) 100307) ((-786 . -906) 100250) ((-786 . -892) NIL) ((-786 . -916) 100229) ((-786 . -1227) 100208) ((-786 . -956) 100177) ((-786 . -927) 100156) ((-786 . -562) 100067) ((-786 . -293) 99978) ((-786 . -173) 99869) ((-786 . -457) 99800) ((-786 . -310) 99779) ((-786 . -289) 99706) ((-786 . -234) T) ((-786 . -131) T) ((-786 . -25) T) ((-786 . -102) T) ((-786 . -618) 99667) ((-786 . -1107) T) ((-786 . -23) T) ((-786 . -21) T) ((-786 . -731) T) ((-786 . -1118) T) ((-786 . -1063) T) ((-786 . -1055) T) ((-786 . -232) 99651) ((-785 . -1071) 99618) ((-785 . -619) 99252) ((-785 . -312) 99239) ((-785 . -519) 99191) ((-785 . -329) 99163) ((-785 . -1044) 99020) 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-731) T) ((-776 . -1118) T) ((-774 . -1107) T) ((-774 . -618) 96881) ((-774 . -102) T) ((-741 . -742) 96865) ((-741 . -1105) 96849) ((-741 . -236) 96833) ((-741 . -619) 96794) ((-741 . -151) 96778) ((-741 . -494) 96762) ((-741 . -102) T) ((-741 . -1107) T) ((-741 . -519) 96695) ((-741 . -312) 96633) ((-741 . -618) 96615) ((-741 . -1222) T) ((-741 . -34) T) ((-741 . -107) 96599) ((-741 . -700) 96583) ((-740 . -1055) T) ((-740 . -1063) T) ((-740 . -1118) T) ((-740 . -731) T) ((-740 . -21) T) ((-740 . -651) 96528) ((-740 . -23) T) ((-740 . -1107) T) ((-740 . -618) 96510) ((-740 . -102) T) ((-740 . -25) T) ((-740 . -131) T) ((-740 . -653) 96470) ((-740 . -621) 96426) ((-740 . -1044) 96397) ((-740 . -147) 96376) ((-740 . -145) 96355) ((-740 . -38) 96325) ((-740 . -111) 96290) ((-740 . -1057) 96260) ((-740 . -1062) 96230) ((-740 . -645) 96200) ((-740 . -722) 96170) ((-740 . -372) 96123) ((-736 . -956) 96076) ((-736 . -621) 95861) ((-736 . -1044) 95737) ((-736 . -1227) 95716) ((-736 . -916) 95695) ((-736 . -892) NIL) ((-736 . -906) 95672) ((-736 . -519) 95615) ((-736 . -457) 95566) ((-736 . -644) 95514) ((-736 . -381) 95498) ((-736 . -47) 95463) ((-736 . -38) 95312) ((-736 . -645) 95161) ((-736 . -722) 95010) ((-736 . -293) 94941) ((-736 . -562) 94872) ((-736 . -111) 94701) ((-736 . -1057) 94544) ((-736 . -1062) 94387) ((-736 . -173) 94298) ((-736 . -147) 94277) ((-736 . -145) 94256) ((-736 . -653) 94181) ((-736 . -651) 94091) ((-736 . -131) T) ((-736 . -25) T) ((-736 . -102) T) ((-736 . -618) 94073) ((-736 . -1107) T) ((-736 . -23) T) ((-736 . -21) T) ((-736 . -1055) T) ((-736 . -1063) T) ((-736 . -1118) T) ((-736 . -731) T) ((-736 . -417) 94057) ((-736 . -329) 94022) ((-736 . -312) 94009) ((-736 . -619) 93870) ((-723 . -478) T) ((-723 . -1118) T) ((-723 . -102) T) ((-723 . -618) 93852) ((-723 . -1107) T) ((-723 . -731) T) ((-720 . -1055) T) ((-720 . -1063) T) ((-720 . -1118) T) ((-720 . -731) T) ((-720 . -21) T) ((-720 . -651) 93824) ((-720 . -23) T) ((-720 . -1107) T) 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90413) ((-716 . -731) T) ((-716 . -1118) T) ((-716 . -1063) T) ((-716 . -1055) T) ((-716 . -111) 90369) ((-716 . -1057) 90334) ((-716 . -1062) 90299) ((-716 . -21) T) ((-716 . -23) T) ((-716 . -1107) T) ((-716 . -618) 90281) ((-716 . -102) T) ((-716 . -25) T) ((-716 . -131) T) ((-716 . -293) T) ((-716 . -244) T) ((-715 . -1107) T) ((-715 . -618) 90263) ((-715 . -102) T) ((-706 . -392) T) ((-706 . -1044) 90245) ((-706 . -855) T) ((-706 . -38) 90232) ((-706 . -621) 90204) ((-706 . -731) T) ((-706 . -1118) T) ((-706 . -1063) T) ((-706 . -1055) T) ((-706 . -111) 90189) ((-706 . -1057) 90176) ((-706 . -1062) 90163) ((-706 . -21) T) ((-706 . -651) 90135) ((-706 . -23) T) ((-706 . -1107) T) ((-706 . -618) 90117) ((-706 . -102) T) ((-706 . -25) T) ((-706 . -131) T) ((-706 . -653) 90104) ((-706 . -645) 90091) ((-706 . -722) 90078) ((-706 . -173) T) ((-706 . -293) T) ((-706 . -562) T) ((-706 . -550) T) ((-706 . -1227) T) ((-706 . -1157) T) ((-706 . -619) 89993) ((-706 . -1026) T) ((-706 . -892) 89975) ((-706 . -853) T) ((-706 . -802) T) ((-706 . -799) T) ((-706 . -797) T) ((-706 . -796) T) ((-706 . -825) T) ((-706 . -644) 89957) ((-706 . -927) T) ((-706 . -457) T) ((-706 . -310) T) ((-706 . -234) T) ((-706 . -143) T) ((-706 . -147) T) ((-704 . -409) T) ((-704 . -147) T) ((-704 . -621) 89892) ((-704 . -653) 89857) ((-704 . -651) 89807) ((-704 . -131) T) ((-704 . -25) T) ((-704 . -102) T) ((-704 . -618) 89789) ((-704 . -1107) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -731) T) ((-704 . -1118) T) ((-704 . -1063) T) ((-704 . -1055) T) ((-704 . -619) 89734) ((-704 . -367) T) ((-704 . -1227) T) ((-704 . -927) T) ((-704 . -562) T) ((-704 . -173) T) ((-704 . -722) 89699) ((-704 . -645) 89664) ((-704 . -38) 89629) ((-704 . -457) T) ((-704 . -310) T) ((-704 . -111) 89585) ((-704 . -1057) 89550) ((-704 . -1062) 89515) ((-704 . -293) T) ((-704 . -244) T) ((-704 . -853) T) ((-704 . -802) T) ((-704 . -799) T) ((-704 . -855) T) ((-704 . -797) T) ((-704 . -796) T) ((-704 . -892) 89497) 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-1089) T) ((-681 . -495) 87933) ((-681 . -618) 87899) ((-681 . -621) 87880) ((-681 . -1107) T) ((-681 . -102) T) ((-681 . -93) T) ((-680 . -494) 87864) ((-680 . -102) 87842) ((-680 . -1107) 87820) ((-680 . -519) 87753) ((-680 . -312) 87691) ((-680 . -618) 87623) ((-680 . -1222) T) ((-680 . -34) T) ((-677 . -855) T) ((-677 . -102) T) ((-677 . -618) 87605) ((-677 . -1107) T) ((-677 . -1044) 87589) ((-677 . -621) 87573) ((-676 . -1089) T) ((-676 . -495) 87554) ((-676 . -618) 87520) ((-676 . -621) 87501) ((-676 . -1107) T) ((-676 . -102) T) ((-676 . -93) T) ((-675 . -1129) 87446) ((-675 . -494) 87430) ((-675 . -519) 87363) ((-675 . -312) 87301) ((-675 . -1222) T) ((-675 . -34) T) ((-675 . -1059) 87241) ((-675 . -1044) 87137) ((-675 . -621) 87055) ((-675 . -417) 87039) ((-675 . -644) 86987) ((-675 . -381) 86971) ((-675 . -234) 86950) ((-675 . -906) 86909) ((-675 . -232) 86893) ((-675 . -722) 86877) ((-675 . -645) 86861) ((-675 . -653) 86835) ((-675 . -651) 86794) ((-675 . -131) T) ((-675 . 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. -1057) 85138) ((-659 . -1062) 85122) ((-659 . -21) T) ((-659 . -23) T) ((-659 . -1107) T) ((-659 . -618) 85104) ((-659 . -102) T) ((-659 . -25) T) ((-659 . -131) T) ((-659 . -645) 85074) ((-659 . -722) 85044) ((-659 . -417) 85028) ((-659 . -1044) 84924) ((-659 . -857) 84908) ((-659 . -289) 84887) ((-657 . -722) 84871) ((-657 . -645) 84855) ((-657 . -653) 84839) ((-657 . -651) 84808) ((-657 . -131) T) ((-657 . -25) T) ((-657 . -102) T) ((-657 . -618) 84790) ((-657 . -1107) T) ((-657 . -23) T) ((-657 . -21) T) ((-657 . -1062) 84774) ((-657 . -1057) 84758) ((-657 . -111) 84737) ((-657 . -796) 84716) ((-657 . -797) 84695) ((-657 . -855) 84674) ((-657 . -799) 84653) ((-657 . -802) 84632) ((-654 . -1107) T) ((-654 . -618) 84614) ((-654 . -102) T) ((-654 . -1044) 84598) ((-654 . -621) 84582) ((-652 . -700) 84566) ((-652 . -107) 84550) ((-652 . -34) T) ((-652 . -1222) T) ((-652 . -618) 84482) ((-652 . -312) 84420) ((-652 . -519) 84353) ((-652 . -1107) 84331) ((-652 . -102) 84309) ((-652 . 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-653) 82305) ((-628 . -621) 82200) ((-628 . -234) 82179) ((-628 . -562) T) ((-628 . -293) T) ((-628 . -173) T) ((-628 . -722) 82166) ((-628 . -645) 82153) ((-628 . -1062) 82140) ((-628 . -1057) 82127) ((-628 . -111) 82112) ((-628 . -38) 82099) ((-628 . -619) 82076) ((-628 . -417) 82060) ((-628 . -1044) 81943) ((-628 . -147) 81922) ((-628 . -145) 81901) ((-628 . -310) 81880) ((-628 . -457) 81859) ((-628 . -927) 81838) ((-624 . -38) 81822) ((-624 . -621) 81791) ((-624 . -653) 81765) ((-624 . -651) 81724) ((-624 . -731) T) ((-624 . -1118) T) ((-624 . -1063) T) ((-624 . -1055) T) ((-624 . -111) 81703) ((-624 . -1057) 81687) ((-624 . -1062) 81671) ((-624 . -21) T) ((-624 . -23) T) ((-624 . -1107) T) ((-624 . -618) 81653) ((-624 . -102) T) ((-624 . -25) T) ((-624 . -131) T) ((-624 . -645) 81637) ((-624 . -722) 81621) ((-624 . -853) 81600) ((-624 . -802) 81579) ((-624 . -799) 81558) ((-624 . -855) 81537) ((-624 . -797) 81516) ((-624 . -796) 81495) ((-622 . -973) T) ((-622 . -102) T) ((-622 . 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((-1237 . -1222) 171341) ((-1237 . -892) 171214) ((-1237 . -825) 171167) ((-1237 . -796) 171120) ((-1237 . -797) 171073) ((-1237 . -855) 170972) ((-1237 . -799) 170925) ((-1237 . -802) 170878) ((-1237 . -853) 170831) ((-1237 . -890) 170801) ((-1237 . -916) 170754) ((-1237 . -1026) 170706) ((-1237 . -1044) 170492) ((-1237 . -1157) 170444) ((-1237 . -997) 170414) ((-1232 . -1236) 170375) ((-1232 . -1008) 170341) ((-1232 . -1208) 170307) ((-1232 . -1211) 170273) ((-1232 . -498) 170239) ((-1232 . -287) 170205) ((-1232 . -95) 170171) ((-1232 . -35) 170137) ((-1232 . -1251) 170114) ((-1232 . -47) 170091) ((-1232 . -621) 169886) ((-1232 . -722) 169682) ((-1232 . -645) 169478) ((-1232 . -653) 169330) ((-1232 . -651) 169167) ((-1232 . -1062) 168957) ((-1232 . -1057) 168747) ((-1232 . -111) 168516) ((-1232 . -38) 168312) ((-1232 . -979) 168281) ((-1232 . -289) 168129) ((-1232 . -1234) 168113) ((-1232 . -731) T) ((-1232 . -1118) T) ((-1232 . -1063) T) ((-1232 . -1055) T) ((-1232 . -21) T) ((-1232 . -23) T) ((-1232 . -1107) T) ((-1232 . -618) 168095) ((-1232 . -102) T) ((-1232 . -25) T) ((-1232 . -131) T) ((-1232 . -145) 168002) ((-1232 . -147) 167909) ((-1232 . -619) NIL) ((-1232 . -232) 167861) ((-1232 . -906) 167694) ((-1232 . -234) 167581) ((-1232 . -367) 167560) ((-1232 . -1227) 167539) ((-1232 . -927) 167518) ((-1232 . -562) 167469) ((-1232 . -173) 167400) ((-1232 . -457) 167379) ((-1232 . -310) 167358) ((-1232 . -293) 167309) ((-1232 . -244) 167288) ((-1232 . -342) 167240) ((-1232 . -519) 167009) ((-1232 . -312) 166894) ((-1232 . -381) 166846) ((-1232 . -644) 166798) ((-1232 . -405) 166750) ((-1232 . -1222) 166729) ((-1232 . -892) NIL) ((-1232 . -825) NIL) ((-1232 . -796) NIL) ((-1232 . -797) NIL) ((-1232 . -855) NIL) ((-1232 . -799) NIL) ((-1232 . -802) NIL) ((-1232 . -853) NIL) ((-1232 . -890) 166681) ((-1232 . -916) NIL) ((-1232 . -1026) NIL) ((-1232 . -1044) 166647) ((-1232 . -1157) NIL) ((-1232 . -997) 166599) ((-1231 . -849) T) ((-1231 . -855) T) ((-1231 . -1107) T) ((-1231 . -618) 166581) ((-1231 . -102) T) ((-1231 . -372) T) ((-1230 . -849) T) ((-1230 . -855) T) ((-1230 . -1107) T) ((-1230 . -618) 166563) ((-1230 . -102) T) ((-1230 . -372) T) ((-1229 . -849) T) ((-1229 . -855) T) ((-1229 . -1107) T) ((-1229 . -618) 166545) ((-1229 . -102) T) ((-1229 . -372) T) ((-1228 . -849) T) ((-1228 . -855) T) ((-1228 . -1107) T) ((-1228 . -618) 166527) ((-1228 . -102) T) ((-1228 . -372) T) ((-1223 . -1089) T) ((-1223 . -495) 166508) ((-1223 . -618) 166474) ((-1223 . -621) 166455) ((-1223 . -1107) T) ((-1223 . -102) T) ((-1223 . -93) T) ((-1220 . -495) 166432) ((-1220 . -618) 166344) ((-1220 . -621) 166321) ((-1220 . -1107) 166299) ((-1220 . -102) 166277) ((-1215 . -745) 166253) ((-1215 . -35) 166219) ((-1215 . -95) 166185) ((-1215 . -287) 166151) ((-1215 . -498) 166117) ((-1215 . -1211) 166083) ((-1215 . -1208) 166049) ((-1215 . -1008) 166015) ((-1215 . -47) 165984) ((-1215 . -38) 165881) ((-1215 . -645) 165778) ((-1215 . -722) 165675) ((-1215 . -621) 165557) ((-1215 . -293) 165536) ((-1215 . -562) 165515) ((-1215 . -111) 165384) ((-1215 . -1057) 165267) ((-1215 . -1062) 165150) ((-1215 . -173) 165101) ((-1215 . -147) 165080) ((-1215 . -145) 165059) ((-1215 . -653) 164984) ((-1215 . -651) 164894) ((-1215 . -979) 164856) ((-1215 . -1055) T) ((-1215 . -1063) T) ((-1215 . -1118) T) ((-1215 . -731) T) ((-1215 . -21) T) ((-1215 . -23) T) ((-1215 . -1107) T) ((-1215 . -618) 164838) ((-1215 . -102) T) ((-1215 . -25) T) ((-1215 . -131) T) ((-1215 . -906) 164819) ((-1215 . -519) 164786) ((-1215 . -312) 164773) ((-1209 . -1016) 164757) ((-1209 . -34) T) ((-1209 . -1222) T) ((-1209 . -618) 164689) ((-1209 . -312) 164627) ((-1209 . -519) 164560) ((-1209 . -1107) 164538) ((-1209 . -102) 164516) ((-1209 . -494) 164500) ((-1204 . -369) 164474) ((-1204 . -102) T) ((-1204 . -618) 164456) ((-1204 . -1107) T) ((-1202 . -1107) T) ((-1202 . -618) 164438) ((-1202 . -102) T) ((-1202 . -621) 164420) ((-1195 . -1199) 164399) ((-1195 . -230) 164349) ((-1195 . -107) 164299) ((-1195 . -312) 164103) ((-1195 . -519) 163895) ((-1195 . -494) 163832) ((-1195 . -151) 163782) ((-1195 . -619) NIL) ((-1195 . -236) 163732) ((-1195 . -615) 163711) ((-1195 . -291) 163690) ((-1195 . -289) 163669) ((-1195 . -102) T) ((-1195 . -1107) T) ((-1195 . -618) 163651) ((-1195 . -1222) T) ((-1195 . -34) T) ((-1195 . -609) 163630) ((-1193 . -1222) T) ((-1191 . -1107) T) ((-1191 . -618) 163612) ((-1191 . -102) T) ((-1190 . -849) T) ((-1190 . -855) T) ((-1190 . -1107) T) ((-1190 . -618) 163594) ((-1190 . -102) T) ((-1190 . -372) T) ((-1189 . -849) T) ((-1189 . -855) T) ((-1189 . -1107) T) ((-1189 . -618) 163576) ((-1189 . -102) T) ((-1189 . -372) T) ((-1188 . -1268) T) ((-1188 . -1107) T) ((-1188 . -618) 163543) ((-1188 . -102) T) ((-1188 . -1044) 163479) ((-1188 . -621) 163415) ((-1187 . -618) 163397) ((-1186 . -618) 163379) ((-1185 . -329) 163356) ((-1185 . -1044) 163252) ((-1185 . -417) 163236) ((-1185 . -38) 163133) ((-1185 . -621) 162986) ((-1185 . -653) 162911) ((-1185 . -651) 162821) ((-1185 . -731) T) ((-1185 . -1118) T) ((-1185 . -1063) T) ((-1185 . -1055) T) ((-1185 . -111) 162690) ((-1185 . -1057) 162573) ((-1185 . -1062) 162456) ((-1185 . -21) T) ((-1185 . -23) T) ((-1185 . -1107) T) ((-1185 . -618) 162438) ((-1185 . -102) T) ((-1185 . -25) T) ((-1185 . -131) T) ((-1185 . -645) 162335) ((-1185 . -722) 162232) ((-1185 . -145) 162211) ((-1185 . -147) 162190) ((-1185 . -173) 162141) ((-1185 . -562) 162120) ((-1185 . -293) 162099) ((-1185 . -47) 162076) ((-1183 . -855) T) ((-1183 . -102) T) ((-1183 . -618) 162058) ((-1183 . -1107) T) ((-1183 . -619) 161980) ((-1183 . -826) T) ((-1183 . -621) 161961) ((-1183 . -892) 161928) ((-1182 . -618) 161910) ((-1181 . -1265) 161894) ((-1181 . -234) 161853) ((-1181 . -621) 161735) ((-1181 . -653) 161660) ((-1181 . -651) 161570) ((-1181 . -131) T) ((-1181 . -25) T) ((-1181 . -102) T) ((-1181 . -618) 161552) ((-1181 . -1107) T) ((-1181 . -23) T) ((-1181 . -21) T) ((-1181 . -731) T) ((-1181 . -1118) T) ((-1181 . -1063) T) ((-1181 . -1055) T) ((-1181 . -289) 161537) ((-1181 . -906) 161450) ((-1181 . -979) 161419) ((-1181 . -38) 161316) ((-1181 . -111) 161185) ((-1181 . -1057) 161068) ((-1181 . -1062) 160951) ((-1181 . -645) 160848) ((-1181 . -722) 160745) ((-1181 . -145) 160724) ((-1181 . -147) 160703) ((-1181 . -173) 160654) ((-1181 . -562) 160633) ((-1181 . -293) 160612) ((-1181 . -47) 160589) ((-1181 . -1251) 160566) ((-1181 . -35) 160532) ((-1181 . -95) 160498) ((-1181 . -287) 160464) ((-1181 . -498) 160430) ((-1181 . -1211) 160396) ((-1181 . -1208) 160362) ((-1181 . -1008) 160328) ((-1180 . -1257) 160289) ((-1180 . -367) 160268) ((-1180 . -1227) 160247) ((-1180 . -927) 160226) ((-1180 . -562) 160177) ((-1180 . -173) 160108) ((-1180 . -621) 159851) ((-1180 . -722) 159692) ((-1180 . -645) 159533) ((-1180 . -38) 159374) ((-1180 . -457) 159353) ((-1180 . -310) 159332) ((-1180 . -653) 159229) ((-1180 . -651) 159111) ((-1180 . -731) T) ((-1180 . -1118) T) ((-1180 . -1063) T) ((-1180 . -1055) T) ((-1180 . -111) 158932) ((-1180 . -1057) 158767) ((-1180 . -1062) 158602) ((-1180 . -21) T) ((-1180 . -23) T) ((-1180 . -1107) T) ((-1180 . -618) 158584) ((-1180 . -102) T) ((-1180 . -25) T) ((-1180 . -131) T) ((-1180 . -293) 158535) ((-1180 . -244) 158514) ((-1180 . -1008) 158480) ((-1180 . -1208) 158446) ((-1180 . -1211) 158412) ((-1180 . -498) 158378) ((-1180 . -287) 158344) ((-1180 . -95) 158310) ((-1180 . -35) 158276) ((-1180 . -1251) 158246) ((-1180 . -47) 158216) ((-1180 . -147) 158195) ((-1180 . -145) 158174) ((-1180 . -979) 158136) ((-1180 . -906) 158042) ((-1180 . -289) 158027) ((-1180 . -234) 157979) ((-1180 . -1255) 157963) ((-1180 . -1044) 157898) ((-1177 . -1248) 157882) ((-1177 . -1157) 157860) ((-1177 . -619) NIL) ((-1177 . -312) 157847) ((-1177 . -519) 157794) ((-1177 . -329) 157771) ((-1177 . -1044) 157651) ((-1177 . -417) 157635) ((-1177 . -38) 157464) ((-1177 . -111) 157273) ((-1177 . -1057) 157096) ((-1177 . -1062) 156919) ((-1177 . -651) 156829) ((-1177 . -653) 156754) ((-1177 . -645) 156583) ((-1177 . -722) 156412) ((-1177 . -621) 156181) ((-1177 . -145) 156160) ((-1177 . -147) 156139) ((-1177 . -47) 156116) ((-1177 . -381) 156100) ((-1177 . -644) 156048) ((-1177 . -906) 155991) ((-1177 . -892) NIL) ((-1177 . -916) 155970) ((-1177 . -1227) 155949) ((-1177 . -956) 155918) ((-1177 . -927) 155897) ((-1177 . -562) 155808) ((-1177 . -293) 155719) ((-1177 . -173) 155610) ((-1177 . -457) 155541) ((-1177 . -310) 155520) ((-1177 . -289) 155447) ((-1177 . -234) T) ((-1177 . -131) T) ((-1177 . -25) T) ((-1177 . -102) T) ((-1177 . -618) 155429) ((-1177 . -1107) T) ((-1177 . -23) T) ((-1177 . -21) T) ((-1177 . -731) T) ((-1177 . -1118) T) ((-1177 . -1063) T) ((-1177 . -1055) T) ((-1177 . -232) 155413) ((-1174 . -1236) 155374) ((-1174 . -1008) 155340) ((-1174 . -1208) 155306) ((-1174 . -1211) 155272) ((-1174 . -498) 155238) ((-1174 . -287) 155204) ((-1174 . -95) 155170) ((-1174 . -35) 155136) ((-1174 . -1251) 155113) ((-1174 . -47) 155090) ((-1174 . -621) 154885) ((-1174 . -722) 154681) ((-1174 . -645) 154477) ((-1174 . -653) 154329) ((-1174 . -651) 154166) ((-1174 . -1062) 153956) ((-1174 . -1057) 153746) ((-1174 . -111) 153515) ((-1174 . -38) 153311) ((-1174 . -979) 153280) ((-1174 . -289) 153128) ((-1174 . -1234) 153112) ((-1174 . -731) T) ((-1174 . -1118) T) ((-1174 . -1063) T) ((-1174 . -1055) T) ((-1174 . -21) T) ((-1174 . -23) T) ((-1174 . -1107) T) ((-1174 . -618) 153094) ((-1174 . -102) T) ((-1174 . -25) T) ((-1174 . -131) T) ((-1174 . -145) 153001) ((-1174 . -147) 152908) ((-1174 . -619) NIL) ((-1174 . -232) 152860) ((-1174 . -906) 152693) ((-1174 . -234) 152580) ((-1174 . -367) 152559) ((-1174 . -1227) 152538) ((-1174 . -927) 152517) ((-1174 . -562) 152468) ((-1174 . -173) 152399) ((-1174 . -457) 152378) ((-1174 . -310) 152357) ((-1174 . -293) 152308) ((-1174 . -244) 152287) ((-1174 . -342) 152239) ((-1174 . -519) 152008) ((-1174 . -312) 151893) ((-1174 . -381) 151845) ((-1174 . -644) 151797) ((-1174 . -405) 151749) ((-1174 . -1222) 151728) ((-1174 . -892) NIL) ((-1174 . -825) NIL) ((-1174 . -796) NIL) ((-1174 . -797) NIL) ((-1174 . -855) NIL) ((-1174 . -799) NIL) ((-1174 . -802) NIL) ((-1174 . -853) NIL) ((-1174 . -890) 151680) ((-1174 . -916) NIL) ((-1174 . -1026) NIL) ((-1174 . -1044) 151646) ((-1174 . -1157) NIL) ((-1174 . -997) 151598) ((-1173 . -1089) T) ((-1173 . -495) 151579) ((-1173 . -618) 151545) ((-1173 . -621) 151526) ((-1173 . -1107) T) ((-1173 . -102) T) ((-1173 . -93) T) ((-1172 . -1107) T) ((-1172 . -618) 151508) ((-1172 . -102) T) ((-1171 . -1107) T) ((-1171 . -618) 151490) ((-1171 . -102) T) ((-1166 . -1199) 151466) ((-1166 . -230) 151413) ((-1166 . -107) 151360) ((-1166 . -312) 151155) ((-1166 . -519) 150938) ((-1166 . -494) 150872) ((-1166 . -151) 150819) ((-1166 . -619) NIL) ((-1166 . -236) 150766) ((-1166 . -615) 150742) ((-1166 . -291) 150718) ((-1166 . -289) 150694) ((-1166 . -102) T) ((-1166 . -1107) T) ((-1166 . -618) 150676) ((-1166 . -1222) T) ((-1166 . -34) T) ((-1166 . -609) 150652) ((-1165 . -1164) T) ((-1165 . -19) 150634) ((-1165 . -656) 150616) ((-1165 . -291) 150591) ((-1165 . -289) 150566) ((-1165 . -609) 150541) ((-1165 . -619) NIL) ((-1165 . -494) 150523) ((-1165 . -519) NIL) ((-1165 . -312) NIL) ((-1165 . -1222) T) ((-1165 . -34) T) ((-1165 . -151) 150505) ((-1165 . -855) T) ((-1165 . -376) 150487) ((-1165 . -1150) T) ((-1165 . -102) T) ((-1165 . -618) 150469) ((-1165 . -1107) T) ((-1165 . -826) T) ((-1160 . -679) 150453) ((-1160 . -656) 150437) ((-1160 . -291) 150414) ((-1160 . -289) 150391) ((-1160 . -609) 150368) ((-1160 . -619) 150329) ((-1160 . -494) 150313) ((-1160 . -102) 150291) ((-1160 . -1107) 150269) ((-1160 . -519) 150202) ((-1160 . -312) 150140) ((-1160 . -618) 150072) ((-1160 . -1222) T) ((-1160 . -34) T) ((-1160 . -151) 150056) ((-1160 . -1261) 150040) ((-1160 . -1016) 150024) ((-1160 . -1155) 150008) ((-1160 . -621) 149985) ((-1158 . -1089) T) ((-1158 . -495) 149966) ((-1158 . -618) 149932) ((-1158 . -621) 149913) ((-1158 . -1107) T) ((-1158 . -102) T) ((-1158 . -93) T) ((-1156 . -1199) 149892) ((-1156 . -230) 149842) ((-1156 . -107) 149792) ((-1156 . -312) 149596) ((-1156 . -519) 149388) ((-1156 . -494) 149325) ((-1156 . -151) 149275) ((-1156 . -619) NIL) ((-1156 . -236) 149225) ((-1156 . -615) 149204) ((-1156 . -291) 149183) ((-1156 . -289) 149162) ((-1156 . -102) T) ((-1156 . -1107) T) ((-1156 . -618) 149144) ((-1156 . -1222) T) ((-1156 . -34) T) ((-1156 . -609) 149123) ((-1153 . -1127) 149107) ((-1153 . -494) 149091) ((-1153 . -102) 149069) ((-1153 . -1107) 149047) ((-1153 . -519) 148980) ((-1153 . -312) 148918) ((-1153 . -618) 148850) ((-1153 . -1222) T) ((-1153 . -34) T) ((-1153 . -107) 148834) ((-1152 . -1115) 148803) ((-1152 . -1217) 148772) ((-1152 . -618) 148734) ((-1152 . -151) 148718) ((-1152 . -34) T) ((-1152 . -1222) T) ((-1152 . -312) 148656) ((-1152 . -519) 148589) ((-1152 . -1107) T) ((-1152 . -102) T) ((-1152 . -494) 148573) ((-1152 . -619) 148534) ((-1152 . -982) 148503) ((-1152 . -1077) 148472) ((-1148 . -1129) 148417) ((-1148 . -494) 148401) ((-1148 . -519) 148334) ((-1148 . -312) 148272) ((-1148 . -1222) T) ((-1148 . -34) T) ((-1148 . -1059) 148212) ((-1148 . -1044) 148108) ((-1148 . -621) 148026) ((-1148 . -417) 148010) ((-1148 . -644) 147958) ((-1148 . -381) 147942) ((-1148 . -234) 147921) ((-1148 . -906) 147880) ((-1148 . -232) 147864) ((-1148 . -722) 147796) ((-1148 . -645) 147728) ((-1148 . -653) 147702) ((-1148 . -651) 147661) ((-1148 . -131) T) ((-1148 . -25) T) ((-1148 . -102) T) ((-1148 . -618) 147623) ((-1148 . -1107) T) ((-1148 . -23) T) ((-1148 . -21) T) ((-1148 . -1062) 147607) ((-1148 . -1057) 147591) ((-1148 . -111) 147570) ((-1148 . -1055) T) ((-1148 . -1063) T) ((-1148 . -1118) T) ((-1148 . -731) T) ((-1148 . -38) 147530) ((-1148 . -619) 147491) ((-1147 . -1016) 147462) ((-1147 . -34) T) ((-1147 . -1222) T) ((-1147 . -618) 147444) ((-1147 . -312) 147370) ((-1147 . -519) 147289) ((-1147 . -1107) T) ((-1147 . -102) T) ((-1147 . -494) 147260) ((-1146 . -1107) T) ((-1146 . -618) 147242) ((-1146 . -102) T) ((-1141 . -1143) T) ((-1141 . -1268) T) ((-1141 . -93) T) ((-1141 . -102) T) ((-1141 . -618) 147208) ((-1141 . -1107) T) ((-1141 . -621) 147189) ((-1141 . -495) 147170) ((-1141 . -1089) T) ((-1139 . -1140) 147154) ((-1139 . -102) T) ((-1139 . -618) 147136) ((-1139 . -1107) T) ((-1132 . -745) 147115) ((-1132 . -35) 147081) ((-1132 . -95) 147047) ((-1132 . -287) 147013) ((-1132 . -498) 146979) ((-1132 . -1211) 146945) ((-1132 . -1208) 146911) ((-1132 . -1008) 146877) ((-1132 . -47) 146849) ((-1132 . -38) 146746) ((-1132 . -645) 146643) ((-1132 . -722) 146540) ((-1132 . -621) 146422) ((-1132 . -293) 146401) ((-1132 . -562) 146380) ((-1132 . -111) 146249) ((-1132 . -1057) 146132) ((-1132 . -1062) 146015) ((-1132 . -173) 145966) ((-1132 . -147) 145945) ((-1132 . -145) 145924) ((-1132 . -653) 145849) ((-1132 . -651) 145759) ((-1132 . -979) 145726) ((-1132 . -1055) T) ((-1132 . -1063) T) ((-1132 . -1118) T) ((-1132 . -731) T) ((-1132 . -21) T) ((-1132 . -23) T) ((-1132 . -1107) T) ((-1132 . -618) 145708) ((-1132 . -102) T) ((-1132 . -25) T) ((-1132 . -131) T) ((-1132 . -906) 145692) ((-1132 . -519) 145662) ((-1132 . -312) 145649) ((-1131 . -956) 145616) ((-1131 . -621) 145408) ((-1131 . -1044) 145291) ((-1131 . -1227) 145270) ((-1131 . -916) 145249) ((-1131 . -892) 145108) ((-1131 . -906) 145092) ((-1131 . -519) 145044) ((-1131 . -457) 144995) ((-1131 . -644) 144943) ((-1131 . -381) 144927) ((-1131 . -47) 144899) ((-1131 . -38) 144748) ((-1131 . -645) 144597) ((-1131 . -722) 144446) ((-1131 . -293) 144377) ((-1131 . -562) 144308) ((-1131 . -111) 144137) ((-1131 . -1057) 143980) ((-1131 . -1062) 143823) ((-1131 . -173) 143734) ((-1131 . -147) 143713) ((-1131 . -145) 143692) ((-1131 . -653) 143617) ((-1131 . -651) 143527) ((-1131 . -131) T) ((-1131 . -25) T) ((-1131 . -102) T) ((-1131 . -618) 143509) ((-1131 . -1107) T) ((-1131 . -23) T) ((-1131 . -21) T) ((-1131 . -1055) T) ((-1131 . -1063) T) ((-1131 . -1118) T) ((-1131 . -731) T) ((-1131 . -417) 143493) ((-1131 . -329) 143465) ((-1131 . -312) 143452) ((-1131 . -619) 143200) ((-1126 . -550) T) ((-1126 . -1227) T) ((-1126 . -1157) T) ((-1126 . -1044) 143182) ((-1126 . -619) 143097) ((-1126 . -1026) T) ((-1126 . -892) 143079) ((-1126 . -853) T) ((-1126 . -802) T) ((-1126 . -799) T) ((-1126 . -855) T) ((-1126 . -797) T) ((-1126 . -796) T) ((-1126 . -825) T) ((-1126 . -644) 143061) ((-1126 . -927) T) ((-1126 . -562) T) ((-1126 . -293) T) ((-1126 . -173) T) ((-1126 . -621) 143033) ((-1126 . -722) 143020) ((-1126 . -645) 143007) ((-1126 . -1062) 142994) ((-1126 . -1057) 142981) ((-1126 . -111) 142966) ((-1126 . -38) 142953) ((-1126 . -457) T) ((-1126 . -310) T) ((-1126 . -234) T) ((-1126 . -143) T) ((-1126 . -1055) T) ((-1126 . -1063) T) ((-1126 . -1118) T) ((-1126 . -731) T) ((-1126 . -21) T) ((-1126 . -651) 142925) ((-1126 . -23) T) ((-1126 . -1107) T) ((-1126 . -618) 142907) ((-1126 . -102) T) ((-1126 . -25) T) ((-1126 . -131) T) ((-1126 . -653) 142894) ((-1126 . -147) T) ((-1126 . -849) T) ((-1126 . -372) T) ((-1126 . -667) T) ((-1126 . -826) T) ((-1122 . -1089) T) ((-1122 . -495) 142875) ((-1122 . -618) 142841) ((-1122 . -621) 142822) ((-1122 . -1107) T) ((-1122 . -102) T) ((-1122 . -93) T) ((-1121 . -1107) T) ((-1121 . -618) 142804) ((-1121 . -102) T) ((-1119 . -239) 142783) ((-1119 . -1280) 142753) ((-1119 . -796) 142732) ((-1119 . -853) 142711) ((-1119 . -802) 142662) ((-1119 . -799) 142613) ((-1119 . -855) 142564) ((-1119 . -797) 142515) ((-1119 . -798) 142494) ((-1119 . -291) 142471) ((-1119 . -289) 142448) ((-1119 . -494) 142432) ((-1119 . -519) 142365) ((-1119 . -312) 142303) ((-1119 . -1222) T) ((-1119 . -34) T) ((-1119 . -609) 142280) ((-1119 . -1044) 142107) ((-1119 . -621) 141837) ((-1119 . -417) 141806) ((-1119 . -644) 141712) ((-1119 . -381) 141681) ((-1119 . -372) 141660) ((-1119 . -234) 141612) ((-1119 . -906) 141544) ((-1119 . -232) 141513) ((-1119 . -111) 141403) ((-1119 . -1057) 141300) ((-1119 . -1062) 141197) ((-1119 . -173) 141176) ((-1119 . -618) 140907) ((-1119 . -722) 140849) ((-1119 . -645) 140791) ((-1119 . -653) 140639) ((-1119 . -651) 140389) ((-1119 . -131) 140259) ((-1119 . -23) 140129) ((-1119 . -21) 140039) ((-1119 . -1055) 139969) ((-1119 . -1063) 139899) ((-1119 . -1118) 139809) ((-1119 . -731) 139719) ((-1119 . -38) 139689) ((-1119 . -1107) 139479) ((-1119 . -102) 139269) ((-1119 . -25) 139120) ((-1112 . -401) T) ((-1112 . -1222) T) ((-1112 . -618) 139102) ((-1111 . -1110) 139066) ((-1111 . -102) T) ((-1111 . -618) 139048) ((-1111 . -1107) T) ((-1111 . -623) 138963) ((-1109 . -1110) 138915) ((-1109 . -102) T) ((-1109 . -618) 138897) ((-1109 . -1107) T) ((-1109 . -623) 138800) ((-1108 . -372) T) ((-1108 . -102) T) ((-1108 . -618) 138782) ((-1108 . -1107) T) ((-1103 . -431) 138766) ((-1103 . -1105) 138750) ((-1103 . -372) 138729) ((-1103 . -236) 138713) ((-1103 . -619) 138674) ((-1103 . -151) 138658) ((-1103 . -494) 138642) ((-1103 . -102) T) ((-1103 . -1107) T) ((-1103 . -519) 138575) ((-1103 . -312) 138513) ((-1103 . -618) 138495) ((-1103 . -1222) T) ((-1103 . -34) T) ((-1103 . -107) 138479) ((-1103 . -230) 138463) ((-1102 . -1089) T) ((-1102 . -495) 138444) ((-1102 . -618) 138410) ((-1102 . -621) 138391) ((-1102 . -1107) T) ((-1102 . -102) T) ((-1102 . -93) T) ((-1098 . -1222) T) ((-1098 . -1107) 138361) ((-1098 . -618) 138320) ((-1098 . -102) 138290) ((-1097 . -1089) T) ((-1097 . -495) 138271) ((-1097 . -618) 138237) ((-1097 . -621) 138218) ((-1097 . -1107) T) ((-1097 . -102) T) ((-1097 . -93) T) ((-1095 . -1100) 138202) ((-1095 . -623) 138186) ((-1095 . -1107) 138164) ((-1095 . -618) 138131) ((-1095 . -102) 138109) ((-1095 . -1101) 138067) ((-1094 . -268) 138051) ((-1094 . -621) 138035) ((-1094 . -1044) 138019) ((-1094 . -1107) T) ((-1094 . -618) 138001) ((-1094 . -102) T) ((-1094 . -855) T) ((-1093 . -255) 137938) ((-1093 . -621) 137674) ((-1093 . -1044) 137501) ((-1093 . -619) NIL) ((-1093 . -329) 137462) ((-1093 . -417) 137446) ((-1093 . -38) 137295) ((-1093 . -111) 137124) ((-1093 . -1057) 136967) ((-1093 . -1062) 136810) ((-1093 . -651) 136720) ((-1093 . -653) 136645) ((-1093 . -645) 136494) ((-1093 . -722) 136343) ((-1093 . -145) 136322) ((-1093 . -147) 136301) ((-1093 . -173) 136212) ((-1093 . -562) 136143) ((-1093 . -293) 136074) ((-1093 . -47) 136035) ((-1093 . -381) 136019) ((-1093 . -644) 135967) ((-1093 . -457) 135918) ((-1093 . -519) 135785) ((-1093 . -906) 135720) ((-1093 . -892) NIL) ((-1093 . -916) 135699) ((-1093 . -1227) 135678) ((-1093 . -956) 135623) ((-1093 . -312) 135610) ((-1093 . -234) 135589) ((-1093 . -131) T) ((-1093 . -25) T) ((-1093 . -102) T) ((-1093 . -618) 135571) ((-1093 . -1107) T) ((-1093 . -23) T) ((-1093 . -21) T) ((-1093 . -731) T) ((-1093 . -1118) T) ((-1093 . -1063) T) ((-1093 . -1055) T) ((-1093 . -232) 135555) ((-1091 . -618) 135537) ((-1088 . -855) T) ((-1088 . -102) T) ((-1088 . -618) 135519) ((-1088 . -1107) T) ((-1088 . -619) 135500) ((-1085 . -729) 135479) 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. -731) T) ((-1085 . -173) T) ((-1083 . -1107) T) ((-1083 . -618) 133394) ((-1083 . -102) T) ((-1083 . -289) 133373) ((-1082 . -1107) T) ((-1082 . -618) 133355) ((-1082 . -102) T) ((-1081 . -1107) T) ((-1081 . -618) 133337) ((-1081 . -102) T) ((-1081 . -289) 133316) ((-1081 . -1044) 133293) ((-1081 . -621) 133270) ((-1080 . -1222) T) ((-1079 . -1089) T) ((-1079 . -495) 133251) ((-1079 . -618) 133217) ((-1079 . -621) 133198) ((-1079 . -1107) T) ((-1079 . -102) T) ((-1079 . -93) T) ((-1072 . -1089) T) ((-1072 . -495) 133179) ((-1072 . -618) 133145) ((-1072 . -621) 133126) ((-1072 . -1107) T) ((-1072 . -102) T) ((-1072 . -93) T) ((-1069 . -1199) 133101) ((-1069 . -230) 133047) ((-1069 . -107) 132993) ((-1069 . -312) 132844) ((-1069 . -519) 132688) ((-1069 . -494) 132619) ((-1069 . -151) 132565) ((-1069 . -619) NIL) ((-1069 . -236) 132511) ((-1069 . -615) 132486) ((-1069 . -291) 132461) ((-1069 . -289) 132436) ((-1069 . -102) T) ((-1069 . -1107) T) ((-1069 . -618) 132418) ((-1069 . -1222) T) ((-1069 . -34) T) ((-1069 . -609) 132393) ((-1068 . -550) T) ((-1068 . -1227) T) ((-1068 . -1157) T) ((-1068 . -1044) 132375) ((-1068 . -619) 132290) ((-1068 . -1026) T) ((-1068 . -892) 132272) ((-1068 . -853) T) ((-1068 . -802) T) ((-1068 . -799) T) ((-1068 . -855) T) ((-1068 . -797) T) ((-1068 . -796) T) ((-1068 . -825) T) ((-1068 . -644) 132254) ((-1068 . -927) T) ((-1068 . -562) T) ((-1068 . -293) T) ((-1068 . -173) T) ((-1068 . -621) 132226) ((-1068 . -722) 132213) ((-1068 . -645) 132200) ((-1068 . -1062) 132187) ((-1068 . -1057) 132174) ((-1068 . -111) 132159) ((-1068 . -38) 132146) ((-1068 . -457) T) ((-1068 . -310) T) ((-1068 . -234) T) ((-1068 . -143) T) ((-1068 . -1055) T) ((-1068 . -1063) T) ((-1068 . -1118) T) ((-1068 . -731) T) ((-1068 . -21) T) ((-1068 . -651) 132118) ((-1068 . -23) T) ((-1068 . -1107) T) ((-1068 . -618) 132100) ((-1068 . -102) T) ((-1068 . -25) T) ((-1068 . -131) T) ((-1068 . -653) 132087) ((-1068 . -147) T) ((-1068 . -623) 132068) ((-1067 . -1074) 132047) ((-1067 . -102) T) ((-1067 . -618) 132029) ((-1067 . -1107) T) ((-1064 . -1222) T) ((-1064 . -1107) 132007) ((-1064 . -618) 131974) ((-1064 . -102) 131952) ((-1060 . -1059) 131892) ((-1060 . -645) 131834) ((-1060 . -722) 131776) ((-1060 . -34) T) ((-1060 . -1222) T) ((-1060 . -312) 131714) ((-1060 . -519) 131647) ((-1060 . -494) 131631) ((-1060 . -653) 131615) ((-1060 . -651) 131584) ((-1060 . -131) T) ((-1060 . -25) T) ((-1060 . -102) T) ((-1060 . -618) 131546) ((-1060 . -1107) T) ((-1060 . -23) T) ((-1060 . -21) T) ((-1060 . -1062) 131530) ((-1060 . -1057) 131514) ((-1060 . -111) 131493) ((-1060 . -1280) 131463) ((-1060 . -619) 131424) ((-1052 . -1077) 131353) ((-1052 . -982) 131282) ((-1052 . -619) 131224) ((-1052 . -494) 131189) ((-1052 . -102) T) ((-1052 . -1107) T) ((-1052 . -519) 131090) ((-1052 . -312) 130998) ((-1052 . -618) 130941) ((-1052 . -1222) T) ((-1052 . -34) T) ((-1052 . -151) 130906) ((-1052 . -1217) 130835) ((-1042 . -1089) T) ((-1042 . -495) 130816) ((-1042 . -618) 130782) ((-1042 . -621) 130763) ((-1042 . -1107) T) ((-1042 . -102) T) ((-1042 . -93) T) ((-1041 . -1199) 130738) ((-1041 . -230) 130684) ((-1041 . -107) 130630) ((-1041 . -312) 130481) ((-1041 . -519) 130325) ((-1041 . -494) 130256) ((-1041 . -151) 130202) ((-1041 . -619) NIL) ((-1041 . -236) 130148) ((-1041 . -615) 130123) ((-1041 . -291) 130098) ((-1041 . -289) 130073) ((-1041 . -102) T) ((-1041 . -1107) T) ((-1041 . -618) 130055) ((-1041 . -1222) T) ((-1041 . -34) T) ((-1041 . -609) 130030) ((-1040 . -173) T) ((-1040 . -621) 129999) ((-1040 . -731) T) ((-1040 . -1118) T) ((-1040 . -1063) T) ((-1040 . -1055) T) ((-1040 . -653) 129973) ((-1040 . -651) 129932) ((-1040 . -131) T) ((-1040 . -25) T) ((-1040 . -102) T) ((-1040 . -618) 129914) ((-1040 . -1107) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -1062) 129888) ((-1040 . -1057) 129862) ((-1040 . -111) 129829) ((-1040 . -38) 129813) ((-1040 . -645) 129797) ((-1040 . -722) 129781) ((-1033 . -1077) 129750) ((-1033 . -982) 129719) ((-1033 . -619) 129680) ((-1033 . -494) 129664) ((-1033 . -102) T) ((-1033 . -1107) T) ((-1033 . -519) 129597) ((-1033 . -312) 129535) ((-1033 . -618) 129497) ((-1033 . -1222) T) ((-1033 . -34) T) ((-1033 . -151) 129481) ((-1033 . -1217) 129450) ((-1032 . -1222) T) ((-1032 . -1107) 129428) ((-1032 . -618) 129395) ((-1032 . -102) 129373) ((-1030 . -1018) T) ((-1030 . -1008) T) ((-1030 . -796) T) ((-1030 . -797) T) ((-1030 . -855) T) ((-1030 . -799) T) ((-1030 . -802) T) ((-1030 . -853) T) ((-1030 . -1044) 129253) ((-1030 . -417) 129215) ((-1030 . -244) T) ((-1030 . -293) T) ((-1030 . -310) T) ((-1030 . -457) T) ((-1030 . -38) 129152) ((-1030 . -645) 129089) ((-1030 . -722) 129026) ((-1030 . -621) 128963) ((-1030 . -562) T) ((-1030 . -927) T) ((-1030 . -1227) T) ((-1030 . -367) T) ((-1030 . -111) 128879) ((-1030 . -1057) 128816) ((-1030 . -1062) 128753) ((-1030 . -173) T) ((-1030 . -147) T) ((-1030 . -653) 128690) ((-1030 . -651) 128627) ((-1030 . -131) T) ((-1030 . -25) T) ((-1030 . -102) T) ((-1030 . -618) 128609) ((-1030 . -1107) T) ((-1030 . -23) T) ((-1030 . -21) T) ((-1030 . -1055) T) ((-1030 . -1063) T) ((-1030 . -1118) T) ((-1030 . -731) T) ((-1025 . -1089) T) ((-1025 . -495) 128590) ((-1025 . -618) 128556) ((-1025 . -621) 128537) ((-1025 . -1107) T) ((-1025 . -102) T) ((-1025 . -93) T) ((-1010 . -997) 128519) ((-1010 . -1157) T) ((-1010 . -621) 128469) ((-1010 . -1044) 128429) ((-1010 . -619) 128359) ((-1010 . -1026) T) ((-1010 . -916) NIL) ((-1010 . -890) 128341) ((-1010 . -853) T) ((-1010 . -802) T) ((-1010 . -799) T) ((-1010 . -855) T) ((-1010 . -797) T) ((-1010 . -796) T) ((-1010 . -825) T) ((-1010 . -892) 128323) ((-1010 . -1222) T) ((-1010 . -405) 128305) ((-1010 . -644) 128287) ((-1010 . -381) 128269) ((-1010 . -289) NIL) ((-1010 . -312) NIL) ((-1010 . -519) NIL) ((-1010 . -342) 128251) ((-1010 . -244) T) ((-1010 . -111) 128185) ((-1010 . -1057) 128135) ((-1010 . -1062) 128085) ((-1010 . -293) T) ((-1010 . -722) 128035) ((-1010 . -645) 127985) ((-1010 . -653) 127935) ((-1010 . -651) 127885) ((-1010 . -38) 127835) ((-1010 . -310) T) ((-1010 . -457) T) ((-1010 . -173) T) ((-1010 . -562) T) ((-1010 . -927) T) ((-1010 . -1227) T) ((-1010 . -367) T) ((-1010 . -234) T) ((-1010 . -906) NIL) ((-1010 . -232) 127817) ((-1010 . -147) T) ((-1010 . -145) NIL) ((-1010 . -131) T) ((-1010 . -25) T) ((-1010 . -102) T) ((-1010 . -618) 127777) ((-1010 . -1107) T) ((-1010 . -23) T) ((-1010 . -21) T) ((-1010 . -1055) T) ((-1010 . -1063) T) ((-1010 . -1118) T) ((-1010 . -731) T) ((-1009 . -346) 127751) ((-1009 . -173) T) ((-1009 . -621) 127681) ((-1009 . -731) T) ((-1009 . -1118) T) ((-1009 . -1063) T) ((-1009 . -1055) T) ((-1009 . -653) 127626) ((-1009 . -651) 127556) ((-1009 . -131) T) ((-1009 . -25) T) ((-1009 . -102) T) ((-1009 . -618) 127538) ((-1009 . -1107) T) ((-1009 . -23) T) ((-1009 . -21) T) ((-1009 . -1062) 127483) ((-1009 . -1057) 127428) ((-1009 . -111) 127357) ((-1009 . -619) 127341) ((-1009 . -232) 127318) ((-1009 . -906) 127270) ((-1009 . -234) 127242) ((-1009 . -367) T) ((-1009 . -1227) T) ((-1009 . -927) T) ((-1009 . -562) T) ((-1009 . -722) 127187) ((-1009 . -645) 127132) ((-1009 . -38) 127077) ((-1009 . -457) T) ((-1009 . -310) T) ((-1009 . -293) T) ((-1009 . -244) T) ((-1009 . -372) NIL) ((-1009 . -354) NIL) ((-1009 . -1157) NIL) ((-1009 . -145) 127049) ((-1009 . -407) NIL) ((-1009 . -415) 127021) ((-1009 . -147) 126993) ((-1009 . -374) 126965) ((-1009 . -381) 126942) ((-1009 . -644) 126881) ((-1009 . -417) 126858) ((-1009 . -1044) 126746) ((-1009 . -729) 126718) ((-1006 . -1001) 126702) ((-1006 . -494) 126686) ((-1006 . -102) 126664) ((-1006 . -1107) 126642) ((-1006 . -519) 126575) ((-1006 . -312) 126513) ((-1006 . -618) 126445) ((-1006 . -1222) T) ((-1006 . -34) T) ((-1006 . -107) 126429) ((-1002 . -1004) 126413) ((-1002 . -855) 126392) ((-1002 . -1044) 126288) ((-1002 . -417) 126272) ((-1002 . -644) 126220) ((-1002 . -381) 126204) ((-1002 . -289) 126162) ((-1002 . -312) 126127) ((-1002 . -519) 126039) ((-1002 . -342) 126023) ((-1002 . -38) 125971) ((-1002 . -111) 125853) ((-1002 . -1057) 125749) ((-1002 . -1062) 125645) ((-1002 . -651) 125568) ((-1002 . -653) 125506) ((-1002 . -645) 125454) ((-1002 . -722) 125402) ((-1002 . -621) 125292) ((-1002 . -293) 125243) ((-1002 . -244) 125222) ((-1002 . -234) 125201) ((-1002 . -906) 125160) ((-1002 . -232) 125144) ((-1002 . -619) 125105) ((-1002 . -147) 125084) ((-1002 . -145) 125063) ((-1002 . -131) T) ((-1002 . -25) T) ((-1002 . -102) T) ((-1002 . -618) 125045) ((-1002 . -1107) T) ((-1002 . -23) T) ((-1002 . -21) T) ((-1002 . -1055) T) ((-1002 . -1063) T) ((-1002 . -1118) T) ((-1002 . -731) T) ((-1000 . -1089) T) ((-1000 . -495) 125026) ((-1000 . -618) 124992) ((-1000 . -621) 124973) ((-1000 . -1107) T) ((-1000 . -102) T) ((-1000 . -93) T) ((-999 . -21) T) ((-999 . -651) 124955) ((-999 . -23) T) ((-999 . -1107) T) ((-999 . -618) 124937) ((-999 . -102) T) ((-999 . -25) T) ((-999 . -131) T) ((-995 . -618) 124919) ((-992 . -1107) T) 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. -1222) T) ((-878 . -618) 116912) ((-878 . -1107) 116863) ((-878 . -102) 116814) ((-877 . -997) 116798) ((-877 . -1157) 116776) ((-877 . -1044) 116642) ((-877 . -621) 116540) ((-877 . -619) 116347) ((-877 . -1026) 116325) ((-877 . -916) 116304) ((-877 . -890) 116288) ((-877 . -853) 116267) ((-877 . -802) 116246) ((-877 . -799) 116225) ((-877 . -855) 116176) ((-877 . -797) 116155) ((-877 . -796) 116134) ((-877 . -825) 116113) ((-877 . -892) 116038) ((-877 . -1222) T) ((-877 . -405) 116022) ((-877 . -644) 115970) ((-877 . -381) 115954) ((-877 . -289) 115912) ((-877 . -312) 115877) ((-877 . -519) 115789) ((-877 . -342) 115773) ((-877 . -244) T) ((-877 . -111) 115711) ((-877 . -1057) 115663) ((-877 . -1062) 115615) ((-877 . -293) T) ((-877 . -722) 115567) ((-877 . -645) 115519) ((-877 . -653) 115471) ((-877 . -651) 115408) ((-877 . -38) 115360) ((-877 . -310) T) ((-877 . -457) T) ((-877 . -173) T) ((-877 . -562) T) ((-877 . -927) T) ((-877 . -1227) T) ((-877 . -367) T) ((-877 . -234) 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. -651) 93878) ((-720 . -23) T) ((-720 . -1107) T) ((-720 . -618) 93860) ((-720 . -102) T) ((-720 . -25) T) ((-720 . -131) T) ((-720 . -653) 93847) ((-720 . -621) 93829) ((-719 . -1055) T) ((-719 . -1063) T) ((-719 . -1118) T) ((-719 . -731) T) ((-719 . -21) T) ((-719 . -651) 93774) ((-719 . -23) T) ((-719 . -1107) T) ((-719 . -618) 93756) ((-719 . -102) T) ((-719 . -25) T) ((-719 . -131) T) ((-719 . -653) 93716) ((-719 . -621) 93670) ((-719 . -1044) 93639) ((-719 . -289) 93618) ((-719 . -147) 93597) ((-719 . -145) 93576) ((-719 . -38) 93546) ((-719 . -111) 93511) ((-719 . -1057) 93481) ((-719 . -1062) 93451) ((-719 . -645) 93421) ((-719 . -722) 93391) ((-718 . -855) T) ((-718 . -102) T) ((-718 . -618) 93326) ((-718 . -1107) T) ((-718 . -495) 93276) ((-718 . -621) 93226) ((-717 . -1248) 93210) ((-717 . -1157) 93188) ((-717 . -619) NIL) ((-717 . -312) 93175) ((-717 . -519) 93122) ((-717 . -329) 93099) ((-717 . -1044) 92979) ((-717 . -417) 92963) ((-717 . -38) 92792) ((-717 . -111) 92601) ((-717 . -1057) 92424) ((-717 . -1062) 92247) ((-717 . -651) 92157) ((-717 . -653) 92082) ((-717 . -645) 91911) ((-717 . -722) 91740) ((-717 . -621) 91496) ((-717 . -145) 91475) ((-717 . -147) 91454) ((-717 . -47) 91431) ((-717 . -381) 91415) ((-717 . -644) 91363) ((-717 . -906) 91306) ((-717 . -892) NIL) ((-717 . -916) 91285) ((-717 . -1227) 91264) ((-717 . -956) 91233) ((-717 . -927) 91212) ((-717 . -562) 91123) ((-717 . -293) 91034) ((-717 . -173) 90925) ((-717 . -457) 90856) ((-717 . -310) 90835) ((-717 . -289) 90762) ((-717 . -234) T) ((-717 . -131) T) ((-717 . -25) T) ((-717 . -102) T) ((-717 . -618) 90744) ((-717 . -1107) T) ((-717 . -23) T) ((-717 . -21) T) ((-717 . -731) T) ((-717 . -1118) T) ((-717 . -1063) T) ((-717 . -1055) T) ((-717 . -232) 90728) ((-717 . -372) 90707) ((-716 . -367) T) ((-716 . -1227) T) ((-716 . -927) T) ((-716 . -562) T) ((-716 . -173) T) ((-716 . -621) 90657) ((-716 . -722) 90622) ((-716 . -645) 90587) ((-716 . -38) 90552) ((-716 . -457) T) 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86889) ((-675 . -651) 86848) ((-675 . -131) T) ((-675 . -25) T) ((-675 . -102) T) ((-675 . -618) 86810) ((-675 . -1107) T) ((-675 . -23) T) ((-675 . -21) T) ((-675 . -1062) 86794) ((-675 . -1057) 86778) ((-675 . -111) 86757) ((-675 . -1055) T) ((-675 . -1063) T) ((-675 . -1118) T) ((-675 . -731) T) ((-675 . -38) 86717) ((-675 . -423) 86701) ((-675 . -749) 86685) ((-675 . -725) T) ((-675 . -766) T) ((-675 . -371) 86669) ((-669 . -378) 86648) ((-669 . -722) 86632) ((-669 . -645) 86616) ((-669 . -653) 86600) ((-669 . -651) 86569) ((-669 . -131) T) ((-669 . -25) T) ((-669 . -102) T) ((-669 . -618) 86551) ((-669 . -1107) T) ((-669 . -23) T) ((-669 . -21) T) ((-669 . -1062) 86535) ((-669 . -1057) 86519) ((-669 . -111) 86498) ((-669 . -640) 86482) ((-669 . -388) 86454) ((-669 . -621) 86431) ((-669 . -1044) 86408) ((-661 . -663) 86392) ((-661 . -38) 86362) ((-661 . -621) 86280) ((-661 . -653) 86254) ((-661 . -651) 86213) ((-661 . -731) T) ((-661 . -1118) T) ((-661 . -1063) T) ((-661 . -1055) T) ((-661 . -111) 86192) ((-661 . -1057) 86176) ((-661 . -1062) 86160) ((-661 . -21) T) ((-661 . -23) T) ((-661 . -1107) T) ((-661 . -618) 86142) ((-661 . -102) T) ((-661 . -25) T) ((-661 . -131) T) ((-661 . -645) 86112) ((-661 . -722) 86082) ((-661 . -417) 86066) ((-661 . -1044) 85962) ((-661 . -857) 85946) ((-661 . -289) 85907) ((-660 . -663) 85891) ((-660 . -38) 85861) ((-660 . -621) 85779) ((-660 . -653) 85753) ((-660 . -651) 85712) ((-660 . -731) T) ((-660 . -1118) T) ((-660 . -1063) T) ((-660 . -1055) T) ((-660 . -111) 85691) ((-660 . -1057) 85675) ((-660 . -1062) 85659) ((-660 . -21) T) ((-660 . -23) T) ((-660 . -1107) T) ((-660 . -618) 85641) ((-660 . -102) T) ((-660 . -25) T) ((-660 . -131) T) ((-660 . -645) 85611) ((-660 . -722) 85581) ((-660 . -417) 85565) ((-660 . -1044) 85461) ((-660 . -857) 85445) ((-660 . -289) 85424) ((-659 . -663) 85408) ((-659 . -38) 85378) ((-659 . -621) 85296) ((-659 . -653) 85270) ((-659 . -651) 85229) ((-659 . -731) T) ((-659 . -1118) T) ((-659 . 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. -644) 53823) ((-412 . -381) 53807) ((-412 . -289) 53765) ((-412 . -312) 53730) ((-412 . -519) 53642) ((-412 . -342) 53626) ((-412 . -244) T) ((-412 . -111) 53564) ((-412 . -1057) 53516) ((-412 . -1062) 53468) ((-412 . -293) T) ((-412 . -722) 53420) ((-412 . -645) 53372) ((-412 . -653) 53324) ((-412 . -651) 53261) ((-412 . -38) 53213) ((-412 . -310) T) ((-412 . -457) T) ((-412 . -173) T) ((-412 . -562) T) ((-412 . -927) T) ((-412 . -1227) T) ((-412 . -367) T) ((-412 . -234) 53192) ((-412 . -906) 53151) ((-412 . -232) 53135) ((-412 . -147) 53114) ((-412 . -145) 53093) ((-412 . -131) T) ((-412 . -25) T) ((-412 . -102) T) ((-412 . -618) 53075) ((-412 . -1107) T) ((-412 . -23) T) ((-412 . -21) T) ((-412 . -1055) T) ((-412 . -1063) T) ((-412 . -1118) T) ((-412 . -731) T) ((-412 . -826) 53028) ((-410 . -562) T) ((-410 . -293) T) ((-410 . -173) T) ((-410 . -621) 52936) ((-410 . -722) 52910) ((-410 . -645) 52884) ((-410 . -653) 52858) ((-410 . -651) 52817) ((-410 . -131) T) ((-410 . -25) T) 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. -346) 1225) ((-40 . -173) T) ((-40 . -621) 1155) ((-40 . -731) T) ((-40 . -1118) T) ((-40 . -1063) T) ((-40 . -1055) T) ((-40 . -653) 1100) ((-40 . -651) 1030) ((-40 . -131) T) ((-40 . -25) T) ((-40 . -102) T) ((-40 . -618) 1012) ((-40 . -1107) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -1062) 957) ((-40 . -1057) 902) ((-40 . -111) 831) ((-40 . -619) 815) ((-40 . -232) 792) ((-40 . -906) 744) ((-40 . -234) 716) ((-40 . -367) T) ((-40 . -1227) T) ((-40 . -927) T) ((-40 . -562) T) ((-40 . -722) 661) ((-40 . -645) 606) ((-40 . -38) 551) ((-40 . -457) T) ((-40 . -310) T) ((-40 . -293) T) ((-40 . -244) T) ((-40 . -372) NIL) ((-40 . -354) NIL) ((-40 . -1157) NIL) ((-40 . -145) 523) ((-40 . -407) NIL) ((-40 . -415) 495) ((-40 . -147) 467) ((-40 . -374) 439) ((-40 . -381) 416) ((-40 . -644) 355) ((-40 . -417) 332) ((-40 . -1044) 220) ((-40 . -729) 192) ((-31 . -1089) T) ((-31 . -495) 173) ((-31 . -618) 139) ((-31 . -621) 120) ((-31 . -1107) T) ((-31 . -102) T) ((-31 . -93) T) ((-30 . -961) T) ((-30 . -618) 102) ((0 . |EnumerationCategory|) T) ((0 . -618) 84) ((0 . -1107) T) ((0 . -102) T) ((-2 . |RecordCategory|) T) ((-2 . -618) 66) ((-2 . -1107) T) ((-2 . -102) T) ((-3 . |UnionCategory|) T) ((-3 . -618) 48) ((-3 . -1107) T) ((-3 . -102) T) ((-1 . -1107) T) ((-1 . -618) 30) ((-1 . -102) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 2e9add15..0bf572b7 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3477425182) -(4437 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3477435920) +(4440 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -633,22 +633,22 @@ |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| - |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| GF2FG FG2F F2FG - |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| - |indices| |index?| |entries| |categories| |search| |key?| |symbolIfCan| - |kernel| |argument| |constantKernel| |constantIfCan| |kovacic| |unknown| - |laplace| |trailingCoefficient| |normalizeIfCan| |polCase| |distFact| - |identification| |LyndonCoordinates| |LyndonBasis| |zeroDimensional?| - |fglmIfCan| |groebner| |lexTriangular| |squareFreeLexTriangular| |belong?| - |erf| |dilog| |li| |Ci| |Si| |Ei| |linGenPos| |groebgen| |totolex| |minPol| - |computeBasis| |coord| |anticoord| |intcompBasis| |choosemon| |transform| - |pack!| |library| |complexLimit| |limit| |linearlyDependent?| - |linearDependence| |solveLinear| |reducedSystem| |setDifference| - |setIntersection| |setUnion| |append| |null| |nil| |substitute| |duplicates?| - |mapGen| |mapExpon| |commutativeEquality| |leftMult| |rightMult| |makeUnit| - |reverse!| |reverse| |nthFactor| |nthExpon| |makeMulti| |makeTerm| - |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| - |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ + |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| |voidMode| + |noValueMode| |jokerMode| GF2FG FG2F F2FG |explogs2trigs| |trigs2explogs| + |swap!| |fill!| |minIndex| |maxIndex| |entry?| |indices| |index?| |entries| + |categories| |search| |key?| |symbolIfCan| |kernel| |argument| + |constantKernel| |constantIfCan| |kovacic| |unknown| |laplace| + |trailingCoefficient| |normalizeIfCan| |polCase| |distFact| |identification| + |LyndonCoordinates| |LyndonBasis| |zeroDimensional?| |fglmIfCan| |groebner| + |lexTriangular| |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| + |Si| |Ei| |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| + |anticoord| |intcompBasis| |choosemon| |transform| |pack!| |library| + |complexLimit| |limit| |linearlyDependent?| |linearDependence| |solveLinear| + |reducedSystem| |setDifference| |setIntersection| |setUnion| |append| |null| + |nil| |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| + |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |nthFactor| |nthExpon| + |makeMulti| |makeTerm| |listOfMonoms| |insert| |delete| |symmetricSquare| + |factor1| |symmetricProduct| |symmetricPower| |directSum| |\\/| |/\\| ~ |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 4d8cafb6..c1210d39 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,342 +1,342 @@ -(3215100 . 3477425203) -((-1909 (((-112) (-1 (-112) |#2| |#2|) $) 87) (((-112) $) NIL)) (-1907 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-4228 ((|#2| $ (-551) |#2|) NIL) ((|#2| $ (-1239 (-551)) |#2|) 44)) (-2451 (($ $) 81)) (-4283 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) 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T) ((-23) . T) ((-25) . T) ((-38 #1=(-412 (-551))) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-38 |#1|) . T) ((-38 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-35) |has| |#1| (-1208)) ((-95) |has| |#1| (-1208)) ((-102) . T) ((-111 #1# #1#) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -3972 (|has| |#1| (-354)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-621 #1#) -3972 (|has| |#1| (-1044 (-412 (-551)))) (|has| |#1| (-354)) (|has| |#1| (-367))) ((-621 (-551)) . T) ((-621 |#1|) . T) ((-621 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-618 (-868)) . T) ((-173) . T) ((-619 (-169 (-226))) |has| |#1| (-1026)) ((-619 (-169 (-382))) |has| |#1| (-1026)) ((-619 (-540)) |has| |#1| (-619 (-540))) ((-619 (-896 (-382))) |has| |#1| (-619 (-896 (-382)))) ((-619 (-896 (-551))) |has| |#1| (-619 (-896 (-551)))) ((-619 #2=(-1177 |#1|)) . 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T) ((-457) -3972 (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-498) |has| |#1| (-1208)) ((-519 (-1183) |#1|) |has| |#1| (-519 (-1183) |#1|)) ((-519 |#1| |#1|) |has| |#1| (-312 |#1|)) ((-562) -3972 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-651 #1#) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-651 (-551)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-645 |#1|) . T) ((-645 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) -3972 (|has| |#1| (-354)) (|has| |#1| (-367))) ((-722 |#1|) . T) ((-722 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-354)) (|has| |#1| (-367)) (|has| |#1| (-310))) ((-729 |#1| #2#) . T) ((-731) . 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T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #2=(-551) |#2|) . T) ((-291 #2# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-417 |#2|) |has| |#2| (-1107)) ((-494 |#2|) . T) ((-609 #2# |#2|) . 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T) ((-1280 |#2|) |has| |#2| (-367))) -((-2977 (((-112) $ $) NIL (|has| |#2| (-1107)))) (-3617 (((-112) $) NIL (|has| |#2| (-131)))) (-4148 (($ (-925)) 65 (|has| |#2| (-1055)))) (-2381 (((-1278) $ (-551) (-551)) NIL (|has| $ (-6 -4435)))) (-2814 (($ $ $) 70 (|has| |#2| (-798)))) (-1410 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-1312 (((-112) $ (-776)) 17)) (-3549 (((-776)) NIL (|has| |#2| (-372)))) (-4064 (((-551) $) NIL (|has| |#2| (-853)))) (-4228 ((|#2| $ (-551) |#2|) NIL (|has| $ (-6 -4435)))) (-4165 (($) NIL T CONST)) (-3586 (((-3 (-551) #1="failed") $) NIL (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107)))) (((-3 (-412 (-551)) #1#) $) NIL (-12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107)))) (((-3 |#2| #1#) $) 34 (|has| |#2| (-1107)))) (-3585 (((-551) $) NIL (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107)))) (((-412 (-551)) $) NIL (-12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107)))) ((|#2| $) 32 (|has| |#2| (-1107)))) (-2436 (((-694 (-551)) (-694 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(|has| |#2| (-1107))))) (-3833 (($ $) NIL)) (-4387 (((-1272 |#2|) $) 10) (($ (-551)) NIL (-3969 (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107))) (|has| |#2| (-1055)))) (($ (-412 (-551))) NIL (-12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107)))) (($ |#2|) 13 (|has| |#2| (-1107))) (((-868) $) NIL (|has| |#2| (-618 (-868))))) (-3539 (((-776)) NIL (|has| |#2| (-1055)) CONST)) (-3671 (((-112) $ $) NIL (|has| |#2| (-1107)))) (-2136 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4434)))) (-3816 (($ $) NIL (|has| |#2| (-853)))) (-3519 (($) 40 (|has| |#2| (-131)) CONST)) (-3076 (($) 44 (|has| |#2| (-731)) CONST)) (-3081 (($ $) NIL (-12 (|has| |#2| (-234)) (|has| |#2| (-1055)))) (($ $ (-776)) NIL (-12 (|has| |#2| (-234)) (|has| |#2| (-1055)))) (($ $ (-1183)) NIL (-12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055)))) (($ $ (-646 (-1183))) NIL (-12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055)))) (($ $ (-1183) (-776)) NIL (-12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055)))) 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(|has| |#2| (-25)))) (-4398 (((-776) $) NIL (|has| $ (-6 -4434))))) +((-1574 (*1 *1 *2) (-12 (-5 *2 (-1272 *4)) (-4 *4 (-1222)) (-4 *1 (-239 *3 *4)))) (-4151 (*1 *1 *2) (-12 (-5 *2 (-925)) (-4 *1 (-239 *3 *4)) (-4 *4 (-1055)) (-4 *4 (-1222)))) (-4280 (*1 *2 *1 *1) (-12 (-4 *1 (-239 *3 *2)) (-4 *2 (-1222)) (-4 *2 (-1055)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-239 *3 *2)) (-4 *2 (-1222)) (-4 *2 (-731)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-239 *3 *2)) (-4 *2 (-1222)) (-4 *2 (-731))))) +(-13 (-609 (-551) |t#2|) (-618 (-1272 |t#2|)) (-10 -8 (-6 -4437) (-15 -1574 ($ (-1272 |t#2|))) (IF (|has| |t#2| (-1107)) (-6 (-417 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1055)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-381 |t#2|)) (-15 -4151 ($ (-925))) (-15 -4280 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-731)) (PROGN (-6 (-731)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-372)) (-6 (-372)) |%noBranch|) (IF (|has| |t#2| (-173)) (PROGN (-6 (-38 |t#2|)) (-6 (-173))) |%noBranch|) (IF (|has| |t#2| (-6 -4434)) (-6 -4434) |%noBranch|) (IF (|has| |t#2| (-853)) (-6 (-853)) |%noBranch|) (IF (|has| |t#2| (-798)) (-6 (-798)) |%noBranch|) (IF (|has| |t#2| (-367)) (-6 (-1280 |t#2|)) |%noBranch|))) +(((-21) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-23) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-25) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -3972 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3972 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #1=(-412 (-551))) -12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107))) ((-621 (-551)) -3972 (|has| |#2| (-1055)) (-12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -3972 (|has| |#2| (-1107)) (|has| |#2| (-173))) ((-618 (-868)) -3972 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-868))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1272 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #2=(-551) |#2|) . T) ((-291 #2# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-417 |#2|) |has| |#2| (-1107)) ((-494 |#2|) . T) ((-609 #2# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1107))) ((-651 (-551)) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -3972 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -3972 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -3972 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-551)) -12 (|has| |#2| (-644 (-551))) (|has| |#2| (-1055))) ((-644 |#2|) |has| |#2| (-1055)) ((-722 |#2|) -3972 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -3972 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -3972 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-802) -3972 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -3972 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055))) ((-1044 #1#) -12 (|has| |#2| (-1044 (-412 (-551)))) (|has| |#2| (-1107))) ((-1044 (-551)) -12 (|has| |#2| (-1044 (-551))) (|has| |#2| (-1107))) ((-1044 |#2|) |has| |#2| (-1107)) ((-1057 |#2|) -3972 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1057 $) |has| |#2| (-173)) ((-1062 |#2|) -3972 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1062 $) |has| |#2| (-173)) ((-1055) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1063) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1118) -3972 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1107) -3972 (|has| |#2| (-1107)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1222) . 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T) ((-173) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-619 (-540)) -12 (|has| |#1| (-619 (-540))) (|has| |#3| (-619 (-540)))) ((-619 (-896 (-382))) -12 (|has| |#1| (-619 (-896 (-382)))) (|has| |#3| (-619 (-896 (-382))))) ((-619 (-896 (-551))) -12 (|has| |#1| (-619 (-896 (-551)))) (|has| |#3| (-619 (-896 (-551))))) ((-232 |#1|) . T) ((-234) |has| |#1| (-234)) ((-293) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-312 $) . T) ((-329 |#1| |#4|) . T) ((-381 |#1|) . T) ((-417 |#1|) . T) ((-457) -3969 (|has| |#1| (-916)) (|has| |#1| (-457))) ((-519 |#2| |#1|) |has| |#1| (-234)) ((-519 |#2| $) |has| |#1| (-234)) ((-519 |#3| |#1|) . T) ((-519 |#3| $) . T) ((-519 $ $) . T) ((-562) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-651 #1#) |has| |#1| (-38 (-412 (-551)))) ((-651 (-551)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#2|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #1=(-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-412 (-551)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #1#) -3972 (|has| |#1| (-1044 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 |#1|) . T) ((-621 |#2|) . T) ((-621 |#3|) . T) ((-621 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-618 (-868)) . T) ((-173) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-619 (-540)) -12 (|has| |#1| (-619 (-540))) (|has| |#3| (-619 (-540)))) ((-619 (-896 (-382))) -12 (|has| |#1| (-619 (-896 (-382)))) (|has| |#3| (-619 (-896 (-382))))) ((-619 (-896 (-551))) -12 (|has| |#1| (-619 (-896 (-551)))) (|has| |#3| (-619 (-896 (-551))))) ((-232 |#1|) . T) ((-234) |has| |#1| (-234)) ((-293) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-312 $) . T) ((-329 |#1| |#4|) . T) ((-381 |#1|) . T) ((-417 |#1|) . T) ((-457) -3972 (|has| |#1| (-916)) (|has| |#1| (-457))) ((-519 |#2| |#1|) |has| |#1| (-234)) ((-519 |#2| $) |has| |#1| (-234)) ((-519 |#3| |#1|) . T) ((-519 |#3| $) . T) ((-519 $ $) . T) ((-562) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-651 #1#) |has| |#1| (-38 (-412 (-551)))) ((-651 (-551)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 (-1183)) |has| |#1| (-906 (-1183))) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#2|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . T) ((-1227) |has| |#1| (-916))) +((-2980 (((-112) $ $) 19 (|has| |#1| (-1107)))) (-1601 ((|#1| $) 55)) (-3760 ((|#1| $) 45)) (-1312 (((-112) $ (-776)) 8)) (-4168 (($) 7 T CONST)) (-3415 (($ $) 61)) (-2454 (($ $) 49)) (-3762 ((|#1| |#1| $) 47)) (-3761 ((|#1| $) 46)) (-2133 (((-646 |#1|) $) 31 (|has| $ (-6 -4437)))) (-4163 (((-112) $ (-776)) 9)) (-3020 (((-646 |#1|) $) 30 (|has| $ (-6 -4437)))) (-3678 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4437))))) (-2137 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4438)))) (-4402 (($ (-1 |#1| |#1|) $) 36)) (-4160 (((-112) $ (-776)) 10)) (-4277 (((-776) $) 62)) (-3675 (((-1165) $) 22 (|has| |#1| (-1107)))) (-1372 ((|#1| $) 40)) (-1599 ((|#1| |#1| $) 53)) (-1598 ((|#1| |#1| $) 52)) (-4051 (($ |#1| $) 41)) (-3015 (((-776) $) 56)) (-3676 (((-1126) $) 21 (|has| |#1| (-1107)))) (-3414 ((|#1| $) 63)) (-1597 ((|#1| $) 51)) (-1596 ((|#1| $) 50)) (-1373 ((|#1| $) 42)) (-2135 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4437)))) (-4211 (($ $ (-646 (-296 |#1|))) 27 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-296 |#1|)) 26 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107)))) (($ $ (-646 |#1|) (-646 |#1|)) 24 (-12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))))) (-1313 (((-112) $ $) 14)) (-3417 ((|#1| |#1| $) 59)) (-3839 (((-112) $) 11)) (-4008 (($) 12)) (-3416 ((|#1| $) 60)) (-1602 (($) 58) (($ (-646 |#1|)) 57)) (-3759 (((-776) $) 44)) (-2134 (((-776) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4437))) (((-776) |#1| $) 29 (-12 (|has| |#1| (-1107)) (|has| $ (-6 -4437))))) (-3836 (($ $) 13)) (-4390 (((-868) $) 18 (|has| |#1| (-618 (-868))))) (-1600 ((|#1| $) 54)) (-3674 (((-112) $ $) 23 (|has| |#1| (-1107)))) (-1374 (($ (-646 |#1|)) 43)) (-3413 ((|#1| $) 64)) (-2136 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4437)))) (-3467 (((-112) $ $) 20 (|has| |#1| (-1107)))) (-4401 (((-776) $) 6 (|has| $ (-6 -4437))))) (((-256 |#1|) (-140) (-1222)) (T -256)) -((-1602 (*1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1602 (*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-4 *1 (-256 *3)))) (-3012 (*1 *2 *1) (-12 (-4 *1 (-256 *3)) (-4 *3 (-1222)) (-5 *2 (-776)))) (-1601 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1600 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1599 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1598 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1597 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1596 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-2451 (*1 *1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222))))) -(-13 (-1127 |t#1|) (-1001 |t#1|) (-10 -8 (-15 -1602 ($)) (-15 -1602 ($ (-646 |t#1|))) (-15 -3012 ((-776) $)) (-15 -1601 (|t#1| $)) (-15 -1600 (|t#1| $)) (-15 -1599 (|t#1| |t#1| $)) (-15 -1598 (|t#1| |t#1| $)) (-15 -1597 (|t#1| $)) (-15 -1596 (|t#1| $)) (-15 -2451 ($ $)))) -(((-34) . T) ((-107 |#1|) . T) ((-102) |has| |#1| (-1107)) ((-618 (-868)) -3969 (|has| |#1| (-1107)) (|has| |#1| (-618 (-868)))) ((-312 |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-494 |#1|) . T) ((-519 |#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-1001 |#1|) . T) ((-1107) |has| |#1| (-1107)) ((-1127 |#1|) . T) ((-1222) . T)) +((-1602 (*1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1602 (*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-4 *1 (-256 *3)))) (-3015 (*1 *2 *1) (-12 (-4 *1 (-256 *3)) (-4 *3 (-1222)) (-5 *2 (-776)))) (-1601 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1600 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1599 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1598 (*1 *2 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1597 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-1596 (*1 *2 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) (-2454 (*1 *1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222))))) +(-13 (-1127 |t#1|) (-1001 |t#1|) (-10 -8 (-15 -1602 ($)) (-15 -1602 ($ (-646 |t#1|))) (-15 -3015 ((-776) $)) (-15 -1601 (|t#1| $)) (-15 -1600 (|t#1| $)) (-15 -1599 (|t#1| |t#1| $)) (-15 -1598 (|t#1| |t#1| $)) (-15 -1597 (|t#1| $)) (-15 -1596 (|t#1| $)) (-15 -2454 ($ $)))) +(((-34) . T) ((-107 |#1|) . T) ((-102) |has| |#1| (-1107)) ((-618 (-868)) -3972 (|has| |#1| (-1107)) (|has| |#1| (-618 (-868)))) ((-312 |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-494 |#1|) . T) ((-519 |#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1107))) ((-1001 |#1|) . T) ((-1107) |has| |#1| (-1107)) ((-1127 |#1|) . T) ((-1222) . 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(-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))))) (T -565)) -((-2263 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1612 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))) (-5 *1 (-565)))) (-2388 (*1 *2 *1) (-12 (-5 *2 (-646 (-2 (|:| -4301 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (|:| -2263 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1160 (-226))) (|:| |notEvaluated| #6#))) (|:| -1612 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-5 *1 (-565)))) (-2262 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| 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T) ((-653 #1#) |has| |#1| (-38 (-412 (-551)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-551)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-644 (-551)) |has| |#1| (-644 (-551))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-551)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457))) ((-731) . T) ((-906 |#3|) . T) ((-892 (-382)) -12 (|has| |#1| (-892 (-382))) (|has| |#3| (-892 (-382)))) ((-892 (-551)) -12 (|has| |#1| (-892 (-551))) (|has| |#3| (-892 (-551)))) ((-956 |#1| |#2| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1044 (-412 (-551))) |has| |#1| (-1044 (-412 (-551)))) ((-1044 (-551)) |has| |#1| (-1044 (-551))) ((-1044 |#1|) . T) ((-1044 |#3|) . T) ((-1057 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1062 #1#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . T) ((-1227) |has| |#1| (-916))) +((-2980 (((-112) $ $) NIL)) (-3675 (((-1165) $) NIL)) (-3613 (((-646 (-1141)) $) 18)) (-3676 (((-1126) $) NIL)) (-4390 (((-868) $) 27) (($ (-1188)) NIL) (((-1188) $) NIL)) (-3665 (((-1141) $) 20)) (-3674 (((-112) $ $) NIL)) (-3467 (((-112) $ $) NIL))) +(((-1072) (-13 (-1089) (-10 -8 (-15 -3613 ((-646 (-1141)) $)) (-15 -3665 ((-1141) $))))) (T -1072)) +((-3613 (*1 *2 *1) (-12 (-5 *2 (-646 (-1141))) (-5 *1 (-1072)))) (-3665 (*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1072))))) +(-13 (-1089) (-10 -8 (-15 -3613 ((-646 (-1141)) $)) (-15 -3665 ((-1141) $)))) +((-3620 (((-112) |#3| $) 15)) (-3615 (((-3 $ "failed") |#3| (-925)) 29)) (-3902 (((-3 |#3| "failed") |#3| $) 45)) (-3618 (((-112) |#3| $) 19)) (-3619 (((-112) |#3| $) 17))) +(((-1073 |#1| |#2| |#3|) (-10 -8 (-15 -3615 ((-3 |#1| "failed") |#3| (-925))) (-15 -3902 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3618 ((-112) |#3| |#1|)) (-15 -3619 ((-112) |#3| |#1|)) (-15 -3620 ((-112) |#3| |#1|))) (-1074 |#2| |#3|) (-13 (-853) (-367)) (-1248 |#2|)) (T -1073)) +NIL +(-10 -8 (-15 -3615 ((-3 |#1| "failed") |#3| (-925))) (-15 -3902 ((-3 |#3| "failed") |#3| |#1|)) (-15 -3618 ((-112) |#3| |#1|)) (-15 -3619 ((-112) |#3| |#1|)) (-15 -3620 ((-112) |#3| |#1|))) +((-2980 (((-112) $ $) 7)) (-3620 (((-112) |#2| $) 22)) (-4067 (((-551) |#2| $) 23)) (-3615 (((-3 $ "failed") |#2| (-925)) 16)) (-3614 ((|#1| |#2| $ |#1|) 14)) (-3902 (((-3 |#2| "failed") |#2| $) 19)) (-3618 (((-112) |#2| $) 20)) (-3619 (((-112) |#2| $) 21)) (-3675 (((-1165) $) 10)) (-3676 (((-1126) $) 11)) (-3617 ((|#2| $) 18)) (-4390 (((-868) $) 12)) (-3674 (((-112) $ $) 9)) (-4213 ((|#1| |#2| $ |#1|) 15)) (-3616 (((-646 $) |#2|) 17)) (-3467 (((-112) $ $) 6))) (((-1074 |#1| |#2|) (-140) (-13 (-853) (-367)) (-1248 |t#1|)) (T -1074)) -((-4064 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-551)))) (-3617 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3616 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3615 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3899 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3614 (*1 *2 *1) (-12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3613 (*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-646 *1)) (-4 *1 (-1074 *4 *3)))) (-3612 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-925)) (-4 *4 (-13 (-853) (-367))) (-4 *1 (-1074 *4 *2)) (-4 *2 (-1248 *4)))) (-4210 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) (-3611 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2))))) -(-13 (-1107) (-10 -8 (-15 -4064 ((-551) |t#2| $)) (-15 -3617 ((-112) |t#2| $)) (-15 -3616 ((-112) |t#2| $)) (-15 -3615 ((-112) |t#2| $)) (-15 -3899 ((-3 |t#2| "failed") |t#2| $)) (-15 -3614 (|t#2| $)) (-15 -3613 ((-646 $) |t#2|)) (-15 -3612 ((-3 $ "failed") |t#2| (-925))) (-15 -4210 (|t#1| |t#2| $ |t#1|)) (-15 -3611 (|t#1| |t#2| $ |t#1|)))) +((-4067 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-551)))) (-3620 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3619 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3618 (*1 *2 *3 *1) (-12 (-4 *1 (-1074 *4 *3)) (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-112)))) (-3902 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3617 (*1 *2 *1) (-12 (-4 *1 (-1074 *3 *2)) (-4 *3 (-13 (-853) (-367))) (-4 *2 (-1248 *3)))) (-3616 (*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-367))) (-4 *3 (-1248 *4)) (-5 *2 (-646 *1)) (-4 *1 (-1074 *4 *3)))) (-3615 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-925)) (-4 *4 (-13 (-853) (-367))) (-4 *1 (-1074 *4 *2)) (-4 *2 (-1248 *4)))) (-4213 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) (-3614 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2))))) +(-13 (-1107) (-10 -8 (-15 -4067 ((-551) |t#2| $)) (-15 -3620 ((-112) |t#2| $)) (-15 -3619 ((-112) |t#2| $)) (-15 -3618 ((-112) |t#2| $)) (-15 -3902 ((-3 |t#2| "failed") |t#2| $)) (-15 -3617 (|t#2| $)) (-15 -3616 ((-646 $) |t#2|)) (-15 -3615 ((-3 $ "failed") |t#2| (-925))) (-15 -4213 (|t#1| |t#2| $ |t#1|)) (-15 -3614 (|t#1| |t#2| $ |t#1|)))) (((-102) . 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T) ((-23) . T) ((-47 |#1| #1=(-551)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -3969 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-551)))) ((-95) |has| |#1| (-38 (-412 (-551)))) ((-102) . T) ((-111 #2# #2#) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -3969 (|has| |#1| (-562)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -3969 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -3969 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #2#) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #2#) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #2#) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -3969 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-644 (-551)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-551)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #2#) -3969 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -3969 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-731) . 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T) ((-23) . T) ((-47 |#1| #1=(-551)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-551)))) ((-95) |has| |#1| (-38 (-412 (-551)))) ((-102) . T) ((-111 #2# #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -3972 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -3972 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-644 (-551)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-551)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #2#) -3972 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-551))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -3972 (|has| |#1| (-562)) (|has| |#1| (-367))) ((-731) . 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T) ((-23) . T) ((-47 |#1| #1=(-776)) . T) ((-25) . T) ((-38 #2=(-412 (-551))) |has| |#1| (-38 (-412 (-551)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-412 (-551)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #2#) -3969 (|has| |#1| (-1044 (-412 (-551)))) (|has| |#1| (-38 (-412 (-551))))) ((-621 (-551)) . T) ((-621 #3=(-1088)) . T) ((-621 |#1|) . T) ((-621 $) -3969 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-618 (-868)) . 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T) ((-1057 #2#) |has| |#1| (-38 (-412 (-551)))) ((-1057 |#1|) . T) ((-1057 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1062 #2#) |has| |#1| (-38 (-412 (-551)))) ((-1062 |#1|) . T) ((-1062 $) -3972 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1055) . T) ((-1063) . T) ((-1118) . T) ((-1107) . 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3214992 "ZMOD" 3214997 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1300 3213293 3213457 3213666 "ZLINDEP" 3214015 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1299 3202593 3204361 3206333 "ZDSOLVE" 3211423 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1298 3201839 3201980 3202169 "YSTREAM" 3202439 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1297 3199613 3201140 3201344 "XRPOLY" 3201682 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196166 3197484 3198059 "XPR" 3199085 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1295 3193819 3195187 3195242 "XPOLYC" 3195530 NIL XPOLYC (NIL T T) -9 NIL 3195643 NIL) (-1294 3191549 3193159 3193363 "XPOLY" 3193659 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1293 3187927 3190066 3190454 "XPBWPOLY" 3191207 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3183123 3184412 3184467 "XFALG" 3186639 NIL XFALG (NIL T T) -9 NIL 3187428 NIL) (-1291 3178820 3181113 3181155 "XF" 3181776 NIL XF (NIL T) -9 NIL 3182176 NIL) (-1290 3178441 3178529 3178698 "XF-" 3178703 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1289 3177574 3177678 3177883 "XEXPPKG" 3178333 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3175683 3177424 3177520 "XDPOLY" 3177525 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3174490 3175090 3175133 "XALG" 3175138 NIL XALG (NIL T) -9 NIL 3175249 NIL) (-1286 3167959 3172467 3172961 "WUTSET" 3174082 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3166215 3167011 3167334 "WP" 3167770 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3165817 3166037 3166107 "WHILEAST" 3166167 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3165289 3165534 3165628 "WHEREAST" 3165745 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3164175 3164373 3164668 "WFFINTBS" 3165086 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3162079 3162506 3162968 "WEIER" 3163747 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3161125 3161575 3161617 "VSPACE" 3161753 NIL VSPACE (NIL T) -9 NIL 3161827 NIL) (-1279 3160963 3160990 3161081 "VSPACE-" 3161086 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3160772 3160814 3160882 "VOID" 3160917 T VOID (NIL) -8 NIL NIL NIL) (-1277 3157196 3157835 3158572 "VIEWDEF" 3160057 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1276 3146500 3148744 3150917 "VIEW3D" 3155045 T VIEW3D (NIL) -8 NIL NIL NIL) (-1275 3138751 3140411 3141990 "VIEW2D" 3144943 T VIEW2D (NIL) -8 NIL NIL NIL) (-1274 3136887 3137246 3137652 "VIEW" 3138367 T VIEW (NIL) -7 NIL NIL NIL) (-1273 3135464 3135723 3136041 "VECTOR2" 3136617 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1272 3130817 3135234 3135326 "VECTOR" 3135407 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1271 3124291 3128598 3128641 "VECTCAT" 3129636 NIL VECTCAT (NIL T) -9 NIL 3130223 NIL) (-1270 3123305 3123559 3123949 "VECTCAT-" 3123954 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3122759 3122956 3123076 "VARIABLE" 3123220 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3122692 3122697 3122727 "UTYPE" 3122732 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3121522 3121676 3121938 "UTSODETL" 3122518 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3118962 3119422 3119946 "UTSODE" 3121063 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3109836 3115203 3115246 "UTSCAT" 3116358 NIL UTSCAT (NIL T) -9 NIL 3117116 NIL) (-1264 3107183 3107906 3108895 "UTSCAT-" 3108900 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1263 3106810 3106853 3106986 "UTS2" 3107134 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3098647 3104436 3104925 "UTS" 3106379 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3092874 3095485 3095528 "URAGG" 3097598 NIL URAGG (NIL T) -9 NIL 3098321 NIL) (-1260 3089816 3090678 3091800 "URAGG-" 3091805 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3085532 3088451 3088916 "UPXSSING" 3089480 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3078607 3085436 3085508 "UPXSCONS" 3085513 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1257 3068354 3075145 3075207 "UPXSCCA" 3075781 NIL UPXSCCA (NIL T T) -9 NIL 3076014 NIL) (-1256 3067992 3068077 3068251 "UPXSCCA-" 3068256 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1255 3057591 3064155 3064198 "UPXSCAT" 3064846 NIL UPXSCAT (NIL T) -9 NIL 3065455 NIL) (-1254 3057021 3057100 3057279 "UPXS2" 3057506 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1253 3049091 3056268 3056541 "UPXS" 3056806 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3047748 3048000 3048350 "UPSQFREE" 3048835 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3041169 3044226 3044281 "UPSCAT" 3045442 NIL UPSCAT (NIL T T) -9 NIL 3046216 NIL) (-1250 3040373 3040580 3040907 "UPSCAT-" 3040912 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3040000 3040043 3040176 "UPOLYC2" 3040324 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1248 3025688 3033423 3033466 "UPOLYC" 3035567 NIL UPOLYC (NIL T) -9 NIL 3036788 NIL) (-1247 3017052 3019466 3022601 "UPOLYC-" 3022606 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1246 3016391 3016498 3016662 "UPMP" 3016941 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1245 3015944 3016025 3016164 "UPDIVP" 3016304 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1244 3014512 3014761 3015077 "UPDECOMP" 3015693 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1243 3013747 3013859 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2930626 2931145 2931684 "TUBETOOL" 2932418 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2929475 2929680 2929921 "TUBE" 2930419 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2918115 2922234 2922331 "TSETCAT" 2927600 NIL TSETCAT (NIL T T T T) -9 NIL 2929131 NIL) (-1216 2912847 2914447 2916338 "TSETCAT-" 2916343 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1215 2907576 2911819 2912102 "TS" 2912599 NIL TS (NIL T) -8 NIL NIL NIL) (-1214 2902215 2903062 2903991 "TRMANIP" 2906712 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2901656 2901719 2901882 "TRIMAT" 2902147 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2899522 2899759 2900116 "TRIGMNIP" 2901405 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2899042 2899155 2899185 "TRIGCAT" 2899398 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2898711 2898790 2898931 "TRIGCAT-" 2898936 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2895557 2897569 2897850 "TREE" 2898465 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2894831 2895359 2895389 "TRANFUN" 2895424 T TRANFUN (NIL) -9 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NIL NIL) (-1183 2836423 2837715 2838528 "SYMBOL" 2839612 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2829962 2831651 2833371 "SWITCH" 2834725 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2823196 2828783 2829086 "SUTS" 2829717 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2815266 2822443 2822716 "SUPXS" 2822981 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2814425 2814552 2814769 "SUPFRACF" 2815134 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1178 2814046 2814105 2814218 "SUP2" 2814360 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1177 2805845 2813664 2813790 "SUP" 2813955 NIL SUP (NIL T) -8 NIL NIL NIL) (-1176 2804293 2804567 2804923 "SUMRF" 2805544 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2803628 2803694 2803886 "SUMFS" 2804214 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2787611 2802805 2803056 "SULS" 2803435 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2787213 2787433 2787503 "SUCHTAST" 2787563 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2786508 2786738 2786878 "SUCH" 2787121 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2780374 2781414 2782373 "SUBSPACE" 2785596 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2779804 2779894 2780058 "SUBRESP" 2780262 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2773977 2775097 2776244 "STTFNC" 2778704 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1168 2767343 2768642 2769953 "STTF" 2772713 NIL STTF (NIL T) -7 NIL NIL NIL) (-1167 2758654 2760525 2762319 "STTAYLOR" 2765584 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2751786 2758518 2758601 "STRTBL" 2758606 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2747150 2751741 2751772 "STRING" 2751777 T STRING (NIL) -8 NIL NIL NIL) (-1164 2742011 2746523 2746553 "STRICAT" 2746612 T STRICAT (NIL) -9 NIL 2746674 NIL) (-1163 2741521 2741598 2741742 "STREAM3" 2741928 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1162 2740503 2740686 2740921 "STREAM2" 2741334 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1161 2740191 2740243 2740336 "STREAM1" 2740445 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1160 2732946 2737810 2738421 "STREAM" 2739615 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1159 2731962 2732143 2732374 "STINPROD" 2732762 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2731149 2731451 2731599 "STEPAST" 2731836 T STEPAST (NIL) -8 NIL NIL NIL) (-1157 2730701 2730911 2730941 "STEP" 2731021 T STEP (NIL) -9 NIL 2731099 NIL) (-1156 2724135 2730600 2730677 "STBL" 2730682 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2719263 2723356 2723399 "STAGG" 2723552 NIL STAGG (NIL T) -9 NIL 2723641 NIL) (-1154 2716971 2717571 2718441 "STAGG-" 2718446 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2715118 2716741 2716833 "STACK" 2716914 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2707840 2713259 2713715 "SREGSET" 2714748 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2700265 2701634 2703147 "SRDCMPK" 2706446 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2693182 2697705 2697735 "SRAGG" 2699038 T SRAGG (NIL) -9 NIL 2699646 NIL) (-1149 2692199 2692454 2692833 "SRAGG-" 2692838 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2686663 2691146 2691567 "SQMATRIX" 2691825 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2680349 2683381 2684108 "SPLTREE" 2686008 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2676312 2677005 2677651 "SPLNODE" 2679775 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2675359 2675592 2675622 "SPFCAT" 2676066 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2674096 2674306 2674570 "SPECOUT" 2675117 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2665206 2667078 2667108 "SPADXPT" 2671784 T SPADXPT (NIL) -9 NIL 2673948 NIL) (-1142 2664967 2665007 2665076 "SPADPRSR" 2665159 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2663016 2664922 2664953 "SPADAST" 2664958 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2654961 2656734 2656777 "SPACEC" 2661150 NIL SPACEC (NIL T) -9 NIL 2662966 NIL) (-1139 2653091 2654893 2654942 "SPACE3" 2654947 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2651843 2652014 2652305 "SORTPAK" 2652896 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2649935 2650238 2650650 "SOLVETRA" 2651507 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2648985 2649207 2649468 "SOLVESER" 2649708 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2644289 2645177 2646172 "SOLVERAD" 2648037 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2640104 2640713 2641442 "SOLVEFOR" 2643656 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2634401 2639453 2639550 "SNTSCAT" 2639555 NIL SNTSCAT (NIL T T T T) -9 NIL 2639625 NIL) (-1132 2628507 2632724 2633115 "SMTS" 2634091 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2623218 2628395 2628472 "SMP" 2628477 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2621377 2621678 2622076 "SMITH" 2622915 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2614088 2618280 2618383 "SMATCAT" 2619737 NIL SMATCAT (NIL NIL T T T) -9 NIL 2620287 NIL) (-1128 2611049 2611865 2613036 "SMATCAT-" 2613041 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2608715 2610285 2610328 "SKAGG" 2610589 NIL SKAGG (NIL T) -9 NIL 2610724 NIL) (-1126 2605028 2608131 2608326 "SINT" 2608513 T SINT (NIL) -8 NIL NIL 2608686) (-1125 2604800 2604838 2604904 "SIMPAN" 2604984 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2603659 2603873 2604141 "SIGNRF" 2604566 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1123 2602513 2602657 2602934 "SIGNEF" 2603495 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1122 2601819 2602096 2602220 "SIGAST" 2602411 T SIGAST (NIL) -8 NIL NIL NIL) (-1121 2601098 2601354 2601494 "SIG" 2601701 T SIG (NIL) -8 NIL NIL NIL) (-1120 2598788 2599242 2599748 "SHP" 2600639 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2592647 2598689 2598765 "SHDP" 2598770 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2592220 2592412 2592442 "SGROUP" 2592535 T SGROUP (NIL) -9 NIL 2592597 NIL) (-1117 2592078 2592104 2592177 "SGROUP-" 2592182 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2588913 2589611 2590334 "SGCF" 2591377 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2583308 2588360 2588457 "SFRTCAT" 2588462 NIL SFRTCAT (NIL T T T T) -9 NIL 2588501 NIL) (-1114 2576729 2577747 2578883 "SFRGCD" 2582291 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2569855 2570928 2572114 "SFQCMPK" 2575662 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2569475 2569564 2569675 "SFORT" 2569796 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2568593 2569315 2569436 "SEXOF" 2569441 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2564106 2564821 2564916 "SEXCAT" 2567853 NIL SEXCAT (NIL T T T T T) -9 NIL 2568431 NIL) (-1109 2563213 2563987 2564055 "SEX" 2564060 T SEX (NIL) -8 NIL NIL NIL) (-1108 2561443 2561930 2562233 "SETMN" 2562956 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1107 2560939 2561091 2561121 "SETCAT" 2561297 T SETCAT (NIL) -9 NIL 2561407 NIL) (-1106 2560631 2560709 2560839 "SETCAT-" 2560844 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1105 2556992 2559092 2559135 "SETAGG" 2560005 NIL SETAGG (NIL T) -9 NIL 2560345 NIL) (-1104 2556450 2556566 2556803 "SETAGG-" 2556808 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1103 2553603 2556384 2556432 "SET" 2556437 NIL SET (NIL T) -8 NIL NIL NIL) (-1102 2553046 2553299 2553400 "SEQAST" 2553524 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2552245 2552539 2552600 "SEGXCAT" 2552886 NIL SEGXCAT (NIL T T) -9 NIL 2553006 NIL) (-1100 2551224 2551438 2551481 "SEGCAT" 2552003 NIL SEGCAT (NIL T) -9 NIL 2552224 NIL) (-1099 2550845 2550904 2551017 "SEGBIND2" 2551159 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1098 2549777 2550208 2550416 "SEGBIND" 2550672 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2549350 2549578 2549655 "SEGAST" 2549722 T SEGAST (NIL) -8 NIL NIL NIL) (-1096 2548569 2548695 2548899 "SEG2" 2549194 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1095 2547575 2548235 2548417 "SEG" 2548422 NIL SEG (NIL T) -8 NIL NIL NIL) (-1094 2546985 2547510 2547557 "SDVAR" 2547562 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2539553 2546755 2546885 "SDPOL" 2546890 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2538146 2538412 2538731 "SCPKG" 2539268 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2537310 2537482 2537674 "SCOPE" 2537976 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2536530 2536664 2536843 "SCACHE" 2537165 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2536176 2536362 2536392 "SASTCAT" 2536397 T SASTCAT (NIL) -9 NIL 2536410 NIL) (-1088 2535663 2536011 2536087 "SAOS" 2536122 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2535228 2535263 2535436 "SAERFFC" 2535622 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2534821 2534856 2535015 "SAEFACT" 2535187 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1085 2528769 2534718 2534798 "SAE" 2534803 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1084 2527090 2527404 2527805 "RURPK" 2528435 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2525727 2526033 2526338 "RULESET" 2526924 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2525339 2525521 2525604 "RULECOLD" 2525679 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1081 2522562 2523092 2523550 "RULE" 2525020 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1080 2522352 2522380 2522451 "RTVALUE" 2522513 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2521823 2522069 2522163 "RSTRCAST" 2522280 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2516671 2517466 2518386 "RSETGCD" 2521022 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2505928 2510980 2511077 "RSETCAT" 2515196 NIL RSETCAT (NIL T T T T) -9 NIL 2516293 NIL) (-1076 2503855 2504394 2505218 "RSETCAT-" 2505223 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2496241 2497617 2499137 "RSDCMPK" 2502454 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2494220 2494687 2494761 "RRCC" 2495847 NIL RRCC (NIL T T) -9 NIL 2496191 NIL) (-1073 2493571 2493745 2494024 "RRCC-" 2494029 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2493014 2493267 2493368 "RPTAST" 2493492 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2466896 2476222 2476289 "RPOLCAT" 2486953 NIL RPOLCAT (NIL T T T) -9 NIL 2490112 NIL) (-1070 2458430 2460758 2463868 "RPOLCAT-" 2463873 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2449363 2456641 2457123 "ROUTINE" 2457970 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2446163 2448989 2449129 "ROMAN" 2449245 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2444409 2445023 2445283 "ROIRC" 2445968 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2440645 2442925 2442955 "RNS" 2443259 T RNS (NIL) -9 NIL 2443533 NIL) (-1065 2439154 2439537 2440071 "RNS-" 2440146 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2438157 2438519 2438721 "RNGBIND" 2439005 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1063 2437560 2437968 2437998 "RNG" 2438003 T RNG (NIL) -9 NIL 2438024 NIL) (-1062 2436959 2437347 2437390 "RMODULE" 2437395 NIL RMODULE (NIL T) -9 NIL 2437422 NIL) (-1061 2435795 2435889 2436225 "RMCAT2" 2436860 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2432645 2435141 2435438 "RMATRIX" 2435557 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2425472 2427732 2427847 "RMATCAT" 2431206 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2432188 NIL) (-1058 2424847 2424994 2425301 "RMATCAT-" 2425306 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2424248 2424469 2424512 "RLINSET" 2424706 NIL RLINSET (NIL T) -9 NIL 2424797 NIL) (-1056 2423815 2423890 2424018 "RINTERP" 2424167 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2422873 2423427 2423457 "RING" 2423513 T RING (NIL) -9 NIL 2423605 NIL) (-1054 2422665 2422709 2422806 "RING-" 2422811 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2421506 2421743 2422001 "RIDIST" 2422429 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2412822 2420974 2421180 "RGCHAIN" 2421354 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2412172 2412578 2412619 "RGBCSPC" 2412677 NIL RGBCSPC (NIL T) -9 NIL 2412729 NIL) (-1050 2411330 2411711 2411752 "RGBCMDL" 2411984 NIL RGBCMDL (NIL T) -9 NIL 2412098 NIL) (-1049 2410976 2411039 2411142 "RFFACTOR" 2411261 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1048 2410701 2410736 2410833 "RFFACT" 2410935 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1047 2408818 2409182 2409564 "RFDIST" 2410341 T RFDIST (NIL) -7 NIL NIL NIL) (-1046 2405812 2406426 2407096 "RF" 2408182 NIL RF (NIL T) -7 NIL NIL NIL) (-1045 2405265 2405357 2405520 "RETSOL" 2405714 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2404901 2404981 2405024 "RETRACT" 2405157 NIL RETRACT (NIL T) -9 NIL 2405244 NIL) (-1043 2404750 2404775 2404862 "RETRACT-" 2404867 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2404352 2404572 2404642 "RETAST" 2404702 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2397092 2404005 2404132 "RESULT" 2404247 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2395683 2396361 2396560 "RESRING" 2396995 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2395319 2395368 2395466 "RESLATC" 2395620 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2395024 2395059 2395166 "REPSQ" 2395278 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2394721 2394756 2394867 "REPDB" 2394983 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1036 2388621 2390010 2391233 "REP2" 2393533 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1035 2384998 2385679 2386487 "REP1" 2387848 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1034 2382420 2383000 2383602 "REP" 2384418 T REP (NIL) -7 NIL NIL NIL) (-1033 2375143 2380561 2381017 "REGSET" 2382050 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2373908 2374291 2374541 "REF" 2374928 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2373285 2373388 2373555 "REDORDER" 2373792 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2369284 2372498 2372725 "RECLOS" 2373113 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2368336 2368517 2368732 "REALSOLV" 2369091 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2364819 2365621 2366505 "REAL0Q" 2367501 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1027 2360420 2361408 2362469 "REAL0" 2363800 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1026 2360266 2360307 2360337 "REAL" 2360342 T REAL (NIL) -9 NIL 2360377 NIL) (-1025 2359737 2359983 2360077 "RDUCEAST" 2360194 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2359142 2359214 2359421 "RDIV" 2359659 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2358210 2358384 2358597 "RDIST" 2358964 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2356807 2357094 2357466 "RDETRS" 2357918 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2354619 2355073 2355611 "RDETR" 2356349 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2353244 2353522 2353919 "RDEEFS" 2354335 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2351753 2352059 2352484 "RDEEF" 2352932 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2345823 2348734 2348764 "RCFIELD" 2350059 T RCFIELD (NIL) -9 NIL 2350790 NIL) (-1017 2343887 2344391 2345087 "RCFIELD-" 2345162 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2340156 2341988 2342031 "RCAGG" 2343115 NIL RCAGG (NIL T) -9 NIL 2343580 NIL) (-1015 2339784 2339878 2340041 "RCAGG-" 2340046 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2339119 2339231 2339396 "RATRET" 2339668 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2338672 2338739 2338860 "RATFACT" 2339047 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2337980 2338100 2338252 "RANDSRC" 2338542 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2337714 2337758 2337831 "RADUTIL" 2337929 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2330851 2336547 2336857 "RADIX" 2337438 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2322481 2330693 2330823 "RADFF" 2330828 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2322128 2322203 2322233 "RADCAT" 2322393 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2321910 2321958 2322058 "RADCAT-" 2322063 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2320008 2321680 2321772 "QUEUE" 2321853 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2319639 2319682 2319813 "QUATCT2" 2319959 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1004 2313095 2316433 2316475 "QUATCAT" 2317266 NIL QUATCAT (NIL T) -9 NIL 2318032 NIL) (-1003 2309255 2310285 2311668 "QUATCAT-" 2311764 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1002 2305799 2309188 2309236 "QUAT" 2309241 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1001 2303264 2304875 2304918 "QUAGG" 2305299 NIL QUAGG (NIL T) -9 NIL 2305474 NIL) (-1000 2302866 2303086 2303156 "QQUTAST" 2303216 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2301764 2302264 2302436 "QFORM" 2302738 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2301402 2301445 2301572 "QFCAT2" 2301715 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2292423 2297646 2297686 "QFCAT" 2298344 NIL QFCAT (NIL T) -9 NIL 2299345 NIL) (-996 2288031 2289220 2290799 "QFCAT-" 2290893 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-995 2287491 2287601 2287731 "QEQUAT" 2287921 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2280637 2281710 2282894 "QCMPACK" 2286424 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2279882 2280056 2280288 "QALGSET2" 2280457 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-992 2277437 2277883 2278309 "QALGSET" 2279539 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-991 2276127 2276351 2276668 "PWFFINTB" 2277210 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2274326 2274494 2274848 "PUSHVAR" 2275941 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2270244 2271298 2271339 "PTRANFN" 2273223 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2268646 2268937 2269259 "PTPACK" 2269955 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2268278 2268335 2268444 "PTFUNC2" 2268583 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2262755 2267150 2267191 "PTCAT" 2267487 NIL PTCAT (NIL T) -9 NIL 2267640 NIL) (-985 2262413 2262448 2262572 "PSQFR" 2262714 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2261008 2261306 2261640 "PSEUDLIN" 2262111 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2247771 2250142 2252466 "PSETPK" 2258768 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2240789 2243529 2243625 "PSETCAT" 2246646 NIL PSETCAT (NIL T T T T) -9 NIL 2247460 NIL) (-981 2238625 2239259 2240080 "PSETCAT-" 2240085 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2237974 2238139 2238167 "PSCURVE" 2238435 T PSCURVE (NIL) -9 NIL 2238602 NIL) (-979 2233972 2235488 2235553 "PSCAT" 2236397 NIL PSCAT (NIL T T T) -9 NIL 2236637 NIL) (-978 2233035 2233251 2233651 "PSCAT-" 2233656 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2231740 2232400 2232605 "PRTITION" 2232850 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2231215 2231461 2231553 "PRTDAST" 2231668 T PRTDAST (NIL) -8 NIL NIL NIL) (-975 2220305 2222519 2224707 "PRS" 2229077 NIL PRS (NIL T T) -7 NIL NIL NIL) (-974 2218116 2219655 2219695 "PRQAGG" 2219878 NIL PRQAGG (NIL T) -9 NIL 2219980 NIL) (-973 2217320 2217625 2217653 "PROPLOG" 2217900 T PROPLOG (NIL) -9 NIL 2218066 NIL) (-972 2215501 2216067 2216364 "PROPFRML" 2217056 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2214970 2215077 2215205 "PROPERTY" 2215393 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2209028 2213136 2213956 "PRODUCT" 2214196 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2208824 2208856 2208915 "PRINT" 2208989 T PRINT (NIL) -7 NIL NIL NIL) (-968 2208164 2208281 2208433 "PRIMES" 2208704 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-967 2206229 2206630 2207096 "PRIMELT" 2207743 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-966 2205958 2206007 2206035 "PRIMCAT" 2206159 T PRIMCAT (NIL) -9 NIL NIL NIL) (-965 2204965 2205143 2205371 "PRIMARR2" 2205776 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-964 2201080 2204903 2204948 "PRIMARR" 2204953 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2200723 2200779 2200890 "PREASSOC" 2201018 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-962 2198008 2200181 2200415 "PR" 2200534 NIL PR (NIL T T) -8 NIL NIL NIL) (-961 2197483 2197616 2197644 "PPCURVE" 2197849 T PPCURVE (NIL) -9 NIL 2197985 NIL) (-960 2197078 2197278 2197361 "PORTNUM" 2197420 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2194437 2194836 2195428 "POLYROOT" 2196659 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2193820 2193878 2194112 "POLYLIFT" 2194373 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-957 2190095 2190544 2191173 "POLYCATQ" 2193365 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-956 2176821 2181935 2182000 "POLYCAT" 2185514 NIL POLYCAT (NIL T T T) -9 NIL 2187392 NIL) (-955 2170327 2172170 2174535 "POLYCAT-" 2174540 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-954 2169914 2169982 2170102 "POLY2UP" 2170253 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-953 2169546 2169603 2169712 "POLY2" 2169851 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-952 2163759 2169150 2169310 "POLY" 2169419 NIL POLY (NIL T) -8 NIL NIL NIL) (-951 2162444 2162683 2162959 "POLUTIL" 2163533 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2160799 2161076 2161407 "POLTOPOL" 2162166 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2156264 2160735 2160781 "POINT" 2160786 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2154451 2154808 2155183 "PNTHEORY" 2155909 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2152909 2153206 2153605 "PMTOOLS" 2154149 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2152502 2152580 2152697 "PMSYM" 2152825 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2152012 2152081 2152255 "PMQFCAT" 2152427 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2151405 2151491 2151653 "PMPREDFS" 2151913 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-943 2150760 2150870 2151026 "PMPRED" 2151282 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-942 2149424 2149632 2150010 "PMPLCAT" 2150522 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2148956 2149035 2149187 "PMLSAGG" 2149339 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2148429 2148505 2148687 "PMKERNEL" 2148874 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2148046 2148121 2148234 "PMINS" 2148348 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2147488 2147557 2147766 "PMFS" 2147971 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2146716 2146834 2147039 "PMDOWN" 2147365 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2145989 2146099 2146262 "PMASSFS" 2146603 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-935 2145156 2145314 2145495 "PMASS" 2145828 T PMASS (NIL) -7 NIL NIL NIL) (-934 2144811 2144879 2144973 "PLOTTOOL" 2145082 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2140615 2141659 2142580 "PLOT3D" 2143910 T PLOT3D (NIL) -8 NIL NIL NIL) (-932 2139527 2139704 2139939 "PLOT1" 2140419 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-931 2134134 2135338 2136486 "PLOT" 2138399 T PLOT (NIL) -8 NIL NIL NIL) (-930 2109523 2114200 2119051 "PLEQN" 2129400 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2109216 2109263 2109366 "PINTERPA" 2109470 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-928 2108534 2108656 2108836 "PINTERP" 2109081 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-927 2106831 2107806 2107834 "PID" 2108016 T PID (NIL) -9 NIL 2108150 NIL) (-926 2106582 2106619 2106694 "PICOERCE" 2106788 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-925 2105803 2106351 2106438 "PI" 2106478 T PI (NIL) -8 NIL NIL 2106545) (-924 2105123 2105262 2105438 "PGROEB" 2105659 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2100710 2101524 2102429 "PGE" 2104238 T PGE (NIL) -7 NIL NIL NIL) (-922 2098833 2099080 2099446 "PGCD" 2100427 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2098171 2098274 2098435 "PFRPAC" 2098717 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2094813 2096719 2097072 "PFR" 2097850 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2093202 2093446 2093771 "PFOTOOLS" 2094560 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2091735 2091974 2092325 "PFOQ" 2092959 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2090236 2090448 2090804 "PFO" 2091519 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2087570 2088841 2088869 "PFECAT" 2089454 T PFECAT (NIL) -9 NIL 2089838 NIL) (-915 2087015 2087169 2087383 "PFECAT-" 2087388 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2085618 2085870 2086171 "PFBRU" 2086764 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2083484 2083836 2084268 "PFBR" 2085269 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2080039 2083373 2083442 "PF" 2083447 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2075273 2076246 2077116 "PERMGRP" 2079202 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2073379 2074336 2074377 "PERMCAT" 2074823 NIL PERMCAT (NIL T) -9 NIL 2075128 NIL) (-909 2073032 2073073 2073197 "PERMAN" 2073332 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2068914 2070408 2071084 "PERM" 2072389 NIL PERM (NIL T) -8 NIL NIL NIL) (-907 2066404 2068579 2068701 "PENDTREE" 2068825 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2064428 2065196 2065237 "PDRING" 2065894 NIL PDRING (NIL T) -9 NIL 2066180 NIL) (-905 2063531 2063749 2064111 "PDRING-" 2064116 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2060746 2061524 2062192 "PDEPROB" 2062883 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2058291 2058795 2059350 "PDEPACK" 2060211 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2057203 2057393 2057644 "PDECOMP" 2058090 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2054782 2055625 2055653 "PDECAT" 2056440 T PDECAT (NIL) -9 NIL 2057153 NIL) (-900 2054533 2054566 2054656 "PCOMP" 2054743 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2052711 2053334 2053631 "PBWLB" 2054262 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2052343 2052400 2052509 "PATTERN2" 2052648 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2050100 2050488 2050945 "PATTERN1" 2051932 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2042575 2044173 2045511 "PATTERN" 2048783 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-895 2042139 2042206 2042338 "PATRES2" 2042502 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2039507 2040088 2040569 "PATRES" 2041704 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-893 2037390 2037795 2038202 "PATMATCH" 2039174 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 2036900 2037109 2037150 "PATMAB" 2037257 NIL PATMAB (NIL T) -9 NIL 2037340 NIL) (-891 2035418 2035754 2036012 "PATLRES" 2036705 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-890 2034964 2035087 2035128 "PATAB" 2035133 NIL PATAB (NIL T) -9 NIL 2035305 NIL) (-889 2032445 2032977 2033550 "PARTPERM" 2034411 T PARTPERM (NIL) -7 NIL NIL NIL) (-888 2032066 2032129 2032231 "PARSURF" 2032376 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-887 2031698 2031755 2031864 "PARSU2" 2032003 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-886 2031462 2031502 2031569 "PARSER" 2031651 T PARSER (NIL) -7 NIL NIL NIL) (-885 2031083 2031146 2031248 "PARSCURV" 2031393 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-884 2030715 2030772 2030881 "PARSC2" 2031020 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-883 2030354 2030412 2030509 "PARPCURV" 2030651 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-882 2029986 2030043 2030152 "PARPC2" 2030291 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-881 2029047 2029359 2029541 "PARAMAST" 2029824 T PARAMAST (NIL) -8 NIL NIL NIL) (-880 2028567 2028653 2028772 "PAN2EXPR" 2028948 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2027344 2027688 2027916 "PALETTE" 2028359 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2025737 2026349 2026709 "PAIR" 2027030 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2019628 2024996 2025190 "PADICRC" 2025592 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2012878 2018974 2019158 "PADICRAT" 2019476 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2009990 2011552 2011592 "PADICCT" 2012173 NIL PADICCT (NIL NIL) -9 NIL 2012455 NIL) (-874 2008307 2009927 2009972 "PADIC" 2009977 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-873 2007264 2007464 2007732 "PADEPAC" 2008094 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2006476 2006609 2006815 "PADE" 2007126 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2004863 2005684 2005964 "OWP" 2006280 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2004356 2004569 2004666 "OVERSET" 2004786 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2003402 2003961 2004133 "OVAR" 2004224 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-868 1992274 1994511 1996711 "OUTFORM" 2001222 T OUTFORM (NIL) -8 NIL NIL NIL) (-867 1991610 1991871 1991998 "OUTBFILE" 1992167 T OUTBFILE (NIL) -8 NIL NIL NIL) (-866 1990917 1991082 1991110 "OUTBCON" 1991428 T OUTBCON (NIL) -9 NIL 1991594 NIL) (-865 1990518 1990630 1990787 "OUTBCON-" 1990792 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-864 1989782 1989903 1990064 "OUT" 1990377 T OUT (NIL) -7 NIL NIL NIL) (-863 1989162 1989511 1989600 "OSI" 1989713 T OSI (NIL) -8 NIL NIL NIL) (-862 1988692 1989030 1989058 "OSGROUP" 1989063 T OSGROUP (NIL) -9 NIL 1989085 NIL) (-861 1987437 1987664 1987949 "ORTHPOL" 1988439 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1985002 1987272 1987393 "OREUP" 1987398 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1982419 1984693 1984820 "ORESUP" 1984944 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1979947 1980447 1981008 "OREPCTO" 1981908 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1973640 1975834 1975875 "OREPCAT" 1978223 NIL OREPCAT (NIL T) -9 NIL 1979327 NIL) (-856 1970808 1971583 1972634 "OREPCAT-" 1972639 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1969959 1970257 1970285 "ORDSET" 1970594 T ORDSET (NIL) -9 NIL 1970758 NIL) (-854 1969390 1969538 1969762 "ORDSET-" 1969767 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1967955 1968746 1968774 "ORDRING" 1968976 T ORDRING (NIL) -9 NIL 1969101 NIL) (-852 1967600 1967694 1967838 "ORDRING-" 1967843 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1966980 1967443 1967471 "ORDMON" 1967476 T ORDMON (NIL) -9 NIL 1967497 NIL) (-850 1966142 1966289 1966484 "ORDFUNS" 1966829 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1965480 1965899 1965927 "ORDFIN" 1965992 T ORDFIN (NIL) -9 NIL 1966066 NIL) (-848 1964746 1964873 1965059 "ORDCOMP2" 1965340 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1961312 1963332 1963741 "ORDCOMP" 1964370 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-846 1957893 1958803 1959617 "OPTPROB" 1960518 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1954695 1955334 1956038 "OPTPACK" 1957209 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1952382 1953148 1953176 "OPTCAT" 1953995 T OPTCAT (NIL) -9 NIL 1954645 NIL) (-843 1951766 1952059 1952164 "OPSIG" 1952297 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1951534 1951573 1951639 "OPQUERY" 1951720 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1950908 1951134 1951175 "OPERCAT" 1951387 NIL OPERCAT (NIL T) -9 NIL 1951484 NIL) (-840 1950663 1950719 1950836 "OPERCAT-" 1950841 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1947796 1948974 1949478 "OP" 1950192 NIL OP (NIL T) -8 NIL NIL NIL) (-838 1947101 1947216 1947390 "ONECOMP2" 1947668 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1943921 1945898 1946267 "ONECOMP" 1946765 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-836 1943340 1943446 1943576 "OMSERVER" 1943811 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1940202 1942780 1942820 "OMSAGG" 1942881 NIL OMSAGG (NIL T) -9 NIL 1942945 NIL) (-834 1938825 1939088 1939370 "OMPKG" 1939940 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1937372 1938374 1938543 "OMLO" 1938706 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1936332 1936479 1936699 "OMEXPR" 1937198 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1935483 1935753 1935913 "OMERRK" 1936192 T OMERRK (NIL) -8 NIL NIL NIL) (-830 1934774 1935029 1935165 "OMERR" 1935367 T OMERR (NIL) -8 NIL NIL NIL) (-829 1934225 1934451 1934559 "OMENC" 1934686 T OMENC (NIL) -8 NIL NIL NIL) (-828 1928120 1929305 1930476 "OMDEV" 1933074 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1927189 1927360 1927554 "OMCONN" 1927946 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1926619 1926722 1926750 "OM" 1927049 T OM (NIL) -9 NIL NIL NIL) (-825 1925140 1926116 1926144 "OINTDOM" 1926149 T OINTDOM (NIL) -9 NIL 1926170 NIL) (-824 1922485 1923828 1924165 "OFMONOID" 1924835 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1921896 1922422 1922467 "ODVAR" 1922472 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1919321 1921641 1921796 "ODR" 1921801 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1911943 1919097 1919223 "ODPOL" 1919228 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1905772 1911815 1911920 "ODP" 1911925 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1904538 1904753 1905028 "ODETOOLS" 1905546 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1901505 1902163 1902879 "ODESYS" 1903871 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1896387 1897295 1898320 "ODERTRIC" 1900580 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1895813 1895895 1896089 "ODERED" 1896299 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1892709 1893255 1893930 "ODERAT" 1895238 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1889666 1890133 1890730 "ODEPRRIC" 1892238 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1887609 1888205 1888691 "ODEPROB" 1889200 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1884129 1884614 1885261 "ODEPRIM" 1887088 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1883378 1883480 1883740 "ODEPAL" 1884021 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1879540 1880331 1881195 "ODEPACK" 1882534 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1878601 1878708 1878930 "ODEINT" 1879429 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1872702 1874127 1875574 "ODEIFTBL" 1877174 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1868114 1868896 1869844 "ODEEF" 1871865 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1867463 1867552 1867775 "ODECONST" 1868019 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1865588 1866249 1866277 "ODECAT" 1866882 T ODECAT (NIL) -9 NIL 1867413 NIL) (-804 1865226 1865269 1865396 "OCTCT2" 1865539 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1862093 1864931 1865053 "OCT" 1865136 NIL OCT (NIL T) -8 NIL NIL NIL) (-802 1861445 1861913 1861941 "OCAMON" 1861946 T OCAMON (NIL) -9 NIL 1861967 NIL) (-801 1856101 1858529 1858569 "OC" 1859666 NIL OC (NIL T) -9 NIL 1860524 NIL) (-800 1853349 1854090 1855073 "OC-" 1855167 NIL OC- (NIL T T) -8 NIL NIL NIL) (-799 1852880 1853221 1853249 "OASGP" 1853254 T OASGP (NIL) -9 NIL 1853274 NIL) (-798 1852141 1852630 1852658 "OAMONS" 1852698 T OAMONS (NIL) -9 NIL 1852741 NIL) (-797 1851555 1851988 1852016 "OAMON" 1852021 T OAMON (NIL) -9 NIL 1852041 NIL) (-796 1850813 1851331 1851359 "OAGROUP" 1851364 T OAGROUP (NIL) -9 NIL 1851384 NIL) (-795 1850503 1850553 1850641 "NUMTUBE" 1850757 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1844076 1845594 1847130 "NUMQUAD" 1848987 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1839832 1840820 1841845 "NUMODE" 1843071 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1837187 1838067 1838095 "NUMINT" 1839018 T NUMINT (NIL) -9 NIL 1839782 NIL) (-791 1836135 1836332 1836550 "NUMFMT" 1836989 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1822494 1825439 1827971 "NUMERIC" 1833642 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1816891 1821943 1822038 "NTSCAT" 1822043 NIL NTSCAT (NIL T T T T) -9 NIL 1822082 NIL) (-788 1816085 1816250 1816443 "NTPOLFN" 1816730 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1815717 1815774 1815883 "NSUP2" 1816022 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1803839 1812542 1813354 "NSUP" 1814938 NIL NSUP (NIL T) -8 NIL NIL NIL) (-785 1794115 1803613 1803746 "NSMP" 1803751 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1792547 1792848 1793205 "NREP" 1793803 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1791138 1791390 1791748 "NPCOEF" 1792290 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1790204 1790319 1790535 "NORMRETR" 1791019 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1788245 1788535 1788944 "NORMPK" 1789912 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1787930 1787958 1788082 "NORMMA" 1788211 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1787719 1787748 1787817 "NONE1" 1787894 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1787519 1787676 1787705 "NONE" 1787710 T NONE (NIL) -8 NIL NIL NIL) (-777 1787016 1787078 1787257 "NODE1" 1787451 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1785301 1786152 1786407 "NNI" 1786754 T NNI (NIL) -8 NIL NIL 1786989) (-775 1783721 1784034 1784398 "NLINSOL" 1784969 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1779962 1780957 1781856 "NIPROB" 1782842 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1778719 1778953 1779255 "NFINTBAS" 1779724 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1777893 1778369 1778410 "NETCLT" 1778582 NIL NETCLT (NIL T) -9 NIL 1778664 NIL) (-771 1776601 1776832 1777113 "NCODIV" 1777661 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1776363 1776400 1776475 "NCNTFRAC" 1776558 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1774543 1774907 1775327 "NCEP" 1775988 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1773401 1774167 1774195 "NASRING" 1774305 T NASRING (NIL) -9 NIL 1774385 NIL) (-767 1773196 1773240 1773334 "NASRING-" 1773339 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1772303 1772828 1772856 "NARNG" 1772973 T NARNG (NIL) -9 NIL 1773064 NIL) (-765 1771995 1772062 1772196 "NARNG-" 1772201 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1770874 1771081 1771316 "NAGSP" 1771780 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1762146 1763830 1765503 "NAGS" 1769221 T NAGS (NIL) -7 NIL NIL NIL) (-762 1760694 1761002 1761333 "NAGF07" 1761835 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1755232 1756523 1757830 "NAGF04" 1759407 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1748200 1749814 1751447 "NAGF02" 1753619 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1743424 1744524 1745641 "NAGF01" 1747103 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1737052 1738618 1740203 "NAGE04" 1741859 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1728221 1730342 1732472 "NAGE02" 1734942 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1724174 1725121 1726085 "NAGE01" 1727277 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1721969 1722503 1723061 "NAGD03" 1723636 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1713719 1715647 1717601 "NAGD02" 1720035 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1707530 1708955 1710395 "NAGD01" 1712299 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1703739 1704561 1705398 "NAGC06" 1706713 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1702204 1702536 1702892 "NAGC05" 1703403 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1701580 1701699 1701843 "NAGC02" 1702080 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1700539 1701122 1701162 "NAALG" 1701241 NIL NAALG (NIL T) -9 NIL 1701302 NIL) (-748 1700374 1700403 1700493 "NAALG-" 1700498 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1694324 1695432 1696619 "MULTSQFR" 1699270 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1693643 1693718 1693902 "MULTFACT" 1694236 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1686367 1690280 1690333 "MTSCAT" 1691403 NIL MTSCAT (NIL T T) -9 NIL 1691918 NIL) (-744 1686079 1686133 1686225 "MTHING" 1686307 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1685871 1685904 1685964 "MSYSCMD" 1686039 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1682940 1685432 1685473 "MSETAGG" 1685478 NIL MSETAGG (NIL T) -9 NIL 1685512 NIL) (-741 1679022 1681695 1682015 "MSET" 1682653 NIL MSET (NIL T) -8 NIL NIL NIL) (-740 1674865 1676401 1677146 "MRING" 1678322 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1674431 1674498 1674629 "MRF2" 1674792 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1674049 1674084 1674228 "MRATFAC" 1674390 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1671661 1671956 1672387 "MPRFF" 1673754 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1665984 1671515 1671612 "MPOLY" 1671617 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1665474 1665509 1665717 "MPCPF" 1665943 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1664988 1665031 1665215 "MPC3" 1665425 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1664183 1664264 1664485 "MPC2" 1664903 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1662484 1662821 1663211 "MONOTOOL" 1663843 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1661709 1662026 1662054 "MONOID" 1662273 T MONOID (NIL) -9 NIL 1662420 NIL) (-730 1661255 1661374 1661555 "MONOID-" 1661560 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1651739 1657681 1657740 "MONOGEN" 1658414 NIL MONOGEN (NIL T T) -9 NIL 1658870 NIL) (-728 1648978 1649706 1650699 "MONOGEN-" 1650818 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1647811 1648257 1648285 "MONADWU" 1648677 T MONADWU (NIL) -9 NIL 1648915 NIL) (-726 1647183 1647342 1647590 "MONADWU-" 1647595 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1646542 1646786 1646814 "MONAD" 1647021 T MONAD (NIL) -9 NIL 1647133 NIL) (-724 1646227 1646305 1646437 "MONAD-" 1646442 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1644516 1645140 1645419 "MOEBIUS" 1645980 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1643794 1644198 1644238 "MODULE" 1644243 NIL MODULE (NIL T) -9 NIL 1644282 NIL) (-721 1643362 1643458 1643648 "MODULE-" 1643653 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1641086 1641770 1642097 "MODRING" 1643186 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1638032 1639191 1639712 "MODOP" 1640615 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1636620 1637099 1637376 "MODMONOM" 1637895 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1626702 1634911 1635325 "MODMON" 1636257 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1623884 1625570 1625846 "MODFIELD" 1626577 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1622861 1623165 1623355 "MMLFORM" 1623714 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1622387 1622430 1622609 "MMAP" 1622812 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1620466 1621233 1621274 "MLO" 1621697 NIL MLO (NIL T) -9 NIL 1621939 NIL) (-712 1617832 1618348 1618950 "MLIFT" 1619947 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1617223 1617307 1617461 "MKUCFUNC" 1617743 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1616822 1616892 1617015 "MKRECORD" 1617146 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1615869 1616031 1616259 "MKFUNC" 1616633 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1615257 1615361 1615517 "MKFLCFN" 1615752 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1614534 1614636 1614821 "MKBCFUNC" 1615150 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1611243 1614088 1614224 "MINT" 1614418 T MINT (NIL) -8 NIL NIL NIL) (-705 1610055 1610298 1610575 "MHROWRED" 1610998 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1605444 1608590 1608995 "MFLOAT" 1609670 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1604801 1604877 1605048 "MFINFACT" 1605356 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1601136 1601979 1602858 "MESH" 1603942 T MESH (NIL) -7 NIL NIL NIL) (-701 1599526 1599838 1600191 "MDDFACT" 1600823 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1596321 1598685 1598726 "MDAGG" 1598981 NIL MDAGG (NIL T) -9 NIL 1599124 NIL) (-699 1586079 1595614 1595821 "MCMPLX" 1596134 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1585220 1585366 1585566 "MCDEN" 1585928 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1583110 1583380 1583760 "MCALCFN" 1584950 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1582035 1582275 1582508 "MAYBE" 1582916 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1579647 1580170 1580732 "MATSTOR" 1581506 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1575603 1579019 1579267 "MATRIX" 1579432 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1571367 1572076 1572812 "MATLIN" 1574960 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1569961 1570114 1570447 "MATCAT2" 1571202 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-691 1560061 1563250 1563327 "MATCAT" 1568210 NIL MATCAT (NIL T T T) -9 NIL 1569627 NIL) (-690 1556417 1557438 1558794 "MATCAT-" 1558799 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-689 1554529 1554853 1555237 "MAPPKG3" 1556092 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1553510 1553683 1553905 "MAPPKG2" 1554353 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1552009 1552293 1552620 "MAPPKG1" 1553216 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1551088 1551415 1551592 "MAPPAST" 1551852 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1550699 1550757 1550880 "MAPHACK3" 1551024 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1550291 1550352 1550466 "MAPHACK2" 1550631 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1549728 1549832 1549974 "MAPHACK1" 1550182 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1547807 1548428 1548732 "MAGMA" 1549456 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1547286 1547531 1547622 "MACROAST" 1547736 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1543704 1545525 1545986 "M3D" 1546858 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1537812 1542073 1542114 "LZSTAGG" 1542896 NIL LZSTAGG (NIL T) -9 NIL 1543191 NIL) (-678 1533769 1534943 1536400 "LZSTAGG-" 1536405 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1530856 1531660 1532147 "LWORD" 1533314 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1530432 1530660 1530735 "LSTAST" 1530801 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1523629 1530203 1530337 "LSQM" 1530342 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1522853 1522992 1523220 "LSPP" 1523484 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1519695 1520352 1521065 "LSMP1" 1522172 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1517530 1517824 1518273 "LSMP" 1519391 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-671 1511409 1516697 1516738 "LSAGG" 1516800 NIL LSAGG (NIL T) -9 NIL 1516878 NIL) (-670 1508104 1509028 1510241 "LSAGG-" 1510246 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1505703 1507248 1507497 "LPOLY" 1507899 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1505285 1505370 1505493 "LPEFRAC" 1505612 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1504937 1505049 1505077 "LOGIC" 1505188 T LOGIC (NIL) -9 NIL 1505269 NIL) (-666 1504799 1504822 1504893 "LOGIC-" 1504898 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1503992 1504132 1504325 "LODOOPS" 1504655 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1502530 1502765 1503118 "LODOF" 1503739 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-663 1498762 1501179 1501220 "LODOCAT" 1501658 NIL LODOCAT (NIL T) -9 NIL 1501869 NIL) (-662 1498495 1498553 1498680 "LODOCAT-" 1498685 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-661 1495829 1498336 1498454 "LODO2" 1498459 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-660 1493278 1495766 1495811 "LODO1" 1495816 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-659 1490715 1493194 1493260 "LODO" 1493265 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1489596 1489761 1490066 "LODEEF" 1490538 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1487917 1488690 1488943 "LO" 1489428 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1483156 1486047 1486088 "LNAGG" 1487035 NIL LNAGG (NIL T) -9 NIL 1487479 NIL) (-655 1482303 1482517 1482859 "LNAGG-" 1482864 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1478439 1479228 1479867 "LMOPS" 1481718 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1477842 1478230 1478271 "LMODULE" 1478276 NIL LMODULE (NIL T) -9 NIL 1478302 NIL) (-652 1475040 1477487 1477610 "LMDICT" 1477752 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1474446 1474667 1474708 "LLINSET" 1474899 NIL LLINSET (NIL T) -9 NIL 1474990 NIL) (-650 1474145 1474354 1474414 "LITERAL" 1474419 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1473670 1473744 1473883 "LIST3" 1474065 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1471804 1472116 1472515 "LIST2MAP" 1473317 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-647 1470811 1470989 1471217 "LIST2" 1471622 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1463976 1469745 1470049 "LIST" 1470540 NIL LIST (NIL T) -8 NIL NIL NIL) (-645 1463572 1463809 1463850 "LINSET" 1463855 NIL LINSET (NIL T) -9 NIL 1463889 NIL) (-644 1462233 1462903 1462944 "LINEXP" 1463199 NIL LINEXP (NIL T) -9 NIL 1463348 NIL) (-643 1460880 1461140 1461437 "LINDEP" 1461985 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1457718 1458418 1459176 "LIMITRF" 1460154 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1456044 1456333 1456735 "LIMITPS" 1457420 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1454992 1455461 1455501 "LIECAT" 1455641 NIL LIECAT (NIL T) -9 NIL 1455792 NIL) (-639 1454833 1454860 1454948 "LIECAT-" 1454953 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1449293 1454344 1454572 "LIE" 1454654 NIL LIE (NIL T T) -8 NIL NIL NIL) (-637 1441791 1448742 1448907 "LIB" 1449148 T LIB (NIL) -8 NIL NIL NIL) (-636 1437426 1438309 1439244 "LGROBP" 1440908 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1436266 1436958 1436986 "LFCAT" 1437193 T LFCAT (NIL) -9 NIL 1437332 NIL) (-634 1434264 1434538 1434888 "LF" 1435987 NIL LF (NIL T T) -7 NIL NIL NIL) (-633 1431166 1431796 1432484 "LEXTRIPK" 1433628 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1427910 1428736 1429239 "LEXP" 1430746 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1427386 1427631 1427723 "LETAST" 1427838 T LETAST (NIL) -8 NIL NIL NIL) (-630 1425784 1426097 1426498 "LEADCDET" 1427068 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1424974 1425048 1425277 "LAZM3PK" 1425705 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1419905 1423051 1423589 "LAUPOL" 1424486 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1419484 1419528 1419689 "LAPLACE" 1419855 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1418478 1419062 1419103 "LALG" 1419165 NIL LALG (NIL T) -9 NIL 1419224 NIL) (-625 1418192 1418251 1418387 "LALG-" 1418392 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1416131 1417293 1417544 "LA" 1418025 NIL LA (NIL T T T) -8 NIL NIL NIL) (-623 1415966 1415990 1416031 "KVTFROM" 1416093 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1414889 1415333 1415518 "KTVLOGIC" 1415801 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1414724 1414748 1414789 "KRCFROM" 1414851 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1413628 1413815 1414114 "KOVACIC" 1414524 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1413463 1413487 1413528 "KONVERT" 1413590 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1413298 1413322 1413363 "KOERCE" 1413425 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1412794 1412875 1413007 "KERNEL2" 1413212 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1410624 1411387 1411764 "KERNEL" 1412450 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-615 1404394 1409163 1409217 "KDAGG" 1409594 NIL KDAGG (NIL T T) -9 NIL 1409800 NIL) (-614 1403923 1404047 1404252 "KDAGG-" 1404257 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1397073 1403584 1403739 "KAFILE" 1403801 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1391533 1396584 1396812 "JORDAN" 1396894 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1390912 1391182 1391303 "JOINAST" 1391432 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1390758 1390817 1390872 "JAVACODE" 1390877 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1387010 1388963 1389017 "IXAGG" 1389946 NIL IXAGG (NIL T T) -9 NIL 1390405 NIL) (-608 1385929 1386235 1386654 "IXAGG-" 1386659 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1381459 1385851 1385910 "IVECTOR" 1385915 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1380225 1380462 1380728 "ITUPLE" 1381226 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1378727 1378904 1379199 "ITRIGMNP" 1380047 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1377472 1377676 1377959 "ITFUN3" 1378503 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1377104 1377161 1377270 "ITFUN2" 1377409 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1377021 1377049 1377084 "ITFORM" 1377089 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1374982 1376041 1376319 "ITAYLOR" 1376776 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1363927 1369119 1370282 "ISUPS" 1373852 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1363031 1363171 1363407 "ISUMP" 1363774 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1358406 1362976 1363017 "ISTRING" 1363022 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1357882 1358127 1358219 "ISAST" 1358334 T ISAST (NIL) -8 NIL NIL NIL) (-596 1357091 1357173 1357389 "IRURPK" 1357796 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1356027 1356228 1356468 "IRSN" 1356871 T IRSN (NIL) -7 NIL NIL NIL) (-594 1354098 1354453 1354882 "IRRF2F" 1355665 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1353845 1353883 1353959 "IRREDFFX" 1354054 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1352460 1352719 1353018 "IROOT" 1353578 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1352304 1352363 1352419 "IRFORM" 1352424 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1351404 1351517 1351731 "IR2F" 1352187 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-589 1349017 1349512 1350078 "IR2" 1350882 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1345621 1346701 1347393 "IR" 1348357 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1345412 1345446 1345506 "IPRNTPK" 1345581 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1341995 1345301 1345370 "IPF" 1345375 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1340324 1341920 1341977 "IPADIC" 1341982 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1339636 1339884 1340014 "IP4ADDR" 1340214 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1339109 1339340 1339450 "IOMODE" 1339546 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1338182 1338706 1338833 "IOBFILE" 1339002 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1337670 1338086 1338114 "IOBCON" 1338119 T IOBCON (NIL) -9 NIL 1338140 NIL) (-580 1337181 1337239 1337422 "INVLAPLA" 1337606 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1326877 1329219 1331593 "INTTR" 1334857 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1323212 1323954 1324819 "INTTOOLS" 1326062 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1322798 1322889 1323006 "INTSLPE" 1323115 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1320751 1322721 1322780 "INTRVL" 1322785 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1318353 1318865 1319440 "INTRF" 1320236 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1317764 1317861 1318003 "INTRET" 1318251 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1315761 1316150 1316620 "INTRAT" 1317372 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1313024 1313607 1314226 "INTPM" 1315246 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1309792 1310384 1311115 "INTPAF" 1312417 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1304971 1305933 1306984 "INTPACK" 1308761 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1304223 1304375 1304583 "INTHERTR" 1304813 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1303662 1303742 1303930 "INTHERAL" 1304137 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1301508 1301951 1302408 "INTHEORY" 1303225 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1292972 1294575 1296329 "INTG0" 1299878 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1279245 1282610 1285995 "INTFTBL" 1289607 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278494 1278632 1278805 "INTFACT" 1279104 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275927 1276371 1276926 "INTEF" 1278050 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1274294 1275033 1275061 "INTDOM" 1275362 T INTDOM (NIL) -9 NIL 1275569 NIL) (-561 1273663 1273837 1274079 "INTDOM-" 1274084 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1270051 1271979 1272033 "INTCAT" 1272832 NIL INTCAT (NIL T) -9 NIL 1273153 NIL) (-559 1269523 1269626 1269754 "INTBIT" 1269943 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1268222 1268376 1268683 "INTALG" 1269368 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267705 1267795 1267952 "INTAF" 1268126 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1261050 1267515 1267655 "INTABL" 1267660 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260391 1260857 1260922 "INT8" 1260956 T INT8 (NIL) -8 NIL NIL 1261001) (-554 1259731 1260197 1260262 "INT64" 1260296 T INT64 (NIL) -8 NIL NIL 1260341) (-553 1259071 1259537 1259602 "INT32" 1259636 T INT32 (NIL) -8 NIL NIL 1259681) (-552 1258411 1258877 1258942 "INT16" 1258976 T INT16 (NIL) -8 NIL NIL 1259021) (-551 1255361 1258208 1258317 "INT" 1258322 T INT (NIL) -8 NIL NIL NIL) (-550 1250273 1252984 1253012 "INS" 1253946 T INS (NIL) -9 NIL 1254611 NIL) (-549 1247513 1248284 1249258 "INS-" 1249331 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1246361 1246566 1246842 "INPSIGN" 1247288 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1245479 1245596 1245793 "INPRODPF" 1246241 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1244373 1244490 1244727 "INPRODFF" 1245359 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1243373 1243525 1243785 "INNMFACT" 1244209 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1242570 1242667 1242855 "INMODGCD" 1243272 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1241078 1241323 1241647 "INFSP" 1242315 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1240262 1240379 1240562 "INFPROD0" 1240958 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239872 1239932 1240030 "INFORM1" 1240197 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1236727 1237937 1238452 "INFORM" 1239365 T INFORM (NIL) -8 NIL NIL NIL) (-539 1236250 1236339 1236453 "INFINITY" 1236633 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1235426 1235970 1236071 "INETCLTS" 1236169 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1234042 1234292 1234613 "INEP" 1235174 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1233291 1233939 1234004 "INDE" 1234009 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1232855 1232923 1233040 "INCRMAPS" 1233218 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1231673 1232124 1232330 "INBFILE" 1232669 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1226973 1227909 1228853 "INBFF" 1230761 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1225881 1226150 1226178 "INBCON" 1226691 T INBCON (NIL) -9 NIL 1226957 NIL) (-531 1225133 1225356 1225632 "INBCON-" 1225637 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1224612 1224857 1224948 "INAST" 1225062 T INAST (NIL) -8 NIL NIL NIL) (-529 1224039 1224291 1224397 "IMPTAST" 1224526 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1220484 1223883 1223987 "IMATRIX" 1223992 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1219196 1219319 1219634 "IMATQF" 1220340 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1217416 1217643 1217980 "IMATLIN" 1218952 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1211996 1217340 1217398 "ILIST" 1217403 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1209901 1211856 1211969 "IIARRAY2" 1211974 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1205301 1209812 1209876 "IFF" 1209881 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1204648 1204918 1205034 "IFAST" 1205205 T IFAST (NIL) -8 NIL NIL NIL) (-521 1199643 1203940 1204128 "IFARRAY" 1204505 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1198823 1199547 1199620 "IFAMON" 1199625 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1198407 1198472 1198526 "IEVALAB" 1198733 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1198082 1198150 1198310 "IEVALAB-" 1198315 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1197332 1197971 1198046 "IDPOAMS" 1198051 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1196639 1197221 1197296 "IDPOAM" 1197301 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1196270 1196553 1196616 "IDPO" 1196621 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1195329 1195605 1195658 "IDPC" 1196071 NIL IDPC (NIL T T) -9 NIL 1196220 NIL) (-513 1194798 1195221 1195294 "IDPAM" 1195299 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1194174 1194690 1194763 "IDPAG" 1194768 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1193819 1194010 1194085 "IDENT" 1194119 T IDENT (NIL) -8 NIL NIL NIL) (-510 1190074 1190922 1191817 "IDECOMP" 1192976 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1182912 1183997 1185044 "IDEAL" 1189110 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1182076 1182188 1182387 "ICDEN" 1182796 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1181147 1181556 1181703 "ICARD" 1181949 T ICARD (NIL) -8 NIL NIL NIL) (-506 1179207 1179520 1179925 "IBPTOOLS" 1180824 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1174814 1178827 1178940 "IBITS" 1179126 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1171537 1172113 1172808 "IBATOOL" 1174231 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1169316 1169778 1170311 "IBACHIN" 1171072 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1167145 1169162 1169265 "IARRAY2" 1169270 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1163251 1167071 1167128 "IARRAY1" 1167133 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1157369 1161663 1162144 "IAN" 1162790 T IAN (NIL) -8 NIL NIL NIL) (-499 1156880 1156937 1157110 "IALGFACT" 1157306 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1156408 1156521 1156549 "HYPCAT" 1156756 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1155946 1156063 1156249 "HYPCAT-" 1156254 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1155541 1155741 1155824 "HOSTNAME" 1155883 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1155386 1155423 1155464 "HOMOTOP" 1155469 NIL HOMOTOP (NIL T) -9 NIL 1155502 NIL) (-494 1152018 1153396 1153437 "HOAGG" 1154418 NIL HOAGG (NIL T) -9 NIL 1155097 NIL) (-493 1150612 1151011 1151537 "HOAGG-" 1151542 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1144637 1150207 1150356 "HEXADEC" 1150483 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1143385 1143607 1143870 "HEUGCD" 1144414 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1142461 1143222 1143352 "HELLFDIV" 1143357 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1140640 1142238 1142326 "HEAP" 1142405 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1139903 1140192 1140326 "HEADAST" 1140526 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1133776 1139818 1139880 "HDP" 1139885 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1127795 1133411 1133563 "HDMP" 1133677 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1127119 1127259 1127423 "HB" 1127651 T HB (NIL) -7 NIL NIL NIL) (-484 1120507 1126965 1127069 "HASHTBL" 1127074 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1119983 1120228 1120320 "HASAST" 1120435 T HASAST (NIL) -8 NIL NIL NIL) (-482 1117765 1119605 1119787 "HACKPI" 1119821 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1113460 1117618 1117731 "GTSET" 1117736 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1106877 1113338 1113436 "GSTBL" 1113441 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1099157 1105908 1106173 "GSERIES" 1106668 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1098298 1098715 1098743 "GROUP" 1098946 T GROUP (NIL) -9 NIL 1099080 NIL) (-477 1097664 1097823 1098074 "GROUP-" 1098079 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1096031 1096352 1096739 "GROEBSOL" 1097341 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1094945 1095233 1095284 "GRMOD" 1095813 NIL GRMOD (NIL T T) -9 NIL 1095981 NIL) (-474 1094713 1094749 1094877 "GRMOD-" 1094882 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1090003 1091067 1092067 "GRIMAGE" 1093733 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1088469 1088730 1089054 "GRDEF" 1089699 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1087913 1088029 1088170 "GRAY" 1088348 T GRAY (NIL) -7 NIL NIL NIL) (-470 1087100 1087506 1087557 "GRALG" 1087710 NIL GRALG (NIL T T) -9 NIL 1087803 NIL) (-469 1086761 1086834 1086997 "GRALG-" 1087002 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1083538 1086346 1086524 "GPOLSET" 1086668 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1082892 1082949 1083207 "GOSPER" 1083475 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1078624 1079330 1079856 "GMODPOL" 1082591 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1077629 1077813 1078051 "GHENSEL" 1078436 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1071785 1072628 1073648 "GENUPS" 1076713 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1071482 1071533 1071622 "GENUFACT" 1071728 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1070894 1070971 1071136 "GENPGCD" 1071400 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1070368 1070403 1070616 "GENMFACT" 1070853 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1068934 1069191 1069498 "GENEEZ" 1070111 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1063111 1068545 1068707 "GDMP" 1068857 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1052475 1056882 1057988 "GCNAALG" 1062094 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1050802 1051664 1051692 "GCDDOM" 1051947 T GCDDOM (NIL) -9 NIL 1052104 NIL) (-456 1050272 1050399 1050614 "GCDDOM-" 1050619 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1038888 1041218 1043610 "GBINTERN" 1047963 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1036725 1037017 1037438 "GBF" 1038563 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1035506 1035671 1035938 "GBEUCLID" 1036541 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1034178 1034363 1034667 "GB" 1035285 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1033527 1033652 1033801 "GAUSSFAC" 1034049 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1031894 1032196 1032510 "GALUTIL" 1033246 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1030202 1030476 1030800 "GALPOLYU" 1031621 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1027567 1027857 1028264 "GALFACTU" 1029899 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1019372 1020872 1022480 "GALFACT" 1025999 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1016760 1017418 1017446 "FVFUN" 1018602 T FVFUN (NIL) -9 NIL 1019322 NIL) (-445 1016026 1016208 1016236 "FVC" 1016527 T FVC (NIL) -9 NIL 1016710 NIL) (-444 1015669 1015851 1015919 "FUNDESC" 1015978 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1015284 1015466 1015547 "FUNCTION" 1015621 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1014075 1014585 1014788 "FTEM" 1015101 T FTEM (NIL) -8 NIL NIL NIL) (-441 1011831 1012406 1012869 "FT" 1013632 T FT (NIL) -8 NIL NIL NIL) (-440 1010122 1010411 1010808 "FSUPFACT" 1011522 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1008519 1008808 1009140 "FST" 1009810 T FST (NIL) -8 NIL NIL NIL) (-438 1007718 1007824 1008012 "FSRED" 1008401 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1006417 1006673 1007020 "FSPRMELT" 1007433 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1003723 1004161 1004647 "FSPECF" 1005980 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 1003251 1003305 1003475 "FSINT" 1003664 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-434 1001543 1002244 1002547 "FSERIES" 1003030 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-433 1000585 1000701 1000925 "FSCINT" 1001423 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-432 999627 999770 999997 "FSAGG2" 1000438 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-431 995835 998571 998612 "FSAGG" 998982 NIL FSAGG (NIL T) -9 NIL 999241 NIL) (-430 993597 994198 994994 "FSAGG-" 995089 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 991279 991559 992106 "FS2UPS" 993315 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-428 990157 990328 990630 "FS2EXPXP" 991104 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 989791 989834 989963 "FS2" 990108 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 971458 979760 979801 "FS" 983685 NIL FS (NIL T) -9 NIL 985974 NIL) (-425 960182 963148 967178 "FS-" 967478 NIL FS- (NIL T T) -8 NIL NIL NIL) (-424 959608 959723 959875 "FRUTIL" 960062 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 954609 957251 957291 "FRNAALG" 958687 NIL FRNAALG (NIL T) -9 NIL 959294 NIL) (-422 950333 951392 952650 "FRNAALG-" 953400 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 949971 950014 950141 "FRNAAF2" 950284 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 948351 948825 949120 "FRMOD" 949783 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 947546 947633 947922 "FRIDEAL2" 948258 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-418 945297 945929 946246 "FRIDEAL" 947337 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 944437 944844 944885 "FRETRCT" 944890 NIL FRETRCT (NIL T) -9 NIL 945066 NIL) (-416 943570 943794 944138 "FRETRCT-" 944143 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 940658 941868 941927 "FRAMALG" 942809 NIL FRAMALG (NIL T T) -9 NIL 943101 NIL) (-414 938792 939247 939877 "FRAMALG-" 940100 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 938428 938485 938592 "FRAC2" 938729 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-412 932370 937903 938179 "FRAC" 938184 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 932006 932063 932170 "FR2" 932307 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 923534 927582 928913 "FR" 930707 NIL FR (NIL T) -8 NIL NIL NIL) (-409 918051 920940 920968 "FPS" 922087 T FPS (NIL) -9 NIL 922644 NIL) (-408 917500 917609 917773 "FPS-" 917919 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 914804 916471 916499 "FPC" 916724 T FPC (NIL) -9 NIL 916866 NIL) (-406 914597 914637 914734 "FPC-" 914739 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 913387 914085 914126 "FPATMAB" 914131 NIL FPATMAB (NIL T) -9 NIL 914283 NIL) (-404 911060 911563 911989 "FPARFRAC" 913024 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 906493 906991 907673 "FORTRAN" 910492 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 904169 904731 904759 "FORTFN" 905819 T FORTFN (NIL) -9 NIL 906443 NIL) (-401 903933 903983 904011 "FORTCAT" 904070 T FORTCAT (NIL) -9 NIL 904132 NIL) (-400 901649 902149 902688 "FORT" 903414 T FORT (NIL) -7 NIL NIL NIL) (-399 901437 901467 901536 "FORMULA1" 901613 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 899543 900053 900443 "FORMULA" 901067 T FORMULA (NIL) -8 NIL NIL NIL) (-397 899066 899118 899291 "FORDER" 899485 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 898162 898326 898519 "FOP" 898893 T FOP (NIL) -7 NIL NIL NIL) (-395 896743 897442 897616 "FNLA" 898044 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 895472 895887 895915 "FNCAT" 896375 T FNCAT (NIL) -9 NIL 896635 NIL) (-393 895011 895431 895459 "FNAME" 895464 T FNAME (NIL) -8 NIL NIL NIL) (-392 893574 894537 894565 "FMTC" 894570 T FMTC (NIL) -9 NIL 894606 NIL) (-391 892327 893510 893556 "FMONOID" 893561 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 889155 890323 890364 "FMONCAT" 891581 NIL FMONCAT (NIL T) -9 NIL 892186 NIL) (-389 886579 887225 887253 "FMFUN" 888397 T FMFUN (NIL) -9 NIL 889105 NIL) (-388 883658 884518 884572 "FMCAT" 885767 NIL FMCAT (NIL T T) -9 NIL 886262 NIL) (-387 882927 883108 883136 "FMC" 883426 T FMC (NIL) -9 NIL 883608 NIL) (-386 881793 882693 882793 "FM1" 882872 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880985 881535 881684 "FM" 881689 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878759 879175 879669 "FLOATRP" 880536 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 876197 876697 877275 "FLOATCP" 878226 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 869775 873926 874547 "FLOAT" 875596 T FLOAT (NIL) -8 NIL NIL NIL) (-381 868515 869353 869394 "FLINEXP" 869399 NIL FLINEXP (NIL T) -9 NIL 869492 NIL) (-380 867669 867904 868232 "FLINEXP-" 868237 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 866745 866889 867113 "FLASORT" 867521 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 863861 864729 864781 "FLALG" 866008 NIL FLALG (NIL T T) -9 NIL 866475 NIL) (-377 862903 863046 863273 "FLAGG2" 863714 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-376 856639 860389 860430 "FLAGG" 861692 NIL FLAGG (NIL T) -9 NIL 862344 NIL) (-375 855365 855704 856194 "FLAGG-" 856199 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-374 852216 853224 853283 "FINRALG" 854411 NIL FINRALG (NIL T T) -9 NIL 854919 NIL) (-373 851376 851605 851944 "FINRALG-" 851949 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 850756 850995 851023 "FINITE" 851219 T FINITE (NIL) -9 NIL 851326 NIL) (-371 843113 845300 845340 "FINAALG" 849007 NIL FINAALG (NIL T) -9 NIL 850460 NIL) (-370 838445 839495 840639 "FINAALG-" 842018 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 837103 837441 837495 "FILECAT" 838179 NIL FILECAT (NIL T T) -9 NIL 838395 NIL) (-368 836471 836858 836961 "FILE" 837033 NIL FILE (NIL T) -8 NIL NIL NIL) (-367 834189 835715 835743 "FIELD" 835783 T FIELD (NIL) -9 NIL 835863 NIL) (-366 832809 833194 833705 "FIELD-" 833710 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 830659 831444 831791 "FGROUP" 832495 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 829749 829913 830133 "FGLMICPK" 830491 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 825583 829674 829731 "FFX" 829736 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 825184 825245 825380 "FFSLPE" 825516 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 824688 824724 824933 "FFPOLY2" 825142 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 820678 821460 822256 "FFPOLY" 823924 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-359 816524 820597 820660 "FFP" 820665 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 811652 815867 816057 "FFNBX" 816378 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 806582 810787 811045 "FFNBP" 811506 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 801217 805866 806077 "FFNB" 806415 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 800049 800247 800562 "FFINTBAS" 801014 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 796120 798338 798366 "FFIELDC" 798986 T FFIELDC (NIL) -9 NIL 799362 NIL) (-353 794782 795153 795650 "FFIELDC-" 795655 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 794351 794397 794521 "FFHOM" 794724 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 792046 792533 793050 "FFF" 793866 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 787666 791788 791889 "FFCGX" 791989 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 783290 787398 787505 "FFCGP" 787609 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 778475 783017 783125 "FFCG" 783226 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 777886 777929 778164 "FFCAT2" 778426 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 759291 768363 768449 "FFCAT" 773614 NIL FFCAT (NIL T T T) -9 NIL 775065 NIL) (-345 754488 755536 756850 "FFCAT-" 758080 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 749888 754399 754463 "FF" 754468 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-343 739213 742860 744080 "FEXPR" 748740 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 738213 738648 738689 "FEVALAB" 738773 NIL FEVALAB (NIL T) -9 NIL 739034 NIL) (-341 737372 737582 737920 "FEVALAB-" 737925 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 734392 735133 735248 "FDIVCAT" 736816 NIL FDIVCAT (NIL T T T T) -9 NIL 737253 NIL) (-339 734154 734181 734351 "FDIVCAT-" 734356 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733374 733461 733738 "FDIV2" 734061 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 731940 732757 732960 "FDIV" 733273 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-336 730914 731235 731437 "FCTRDATA" 731758 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 729600 729859 730148 "FCPAK1" 730645 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 728699 729100 729241 "FCOMP" 729491 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 712404 715849 719387 "FC" 725181 T FC (NIL) -8 NIL NIL NIL) (-332 704769 708795 708835 "FAXF" 710637 NIL FAXF (NIL T) -9 NIL 711329 NIL) (-331 702045 702703 703528 "FAXF-" 703993 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 697097 701421 701597 "FARRAY" 701902 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 691998 694058 694111 "FAMR" 695134 NIL FAMR (NIL T T) -9 NIL 695594 NIL) (-328 690888 691190 691625 "FAMR-" 691630 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 690057 690810 690863 "FAMONOID" 690868 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 687843 688553 688606 "FAMONC" 689547 NIL FAMONC (NIL T T) -9 NIL 689933 NIL) (-325 686507 687597 687734 "FAGROUP" 687739 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 684302 684621 685024 "FACUTIL" 686188 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 683401 683586 683808 "FACTFUNC" 684112 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 675825 682704 682903 "EXPUPXS" 683257 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 673308 673848 674434 "EXPRTUBE" 675259 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 669579 670171 670901 "EXPRODE" 672647 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 664133 664720 665526 "EXPR2UPS" 668877 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 663765 663822 663931 "EXPR2" 664070 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 649311 662414 662843 "EXPR" 663369 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 640727 648464 648754 "EXPEXPAN" 649148 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 640207 640451 640542 "EXITAST" 640656 T EXITAST (NIL) -8 NIL NIL NIL) (-314 640007 640164 640193 "EXIT" 640198 T EXIT (NIL) -8 NIL NIL NIL) (-313 639634 639696 639809 "EVALCYC" 639939 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 639175 639293 639334 "EVALAB" 639504 NIL EVALAB (NIL T) -9 NIL 639608 NIL) (-311 638656 638778 638999 "EVALAB-" 639004 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 636024 637326 637354 "EUCDOM" 637909 T EUCDOM (NIL) -9 NIL 638259 NIL) (-309 634429 634871 635461 "EUCDOM-" 635466 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 634061 634118 634227 "ESTOOLS2" 634366 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 633812 633854 633934 "ESTOOLS1" 634013 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 621350 624110 626860 "ESTOOLS" 631082 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621095 621127 621209 "ESCONT1" 621312 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 617469 618230 619010 "ESCONT" 620335 T ESCONT (NIL) -7 NIL NIL NIL) (-303 617144 617194 617294 "ES2" 617413 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-302 616774 616832 616941 "ES1" 617080 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-301 610811 612419 612447 "ES" 615215 T ES (NIL) -9 NIL 616625 NIL) (-300 605758 607045 608862 "ES-" 609026 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 604974 605103 605279 "ERROR" 605602 T ERROR (NIL) -7 NIL NIL NIL) (-298 598368 604833 604924 "EQTBL" 604929 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 598000 598057 598166 "EQ2" 598305 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 590503 593314 594763 "EQ" 596584 NIL -3968 (NIL T) -8 NIL NIL NIL) (-295 585793 586841 587934 "EP" 589442 NIL EP (NIL T) -7 NIL NIL NIL) (-294 584393 584684 584990 "ENV" 585507 T ENV (NIL) -8 NIL NIL NIL) (-293 583487 584041 584069 "ENTIRER" 584074 T ENTIRER (NIL) -9 NIL 584120 NIL) (-292 580010 581496 581866 "EMR" 583286 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 579154 579339 579393 "ELTAGG" 579773 NIL ELTAGG (NIL T T) -9 NIL 579984 NIL) (-290 578873 578935 579076 "ELTAGG-" 579081 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 578662 578691 578745 "ELTAB" 578829 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 577788 577934 578133 "ELFUTS" 578513 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 577530 577586 577614 "ELEMFUN" 577719 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 577400 577421 577489 "ELEMFUN-" 577494 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 572244 575500 575541 "ELAGG" 576481 NIL ELAGG (NIL T) -9 NIL 576944 NIL) (-284 570529 570963 571626 "ELAGG-" 571631 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 569841 569978 570134 "ELABOR" 570393 T ELABOR (NIL) -8 NIL NIL NIL) (-282 568502 568781 569075 "ELABEXPR" 569567 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 561493 563169 563996 "EFUPXS" 567778 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 555070 556744 557554 "EFULS" 560769 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 552555 552913 553385 "EFSTRUC" 554702 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 542346 543912 545460 "EF" 551070 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 541420 541831 541980 "EAB" 542217 T EAB (NIL) -8 NIL NIL NIL) (-276 540602 541379 541407 "E04UCFA" 541412 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 539784 540561 540589 "E04NAFA" 540594 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 538966 539743 539771 "E04MBFA" 539776 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 538148 538925 538953 "E04JAFA" 538958 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 537332 538107 538135 "E04GCFA" 538140 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 536516 537291 537319 "E04FDFA" 537324 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 535698 536475 536503 "E04DGFA" 536508 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 529871 531223 532587 "E04AGNT" 534354 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 528551 529057 529097 "DVARCAT" 529572 NIL DVARCAT (NIL T) -9 NIL 529771 NIL) (-267 527755 527967 528281 "DVARCAT-" 528286 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 520933 527554 527683 "DSMP" 527688 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 520598 520657 520755 "DROPT1" 520868 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 515713 516839 517976 "DROPT0" 519481 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510494 511658 512726 "DROPT" 514665 T DROPT (NIL) -8 NIL NIL NIL) (-262 508839 509164 509550 "DRAWPT" 510128 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 508472 508525 508643 "DRAWHACK" 508780 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 507203 507472 507763 "DRAWCX" 508201 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 506718 506787 506938 "DRAWCURV" 507129 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 497186 499148 501263 "DRAWCFUN" 504623 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 491773 492696 493775 "DRAW" 496160 NIL DRAW (NIL T) -7 NIL NIL NIL) (-256 488537 490466 490507 "DQAGG" 491136 NIL DQAGG (NIL T) -9 NIL 491410 NIL) (-255 476697 483130 483213 "DPOLCAT" 485065 NIL DPOLCAT (NIL T T T T) -9 NIL 485610 NIL) (-254 471584 472916 474857 "DPOLCAT-" 474862 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 464713 471445 471543 "DPMO" 471548 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 457745 464493 464660 "DPMM" 464665 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 457223 457437 457535 "DOMTMPLT" 457667 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 456656 457025 457105 "DOMCTOR" 457163 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 455868 456136 456287 "DOMAIN" 456525 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 449887 455503 455655 "DMP" 455769 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 449487 449543 449687 "DLP" 449825 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 443311 448814 449004 "DLIST" 449329 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 440109 442164 442205 "DLAGG" 442755 NIL DLAGG (NIL T) -9 NIL 442985 NIL) (-244 438785 439449 439477 "DIVRING" 439569 T DIVRING (NIL) -9 NIL 439652 NIL) (-243 438022 438212 438512 "DIVRING-" 438517 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 436124 436481 436887 "DISPLAY" 437636 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 434972 435175 435440 "DIRPROD2" 435917 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 428867 434886 434949 "DIRPROD" 434954 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 417649 423648 423701 "DIRPCAT" 424111 NIL DIRPCAT (NIL NIL T) -9 NIL 424951 NIL) (-238 414975 415617 416498 "DIRPCAT-" 416835 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 414262 414422 414608 "DIOSP" 414809 T DIOSP (NIL) -7 NIL NIL NIL) (-236 410917 413174 413215 "DIOPS" 413649 NIL DIOPS (NIL T) -9 NIL 413878 NIL) (-235 410466 410580 410771 "DIOPS-" 410776 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 409289 409917 409945 "DIFRING" 410132 T DIFRING (NIL) -9 NIL 410242 NIL) (-233 408935 409012 409164 "DIFRING-" 409169 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 406671 407943 407984 "DIFEXT" 408347 NIL DIFEXT (NIL T) -9 NIL 408641 NIL) (-231 404956 405384 406050 "DIFEXT-" 406055 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 402231 404488 404529 "DIAGG" 404534 NIL DIAGG (NIL T) -9 NIL 404554 NIL) (-229 401615 401772 402024 "DIAGG-" 402029 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 397031 400574 400851 "DHMATRIX" 401384 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 392643 393552 394562 "DFSFUN" 396041 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 387726 391574 391886 "DFLOAT" 392351 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 385989 386270 386659 "DFINTTLS" 387434 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 383018 384010 384410 "DERHAM" 385655 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 380819 382793 382882 "DEQUEUE" 382962 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 380073 380206 380389 "DEGRED" 380681 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 376683 377383 378184 "DEFINTRF" 379346 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 374350 374791 375355 "DEFINTEF" 376230 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 373700 373970 374085 "DEFAST" 374255 T DEFAST (NIL) -8 NIL NIL NIL) (-218 367725 373295 373444 "DECIMAL" 373571 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 365237 365695 366201 "DDFACT" 367269 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 364833 364876 365027 "DBLRESP" 365188 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 362705 363066 363426 "DBASE" 364600 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 361947 362185 362331 "DATAARY" 362604 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361053 361906 361934 "D03FAFA" 361939 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 360160 361012 361040 "D03EEFA" 361045 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 358110 358576 359065 "D03AGNT" 359691 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 357399 358069 358097 "D02EJFA" 358102 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 356688 357358 357386 "D02CJFA" 357391 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 355977 356647 356675 "D02BHFA" 356680 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 355266 355936 355964 "D02BBFA" 355969 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 348463 350052 351658 "D02AGNT" 353680 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 346231 346754 347300 "D01WGTS" 347937 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 345298 346190 346218 "D01TRNS" 346223 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 344366 345257 345285 "D01GBFA" 345290 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 343434 344325 344353 "D01FCFA" 344358 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 342502 343393 343421 "D01ASFA" 343426 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 341570 342461 342489 "D01AQFA" 342494 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 340638 341529 341557 "D01APFA" 341562 T D01APFA (NIL) -8 NIL NIL NIL) (-198 339706 340597 340625 "D01ANFA" 340630 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 338774 339665 339693 "D01AMFA" 339698 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 337842 338733 338761 "D01ALFA" 338766 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 336910 337801 337829 "D01AKFA" 337834 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 335978 336869 336897 "D01AJFA" 336902 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 329273 330826 332387 "D01AGNT" 334437 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 328610 328738 328890 "CYCLOTOM" 329141 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 325345 326058 326785 "CYCLES" 327903 T CYCLES (NIL) -7 NIL NIL NIL) (-190 324657 324791 324962 "CVMP" 325206 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 322498 322756 323125 "CTRIGMNP" 324385 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322007 322229 322330 "CTORKIND" 322417 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321298 321614 321642 "CTORCAT" 321824 T CTORCAT (NIL) -9 NIL 321937 NIL) (-186 320896 321007 321166 "CTORCAT-" 321171 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320358 320570 320678 "CTORCALL" 320820 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 319794 320152 320225 "CTOR" 320305 T CTOR (NIL) -8 NIL NIL NIL) (-183 319168 319267 319420 "CSTTOOLS" 319691 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 314967 315624 316382 "CRFP" 318480 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 314442 314688 314780 "CRCEAST" 314895 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 313489 313674 313902 "CRAPACK" 314246 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 312873 312974 313178 "CPMATCH" 313365 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 312598 312626 312732 "CPIMA" 312839 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 308946 309618 310337 "COORDSYS" 311933 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 308358 308479 308621 "CONTOUR" 308824 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 304251 306361 306853 "CONTFRAC" 307898 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 304131 304152 304180 "CONDUIT" 304217 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 303219 303773 303801 "COMRING" 303806 T COMRING (NIL) -9 NIL 303858 NIL) (-172 302273 302577 302761 "COMPPROP" 303055 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 301934 301969 302097 "COMPLPAT" 302232 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 301570 301627 301734 "COMPLEX2" 301871 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 291879 301379 301488 "COMPLEX" 301493 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291468 291537 291645 "COMPILER" 291791 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291186 291221 291319 "COMPFACT" 291427 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275275 285260 285300 "COMPCAT" 286304 NIL COMPCAT (NIL T) -9 NIL 287652 NIL) (-165 264808 267728 271348 "COMPCAT-" 271704 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264537 264565 264668 "COMMUPC" 264774 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264331 264365 264424 "COMMONOP" 264498 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263907 264135 264210 "COMMAAST" 264276 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263463 263658 263745 "COMM" 263840 T COMM (NIL) -8 NIL NIL NIL) (-160 262712 262906 262934 "COMBOPC" 263272 T COMBOPC (NIL) -9 NIL 263447 NIL) (-159 261608 261818 262060 "COMBINAT" 262502 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258065 258639 259266 "COMBF" 261030 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256823 257181 257416 "COLOR" 257850 T COLOR (NIL) -8 NIL NIL NIL) (-156 256299 256544 256636 "COLONAST" 256751 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255939 255986 256111 "CMPLXRT" 256246 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255387 255639 255738 "CLLCTAST" 255860 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250886 251917 252997 "CLIP" 254327 T CLIP (NIL) -7 NIL NIL NIL) (-152 249232 249992 250231 "CLIF" 250713 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245407 247378 247419 "CLAGG" 248348 NIL CLAGG (NIL T) -9 NIL 248884 NIL) (-150 243829 244286 244869 "CLAGG-" 244874 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243373 243458 243598 "CINTSLPE" 243738 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240874 241345 241893 "CHVAR" 242901 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240048 240602 240630 "CHARZ" 240635 T CHARZ (NIL) -9 NIL 240650 NIL) (-146 239802 239842 239920 "CHARPOL" 240002 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238860 239447 239475 "CHARNZ" 239522 T CHARNZ (NIL) -9 NIL 239578 NIL) (-144 236766 237514 237867 "CHAR" 238527 T CHAR (NIL) -8 NIL NIL NIL) (-143 236492 236553 236581 "CFCAT" 236692 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235737 235848 236030 "CDEN" 236376 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231702 234890 235170 "CCLASS" 235477 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230953 231110 231287 "CATEGORY" 231545 T -10 (NIL) -8 NIL NIL NIL) (-139 230526 230872 230920 "CATCTOR" 230925 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229977 230229 230327 "CATAST" 230448 T CATAST (NIL) -8 NIL NIL NIL) (-137 229453 229698 229790 "CASEAST" 229905 T CASEAST (NIL) -8 NIL NIL NIL) (-136 228561 228709 228930 "CARTEN2" 229300 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223570 224590 225343 "CARTEN" 227864 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 221886 222720 222977 "CARD" 223333 T CARD (NIL) -8 NIL NIL NIL) (-133 221462 221690 221765 "CAPSLAST" 221831 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220966 221174 221202 "CACHSET" 221334 T CACHSET (NIL) -9 NIL 221412 NIL) (-131 220436 220758 220786 "CABMON" 220836 T CABMON (NIL) -9 NIL 220892 NIL) (-130 219909 220140 220250 "BYTEORD" 220346 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 215259 219414 219586 "BYTEBUF" 219757 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214241 214793 214935 "BYTE" 215098 T BYTE (NIL) -8 NIL NIL 215220) (-127 211752 213933 214040 "BTREE" 214167 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209203 211400 211522 "BTOURN" 211662 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206575 208673 208714 "BTCAT" 208782 NIL BTCAT (NIL T) -9 NIL 208859 NIL) (-124 206242 206322 206471 "BTCAT-" 206476 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201507 205385 205413 "BTAGG" 205635 T BTAGG (NIL) -9 NIL 205796 NIL) (-122 200997 201122 201328 "BTAGG-" 201333 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197994 200275 200490 "BSTREE" 200814 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197132 197258 197442 "BRILL" 197850 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193785 195858 195899 "BRAGG" 196548 NIL BRAGG (NIL T) -9 NIL 196806 NIL) (-118 192317 192722 193276 "BRAGG-" 193281 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185567 191663 191847 "BPADICRT" 192165 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183884 185504 185549 "BPADIC" 185554 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183582 183612 183726 "BOUNDZRO" 183848 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 181363 181767 182242 "BOP1" 183140 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 176591 177789 178701 "BOP" 180471 T BOP (NIL) -8 NIL NIL NIL) (-112 175416 176165 176314 "BOOLEAN" 176462 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174695 175099 175153 "BMODULE" 175158 NIL BMODULE (NIL T T) -9 NIL 175223 NIL) (-110 170496 174493 174566 "BITS" 174642 T BITS (NIL) -8 NIL NIL NIL) (-109 169917 170036 170176 "BINDING" 170376 T BINDING (NIL) -8 NIL NIL NIL) (-108 163945 169514 169662 "BINARY" 169789 T BINARY (NIL) -8 NIL NIL NIL) (-107 161725 163200 163241 "BGAGG" 163501 NIL BGAGG (NIL T) -9 NIL 163638 NIL) (-106 161556 161588 161679 "BGAGG-" 161684 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160627 160940 161145 "BFUNCT" 161371 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159311 159492 159780 "BEZOUT" 160451 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155782 158163 158493 "BBTREE" 159014 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155516 155569 155597 "BASTYPE" 155716 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155368 155397 155470 "BASTYPE-" 155475 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154802 154878 155030 "BALFACT" 155279 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153658 154217 154403 "AUTOMOR" 154647 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153384 153389 153415 "ATTREG" 153420 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151636 152081 152433 "ATTRBUT" 153050 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151244 151464 151530 "ATTRAST" 151588 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150780 150893 150919 "ATRIG" 151120 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150589 150630 150717 "ATRIG-" 150722 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150234 150420 150446 "ASTCAT" 150451 T ASTCAT (NIL) -9 NIL 150481 NIL) (-92 149961 150020 150139 "ASTCAT-" 150144 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148110 149737 149825 "ASTACK" 149904 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146615 146912 147277 "ASSOCEQ" 147792 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145669 146274 146398 "ASP9" 146522 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 144559 145274 145416 "ASP80" 145558 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 144322 144507 144546 "ASP8" 144551 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 143298 143999 144117 "ASP78" 144235 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 142289 142978 143095 "ASP77" 143212 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 141223 141927 142058 "ASP74" 142189 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 140145 140858 140990 "ASP73" 141122 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 139065 139780 139912 "ASP7" 140044 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 138191 138891 138991 "ASP6" 138996 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137158 137868 137986 "ASP55" 138104 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136129 136832 136951 "ASP50" 137070 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135239 135830 135940 "ASP49" 136050 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 134045 134778 134946 "ASP42" 135128 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 132843 133578 133748 "ASP41" 133932 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131953 132544 132654 "ASP4" 132764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 130925 131630 131748 "ASP35" 131866 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130690 130873 130912 "ASP34" 130917 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130427 130494 130570 "ASP33" 130645 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129342 130062 130194 "ASP31" 130326 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129107 129290 129329 "ASP30" 129334 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128842 128911 128987 "ASP29" 129062 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128607 128790 128829 "ASP28" 128834 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128372 128555 128594 "ASP27" 128599 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127478 128070 128181 "ASP24" 128292 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126576 127280 127392 "ASP20" 127397 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125540 126250 126369 "ASP19" 126488 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 125277 125344 125420 "ASP12" 125495 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 124151 124876 125020 "ASP10" 125164 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 123261 123852 123962 "ASP1" 124072 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 121112 123105 123196 "ARRAY2" 123201 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 120144 120317 120538 "ARRAY12" 120935 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 115909 119792 119906 "ARRAY1" 120061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 110221 112139 112214 "ARR2CAT" 114844 NIL ARR2CAT (NIL T T T) -9 NIL 115602 NIL) (-56 107655 108399 109353 "ARR2CAT-" 109358 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106972 107282 107407 "ARITY" 107548 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106199 "APPRULE" 106808 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104677 104800 104957 "ANY1" 105273 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 104031 104270 104390 "ANY" 104575 T ANY (NIL) -8 NIL NIL NIL) (-50 101561 102468 102795 "ANTISYM" 103755 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101053 101268 101364 "ANON" 101483 T ANON (NIL) -8 NIL NIL NIL) (-48 95311 99592 100046 "AN" 100617 T AN (NIL) -8 NIL NIL NIL) (-47 91209 92597 92648 "AMR" 93396 NIL AMR (NIL T T) -9 NIL 93996 NIL) (-46 90321 90542 90905 "AMR-" 90910 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74766 90238 90299 "ALIST" 90304 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71601 74360 74529 "ALGSC" 74684 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68156 68711 69318 "ALGPKG" 71041 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67433 67534 67718 "ALGMFACT" 68042 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63468 64047 64641 "ALGMANIP" 67017 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54849 63094 63244 "ALGFF" 63401 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54045 54176 54355 "ALGFACT" 54707 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52986 53586 53624 "ALGEBRA" 53629 NIL ALGEBRA (NIL T) -9 NIL 53670 NIL) (-37 52704 52763 52895 "ALGEBRA-" 52900 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34803 50706 50758 "ALAGG" 50894 NIL ALAGG (NIL T T) -9 NIL 51055 NIL) (-35 34339 34452 34478 "AHYP" 34679 T AHYP (NIL) -9 NIL NIL NIL) (-34 33270 33518 33544 "AGG" 34043 T AGG (NIL) -9 NIL 34322 NIL) (-33 32704 32866 33080 "AGG-" 33085 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30510 30933 31338 "AF" 32346 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29990 30235 30325 "ADDAST" 30438 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29258 29517 29673 "ACPLOT" 29852 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18637 26385 26423 "ACFS" 27030 NIL ACFS (NIL T) -9 NIL 27269 NIL) (-28 16664 17154 17916 "ACFS-" 17921 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14711 14737 "ACF" 15616 T ACF (NIL) -9 NIL 16029 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3215754 3215759 3215764 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3215739 3215744 3215749 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3215724 3215729 3215734 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3215709 3215714 3215719 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1301 3214852 3215584 3215661 "ZMOD" 3215666 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1300 3213962 3214126 3214335 "ZLINDEP" 3214684 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1299 3203262 3205030 3207002 "ZDSOLVE" 3212092 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1298 3202508 3202649 3202838 "YSTREAM" 3203108 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1297 3200282 3201809 3202013 "XRPOLY" 3202351 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3196835 3198153 3198728 "XPR" 3199754 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1295 3194488 3195856 3195911 "XPOLYC" 3196199 NIL XPOLYC (NIL T T) -9 NIL 3196312 NIL) (-1294 3192218 3193828 3194032 "XPOLY" 3194328 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1293 3188596 3190735 3191123 "XPBWPOLY" 3191876 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1292 3183792 3185081 3185136 "XFALG" 3187308 NIL XFALG (NIL T T) -9 NIL 3188097 NIL) (-1291 3179489 3181782 3181824 "XF" 3182445 NIL XF (NIL T) -9 NIL 3182845 NIL) (-1290 3179110 3179198 3179367 "XF-" 3179372 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1289 3178243 3178347 3178552 "XEXPPKG" 3179002 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1288 3176352 3178093 3178189 "XDPOLY" 3178194 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3175159 3175759 3175802 "XALG" 3175807 NIL XALG (NIL T) -9 NIL 3175918 NIL) (-1286 3168628 3173136 3173630 "WUTSET" 3174751 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1285 3166884 3167680 3168003 "WP" 3168439 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1284 3166486 3166706 3166776 "WHILEAST" 3166836 T WHILEAST (NIL) -8 NIL NIL NIL) (-1283 3165958 3166203 3166297 "WHEREAST" 3166414 T WHEREAST (NIL) -8 NIL NIL NIL) (-1282 3164844 3165042 3165337 "WFFINTBS" 3165755 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1281 3162748 3163175 3163637 "WEIER" 3164416 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1280 3161794 3162244 3162286 "VSPACE" 3162422 NIL VSPACE (NIL T) -9 NIL 3162496 NIL) (-1279 3161632 3161659 3161750 "VSPACE-" 3161755 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1278 3161441 3161483 3161551 "VOID" 3161586 T VOID (NIL) -8 NIL NIL NIL) (-1277 3157865 3158504 3159241 "VIEWDEF" 3160726 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1276 3147169 3149413 3151586 "VIEW3D" 3155714 T VIEW3D (NIL) -8 NIL NIL NIL) (-1275 3139420 3141080 3142659 "VIEW2D" 3145612 T VIEW2D (NIL) -8 NIL NIL NIL) (-1274 3137556 3137915 3138321 "VIEW" 3139036 T VIEW (NIL) -7 NIL NIL NIL) (-1273 3136133 3136392 3136710 "VECTOR2" 3137286 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1272 3131486 3135903 3135995 "VECTOR" 3136076 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1271 3124960 3129267 3129310 "VECTCAT" 3130305 NIL VECTCAT (NIL T) -9 NIL 3130892 NIL) (-1270 3123974 3124228 3124618 "VECTCAT-" 3124623 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1269 3123428 3123625 3123745 "VARIABLE" 3123889 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1268 3123361 3123366 3123396 "UTYPE" 3123401 T UTYPE (NIL) -9 NIL NIL NIL) (-1267 3122191 3122345 3122607 "UTSODETL" 3123187 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1266 3119631 3120091 3120615 "UTSODE" 3121732 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1265 3110505 3115872 3115915 "UTSCAT" 3117027 NIL UTSCAT (NIL T) -9 NIL 3117785 NIL) (-1264 3107852 3108575 3109564 "UTSCAT-" 3109569 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1263 3107479 3107522 3107655 "UTS2" 3107803 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1262 3099316 3105105 3105594 "UTS" 3107048 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3093543 3096154 3096197 "URAGG" 3098267 NIL URAGG (NIL T) -9 NIL 3098990 NIL) (-1260 3090485 3091347 3092469 "URAGG-" 3092474 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1259 3086201 3089120 3089585 "UPXSSING" 3090149 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1258 3079276 3086105 3086177 "UPXSCONS" 3086182 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1257 3069023 3075814 3075876 "UPXSCCA" 3076450 NIL UPXSCCA (NIL T T) -9 NIL 3076683 NIL) (-1256 3068661 3068746 3068920 "UPXSCCA-" 3068925 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1255 3058260 3064824 3064867 "UPXSCAT" 3065515 NIL UPXSCAT (NIL T) -9 NIL 3066124 NIL) (-1254 3057690 3057769 3057948 "UPXS2" 3058175 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1253 3049760 3056937 3057210 "UPXS" 3057475 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1252 3048417 3048669 3049019 "UPSQFREE" 3049504 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1251 3041838 3044895 3044950 "UPSCAT" 3046111 NIL UPSCAT (NIL T T) -9 NIL 3046885 NIL) (-1250 3041042 3041249 3041576 "UPSCAT-" 3041581 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1249 3040669 3040712 3040845 "UPOLYC2" 3040993 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1248 3026357 3034092 3034135 "UPOLYC" 3036236 NIL UPOLYC (NIL T) -9 NIL 3037457 NIL) (-1247 3017721 3020135 3023270 "UPOLYC-" 3023275 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1246 3017060 3017167 3017331 "UPMP" 3017610 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1245 3016613 3016694 3016833 "UPDIVP" 3016973 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1244 3015181 3015430 3015746 "UPDECOMP" 3016362 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1243 3014416 3014528 3014713 "UPCDEN" 3015065 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1242 3013935 3014004 3014153 "UP2" 3014341 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1241 3005786 3013618 3013747 "UP" 3013854 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1240 3005001 3005128 3005333 "UNISEG2" 3005629 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1239 3003468 3004205 3004482 "UNISEG" 3004759 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1238 3002528 3002708 3002934 "UNIFACT" 3003284 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1237 2990542 3002432 3002504 "ULSCONS" 3002509 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1236 2972577 2984546 2984608 "ULSCCAT" 2985246 NIL ULSCCAT (NIL T T) -9 NIL 2985534 NIL) (-1235 2971663 2971896 2972272 "ULSCCAT-" 2972277 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1234 2961039 2967517 2967560 "ULSCAT" 2968423 NIL ULSCAT (NIL T) -9 NIL 2969154 NIL) (-1233 2960469 2960548 2960727 "ULS2" 2960954 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1232 2944417 2959646 2959897 "ULS" 2960276 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1231 2943544 2944054 2944161 "UINT8" 2944272 T UINT8 (NIL) -8 NIL NIL 2944357) (-1230 2942670 2943180 2943287 "UINT64" 2943398 T UINT64 (NIL) -8 NIL NIL 2943483) (-1229 2941796 2942306 2942413 "UINT32" 2942524 T UINT32 (NIL) -8 NIL NIL 2942609) (-1228 2940922 2941432 2941539 "UINT16" 2941650 T UINT16 (NIL) -8 NIL NIL 2941735) (-1227 2939225 2940182 2940212 "UFD" 2940424 T UFD (NIL) -9 NIL 2940538 NIL) (-1226 2939019 2939065 2939160 "UFD-" 2939165 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1225 2938101 2938284 2938500 "UDVO" 2938825 T UDVO (NIL) -7 NIL NIL NIL) (-1224 2935917 2936326 2936797 "UDPO" 2937665 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1223 2935677 2935872 2935903 "TYPEAST" 2935908 T TYPEAST (NIL) -8 NIL NIL NIL) (-1222 2935610 2935615 2935645 "TYPE" 2935650 T TYPE (NIL) -9 NIL NIL NIL) (-1221 2934581 2934783 2935023 "TWOFACT" 2935404 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1220 2933604 2933990 2934225 "TUPLE" 2934381 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1219 2931295 2931814 2932353 "TUBETOOL" 2933087 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1218 2930144 2930349 2930590 "TUBE" 2931088 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1217 2918784 2922903 2923000 "TSETCAT" 2928269 NIL TSETCAT (NIL T T T T) -9 NIL 2929800 NIL) (-1216 2913516 2915116 2917007 "TSETCAT-" 2917012 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1215 2908245 2912488 2912771 "TS" 2913268 NIL TS (NIL T) -8 NIL NIL NIL) (-1214 2902884 2903731 2904660 "TRMANIP" 2907381 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1213 2902325 2902388 2902551 "TRIMAT" 2902816 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1212 2900191 2900428 2900785 "TRIGMNIP" 2902074 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1211 2899711 2899824 2899854 "TRIGCAT" 2900067 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1210 2899380 2899459 2899600 "TRIGCAT-" 2899605 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1209 2896226 2898238 2898519 "TREE" 2899134 NIL TREE (NIL T) -8 NIL NIL NIL) (-1208 2895500 2896028 2896058 "TRANFUN" 2896093 T TRANFUN (NIL) -9 NIL 2896159 NIL) (-1207 2894779 2894970 2895250 "TRANFUN-" 2895255 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1206 2894583 2894615 2894676 "TOPSP" 2894740 T TOPSP (NIL) -7 NIL NIL NIL) (-1205 2893931 2894046 2894200 "TOOLSIGN" 2894464 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1204 2892565 2893108 2893347 "TEXTFILE" 2893714 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1203 2892346 2892377 2892449 "TEX1" 2892528 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1202 2890258 2890799 2891228 "TEX" 2891939 T TEX (NIL) -8 NIL NIL NIL) (-1201 2889906 2889969 2890059 "TEMUTL" 2890190 T TEMUTL (NIL) -7 NIL NIL NIL) (-1200 2888060 2888340 2888665 "TBCMPPK" 2889629 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1199 2879839 2886220 2886276 "TBAGG" 2886676 NIL TBAGG (NIL T T) -9 NIL 2886887 NIL) (-1198 2874909 2876397 2878151 "TBAGG-" 2878156 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1197 2874293 2874400 2874545 "TANEXP" 2874798 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1196 2873705 2873804 2873942 "TABLEAU" 2874190 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1195 2867097 2873562 2873655 "TABLE" 2873660 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1194 2861705 2862925 2864173 "TABLBUMP" 2865883 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1193 2860927 2861074 2861255 "SYSTEM" 2861546 T SYSTEM (NIL) -8 NIL NIL NIL) (-1192 2857386 2858085 2858868 "SYSSOLP" 2860178 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1191 2857184 2857341 2857372 "SYSPTR" 2857377 T SYSPTR (NIL) -8 NIL NIL NIL) (-1190 2856228 2856733 2856852 "SYSNNI" 2857038 NIL SYSNNI (NIL NIL) -8 NIL NIL 2857123) (-1189 2855535 2855994 2856073 "SYSINT" 2856133 NIL SYSINT (NIL NIL) -8 NIL NIL 2856178) (-1188 2851879 2852813 2853523 "SYNTAX" 2854847 T SYNTAX (NIL) -8 NIL NIL NIL) (-1187 2849037 2849639 2850271 "SYMTAB" 2851269 T SYMTAB (NIL) -8 NIL NIL NIL) (-1186 2844310 2845206 2846183 "SYMS" 2848082 T SYMS (NIL) -8 NIL NIL NIL) (-1185 2841555 2843771 2844001 "SYMPOLY" 2844118 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1184 2841072 2841147 2841270 "SYMFUNC" 2841467 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1183 2837092 2838384 2839197 "SYMBOL" 2840281 T SYMBOL (NIL) -8 NIL NIL NIL) (-1182 2830631 2832320 2834040 "SWITCH" 2835394 T SWITCH (NIL) -8 NIL NIL NIL) (-1181 2823865 2829452 2829755 "SUTS" 2830386 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2815935 2823112 2823385 "SUPXS" 2823650 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1179 2815094 2815221 2815438 "SUPFRACF" 2815803 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1178 2814715 2814774 2814887 "SUP2" 2815029 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1177 2806514 2814333 2814459 "SUP" 2814624 NIL SUP (NIL T) -8 NIL NIL NIL) (-1176 2804962 2805236 2805592 "SUMRF" 2806213 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2804297 2804363 2804555 "SUMFS" 2804883 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2788280 2803474 2803725 "SULS" 2804104 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2787882 2788102 2788172 "SUCHTAST" 2788232 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2787177 2787407 2787547 "SUCH" 2787790 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2781043 2782083 2783042 "SUBSPACE" 2786265 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2780473 2780563 2780727 "SUBRESP" 2780931 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2774646 2775766 2776913 "STTFNC" 2779373 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1168 2768012 2769311 2770622 "STTF" 2773382 NIL STTF (NIL T) -7 NIL NIL NIL) (-1167 2759323 2761194 2762988 "STTAYLOR" 2766253 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2752455 2759187 2759270 "STRTBL" 2759275 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2747819 2752410 2752441 "STRING" 2752446 T STRING (NIL) -8 NIL NIL NIL) (-1164 2742680 2747192 2747222 "STRICAT" 2747281 T STRICAT (NIL) -9 NIL 2747343 NIL) (-1163 2742190 2742267 2742411 "STREAM3" 2742597 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1162 2741172 2741355 2741590 "STREAM2" 2742003 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1161 2740860 2740912 2741005 "STREAM1" 2741114 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1160 2733615 2738479 2739090 "STREAM" 2740284 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1159 2732631 2732812 2733043 "STINPROD" 2733431 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2731818 2732120 2732268 "STEPAST" 2732505 T STEPAST (NIL) -8 NIL NIL NIL) (-1157 2731370 2731580 2731610 "STEP" 2731690 T STEP (NIL) -9 NIL 2731768 NIL) (-1156 2724804 2731269 2731346 "STBL" 2731351 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2719932 2724025 2724068 "STAGG" 2724221 NIL STAGG (NIL T) -9 NIL 2724310 NIL) (-1154 2717640 2718240 2719110 "STAGG-" 2719115 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2715787 2717410 2717502 "STACK" 2717583 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2708509 2713928 2714384 "SREGSET" 2715417 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2700934 2702303 2703816 "SRDCMPK" 2707115 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2693851 2698374 2698404 "SRAGG" 2699707 T SRAGG (NIL) -9 NIL 2700315 NIL) (-1149 2692868 2693123 2693502 "SRAGG-" 2693507 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2687332 2691815 2692236 "SQMATRIX" 2692494 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2681018 2684050 2684777 "SPLTREE" 2686677 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2676981 2677674 2678320 "SPLNODE" 2680444 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2676028 2676261 2676291 "SPFCAT" 2676735 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2674765 2674975 2675239 "SPECOUT" 2675786 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2665875 2667747 2667777 "SPADXPT" 2672453 T SPADXPT (NIL) -9 NIL 2674617 NIL) (-1142 2665636 2665676 2665745 "SPADPRSR" 2665828 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2663685 2665591 2665622 "SPADAST" 2665627 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2655630 2657403 2657446 "SPACEC" 2661819 NIL SPACEC (NIL T) -9 NIL 2663635 NIL) (-1139 2653760 2655562 2655611 "SPACE3" 2655616 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2652512 2652683 2652974 "SORTPAK" 2653565 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2650604 2650907 2651319 "SOLVETRA" 2652176 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2649654 2649876 2650137 "SOLVESER" 2650377 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2644958 2645846 2646841 "SOLVERAD" 2648706 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2640773 2641382 2642111 "SOLVEFOR" 2644325 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2635070 2640122 2640219 "SNTSCAT" 2640224 NIL SNTSCAT (NIL T T T T) -9 NIL 2640294 NIL) (-1132 2629176 2633393 2633784 "SMTS" 2634760 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2623887 2629064 2629141 "SMP" 2629146 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2622046 2622347 2622745 "SMITH" 2623584 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2614757 2618949 2619052 "SMATCAT" 2620406 NIL SMATCAT (NIL NIL T T T) -9 NIL 2620956 NIL) (-1128 2611718 2612534 2613705 "SMATCAT-" 2613710 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2609384 2610954 2610997 "SKAGG" 2611258 NIL SKAGG (NIL T) -9 NIL 2611393 NIL) (-1126 2605697 2608800 2608995 "SINT" 2609182 T SINT (NIL) -8 NIL NIL 2609355) (-1125 2605469 2605507 2605573 "SIMPAN" 2605653 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2604328 2604542 2604810 "SIGNRF" 2605235 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1123 2603182 2603326 2603603 "SIGNEF" 2604164 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1122 2602488 2602765 2602889 "SIGAST" 2603080 T SIGAST (NIL) -8 NIL NIL NIL) (-1121 2601767 2602023 2602163 "SIG" 2602370 T SIG (NIL) -8 NIL NIL NIL) (-1120 2599457 2599911 2600417 "SHP" 2601308 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2593316 2599358 2599434 "SHDP" 2599439 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2592889 2593081 2593111 "SGROUP" 2593204 T SGROUP (NIL) -9 NIL 2593266 NIL) (-1117 2592747 2592773 2592846 "SGROUP-" 2592851 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2589582 2590280 2591003 "SGCF" 2592046 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2583977 2589029 2589126 "SFRTCAT" 2589131 NIL SFRTCAT (NIL T T T T) -9 NIL 2589170 NIL) (-1114 2577398 2578416 2579552 "SFRGCD" 2582960 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2570524 2571597 2572783 "SFQCMPK" 2576331 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2570144 2570233 2570344 "SFORT" 2570465 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2569262 2569984 2570105 "SEXOF" 2570110 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2564775 2565490 2565585 "SEXCAT" 2568522 NIL SEXCAT (NIL T T T T T) -9 NIL 2569100 NIL) (-1109 2563882 2564656 2564724 "SEX" 2564729 T SEX (NIL) -8 NIL NIL NIL) (-1108 2562112 2562599 2562902 "SETMN" 2563625 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1107 2561608 2561760 2561790 "SETCAT" 2561966 T SETCAT (NIL) -9 NIL 2562076 NIL) (-1106 2561300 2561378 2561508 "SETCAT-" 2561513 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1105 2557661 2559761 2559804 "SETAGG" 2560674 NIL SETAGG (NIL T) -9 NIL 2561014 NIL) (-1104 2557119 2557235 2557472 "SETAGG-" 2557477 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1103 2554272 2557053 2557101 "SET" 2557106 NIL SET (NIL T) -8 NIL NIL NIL) (-1102 2553715 2553968 2554069 "SEQAST" 2554193 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2552914 2553208 2553269 "SEGXCAT" 2553555 NIL SEGXCAT (NIL T T) -9 NIL 2553675 NIL) (-1100 2551893 2552107 2552150 "SEGCAT" 2552672 NIL SEGCAT (NIL T) -9 NIL 2552893 NIL) (-1099 2551514 2551573 2551686 "SEGBIND2" 2551828 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1098 2550446 2550877 2551085 "SEGBIND" 2551341 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2550019 2550247 2550324 "SEGAST" 2550391 T SEGAST (NIL) -8 NIL NIL NIL) (-1096 2549238 2549364 2549568 "SEG2" 2549863 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1095 2548244 2548904 2549086 "SEG" 2549091 NIL SEG (NIL T) -8 NIL NIL NIL) (-1094 2547654 2548179 2548226 "SDVAR" 2548231 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2540222 2547424 2547554 "SDPOL" 2547559 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2538815 2539081 2539400 "SCPKG" 2539937 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2537979 2538151 2538343 "SCOPE" 2538645 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2537199 2537333 2537512 "SCACHE" 2537834 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2536845 2537031 2537061 "SASTCAT" 2537066 T SASTCAT (NIL) -9 NIL 2537079 NIL) (-1088 2536332 2536680 2536756 "SAOS" 2536791 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2535897 2535932 2536105 "SAERFFC" 2536291 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2535490 2535525 2535684 "SAEFACT" 2535856 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1085 2529438 2535387 2535467 "SAE" 2535472 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1084 2527759 2528073 2528474 "RURPK" 2529104 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2526396 2526702 2527007 "RULESET" 2527593 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2526008 2526190 2526273 "RULECOLD" 2526348 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1081 2523231 2523761 2524219 "RULE" 2525689 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1080 2523021 2523049 2523120 "RTVALUE" 2523182 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2522492 2522738 2522832 "RSTRCAST" 2522949 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2517340 2518135 2519055 "RSETGCD" 2521691 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506597 2511649 2511746 "RSETCAT" 2515865 NIL RSETCAT (NIL T T T T) -9 NIL 2516962 NIL) (-1076 2504524 2505063 2505887 "RSETCAT-" 2505892 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2496910 2498286 2499806 "RSDCMPK" 2503123 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2494889 2495356 2495430 "RRCC" 2496516 NIL RRCC (NIL T T) -9 NIL 2496860 NIL) (-1073 2494240 2494414 2494693 "RRCC-" 2494698 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2493683 2493936 2494037 "RPTAST" 2494161 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2467565 2476891 2476958 "RPOLCAT" 2487622 NIL RPOLCAT (NIL T T T) -9 NIL 2490781 NIL) (-1070 2459099 2461427 2464537 "RPOLCAT-" 2464542 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2450032 2457310 2457792 "ROUTINE" 2458639 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2446832 2449658 2449798 "ROMAN" 2449914 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2445078 2445692 2445952 "ROIRC" 2446637 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2441314 2443594 2443624 "RNS" 2443928 T RNS (NIL) -9 NIL 2444202 NIL) (-1065 2439823 2440206 2440740 "RNS-" 2440815 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2438826 2439188 2439390 "RNGBIND" 2439674 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1063 2438229 2438637 2438667 "RNG" 2438672 T RNG (NIL) -9 NIL 2438693 NIL) (-1062 2437628 2438016 2438059 "RMODULE" 2438064 NIL RMODULE (NIL T) -9 NIL 2438091 NIL) (-1061 2436464 2436558 2436894 "RMCAT2" 2437529 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2433314 2435810 2436107 "RMATRIX" 2436226 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2426141 2428401 2428516 "RMATCAT" 2431875 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2432857 NIL) (-1058 2425516 2425663 2425970 "RMATCAT-" 2425975 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2424917 2425138 2425181 "RLINSET" 2425375 NIL RLINSET (NIL T) -9 NIL 2425466 NIL) (-1056 2424484 2424559 2424687 "RINTERP" 2424836 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2423542 2424096 2424126 "RING" 2424182 T RING (NIL) -9 NIL 2424274 NIL) (-1054 2423334 2423378 2423475 "RING-" 2423480 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2422175 2422412 2422670 "RIDIST" 2423098 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2413491 2421643 2421849 "RGCHAIN" 2422023 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2412841 2413247 2413288 "RGBCSPC" 2413346 NIL RGBCSPC (NIL T) -9 NIL 2413398 NIL) (-1050 2411999 2412380 2412421 "RGBCMDL" 2412653 NIL RGBCMDL (NIL T) -9 NIL 2412767 NIL) (-1049 2411645 2411708 2411811 "RFFACTOR" 2411930 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1048 2411370 2411405 2411502 "RFFACT" 2411604 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1047 2409487 2409851 2410233 "RFDIST" 2411010 T RFDIST (NIL) -7 NIL NIL NIL) (-1046 2406481 2407095 2407765 "RF" 2408851 NIL RF (NIL T) -7 NIL NIL NIL) (-1045 2405934 2406026 2406189 "RETSOL" 2406383 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2405570 2405650 2405693 "RETRACT" 2405826 NIL RETRACT (NIL T) -9 NIL 2405913 NIL) (-1043 2405419 2405444 2405531 "RETRACT-" 2405536 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2405021 2405241 2405311 "RETAST" 2405371 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2397761 2404674 2404801 "RESULT" 2404916 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2396352 2397030 2397229 "RESRING" 2397664 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2395988 2396037 2396135 "RESLATC" 2396289 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2395693 2395728 2395835 "REPSQ" 2395947 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2395390 2395425 2395536 "REPDB" 2395652 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1036 2389290 2390679 2391902 "REP2" 2394202 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1035 2385667 2386348 2387156 "REP1" 2388517 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1034 2383089 2383669 2384271 "REP" 2385087 T REP (NIL) -7 NIL NIL NIL) (-1033 2375812 2381230 2381686 "REGSET" 2382719 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2374577 2374960 2375210 "REF" 2375597 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2373954 2374057 2374224 "REDORDER" 2374461 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2369953 2373167 2373394 "RECLOS" 2373782 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2369005 2369186 2369401 "REALSOLV" 2369760 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2365488 2366290 2367174 "REAL0Q" 2368170 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1027 2361089 2362077 2363138 "REAL0" 2364469 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1026 2360935 2360976 2361006 "REAL" 2361011 T REAL (NIL) -9 NIL 2361046 NIL) (-1025 2360406 2360652 2360746 "RDUCEAST" 2360863 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2359811 2359883 2360090 "RDIV" 2360328 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2358879 2359053 2359266 "RDIST" 2359633 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2357476 2357763 2358135 "RDETRS" 2358587 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2355288 2355742 2356280 "RDETR" 2357018 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2353913 2354191 2354588 "RDEEFS" 2355004 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2352422 2352728 2353153 "RDEEF" 2353601 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2346492 2349403 2349433 "RCFIELD" 2350728 T RCFIELD (NIL) -9 NIL 2351459 NIL) (-1017 2344556 2345060 2345756 "RCFIELD-" 2345831 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2340825 2342657 2342700 "RCAGG" 2343784 NIL RCAGG (NIL T) -9 NIL 2344249 NIL) (-1015 2340453 2340547 2340710 "RCAGG-" 2340715 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2339788 2339900 2340065 "RATRET" 2340337 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2339341 2339408 2339529 "RATFACT" 2339716 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2338649 2338769 2338921 "RANDSRC" 2339211 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2338383 2338427 2338500 "RADUTIL" 2338598 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2331520 2337216 2337526 "RADIX" 2338107 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2323150 2331362 2331492 "RADFF" 2331497 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2322797 2322872 2322902 "RADCAT" 2323062 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2322579 2322627 2322727 "RADCAT-" 2322732 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2320677 2322349 2322441 "QUEUE" 2322522 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2320308 2320351 2320482 "QUATCT2" 2320628 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1004 2313764 2317102 2317144 "QUATCAT" 2317935 NIL QUATCAT (NIL T) -9 NIL 2318701 NIL) (-1003 2309924 2310954 2312337 "QUATCAT-" 2312433 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1002 2306468 2309857 2309905 "QUAT" 2309910 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1001 2303933 2305544 2305587 "QUAGG" 2305968 NIL QUAGG (NIL T) -9 NIL 2306143 NIL) (-1000 2303535 2303755 2303825 "QQUTAST" 2303885 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2302433 2302933 2303105 "QFORM" 2303407 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2302071 2302114 2302241 "QFCAT2" 2302384 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2293092 2298315 2298355 "QFCAT" 2299013 NIL QFCAT (NIL T) -9 NIL 2300014 NIL) (-996 2288700 2289889 2291468 "QFCAT-" 2291562 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-995 2288160 2288270 2288400 "QEQUAT" 2288590 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2281306 2282379 2283563 "QCMPACK" 2287093 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2280551 2280725 2280957 "QALGSET2" 2281126 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-992 2278106 2278552 2278978 "QALGSET" 2280208 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-991 2276796 2277020 2277337 "PWFFINTB" 2277879 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2274995 2275163 2275517 "PUSHVAR" 2276610 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2270913 2271967 2272008 "PTRANFN" 2273892 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2269315 2269606 2269928 "PTPACK" 2270624 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2268947 2269004 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"PFECAT" 2090123 T PFECAT (NIL) -9 NIL 2090507 NIL) (-915 2087684 2087838 2088052 "PFECAT-" 2088057 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-914 2086287 2086539 2086840 "PFBRU" 2087433 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-913 2084153 2084505 2084937 "PFBR" 2085938 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-912 2080708 2084042 2084111 "PF" 2084116 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2075942 2076915 2077785 "PERMGRP" 2079871 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-910 2074048 2075005 2075046 "PERMCAT" 2075492 NIL PERMCAT (NIL T) -9 NIL 2075797 NIL) (-909 2073701 2073742 2073866 "PERMAN" 2074001 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-908 2069583 2071077 2071753 "PERM" 2073058 NIL PERM (NIL T) -8 NIL NIL NIL) (-907 2067073 2069248 2069370 "PENDTREE" 2069494 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2065097 2065865 2065906 "PDRING" 2066563 NIL PDRING (NIL T) -9 NIL 2066849 NIL) (-905 2064200 2064418 2064780 "PDRING-" 2064785 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2061415 2062193 2062861 "PDEPROB" 2063552 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2058960 2059464 2060019 "PDEPACK" 2060880 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2057872 2058062 2058313 "PDECOMP" 2058759 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2055451 2056294 2056322 "PDECAT" 2057109 T PDECAT (NIL) -9 NIL 2057822 NIL) (-900 2055202 2055235 2055325 "PCOMP" 2055412 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2053380 2054003 2054300 "PBWLB" 2054931 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2053012 2053069 2053178 "PATTERN2" 2053317 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-897 2050769 2051157 2051614 "PATTERN1" 2052601 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-896 2043244 2044842 2046180 "PATTERN" 2049452 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-895 2042808 2042875 2043007 "PATRES2" 2043171 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-894 2040176 2040757 2041238 "PATRES" 2042373 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-893 2038059 2038464 2038871 "PATMATCH" 2039843 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 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NIL) (-880 2029236 2029322 2029441 "PAN2EXPR" 2029617 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2028013 2028357 2028585 "PALETTE" 2029028 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2026406 2027018 2027378 "PAIR" 2027699 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2020297 2025665 2025859 "PADICRC" 2026261 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2013547 2019643 2019827 "PADICRAT" 2020145 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2010659 2012221 2012261 "PADICCT" 2012842 NIL PADICCT (NIL NIL) -9 NIL 2013124 NIL) (-874 2008976 2010596 2010641 "PADIC" 2010646 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-873 2007933 2008133 2008401 "PADEPAC" 2008763 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2007145 2007278 2007484 "PADE" 2007795 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2005532 2006353 2006633 "OWP" 2006949 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2005025 2005238 2005335 "OVERSET" 2005455 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2004071 2004630 2004802 "OVAR" 2004893 NIL OVAR (NIL NIL) 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NIL 1979996 NIL) (-856 1971477 1972252 1973303 "OREPCAT-" 1973308 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1970628 1970926 1970954 "ORDSET" 1971263 T ORDSET (NIL) -9 NIL 1971427 NIL) (-854 1970059 1970207 1970431 "ORDSET-" 1970436 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1968624 1969415 1969443 "ORDRING" 1969645 T ORDRING (NIL) -9 NIL 1969770 NIL) (-852 1968269 1968363 1968507 "ORDRING-" 1968512 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1967649 1968112 1968140 "ORDMON" 1968145 T ORDMON (NIL) -9 NIL 1968166 NIL) (-850 1966811 1966958 1967153 "ORDFUNS" 1967498 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1966149 1966568 1966596 "ORDFIN" 1966661 T ORDFIN (NIL) -9 NIL 1966735 NIL) (-848 1965415 1965542 1965728 "ORDCOMP2" 1966009 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1961981 1964001 1964410 "ORDCOMP" 1965039 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-846 1958562 1959472 1960286 "OPTPROB" 1961187 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1955364 1956003 1956707 "OPTPACK" 1957878 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1953051 1953817 1953845 "OPTCAT" 1954664 T OPTCAT (NIL) -9 NIL 1955314 NIL) (-843 1952435 1952728 1952833 "OPSIG" 1952966 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1952203 1952242 1952308 "OPQUERY" 1952389 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1951577 1951803 1951844 "OPERCAT" 1952056 NIL OPERCAT (NIL T) -9 NIL 1952153 NIL) (-840 1951332 1951388 1951505 "OPERCAT-" 1951510 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1948465 1949643 1950147 "OP" 1950861 NIL OP (NIL T) -8 NIL NIL NIL) (-838 1947770 1947885 1948059 "ONECOMP2" 1948337 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1944590 1946567 1946936 "ONECOMP" 1947434 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-836 1944009 1944115 1944245 "OMSERVER" 1944480 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1940871 1943449 1943489 "OMSAGG" 1943550 NIL OMSAGG (NIL T) -9 NIL 1943614 NIL) (-834 1939494 1939757 1940039 "OMPKG" 1940609 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1938041 1939043 1939212 "OMLO" 1939375 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1937001 1937148 1937368 "OMEXPR" 1937867 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1936152 1936422 1936582 "OMERRK" 1936861 T OMERRK (NIL) -8 NIL NIL NIL) (-830 1935443 1935698 1935834 "OMERR" 1936036 T OMERR (NIL) -8 NIL NIL NIL) (-829 1934894 1935120 1935228 "OMENC" 1935355 T OMENC (NIL) -8 NIL NIL NIL) (-828 1928789 1929974 1931145 "OMDEV" 1933743 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1927858 1928029 1928223 "OMCONN" 1928615 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1927288 1927391 1927419 "OM" 1927718 T OM (NIL) -9 NIL NIL NIL) (-825 1925809 1926785 1926813 "OINTDOM" 1926818 T OINTDOM (NIL) -9 NIL 1926839 NIL) (-824 1923154 1924497 1924834 "OFMONOID" 1925504 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1922565 1923091 1923136 "ODVAR" 1923141 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1919990 1922310 1922465 "ODR" 1922470 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1912612 1919766 1919892 "ODPOL" 1919897 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1906441 1912484 1912589 "ODP" 1912594 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1905207 1905422 1905697 "ODETOOLS" 1906215 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1902174 1902832 1903548 "ODESYS" 1904540 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1897056 1897964 1898989 "ODERTRIC" 1901249 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1896482 1896564 1896758 "ODERED" 1896968 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1893378 1893924 1894599 "ODERAT" 1895907 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1890335 1890802 1891399 "ODEPRRIC" 1892907 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1888278 1888874 1889360 "ODEPROB" 1889869 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1884798 1885283 1885930 "ODEPRIM" 1887757 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1884047 1884149 1884409 "ODEPAL" 1884690 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1880209 1881000 1881864 "ODEPACK" 1883203 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1879270 1879377 1879599 "ODEINT" 1880098 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1873371 1874796 1876243 "ODEIFTBL" 1877843 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1868783 1869565 1870513 "ODEEF" 1872534 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1868132 1868221 1868444 "ODECONST" 1868688 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1866257 1866918 1866946 "ODECAT" 1867551 T ODECAT (NIL) -9 NIL 1868082 NIL) (-804 1865895 1865938 1866065 "OCTCT2" 1866208 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1862762 1865600 1865722 "OCT" 1865805 NIL OCT (NIL T) -8 NIL NIL NIL) (-802 1862114 1862582 1862610 "OCAMON" 1862615 T OCAMON (NIL) -9 NIL 1862636 NIL) (-801 1856770 1859198 1859238 "OC" 1860335 NIL OC (NIL T) -9 NIL 1861193 NIL) (-800 1854018 1854759 1855742 "OC-" 1855836 NIL OC- (NIL T T) -8 NIL NIL NIL) (-799 1853549 1853890 1853918 "OASGP" 1853923 T OASGP (NIL) -9 NIL 1853943 NIL) (-798 1852810 1853299 1853327 "OAMONS" 1853367 T OAMONS (NIL) -9 NIL 1853410 NIL) (-797 1852224 1852657 1852685 "OAMON" 1852690 T OAMON (NIL) -9 NIL 1852710 NIL) (-796 1851482 1852000 1852028 "OAGROUP" 1852033 T OAGROUP (NIL) -9 NIL 1852053 NIL) (-795 1851172 1851222 1851310 "NUMTUBE" 1851426 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1844745 1846263 1847799 "NUMQUAD" 1849656 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1840501 1841489 1842514 "NUMODE" 1843740 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1837856 1838736 1838764 "NUMINT" 1839687 T NUMINT (NIL) -9 NIL 1840451 NIL) (-791 1836804 1837001 1837219 "NUMFMT" 1837658 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1823163 1826108 1828640 "NUMERIC" 1834311 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1817560 1822612 1822707 "NTSCAT" 1822712 NIL NTSCAT (NIL T T T T) -9 NIL 1822751 NIL) (-788 1816754 1816919 1817112 "NTPOLFN" 1817399 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1816386 1816443 1816552 "NSUP2" 1816691 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804508 1813211 1814023 "NSUP" 1815607 NIL NSUP (NIL T) -8 NIL NIL NIL) (-785 1794784 1804282 1804415 "NSMP" 1804420 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1793216 1793517 1793874 "NREP" 1794472 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1791807 1792059 1792417 "NPCOEF" 1792959 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1790873 1790988 1791204 "NORMRETR" 1791688 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1788914 1789204 1789613 "NORMPK" 1790581 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1788599 1788627 1788751 "NORMMA" 1788880 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1788388 1788417 1788486 "NONE1" 1788563 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1788188 1788345 1788374 "NONE" 1788379 T NONE (NIL) -8 NIL NIL NIL) (-777 1787685 1787747 1787926 "NODE1" 1788120 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1785970 1786821 1787076 "NNI" 1787423 T NNI (NIL) -8 NIL NIL 1787658) (-775 1784390 1784703 1785067 "NLINSOL" 1785638 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1780631 1781626 1782525 "NIPROB" 1783511 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1779388 1779622 1779924 "NFINTBAS" 1780393 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1778562 1779038 1779079 "NETCLT" 1779251 NIL NETCLT (NIL T) -9 NIL 1779333 NIL) (-771 1777270 1777501 1777782 "NCODIV" 1778330 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1777032 1777069 1777144 "NCNTFRAC" 1777227 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1775212 1775576 1775996 "NCEP" 1776657 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1774070 1774836 1774864 "NASRING" 1774974 T NASRING (NIL) -9 NIL 1775054 NIL) (-767 1773865 1773909 1774003 "NASRING-" 1774008 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1772972 1773497 1773525 "NARNG" 1773642 T NARNG (NIL) -9 NIL 1773733 NIL) (-765 1772664 1772731 1772865 "NARNG-" 1772870 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1771543 1771750 1771985 "NAGSP" 1772449 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1762815 1764499 1766172 "NAGS" 1769890 T NAGS (NIL) -7 NIL NIL NIL) (-762 1761363 1761671 1762002 "NAGF07" 1762504 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1755901 1757192 1758499 "NAGF04" 1760076 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1748869 1750483 1752116 "NAGF02" 1754288 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1744093 1745193 1746310 "NAGF01" 1747772 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1737721 1739287 1740872 "NAGE04" 1742528 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1728890 1731011 1733141 "NAGE02" 1735611 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1724843 1725790 1726754 "NAGE01" 1727946 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1722638 1723172 1723730 "NAGD03" 1724305 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1714388 1716316 1718270 "NAGD02" 1720704 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1708199 1709624 1711064 "NAGD01" 1712968 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1704408 1705230 1706067 "NAGC06" 1707382 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1702873 1703205 1703561 "NAGC05" 1704072 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1702249 1702368 1702512 "NAGC02" 1702749 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1701208 1701791 1701831 "NAALG" 1701910 NIL NAALG (NIL T) -9 NIL 1701971 NIL) (-748 1701043 1701072 1701162 "NAALG-" 1701167 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1694993 1696101 1697288 "MULTSQFR" 1699939 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1694312 1694387 1694571 "MULTFACT" 1694905 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1687036 1690949 1691002 "MTSCAT" 1692072 NIL MTSCAT (NIL T T) -9 NIL 1692587 NIL) (-744 1686748 1686802 1686894 "MTHING" 1686976 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1686540 1686573 1686633 "MSYSCMD" 1686708 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1683609 1686101 1686142 "MSETAGG" 1686147 NIL MSETAGG (NIL T) -9 NIL 1686181 NIL) (-741 1679691 1682364 1682684 "MSET" 1683322 NIL MSET (NIL T) -8 NIL NIL NIL) (-740 1675534 1677070 1677815 "MRING" 1678991 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1675100 1675167 1675298 "MRF2" 1675461 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1674718 1674753 1674897 "MRATFAC" 1675059 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1672330 1672625 1673056 "MPRFF" 1674423 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1666653 1672184 1672281 "MPOLY" 1672286 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1666143 1666178 1666386 "MPCPF" 1666612 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1665657 1665700 1665884 "MPC3" 1666094 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1664852 1664933 1665154 "MPC2" 1665572 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1663153 1663490 1663880 "MONOTOOL" 1664512 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1662378 1662695 1662723 "MONOID" 1662942 T MONOID (NIL) -9 NIL 1663089 NIL) (-730 1661924 1662043 1662224 "MONOID-" 1662229 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1652408 1658350 1658409 "MONOGEN" 1659083 NIL MONOGEN (NIL T T) -9 NIL 1659539 NIL) (-728 1649647 1650375 1651368 "MONOGEN-" 1651487 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1648480 1648926 1648954 "MONADWU" 1649346 T MONADWU (NIL) -9 NIL 1649584 NIL) (-726 1647852 1648011 1648259 "MONADWU-" 1648264 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1647211 1647455 1647483 "MONAD" 1647690 T MONAD (NIL) -9 NIL 1647802 NIL) (-724 1646896 1646974 1647106 "MONAD-" 1647111 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1645185 1645809 1646088 "MOEBIUS" 1646649 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1644463 1644867 1644907 "MODULE" 1644912 NIL MODULE (NIL T) -9 NIL 1644951 NIL) (-721 1644031 1644127 1644317 "MODULE-" 1644322 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1641755 1642439 1642766 "MODRING" 1643855 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1638701 1639860 1640381 "MODOP" 1641284 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1637289 1637768 1638045 "MODMONOM" 1638564 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1627371 1635580 1635994 "MODMON" 1636926 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1624553 1626239 1626515 "MODFIELD" 1627246 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1623530 1623834 1624024 "MMLFORM" 1624383 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1623056 1623099 1623278 "MMAP" 1623481 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1621135 1621902 1621943 "MLO" 1622366 NIL MLO (NIL T) -9 NIL 1622608 NIL) (-712 1618501 1619017 1619619 "MLIFT" 1620616 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1617892 1617976 1618130 "MKUCFUNC" 1618412 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1617491 1617561 1617684 "MKRECORD" 1617815 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1616538 1616700 1616928 "MKFUNC" 1617302 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1615926 1616030 1616186 "MKFLCFN" 1616421 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1615203 1615305 1615490 "MKBCFUNC" 1615819 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1611912 1614757 1614893 "MINT" 1615087 T MINT (NIL) -8 NIL NIL NIL) (-705 1610724 1610967 1611244 "MHROWRED" 1611667 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1606113 1609259 1609664 "MFLOAT" 1610339 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1605470 1605546 1605717 "MFINFACT" 1606025 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1601805 1602648 1603527 "MESH" 1604611 T MESH (NIL) -7 NIL NIL NIL) (-701 1600195 1600507 1600860 "MDDFACT" 1601492 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1596990 1599354 1599395 "MDAGG" 1599650 NIL MDAGG (NIL T) -9 NIL 1599793 NIL) (-699 1586748 1596283 1596490 "MCMPLX" 1596803 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1585889 1586035 1586235 "MCDEN" 1586597 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1583779 1584049 1584429 "MCALCFN" 1585619 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1582704 1582944 1583177 "MAYBE" 1583585 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1580316 1580839 1581401 "MATSTOR" 1582175 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1576272 1579688 1579936 "MATRIX" 1580101 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1572036 1572745 1573481 "MATLIN" 1575629 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1570630 1570783 1571116 "MATCAT2" 1571871 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-691 1560730 1563919 1563996 "MATCAT" 1568879 NIL MATCAT (NIL T T T) -9 NIL 1570296 NIL) (-690 1557086 1558107 1559463 "MATCAT-" 1559468 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-689 1555198 1555522 1555906 "MAPPKG3" 1556761 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1554179 1554352 1554574 "MAPPKG2" 1555022 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1552678 1552962 1553289 "MAPPKG1" 1553885 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1551757 1552084 1552261 "MAPPAST" 1552521 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1551368 1551426 1551549 "MAPHACK3" 1551693 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1550960 1551021 1551135 "MAPHACK2" 1551300 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1550397 1550501 1550643 "MAPHACK1" 1550851 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1548476 1549097 1549401 "MAGMA" 1550125 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1547955 1548200 1548291 "MACROAST" 1548405 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1544373 1546194 1546655 "M3D" 1547527 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1538481 1542742 1542783 "LZSTAGG" 1543565 NIL LZSTAGG (NIL T) -9 NIL 1543860 NIL) (-678 1534438 1535612 1537069 "LZSTAGG-" 1537074 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1531525 1532329 1532816 "LWORD" 1533983 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1531101 1531329 1531404 "LSTAST" 1531470 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1524298 1530872 1531006 "LSQM" 1531011 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1523522 1523661 1523889 "LSPP" 1524153 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1520364 1521021 1521734 "LSMP1" 1522841 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1518199 1518493 1518942 "LSMP" 1520060 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-671 1512078 1517366 1517407 "LSAGG" 1517469 NIL LSAGG (NIL T) -9 NIL 1517547 NIL) (-670 1508773 1509697 1510910 "LSAGG-" 1510915 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1506372 1507917 1508166 "LPOLY" 1508568 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1505954 1506039 1506162 "LPEFRAC" 1506281 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1505606 1505718 1505746 "LOGIC" 1505857 T LOGIC (NIL) -9 NIL 1505938 NIL) (-666 1505468 1505491 1505562 "LOGIC-" 1505567 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1504661 1504801 1504994 "LODOOPS" 1505324 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1503199 1503434 1503787 "LODOF" 1504408 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-663 1499431 1501848 1501889 "LODOCAT" 1502327 NIL LODOCAT (NIL T) -9 NIL 1502538 NIL) (-662 1499164 1499222 1499349 "LODOCAT-" 1499354 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-661 1496498 1499005 1499123 "LODO2" 1499128 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-660 1493947 1496435 1496480 "LODO1" 1496485 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-659 1491384 1493863 1493929 "LODO" 1493934 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1490265 1490430 1490735 "LODEEF" 1491207 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1488586 1489359 1489612 "LO" 1490097 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1483825 1486716 1486757 "LNAGG" 1487704 NIL LNAGG (NIL T) -9 NIL 1488148 NIL) (-655 1482972 1483186 1483528 "LNAGG-" 1483533 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1479108 1479897 1480536 "LMOPS" 1482387 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1478511 1478899 1478940 "LMODULE" 1478945 NIL LMODULE (NIL T) -9 NIL 1478971 NIL) (-652 1475709 1478156 1478279 "LMDICT" 1478421 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1475115 1475336 1475377 "LLINSET" 1475568 NIL LLINSET (NIL T) -9 NIL 1475659 NIL) (-650 1474814 1475023 1475083 "LITERAL" 1475088 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1474339 1474413 1474552 "LIST3" 1474734 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1472473 1472785 1473184 "LIST2MAP" 1473986 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-647 1471480 1471658 1471886 "LIST2" 1472291 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1464645 1470414 1470718 "LIST" 1471209 NIL LIST (NIL T) -8 NIL NIL NIL) (-645 1464241 1464478 1464519 "LINSET" 1464524 NIL LINSET (NIL T) -9 NIL 1464558 NIL) (-644 1462902 1463572 1463613 "LINEXP" 1463868 NIL LINEXP (NIL T) -9 NIL 1464017 NIL) (-643 1461549 1461809 1462106 "LINDEP" 1462654 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1458387 1459087 1459845 "LIMITRF" 1460823 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1456713 1457002 1457404 "LIMITPS" 1458089 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1455661 1456130 1456170 "LIECAT" 1456310 NIL LIECAT (NIL T) -9 NIL 1456461 NIL) (-639 1455502 1455529 1455617 "LIECAT-" 1455622 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1449962 1455013 1455241 "LIE" 1455323 NIL LIE (NIL T T) -8 NIL NIL NIL) (-637 1442460 1449411 1449576 "LIB" 1449817 T LIB (NIL) -8 NIL NIL NIL) (-636 1438095 1438978 1439913 "LGROBP" 1441577 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1436935 1437627 1437655 "LFCAT" 1437862 T LFCAT (NIL) -9 NIL 1438001 NIL) (-634 1434933 1435207 1435557 "LF" 1436656 NIL LF (NIL T T) -7 NIL NIL NIL) (-633 1431835 1432465 1433153 "LEXTRIPK" 1434297 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1428579 1429405 1429908 "LEXP" 1431415 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1428055 1428300 1428392 "LETAST" 1428507 T LETAST (NIL) -8 NIL NIL NIL) (-630 1426453 1426766 1427167 "LEADCDET" 1427737 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1425643 1425717 1425946 "LAZM3PK" 1426374 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1420574 1423720 1424258 "LAUPOL" 1425155 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1420153 1420197 1420358 "LAPLACE" 1420524 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1419147 1419731 1419772 "LALG" 1419834 NIL LALG (NIL T) -9 NIL 1419893 NIL) (-625 1418861 1418920 1419056 "LALG-" 1419061 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1416800 1417962 1418213 "LA" 1418694 NIL LA (NIL T T T) -8 NIL NIL NIL) (-623 1416635 1416659 1416700 "KVTFROM" 1416762 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1415558 1416002 1416187 "KTVLOGIC" 1416470 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1415393 1415417 1415458 "KRCFROM" 1415520 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1414297 1414484 1414783 "KOVACIC" 1415193 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1414132 1414156 1414197 "KONVERT" 1414259 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1413967 1413991 1414032 "KOERCE" 1414094 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1413463 1413544 1413676 "KERNEL2" 1413881 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1411293 1412056 1412433 "KERNEL" 1413119 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-615 1405063 1409832 1409886 "KDAGG" 1410263 NIL KDAGG (NIL T T) -9 NIL 1410469 NIL) (-614 1404592 1404716 1404921 "KDAGG-" 1404926 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1397742 1404253 1404408 "KAFILE" 1404470 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1392202 1397253 1397481 "JORDAN" 1397563 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1391581 1391851 1391972 "JOINAST" 1392101 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1391427 1391486 1391541 "JAVACODE" 1391546 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1387679 1389632 1389686 "IXAGG" 1390615 NIL IXAGG (NIL T T) -9 NIL 1391074 NIL) (-608 1386598 1386904 1387323 "IXAGG-" 1387328 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1382128 1386520 1386579 "IVECTOR" 1386584 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1380894 1381131 1381397 "ITUPLE" 1381895 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1379396 1379573 1379868 "ITRIGMNP" 1380716 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1378141 1378345 1378628 "ITFUN3" 1379172 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1377773 1377830 1377939 "ITFUN2" 1378078 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1377178 1377447 1377572 "ITFORM" 1377668 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1375139 1376198 1376476 "ITAYLOR" 1376933 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1364084 1369276 1370439 "ISUPS" 1374009 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1363188 1363328 1363564 "ISUMP" 1363931 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1358563 1363133 1363174 "ISTRING" 1363179 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1358039 1358284 1358376 "ISAST" 1358491 T ISAST (NIL) -8 NIL NIL NIL) (-596 1357248 1357330 1357546 "IRURPK" 1357953 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1356184 1356385 1356625 "IRSN" 1357028 T IRSN (NIL) -7 NIL NIL NIL) (-594 1354255 1354610 1355039 "IRRF2F" 1355822 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1354002 1354040 1354116 "IRREDFFX" 1354211 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1352617 1352876 1353175 "IROOT" 1353735 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1352339 1352532 1352582 "IRFORM" 1352587 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1351439 1351552 1351766 "IR2F" 1352222 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-589 1349052 1349547 1350113 "IR2" 1350917 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1345656 1346736 1347428 "IR" 1348392 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1345447 1345481 1345541 "IPRNTPK" 1345616 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1342030 1345336 1345405 "IPF" 1345410 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1340359 1341955 1342012 "IPADIC" 1342017 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1339671 1339919 1340049 "IP4ADDR" 1340249 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1339144 1339375 1339485 "IOMODE" 1339581 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1338217 1338741 1338868 "IOBFILE" 1339037 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1337705 1338121 1338149 "IOBCON" 1338154 T IOBCON (NIL) -9 NIL 1338175 NIL) (-580 1337216 1337274 1337457 "INVLAPLA" 1337641 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1326912 1329254 1331628 "INTTR" 1334892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1323247 1323989 1324854 "INTTOOLS" 1326097 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1322833 1322924 1323041 "INTSLPE" 1323150 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1320786 1322756 1322815 "INTRVL" 1322820 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1318388 1318900 1319475 "INTRF" 1320271 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1317799 1317896 1318038 "INTRET" 1318286 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1315796 1316185 1316655 "INTRAT" 1317407 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1313059 1313642 1314261 "INTPM" 1315281 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1309827 1310419 1311150 "INTPAF" 1312452 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1305006 1305968 1307019 "INTPACK" 1308796 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1304258 1304410 1304618 "INTHERTR" 1304848 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1303697 1303777 1303965 "INTHERAL" 1304172 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1301543 1301986 1302443 "INTHEORY" 1303260 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1293007 1294610 1296364 "INTG0" 1299913 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1279280 1282645 1286030 "INTFTBL" 1289642 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278529 1278667 1278840 "INTFACT" 1279139 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275962 1276406 1276961 "INTEF" 1278085 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1274329 1275068 1275096 "INTDOM" 1275397 T INTDOM (NIL) -9 NIL 1275604 NIL) (-561 1273698 1273872 1274114 "INTDOM-" 1274119 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1270086 1272014 1272068 "INTCAT" 1272867 NIL INTCAT (NIL T) -9 NIL 1273188 NIL) (-559 1269558 1269661 1269789 "INTBIT" 1269978 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1268257 1268411 1268718 "INTALG" 1269403 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267740 1267830 1267987 "INTAF" 1268161 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1261085 1267550 1267690 "INTABL" 1267695 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260426 1260892 1260957 "INT8" 1260991 T INT8 (NIL) -8 NIL NIL 1261036) (-554 1259766 1260232 1260297 "INT64" 1260331 T INT64 (NIL) -8 NIL NIL 1260376) (-553 1259106 1259572 1259637 "INT32" 1259671 T INT32 (NIL) -8 NIL NIL 1259716) (-552 1258446 1258912 1258977 "INT16" 1259011 T INT16 (NIL) -8 NIL NIL 1259056) (-551 1255396 1258243 1258352 "INT" 1258357 T INT (NIL) -8 NIL NIL NIL) (-550 1250308 1253019 1253047 "INS" 1253981 T INS (NIL) -9 NIL 1254646 NIL) (-549 1247548 1248319 1249293 "INS-" 1249366 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1246396 1246601 1246877 "INPSIGN" 1247323 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1245514 1245631 1245828 "INPRODPF" 1246276 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1244408 1244525 1244762 "INPRODFF" 1245394 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1243408 1243560 1243820 "INNMFACT" 1244244 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1242605 1242702 1242890 "INMODGCD" 1243307 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1241113 1241358 1241682 "INFSP" 1242350 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1240297 1240414 1240597 "INFPROD0" 1240993 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239907 1239967 1240065 "INFORM1" 1240232 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1236762 1237972 1238487 "INFORM" 1239400 T INFORM (NIL) -8 NIL NIL NIL) (-539 1236285 1236374 1236488 "INFINITY" 1236668 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1235461 1236005 1236106 "INETCLTS" 1236204 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1234077 1234327 1234648 "INEP" 1235209 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1233326 1233974 1234039 "INDE" 1234044 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1232890 1232958 1233075 "INCRMAPS" 1233253 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1231708 1232159 1232365 "INBFILE" 1232704 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1227008 1227944 1228888 "INBFF" 1230796 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1225916 1226185 1226213 "INBCON" 1226726 T INBCON (NIL) -9 NIL 1226992 NIL) (-531 1225168 1225391 1225667 "INBCON-" 1225672 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1224647 1224892 1224983 "INAST" 1225097 T INAST (NIL) -8 NIL NIL NIL) (-529 1224074 1224326 1224432 "IMPTAST" 1224561 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1220519 1223918 1224022 "IMATRIX" 1224027 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1219231 1219354 1219669 "IMATQF" 1220375 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1217451 1217678 1218015 "IMATLIN" 1218987 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1212031 1217375 1217433 "ILIST" 1217438 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1209936 1211891 1212004 "IIARRAY2" 1212009 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1205336 1209847 1209911 "IFF" 1209916 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1204683 1204953 1205069 "IFAST" 1205240 T IFAST (NIL) -8 NIL NIL NIL) (-521 1199678 1203975 1204163 "IFARRAY" 1204540 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1198858 1199582 1199655 "IFAMON" 1199660 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1198442 1198507 1198561 "IEVALAB" 1198768 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1198117 1198185 1198345 "IEVALAB-" 1198350 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1197367 1198006 1198081 "IDPOAMS" 1198086 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1196674 1197256 1197331 "IDPOAM" 1197336 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1196305 1196588 1196651 "IDPO" 1196656 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1195364 1195640 1195693 "IDPC" 1196106 NIL IDPC (NIL T T) -9 NIL 1196255 NIL) (-513 1194833 1195256 1195329 "IDPAM" 1195334 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1194209 1194725 1194798 "IDPAG" 1194803 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1193854 1194045 1194120 "IDENT" 1194154 T IDENT (NIL) -8 NIL NIL NIL) (-510 1190109 1190957 1191852 "IDECOMP" 1193011 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1182947 1184032 1185079 "IDEAL" 1189145 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1182111 1182223 1182422 "ICDEN" 1182831 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1181182 1181591 1181738 "ICARD" 1181984 T ICARD (NIL) -8 NIL NIL NIL) (-506 1179242 1179555 1179960 "IBPTOOLS" 1180859 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1174849 1178862 1178975 "IBITS" 1179161 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1171572 1172148 1172843 "IBATOOL" 1174266 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1169351 1169813 1170346 "IBACHIN" 1171107 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1167180 1169197 1169300 "IARRAY2" 1169305 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1163286 1167106 1167163 "IARRAY1" 1167168 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1157404 1161698 1162179 "IAN" 1162825 T IAN (NIL) -8 NIL NIL NIL) (-499 1156915 1156972 1157145 "IALGFACT" 1157341 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1156443 1156556 1156584 "HYPCAT" 1156791 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1155981 1156098 1156284 "HYPCAT-" 1156289 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1155576 1155776 1155859 "HOSTNAME" 1155918 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1155421 1155458 1155499 "HOMOTOP" 1155504 NIL HOMOTOP (NIL T) -9 NIL 1155537 NIL) (-494 1152053 1153431 1153472 "HOAGG" 1154453 NIL HOAGG (NIL T) -9 NIL 1155132 NIL) (-493 1150647 1151046 1151572 "HOAGG-" 1151577 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1144672 1150242 1150391 "HEXADEC" 1150518 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1143420 1143642 1143905 "HEUGCD" 1144449 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1142496 1143257 1143387 "HELLFDIV" 1143392 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1140675 1142273 1142361 "HEAP" 1142440 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1139938 1140227 1140361 "HEADAST" 1140561 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1133811 1139853 1139915 "HDP" 1139920 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1127830 1133446 1133598 "HDMP" 1133712 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1127154 1127294 1127458 "HB" 1127686 T HB (NIL) -7 NIL NIL NIL) (-484 1120542 1127000 1127104 "HASHTBL" 1127109 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1120018 1120263 1120355 "HASAST" 1120470 T HASAST (NIL) -8 NIL NIL NIL) (-482 1117800 1119640 1119822 "HACKPI" 1119856 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1113495 1117653 1117766 "GTSET" 1117771 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1106912 1113373 1113471 "GSTBL" 1113476 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1099192 1105943 1106208 "GSERIES" 1106703 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1098333 1098750 1098778 "GROUP" 1098981 T GROUP (NIL) -9 NIL 1099115 NIL) (-477 1097699 1097858 1098109 "GROUP-" 1098114 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1096066 1096387 1096774 "GROEBSOL" 1097376 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1094980 1095268 1095319 "GRMOD" 1095848 NIL GRMOD (NIL T T) -9 NIL 1096016 NIL) (-474 1094748 1094784 1094912 "GRMOD-" 1094917 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1090038 1091102 1092102 "GRIMAGE" 1093768 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1088504 1088765 1089089 "GRDEF" 1089734 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1087948 1088064 1088205 "GRAY" 1088383 T GRAY (NIL) -7 NIL NIL NIL) (-470 1087135 1087541 1087592 "GRALG" 1087745 NIL GRALG (NIL T T) -9 NIL 1087838 NIL) (-469 1086796 1086869 1087032 "GRALG-" 1087037 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1083573 1086381 1086559 "GPOLSET" 1086703 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1082927 1082984 1083242 "GOSPER" 1083510 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1078659 1079365 1079891 "GMODPOL" 1082626 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1077664 1077848 1078086 "GHENSEL" 1078471 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1071820 1072663 1073683 "GENUPS" 1076748 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1071517 1071568 1071657 "GENUFACT" 1071763 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1070929 1071006 1071171 "GENPGCD" 1071435 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1070403 1070438 1070651 "GENMFACT" 1070888 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1068969 1069226 1069533 "GENEEZ" 1070146 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1063146 1068580 1068742 "GDMP" 1068892 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1052510 1056917 1058023 "GCNAALG" 1062129 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1050837 1051699 1051727 "GCDDOM" 1051982 T GCDDOM (NIL) -9 NIL 1052139 NIL) (-456 1050307 1050434 1050649 "GCDDOM-" 1050654 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1038923 1041253 1043645 "GBINTERN" 1047998 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1036760 1037052 1037473 "GBF" 1038598 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1035541 1035706 1035973 "GBEUCLID" 1036576 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1034213 1034398 1034702 "GB" 1035320 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1033562 1033687 1033836 "GAUSSFAC" 1034084 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1031929 1032231 1032545 "GALUTIL" 1033281 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1030237 1030511 1030835 "GALPOLYU" 1031656 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1027602 1027892 1028299 "GALFACTU" 1029934 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1019407 1020907 1022515 "GALFACT" 1026034 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1016795 1017453 1017481 "FVFUN" 1018637 T FVFUN (NIL) -9 NIL 1019357 NIL) (-445 1016061 1016243 1016271 "FVC" 1016562 T FVC (NIL) -9 NIL 1016745 NIL) (-444 1015704 1015886 1015954 "FUNDESC" 1016013 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1015319 1015501 1015582 "FUNCTION" 1015656 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1014110 1014620 1014823 "FTEM" 1015136 T FTEM (NIL) -8 NIL NIL NIL) (-441 1011866 1012441 1012904 "FT" 1013667 T FT (NIL) -8 NIL NIL NIL) (-440 1010157 1010446 1010843 "FSUPFACT" 1011557 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1008554 1008843 1009175 "FST" 1009845 T FST (NIL) -8 NIL NIL NIL) (-438 1007753 1007859 1008047 "FSRED" 1008436 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1006452 1006708 1007055 "FSPRMELT" 1007468 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1003758 1004196 1004682 "FSPECF" 1006015 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 1003286 1003340 1003510 "FSINT" 1003699 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-434 1001578 1002279 1002582 "FSERIES" 1003065 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-433 1000620 1000736 1000960 "FSCINT" 1001458 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-432 999662 999805 1000032 "FSAGG2" 1000473 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-431 995870 998606 998647 "FSAGG" 999017 NIL FSAGG (NIL T) -9 NIL 999276 NIL) (-430 993632 994233 995029 "FSAGG-" 995124 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 991314 991594 992141 "FS2UPS" 993350 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-428 990192 990363 990665 "FS2EXPXP" 991139 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 989826 989869 989998 "FS2" 990143 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 971493 979795 979836 "FS" 983720 NIL FS (NIL T) -9 NIL 986009 NIL) (-425 960217 963183 967213 "FS-" 967513 NIL FS- (NIL T T) -8 NIL NIL NIL) (-424 959643 959758 959910 "FRUTIL" 960097 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 954644 957286 957326 "FRNAALG" 958722 NIL FRNAALG (NIL T) -9 NIL 959329 NIL) (-422 950368 951427 952685 "FRNAALG-" 953435 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 950006 950049 950176 "FRNAAF2" 950319 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 948386 948860 949155 "FRMOD" 949818 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 947581 947668 947957 "FRIDEAL2" 948293 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-418 945332 945964 946281 "FRIDEAL" 947372 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 944472 944879 944920 "FRETRCT" 944925 NIL FRETRCT (NIL T) -9 NIL 945101 NIL) (-416 943605 943829 944173 "FRETRCT-" 944178 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 940693 941903 941962 "FRAMALG" 942844 NIL FRAMALG (NIL T T) -9 NIL 943136 NIL) (-414 938827 939282 939912 "FRAMALG-" 940135 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 938463 938520 938627 "FRAC2" 938764 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-412 932405 937938 938214 "FRAC" 938219 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 932041 932098 932205 "FR2" 932342 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 923569 927617 928948 "FR" 930742 NIL FR (NIL T) -8 NIL NIL NIL) (-409 918086 920975 921003 "FPS" 922122 T FPS (NIL) -9 NIL 922679 NIL) (-408 917535 917644 917808 "FPS-" 917954 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 914839 916506 916534 "FPC" 916759 T FPC (NIL) -9 NIL 916901 NIL) (-406 914632 914672 914769 "FPC-" 914774 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 913422 914120 914161 "FPATMAB" 914166 NIL FPATMAB (NIL T) -9 NIL 914318 NIL) (-404 911095 911598 912024 "FPARFRAC" 913059 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 906528 907026 907708 "FORTRAN" 910527 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 904204 904766 904794 "FORTFN" 905854 T FORTFN (NIL) -9 NIL 906478 NIL) (-401 903968 904018 904046 "FORTCAT" 904105 T FORTCAT (NIL) -9 NIL 904167 NIL) (-400 901684 902184 902723 "FORT" 903449 T FORT (NIL) -7 NIL NIL NIL) (-399 901472 901502 901571 "FORMULA1" 901648 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 899578 900088 900478 "FORMULA" 901102 T FORMULA (NIL) -8 NIL NIL NIL) (-397 899101 899153 899326 "FORDER" 899520 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 898197 898361 898554 "FOP" 898928 T FOP (NIL) -7 NIL NIL NIL) (-395 896778 897477 897651 "FNLA" 898079 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 895507 895922 895950 "FNCAT" 896410 T FNCAT (NIL) -9 NIL 896670 NIL) (-393 895046 895466 895494 "FNAME" 895499 T FNAME (NIL) -8 NIL NIL NIL) (-392 893609 894572 894600 "FMTC" 894605 T FMTC (NIL) -9 NIL 894641 NIL) (-391 892362 893545 893591 "FMONOID" 893596 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 889190 890358 890399 "FMONCAT" 891616 NIL FMONCAT (NIL T) -9 NIL 892221 NIL) (-389 886614 887260 887288 "FMFUN" 888432 T FMFUN (NIL) -9 NIL 889140 NIL) (-388 883693 884553 884607 "FMCAT" 885802 NIL FMCAT (NIL T T) -9 NIL 886297 NIL) (-387 882962 883143 883171 "FMC" 883461 T FMC (NIL) -9 NIL 883643 NIL) (-386 881828 882728 882828 "FM1" 882907 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 881020 881570 881719 "FM" 881724 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878794 879210 879704 "FLOATRP" 880571 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 876232 876732 877310 "FLOATCP" 878261 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 869810 873961 874582 "FLOAT" 875631 T FLOAT (NIL) -8 NIL NIL NIL) (-381 868550 869388 869429 "FLINEXP" 869434 NIL FLINEXP (NIL T) -9 NIL 869527 NIL) (-380 867704 867939 868267 "FLINEXP-" 868272 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 866780 866924 867148 "FLASORT" 867556 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 863896 864764 864816 "FLALG" 866043 NIL FLALG (NIL T T) -9 NIL 866510 NIL) (-377 862938 863081 863308 "FLAGG2" 863749 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-376 856674 860424 860465 "FLAGG" 861727 NIL FLAGG (NIL T) -9 NIL 862379 NIL) (-375 855400 855739 856229 "FLAGG-" 856234 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-374 852251 853259 853318 "FINRALG" 854446 NIL FINRALG (NIL T T) -9 NIL 854954 NIL) (-373 851411 851640 851979 "FINRALG-" 851984 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 850791 851030 851058 "FINITE" 851254 T FINITE (NIL) -9 NIL 851361 NIL) (-371 843148 845335 845375 "FINAALG" 849042 NIL FINAALG (NIL T) -9 NIL 850495 NIL) (-370 838480 839530 840674 "FINAALG-" 842053 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 837138 837476 837530 "FILECAT" 838214 NIL FILECAT (NIL T T) -9 NIL 838430 NIL) (-368 836506 836893 836996 "FILE" 837068 NIL FILE (NIL T) -8 NIL NIL NIL) (-367 834224 835750 835778 "FIELD" 835818 T FIELD (NIL) -9 NIL 835898 NIL) (-366 832844 833229 833740 "FIELD-" 833745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 830694 831479 831826 "FGROUP" 832530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 829784 829948 830168 "FGLMICPK" 830526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 825618 829709 829766 "FFX" 829771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 825219 825280 825415 "FFSLPE" 825551 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 824723 824759 824968 "FFPOLY2" 825177 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 820713 821495 822291 "FFPOLY" 823959 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-359 816559 820632 820695 "FFP" 820700 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 811687 815902 816092 "FFNBX" 816413 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 806617 810822 811080 "FFNBP" 811541 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 801252 805901 806112 "FFNB" 806450 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 800084 800282 800597 "FFINTBAS" 801049 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 796155 798373 798401 "FFIELDC" 799021 T FFIELDC (NIL) -9 NIL 799397 NIL) (-353 794817 795188 795685 "FFIELDC-" 795690 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 794386 794432 794556 "FFHOM" 794759 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 792081 792568 793085 "FFF" 793901 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 787701 791823 791924 "FFCGX" 792024 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 783325 787433 787540 "FFCGP" 787644 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 778510 783052 783160 "FFCG" 783261 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 777921 777964 778199 "FFCAT2" 778461 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 759326 768398 768484 "FFCAT" 773649 NIL FFCAT (NIL T T T) -9 NIL 775100 NIL) (-345 754523 755571 756885 "FFCAT-" 758115 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 749923 754434 754498 "FF" 754503 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-343 739248 742895 744115 "FEXPR" 748775 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 738248 738683 738724 "FEVALAB" 738808 NIL FEVALAB (NIL T) -9 NIL 739069 NIL) (-341 737407 737617 737955 "FEVALAB-" 737960 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 734427 735168 735283 "FDIVCAT" 736851 NIL FDIVCAT (NIL T T T T) -9 NIL 737288 NIL) (-339 734189 734216 734386 "FDIVCAT-" 734391 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733409 733496 733773 "FDIV2" 734096 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 731975 732792 732995 "FDIV" 733308 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-336 730949 731270 731472 "FCTRDATA" 731793 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 729635 729894 730183 "FCPAK1" 730680 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 728734 729135 729276 "FCOMP" 729526 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 712439 715884 719422 "FC" 725216 T FC (NIL) -8 NIL NIL NIL) (-332 704804 708830 708870 "FAXF" 710672 NIL FAXF (NIL T) -9 NIL 711364 NIL) (-331 702080 702738 703563 "FAXF-" 704028 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 697132 701456 701632 "FARRAY" 701937 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 692033 694093 694146 "FAMR" 695169 NIL FAMR (NIL T T) -9 NIL 695629 NIL) (-328 690923 691225 691660 "FAMR-" 691665 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 690092 690845 690898 "FAMONOID" 690903 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 687878 688588 688641 "FAMONC" 689582 NIL FAMONC (NIL T T) -9 NIL 689968 NIL) (-325 686542 687632 687769 "FAGROUP" 687774 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 684337 684656 685059 "FACUTIL" 686223 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 683436 683621 683843 "FACTFUNC" 684147 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 675860 682739 682938 "EXPUPXS" 683292 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 673343 673883 674469 "EXPRTUBE" 675294 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 669614 670206 670936 "EXPRODE" 672682 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 664168 664755 665561 "EXPR2UPS" 668912 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 663800 663857 663966 "EXPR2" 664105 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 649346 662449 662878 "EXPR" 663404 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 640762 648499 648789 "EXPEXPAN" 649183 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 640242 640486 640577 "EXITAST" 640691 T EXITAST (NIL) -8 NIL NIL NIL) (-314 640042 640199 640228 "EXIT" 640233 T EXIT (NIL) -8 NIL NIL NIL) (-313 639669 639731 639844 "EVALCYC" 639974 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 639210 639328 639369 "EVALAB" 639539 NIL EVALAB (NIL T) -9 NIL 639643 NIL) (-311 638691 638813 639034 "EVALAB-" 639039 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 636059 637361 637389 "EUCDOM" 637944 T EUCDOM (NIL) -9 NIL 638294 NIL) (-309 634464 634906 635496 "EUCDOM-" 635501 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 634096 634153 634262 "ESTOOLS2" 634401 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 633847 633889 633969 "ESTOOLS1" 634048 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 621385 624145 626895 "ESTOOLS" 631117 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621130 621162 621244 "ESCONT1" 621347 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 617504 618265 619045 "ESCONT" 620370 T ESCONT (NIL) -7 NIL NIL NIL) (-303 617179 617229 617329 "ES2" 617448 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-302 616809 616867 616976 "ES1" 617115 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-301 610846 612454 612482 "ES" 615250 T ES (NIL) -9 NIL 616660 NIL) (-300 605793 607080 608897 "ES-" 609061 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 605009 605138 605314 "ERROR" 605637 T ERROR (NIL) -7 NIL NIL NIL) (-298 598403 604868 604959 "EQTBL" 604964 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 598035 598092 598201 "EQ2" 598340 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 590538 593349 594798 "EQ" 596619 NIL -3971 (NIL T) -8 NIL NIL NIL) (-295 585828 586876 587969 "EP" 589477 NIL EP (NIL T) -7 NIL NIL NIL) (-294 584428 584719 585025 "ENV" 585542 T ENV (NIL) -8 NIL NIL NIL) (-293 583522 584076 584104 "ENTIRER" 584109 T ENTIRER (NIL) -9 NIL 584155 NIL) (-292 580045 581531 581901 "EMR" 583321 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 579189 579374 579428 "ELTAGG" 579808 NIL ELTAGG (NIL T T) -9 NIL 580019 NIL) (-290 578908 578970 579111 "ELTAGG-" 579116 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 578697 578726 578780 "ELTAB" 578864 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 577823 577969 578168 "ELFUTS" 578548 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 577565 577621 577649 "ELEMFUN" 577754 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 577435 577456 577524 "ELEMFUN-" 577529 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 572279 575535 575576 "ELAGG" 576516 NIL ELAGG (NIL T) -9 NIL 576979 NIL) (-284 570564 570998 571661 "ELAGG-" 571666 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 569876 570013 570169 "ELABOR" 570428 T ELABOR (NIL) -8 NIL NIL NIL) (-282 568537 568816 569110 "ELABEXPR" 569602 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 561528 563204 564031 "EFUPXS" 567813 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 555105 556779 557589 "EFULS" 560804 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 552590 552948 553420 "EFSTRUC" 554737 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 542381 543947 545495 "EF" 551105 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 541455 541866 542015 "EAB" 542252 T EAB (NIL) -8 NIL NIL NIL) (-276 540637 541414 541442 "E04UCFA" 541447 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 539819 540596 540624 "E04NAFA" 540629 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 539001 539778 539806 "E04MBFA" 539811 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 538183 538960 538988 "E04JAFA" 538993 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 537367 538142 538170 "E04GCFA" 538175 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 536551 537326 537354 "E04FDFA" 537359 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 535733 536510 536538 "E04DGFA" 536543 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 529906 531258 532622 "E04AGNT" 534389 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 528586 529092 529132 "DVARCAT" 529607 NIL DVARCAT (NIL T) -9 NIL 529806 NIL) (-267 527790 528002 528316 "DVARCAT-" 528321 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 520968 527589 527718 "DSMP" 527723 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 520633 520692 520790 "DROPT1" 520903 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 515748 516874 518011 "DROPT0" 519516 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510529 511693 512761 "DROPT" 514700 T DROPT (NIL) -8 NIL NIL NIL) (-262 508874 509199 509585 "DRAWPT" 510163 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 508507 508560 508678 "DRAWHACK" 508815 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 507238 507507 507798 "DRAWCX" 508236 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 506753 506822 506973 "DRAWCURV" 507164 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 497221 499183 501298 "DRAWCFUN" 504658 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 491808 492731 493810 "DRAW" 496195 NIL DRAW (NIL T) -7 NIL NIL NIL) (-256 488572 490501 490542 "DQAGG" 491171 NIL DQAGG (NIL T) -9 NIL 491445 NIL) (-255 476732 483165 483248 "DPOLCAT" 485100 NIL DPOLCAT (NIL T T T T) -9 NIL 485645 NIL) (-254 471619 472951 474892 "DPOLCAT-" 474897 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 464748 471480 471578 "DPMO" 471583 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 457780 464528 464695 "DPMM" 464700 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 457258 457472 457570 "DOMTMPLT" 457702 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 456691 457060 457140 "DOMCTOR" 457198 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 455903 456171 456322 "DOMAIN" 456560 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 449922 455538 455690 "DMP" 455804 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 449522 449578 449722 "DLP" 449860 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 443346 448849 449039 "DLIST" 449364 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 440144 442199 442240 "DLAGG" 442790 NIL DLAGG (NIL T) -9 NIL 443020 NIL) (-244 438820 439484 439512 "DIVRING" 439604 T DIVRING (NIL) -9 NIL 439687 NIL) (-243 438057 438247 438547 "DIVRING-" 438552 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 436159 436516 436922 "DISPLAY" 437671 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 435007 435210 435475 "DIRPROD2" 435952 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 428902 434921 434984 "DIRPROD" 434989 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 417684 423683 423736 "DIRPCAT" 424146 NIL DIRPCAT (NIL NIL T) -9 NIL 424986 NIL) (-238 415010 415652 416533 "DIRPCAT-" 416870 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 414297 414457 414643 "DIOSP" 414844 T DIOSP (NIL) -7 NIL NIL NIL) (-236 410952 413209 413250 "DIOPS" 413684 NIL DIOPS (NIL T) -9 NIL 413913 NIL) (-235 410501 410615 410806 "DIOPS-" 410811 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 409324 409952 409980 "DIFRING" 410167 T DIFRING (NIL) -9 NIL 410277 NIL) (-233 408970 409047 409199 "DIFRING-" 409204 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 406706 407978 408019 "DIFEXT" 408382 NIL DIFEXT (NIL T) -9 NIL 408676 NIL) (-231 404991 405419 406085 "DIFEXT-" 406090 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 402266 404523 404564 "DIAGG" 404569 NIL DIAGG (NIL T) -9 NIL 404589 NIL) (-229 401650 401807 402059 "DIAGG-" 402064 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 397066 400609 400886 "DHMATRIX" 401419 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 392678 393587 394597 "DFSFUN" 396076 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 387761 391609 391921 "DFLOAT" 392386 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 386024 386305 386694 "DFINTTLS" 387469 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 383053 384045 384445 "DERHAM" 385690 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 380854 382828 382917 "DEQUEUE" 382997 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 380108 380241 380424 "DEGRED" 380716 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 376718 377418 378219 "DEFINTRF" 379381 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 374385 374826 375390 "DEFINTEF" 376265 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 373735 374005 374120 "DEFAST" 374290 T DEFAST (NIL) -8 NIL NIL NIL) (-218 367760 373330 373479 "DECIMAL" 373606 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 365272 365730 366236 "DDFACT" 367304 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 364868 364911 365062 "DBLRESP" 365223 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 362740 363101 363461 "DBASE" 364635 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 361982 362220 362366 "DATAARY" 362639 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361088 361941 361969 "D03FAFA" 361974 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 360195 361047 361075 "D03EEFA" 361080 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 358145 358611 359100 "D03AGNT" 359726 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 357434 358104 358132 "D02EJFA" 358137 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 356723 357393 357421 "D02CJFA" 357426 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356012 356682 356710 "D02BHFA" 356715 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 355301 355971 355999 "D02BBFA" 356004 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 348498 350087 351693 "D02AGNT" 353715 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 346266 346789 347335 "D01WGTS" 347972 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 345333 346225 346253 "D01TRNS" 346258 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 344401 345292 345320 "D01GBFA" 345325 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 343469 344360 344388 "D01FCFA" 344393 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 342537 343428 343456 "D01ASFA" 343461 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 341605 342496 342524 "D01AQFA" 342529 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 340673 341564 341592 "D01APFA" 341597 T D01APFA (NIL) -8 NIL NIL NIL) (-198 339741 340632 340660 "D01ANFA" 340665 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 338809 339700 339728 "D01AMFA" 339733 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 337877 338768 338796 "D01ALFA" 338801 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 336945 337836 337864 "D01AKFA" 337869 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336013 336904 336932 "D01AJFA" 336937 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 329308 330861 332422 "D01AGNT" 334472 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 328645 328773 328925 "CYCLOTOM" 329176 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 325380 326093 326820 "CYCLES" 327938 T CYCLES (NIL) -7 NIL NIL NIL) (-190 324692 324826 324997 "CVMP" 325241 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 322533 322791 323160 "CTRIGMNP" 324420 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322042 322264 322365 "CTORKIND" 322452 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321333 321649 321677 "CTORCAT" 321859 T CTORCAT (NIL) -9 NIL 321972 NIL) (-186 320931 321042 321201 "CTORCAT-" 321206 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320393 320605 320713 "CTORCALL" 320855 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 319829 320187 320260 "CTOR" 320340 T CTOR (NIL) -8 NIL NIL NIL) (-183 319203 319302 319455 "CSTTOOLS" 319726 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315002 315659 316417 "CRFP" 318515 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 314477 314723 314815 "CRCEAST" 314930 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 313524 313709 313937 "CRAPACK" 314281 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 312908 313009 313213 "CPMATCH" 313400 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 312633 312661 312767 "CPIMA" 312874 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 308981 309653 310372 "COORDSYS" 311968 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 308393 308514 308656 "CONTOUR" 308859 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 304286 306396 306888 "CONTFRAC" 307933 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 304166 304187 304215 "CONDUIT" 304252 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 303254 303808 303836 "COMRING" 303841 T COMRING (NIL) -9 NIL 303893 NIL) (-172 302308 302612 302796 "COMPPROP" 303090 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 301969 302004 302132 "COMPLPAT" 302267 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 301605 301662 301769 "COMPLEX2" 301906 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 291914 301414 301523 "COMPLEX" 301528 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291468 291545 291662 "COMPILER" 291817 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291186 291221 291319 "COMPFACT" 291427 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275275 285260 285300 "COMPCAT" 286304 NIL COMPCAT (NIL T) -9 NIL 287652 NIL) (-165 264808 267728 271348 "COMPCAT-" 271704 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264537 264565 264668 "COMMUPC" 264774 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264331 264365 264424 "COMMONOP" 264498 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263907 264135 264210 "COMMAAST" 264276 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263463 263658 263745 "COMM" 263840 T COMM (NIL) -8 NIL NIL NIL) (-160 262712 262906 262934 "COMBOPC" 263272 T COMBOPC (NIL) -9 NIL 263447 NIL) (-159 261608 261818 262060 "COMBINAT" 262502 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258065 258639 259266 "COMBF" 261030 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256823 257181 257416 "COLOR" 257850 T COLOR (NIL) -8 NIL NIL NIL) (-156 256299 256544 256636 "COLONAST" 256751 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255939 255986 256111 "CMPLXRT" 256246 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255387 255639 255738 "CLLCTAST" 255860 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250886 251917 252997 "CLIP" 254327 T CLIP (NIL) -7 NIL NIL NIL) (-152 249232 249992 250231 "CLIF" 250713 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245407 247378 247419 "CLAGG" 248348 NIL CLAGG (NIL T) -9 NIL 248884 NIL) (-150 243829 244286 244869 "CLAGG-" 244874 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243373 243458 243598 "CINTSLPE" 243738 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240874 241345 241893 "CHVAR" 242901 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240048 240602 240630 "CHARZ" 240635 T CHARZ (NIL) -9 NIL 240650 NIL) (-146 239802 239842 239920 "CHARPOL" 240002 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238860 239447 239475 "CHARNZ" 239522 T CHARNZ (NIL) -9 NIL 239578 NIL) (-144 236766 237514 237867 "CHAR" 238527 T CHAR (NIL) -8 NIL NIL NIL) (-143 236492 236553 236581 "CFCAT" 236692 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235737 235848 236030 "CDEN" 236376 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231702 234890 235170 "CCLASS" 235477 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230953 231110 231287 "CATEGORY" 231545 T -10 (NIL) -8 NIL NIL NIL) (-139 230526 230872 230920 "CATCTOR" 230925 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229977 230229 230327 "CATAST" 230448 T CATAST (NIL) -8 NIL NIL NIL) (-137 229453 229698 229790 "CASEAST" 229905 T CASEAST (NIL) -8 NIL NIL NIL) (-136 228561 228709 228930 "CARTEN2" 229300 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223570 224590 225343 "CARTEN" 227864 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 221886 222720 222977 "CARD" 223333 T CARD (NIL) -8 NIL NIL NIL) (-133 221462 221690 221765 "CAPSLAST" 221831 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220966 221174 221202 "CACHSET" 221334 T CACHSET (NIL) -9 NIL 221412 NIL) (-131 220436 220758 220786 "CABMON" 220836 T CABMON (NIL) -9 NIL 220892 NIL) (-130 219909 220140 220250 "BYTEORD" 220346 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 215259 219414 219586 "BYTEBUF" 219757 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214241 214793 214935 "BYTE" 215098 T BYTE (NIL) -8 NIL NIL 215220) (-127 211752 213933 214040 "BTREE" 214167 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209203 211400 211522 "BTOURN" 211662 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206575 208673 208714 "BTCAT" 208782 NIL BTCAT (NIL T) -9 NIL 208859 NIL) (-124 206242 206322 206471 "BTCAT-" 206476 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201507 205385 205413 "BTAGG" 205635 T BTAGG (NIL) -9 NIL 205796 NIL) (-122 200997 201122 201328 "BTAGG-" 201333 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197994 200275 200490 "BSTREE" 200814 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197132 197258 197442 "BRILL" 197850 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193785 195858 195899 "BRAGG" 196548 NIL BRAGG (NIL T) -9 NIL 196806 NIL) (-118 192317 192722 193276 "BRAGG-" 193281 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185567 191663 191847 "BPADICRT" 192165 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183884 185504 185549 "BPADIC" 185554 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183582 183612 183726 "BOUNDZRO" 183848 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 181363 181767 182242 "BOP1" 183140 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 176591 177789 178701 "BOP" 180471 T BOP (NIL) -8 NIL NIL NIL) (-112 175416 176165 176314 "BOOLEAN" 176462 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174695 175099 175153 "BMODULE" 175158 NIL BMODULE (NIL T T) -9 NIL 175223 NIL) (-110 170496 174493 174566 "BITS" 174642 T BITS (NIL) -8 NIL NIL NIL) (-109 169917 170036 170176 "BINDING" 170376 T BINDING (NIL) -8 NIL NIL NIL) (-108 163945 169514 169662 "BINARY" 169789 T BINARY (NIL) -8 NIL NIL NIL) (-107 161725 163200 163241 "BGAGG" 163501 NIL BGAGG (NIL T) -9 NIL 163638 NIL) (-106 161556 161588 161679 "BGAGG-" 161684 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160627 160940 161145 "BFUNCT" 161371 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159311 159492 159780 "BEZOUT" 160451 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155782 158163 158493 "BBTREE" 159014 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155516 155569 155597 "BASTYPE" 155716 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155368 155397 155470 "BASTYPE-" 155475 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154802 154878 155030 "BALFACT" 155279 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153658 154217 154403 "AUTOMOR" 154647 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153384 153389 153415 "ATTREG" 153420 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151636 152081 152433 "ATTRBUT" 153050 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151244 151464 151530 "ATTRAST" 151588 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150780 150893 150919 "ATRIG" 151120 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150589 150630 150717 "ATRIG-" 150722 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150234 150420 150446 "ASTCAT" 150451 T ASTCAT (NIL) -9 NIL 150481 NIL) (-92 149961 150020 150139 "ASTCAT-" 150144 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148110 149737 149825 "ASTACK" 149904 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146615 146912 147277 "ASSOCEQ" 147792 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145669 146274 146398 "ASP9" 146522 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 144559 145274 145416 "ASP80" 145558 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 144322 144507 144546 "ASP8" 144551 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 143298 143999 144117 "ASP78" 144235 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 142289 142978 143095 "ASP77" 143212 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 141223 141927 142058 "ASP74" 142189 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 140145 140858 140990 "ASP73" 141122 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 139065 139780 139912 "ASP7" 140044 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 138191 138891 138991 "ASP6" 138996 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137158 137868 137986 "ASP55" 138104 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136129 136832 136951 "ASP50" 137070 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135239 135830 135940 "ASP49" 136050 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 134045 134778 134946 "ASP42" 135128 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 132843 133578 133748 "ASP41" 133932 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131953 132544 132654 "ASP4" 132764 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 130925 131630 131748 "ASP35" 131866 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130690 130873 130912 "ASP34" 130917 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130427 130494 130570 "ASP33" 130645 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129342 130062 130194 "ASP31" 130326 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129107 129290 129329 "ASP30" 129334 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128842 128911 128987 "ASP29" 129062 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128607 128790 128829 "ASP28" 128834 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128372 128555 128594 "ASP27" 128599 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127478 128070 128181 "ASP24" 128292 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126576 127280 127392 "ASP20" 127397 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125540 126250 126369 "ASP19" 126488 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 125277 125344 125420 "ASP12" 125495 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 124151 124876 125020 "ASP10" 125164 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 123261 123852 123962 "ASP1" 124072 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 121112 123105 123196 "ARRAY2" 123201 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 120144 120317 120538 "ARRAY12" 120935 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 115909 119792 119906 "ARRAY1" 120061 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 110221 112139 112214 "ARR2CAT" 114844 NIL ARR2CAT (NIL T T T) -9 NIL 115602 NIL) (-56 107655 108399 109353 "ARR2CAT-" 109358 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106972 107282 107407 "ARITY" 107548 T ARITY (NIL) -8 NIL NIL NIL) (-54 105748 105900 106199 "APPRULE" 106808 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105399 105447 105566 "APPLYORE" 105694 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104677 104800 104957 "ANY1" 105273 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 104031 104270 104390 "ANY" 104575 T ANY (NIL) -8 NIL NIL NIL) (-50 101561 102468 102795 "ANTISYM" 103755 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101053 101268 101364 "ANON" 101483 T ANON (NIL) -8 NIL NIL NIL) (-48 95311 99592 100046 "AN" 100617 T AN (NIL) -8 NIL NIL NIL) (-47 91209 92597 92648 "AMR" 93396 NIL AMR (NIL T T) -9 NIL 93996 NIL) (-46 90321 90542 90905 "AMR-" 90910 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74766 90238 90299 "ALIST" 90304 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71601 74360 74529 "ALGSC" 74684 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68156 68711 69318 "ALGPKG" 71041 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67433 67534 67718 "ALGMFACT" 68042 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63468 64047 64641 "ALGMANIP" 67017 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54849 63094 63244 "ALGFF" 63401 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54045 54176 54355 "ALGFACT" 54707 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52986 53586 53624 "ALGEBRA" 53629 NIL ALGEBRA (NIL T) -9 NIL 53670 NIL) (-37 52704 52763 52895 "ALGEBRA-" 52900 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34803 50706 50758 "ALAGG" 50894 NIL ALAGG (NIL T T) -9 NIL 51055 NIL) (-35 34339 34452 34478 "AHYP" 34679 T AHYP (NIL) -9 NIL NIL NIL) (-34 33270 33518 33544 "AGG" 34043 T AGG (NIL) -9 NIL 34322 NIL) (-33 32704 32866 33080 "AGG-" 33085 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30510 30933 31338 "AF" 32346 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29990 30235 30325 "ADDAST" 30438 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29258 29517 29673 "ACPLOT" 29852 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18637 26385 26423 "ACFS" 27030 NIL ACFS (NIL T) -9 NIL 27269 NIL) (-28 16664 17154 17916 "ACFS-" 17921 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14711 14737 "ACF" 15616 T ACF (NIL) -9 NIL 16029 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 0f3e38cc..d466d41c 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,5 +1,5 @@ -(724368 . 3477425186) +(724461 . 3477435923) (((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 (-551))) (-5 *2 (-1272 (-412 (-551)))) (-5 *1 (-1300 *4))))) @@ -38,9 +38,9 @@ (-12 (-5 *2 (-952 *3)) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *5 (-619 (-1183))) (-4 *4 (-798)) (-4 *5 (-855)))) ((*1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3755 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -105,7 +105,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-410 *1)) (-4 *1 (-1227)))) ((*1 *2 *3) (-12 (-4 *4 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-1252 *4 *3)) - (-4 *3 (-13 (-1248 *4) (-562) (-10 -8 (-15 -3573 ($ $ $))))))) + (-4 *3 (-13 (-1248 *4) (-562) (-10 -8 (-15 -3576 ($ $ $))))))) ((*1 *2 *3) (-12 (-5 *3 (-1052 *4 *5)) (-4 *4 (-13 (-853) (-310) (-147) (-1026))) (-14 *5 (-646 (-1183))) @@ -158,26 +158,26 @@ (((*1 *2 *3) (-12 (-5 *3 (-1052 *4 *5)) (-4 *4 (-13 (-853) (-310) (-147) (-1026))) (-14 *5 (-646 (-1183))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3653 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) (-5 *1 (-1299 *4 *5 *6)) (-14 *6 (-646 (-1183))))) ((*1 *2 *3 *4 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3653 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3653 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3653 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) (-5 *1 (-1299 *5 *6 *7)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))) (-14 *7 (-646 (-1183))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-853) (-310) (-147) (-1026))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3653 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) (-5 *1 (-1299 *4 *5 *6)) (-5 *3 (-646 (-952 *4))) (-14 *5 (-646 (-1183))) (-14 *6 (-646 (-1183)))))) (((*1 *2 *3 *4 *4) @@ -252,10 +252,10 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-390 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-390 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4398 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4401 *3) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2572 *5) (|:| -2573 *6)) - (-2 (|:| -2572 *5) (|:| -2573 *6)))) + (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) + (-2 (|:| -2575 *5) (|:| -2576 *6)))) (-5 *1 (-466 *3 *4 *5 *6 *7 *2)) (-4 *5 (-855)) (-4 *2 (-956 *4 *6 (-869 *3))))) ((*1 *1 *1 *2) (-12 (-4 *1 (-475 *2 *3)) (-4 *2 (-173)) (-4 *3 (-23)))) @@ -323,10 +323,10 @@ (-14 *3 (-646 (-1183))))) ((*1 *1 *1) (-12 (-4 *1 (-388 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-1107)))) ((*1 *1 *1) - (-12 (-14 *2 (-646 (-1183))) (-4 *3 (-173)) (-4 *5 (-239 (-4398 *2) (-776))) + (-12 (-14 *2 (-646 (-1183))) (-4 *3 (-173)) (-4 *5 (-239 (-4401 *2) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *4) (|:| -2573 *5)) - (-2 (|:| -2572 *4) (|:| -2573 *5)))) + (-1 (-112) (-2 (|:| -2575 *4) (|:| -2576 *5)) + (-2 (|:| -2575 *4) (|:| -2576 *5)))) (-5 *1 (-466 *2 *3 *4 *5 *6 *7)) (-4 *4 (-855)) (-4 *7 (-956 *3 *5 (-869 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-514 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-855)))) @@ -544,7 +544,7 @@ (-4 *6 (-798)) (-4 *2 (-13 (-1107) - (-10 -8 (-15 -4280 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-776)))))) + (-10 -8 (-15 -4283 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-776)))))) (-5 *1 (-958 *6 *7 *8 *5 *2)) (-4 *5 (-956 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-964 *5)) (-4 *5 (-1222)) (-4 *6 (-1222)) @@ -557,7 +557,7 @@ (-4 *5 (-798)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) (-15 -4272 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) (-5 *1 (-990 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-562)) (-4 *6 (-562)) (-4 *2 (-997 *6)) @@ -641,7 +641,7 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1055)) (-5 *1 (-1296 *3 *4)) (-4 *4 (-851))))) -(((*1 *2 *1) (-12 (|has| *1 (-6 -4434)) (-4 *1 (-34)) (-5 *2 (-776)))) +(((*1 *2 *1) (-12 (|has| *1 (-6 -4437)) (-4 *1 (-34)) (-5 *2 (-776)))) ((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-251)))) ((*1 *2 *1) (-12 (-4 *1 (-1110 *3 *4 *5 *6 *7)) (-4 *3 (-1107)) (-4 *4 (-1107)) @@ -684,7 +684,7 @@ (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-797)) (-4 *2 (-367)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-226)))) ((*1 *1 *1 *1) - (-3969 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) + (-3972 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) (-12 (-5 *1 (-296 *2)) (-4 *2 (-478)) (-4 *2 (-1222))))) ((*1 *1 *1 *1) (-4 *1 (-367))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-382)))) @@ -782,61 +782,61 @@ ((*1 *1 *2) (-12 (-5 *2 (-1131 (-551) (-616 (-48)))) (-5 *1 (-48)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-52 *3)) (-4 *3 (-1222)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3962 'X) (-3962) (-704))) (-5 *1 (-61 *3)) + (-12 (-5 *2 (-343 (-3965 'X) (-3965) (-704))) (-5 *1 (-61 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'JINT 'X 'ELAM) (-3962) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3965 'JINT 'X 'ELAM) (-3965) (-704)))) (-5 *1 (-62 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962) (-3962 'XC) (-704)))) (-5 *1 (-64 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'XC) (-704)))) (-5 *1 (-64 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3962) (-3962 'XC) (-704))) (-5 *1 (-66 *3)) + (-12 (-5 *2 (-343 (-3965) (-3965 'XC) (-704))) (-5 *1 (-66 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'X) (-3962 '-4405) (-704)))) (-5 *1 (-71 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965 '-4408) (-704)))) (-5 *1 (-71 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962) (-3962 'X) (-704)))) (-5 *1 (-74 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'X) (-704)))) (-5 *1 (-74 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3962) (-3962 'X) (-704))) (-5 *1 (-75 *3)) + (-12 (-5 *2 (-343 (-3965) (-3965 'X) (-704))) (-5 *1 (-75 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'X 'EPS) (-3962 '-4405) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3965 'X 'EPS) (-3965 '-4408) (-704)))) (-5 *1 (-76 *3 *4 *5)) (-14 *3 (-1183)) (-14 *4 (-1183)) (-14 *5 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'EPS) (-3962 'YA 'YB) (-704)))) + (-12 (-5 *2 (-1272 (-343 (-3965 'EPS) (-3965 'YA 'YB) (-704)))) (-5 *1 (-77 *3 *4 *5)) (-14 *3 (-1183)) (-14 *4 (-1183)) (-14 *5 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3962) (-3962 'X) (-704))) (-5 *1 (-78 *3)) + (-12 (-5 *2 (-343 (-3965) (-3965 'X) (-704))) (-5 *1 (-78 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962) (-3962 'XC) (-704)))) (-5 *1 (-79 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'XC) (-704)))) (-5 *1 (-79 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962) (-3962 'X) (-704)))) (-5 *1 (-80 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965) (-3965 'X) (-704)))) (-5 *1 (-80 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'X) (-3962 '-4405) (-704)))) (-5 *1 (-82 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965 '-4408) (-704)))) (-5 *1 (-82 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'X '-4405) (-3962) (-704)))) (-5 *1 (-83 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965 'X '-4408) (-3965) (-704)))) (-5 *1 (-83 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3962 'X '-4405) (-3962) (-704)))) (-5 *1 (-84 *3)) + (-12 (-5 *2 (-694 (-343 (-3965 'X '-4408) (-3965) (-704)))) (-5 *1 (-84 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3962 'X) (-3962) (-704)))) (-5 *1 (-85 *3)) + (-12 (-5 *2 (-694 (-343 (-3965 'X) (-3965) (-704)))) (-5 *1 (-85 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-1272 (-343 (-3962 'X) (-3962) (-704)))) (-5 *1 (-86 *3)) + (-12 (-5 *2 (-1272 (-343 (-3965 'X) (-3965) (-704)))) (-5 *1 (-86 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-694 (-343 (-3962 'XL 'XR 'ELAM) (-3962) (-704)))) + (-12 (-5 *2 (-694 (-343 (-3965 'XL 'XR 'ELAM) (-3965) (-704)))) (-5 *1 (-88 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) - (-12 (-5 *2 (-343 (-3962 'X) (-3962 '-4405) (-704))) (-5 *1 (-89 *3)) + (-12 (-5 *2 (-343 (-3965 'X) (-3965 '-4408) (-704))) (-5 *1 (-89 *3)) (-14 *3 (-1183)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-135 *3 *4 *5))) (-5 *1 (-135 *3 *4 *5)) (-14 *3 (-551)) @@ -902,64 +902,64 @@ ((*1 *1 *2) (-12 (-5 *2 (-646 (-333))) (-4 *1 (-402)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-169 (-382))))) (-5 *1 (-403 *3 *4 *5 *6)) - (-14 *3 (-1183)) (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1="void"))) + (-14 *3 (-1183)) (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1="void"))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-382)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-551)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-169 (-382)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-382))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-551))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-699)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-704)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-296 (-317 (-706)))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-699))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-704))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-317 (-706))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |localSymbols| (-1187)) (|:| -1787 (-646 (-333))))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-646 (-333))) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-333)) (-5 *1 (-403 *3 *4 *5 *6)) (-14 *3 (-1183)) - (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-14 *5 (-646 (-1183))) + (-14 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-14 *5 (-646 (-1183))) (-14 *6 (-1187)))) ((*1 *1 *2) (-12 (-5 *2 (-412 (-952 (-412 *3)))) (-4 *3 (-562)) (-4 *3 (-1107)) @@ -1054,7 +1054,7 @@ (-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 (-646 (-2 (|:| -4395 *3) (|:| -4379 *4)))) (-4 *3 (-1055)) + (-12 (-5 *2 (-646 (-2 (|:| -4398 *3) (|:| -4382 *4)))) (-4 *3 (-1055)) (-4 *4 (-731)) (-5 *1 (-740 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-768)))) ((*1 *1 *2) @@ -1097,19 +1097,19 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) (-5 *1 (-846)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))) + (-12 (-5 *2 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) (-5 *1 (-846)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *1 (-846)))) @@ -1255,7 +1255,7 @@ ((*1 *1 *1) (-4 *1 (-287))) ((*1 *2 *3) (-12 (-5 *3 (-410 *4)) (-4 *4 (-562)) - (-5 *2 (-646 (-2 (|:| -4395 (-776)) (|:| |logand| *4)))) (-5 *1 (-323 *4)))) + (-5 *2 (-646 (-2 (|:| -4398 (-776)) (|:| |logand| *4)))) (-5 *1 (-323 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-646 (-1183))) (-14 *3 (-646 (-1183))) (-4 *4 (-392)))) @@ -1399,7 +1399,7 @@ (((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1283))))) (((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1283))))) (((*1 *2 *3) - (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *2 (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) @@ -1423,7 +1423,7 @@ (-12 (-4 *3 (-1227)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 (-412 *4))) (-5 *2 (-1272 *1)) (-4 *1 (-346 *3 *4 *5)))) ((*1 *2) - (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *2 (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) @@ -1547,14 +1547,14 @@ (((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4288 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *1 (-263)))) ((*1 *2 *3 *2) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4288 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *3 (-646 (-263))) (-5 *1 (-264)))) @@ -1565,14 +1565,14 @@ ((*1 *2 *1 *3) (-12 (-5 *3 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4288 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *2 (-1278)) (-5 *1 (-1276)))) ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4288 (-226)) + (-2 (|:| |theta| (-226)) (|:| |phi| (-226)) (|:| -4291 (-226)) (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |scaleZ| (-226)) (|:| |deltaX| (-226)) (|:| |deltaY| (-226)))) (-5 *1 (-1276)))) @@ -1636,9 +1636,9 @@ (-5 *2 (-1272 (-2 (|:| |scaleX| (-226)) (|:| |scaleY| (-226)) (|:| |deltaX| (-226)) - (|:| |deltaY| (-226)) (|:| -4291 (-551)) (|:| -4289 (-551)) - (|:| |spline| (-551)) (|:| -4320 (-551)) (|:| |axesColor| (-879)) - (|:| -4292 (-551)) (|:| |unitsColor| (-879)) (|:| |showing| (-551))))) + (|:| |deltaY| (-226)) (|:| -4294 (-551)) (|:| -4292 (-551)) + (|:| |spline| (-551)) (|:| -4323 (-551)) (|:| |axesColor| (-879)) + (|:| -4295 (-551)) (|:| |unitsColor| (-879)) (|:| |showing| (-551))))) (-5 *1 (-1275))))) (((*1 *2 *3) (-12 (-5 *2 (-1185 (-412 (-551)))) (-5 *1 (-191)) (-5 *3 (-551)))) ((*1 *2 *1) (-12 (-5 *2 (-1272 (-3 (-473) "undefined"))) (-5 *1 (-1275))))) @@ -1687,13 +1687,13 @@ (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1222)) (-4 *2 (-1222)) (-5 *1 (-59 *5 *2)))) ((*1 *2 *3 *1 *2 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1107)) (|has| *1 (-6 -4434)) + (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1107)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3 *1 *2) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4434)) (-4 *1 (-151 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4434)) (-4 *1 (-151 *2)) + (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)))) ((*1 *2 *3) (-12 (-4 *4 (-1055)) (-5 *2 (-2 (|:| -2191 (-1177 *4)) (|:| |deg| (-925)))) @@ -1790,7 +1790,7 @@ (-12 (-5 *1 (-215 *2)) (-4 *2 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 ((-1278) $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) (-15 -2152 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-296 *2)) (-4 *2 (-25)) (-4 *2 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-296 *2)) (-4 *2 (-25)) (-4 *2 (-1222)))) @@ -1821,7 +1821,7 @@ (-12 (-5 *1 (-215 *2)) (-4 *2 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 ((-1278) $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) (-15 -2152 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-296 *2)) (-4 *2 (-21)) (-4 *2 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-296 *2)) (-4 *2 (-21)) (-4 *2 (-1222)))) @@ -2177,13 +2177,13 @@ (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1232 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-1183)) (-4 *1 (-1234 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1234 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3494 ((-646 *2) *3))) - (|has| *3 (-15 -4253 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) + (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1234 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551)))))) ((*1 *1 *1) @@ -2192,26 +2192,26 @@ (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1253 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-1183)) (-4 *1 (-1255 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1255 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3494 ((-646 *2) *3))) - (|has| *3 (-15 -4253 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) + (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1255 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551)))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1269 *4)) (-14 *4 (-1183)) (-5 *1 (-1262 *3 *4 *5)) (-4 *3 (-38 (-412 (-551)))) (-4 *3 (-1055)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-1183)) (-4 *1 (-1265 *3)) (-4 *3 (-1055)) (-12 (-4 *3 (-29 (-551))) (-4 *3 (-966)) (-4 *3 (-1208)) (-4 *3 (-38 (-412 (-551)))))) (-12 (-5 *2 (-1183)) (-4 *1 (-1265 *3)) (-4 *3 (-1055)) - (-12 (|has| *3 (-15 -3494 ((-646 *2) *3))) - (|has| *3 (-15 -4253 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) + (-12 (|has| *3 (-15 -3497 ((-646 *2) *3))) + (|has| *3 (-15 -4256 (*3 *3 *2))) (-4 *3 (-38 (-412 (-551)))))))) ((*1 *1 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1055)) (-4 *2 (-38 (-412 (-551))))))) (((*1 *2 *1 *3) @@ -2349,13 +2349,13 @@ (-12 (-5 *3 (-1183)) (-5 *2 (-246 (-1165))) (-5 *1 (-215 *4)) (-4 *4 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ *3)) (-15 -4058 ((-1278) $)) + (-10 -8 (-15 -4243 ((-1165) $ *3)) (-15 -4061 ((-1278) $)) (-15 -2152 ((-1278) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-995)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 ((-1278) $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 ((-1278) $)) (-15 -2152 ((-1278) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-776)) (-5 *1 (-246 *4)) (-4 *4 (-855)))) @@ -2451,50 +2451,50 @@ (((*1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1261 *3)) (-4 *3 (-1222)) (-5 *2 (-776))))) (((*1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-245 *2)) (-4 *2 (-1222)))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) + ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-551)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1222)) (-4 *4 (-376 *2)) (-4 *5 (-376 *2)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "right") (|has| *1 (-6 -4435)) (-4 *1 (-119 *3)) + (-12 (-5 *2 "right") (|has| *1 (-6 -4438)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "left") (|has| *1 (-6 -4435)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) + (-12 (-5 *2 "left") (|has| *1 (-6 -4438)) (-4 *1 (-119 *3)) (-4 *3 (-1222)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4435)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4438)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222)))) ((*1 *2 *1 *3 *2) (-12 (-5 *2 (-51)) (-5 *3 (-1183)) (-5 *1 (-637)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 (-1239 (-551))) (|has| *1 (-6 -4435)) (-4 *1 (-656 *2)) + (-12 (-5 *3 (-1239 (-551))) (|has| *1 (-6 -4438)) (-4 *1 (-656 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2 *2 *1) (-12 (-5 *2 (-646 (-551))) (-4 *1 (-691 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "value") (|has| *1 (-6 -4435)) (-4 *1 (-1016 *2)) + (-12 (-5 *3 "value") (|has| *1 (-6 -4438)) (-4 *1 (-1016 *2)) (-4 *2 (-1222)))) ((*1 *2 *1 *2) (-12 (-5 *1 (-1032 *2)) (-4 *2 (-1222)))) ((*1 *2 *1 *3 *2) (-12 (-4 *1 (-1199 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1107)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "last") (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) + (-12 (-5 *3 "last") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222)))) ((*1 *1 *1 *2 *1) - (-12 (-5 *2 "rest") (|has| *1 (-6 -4435)) (-4 *1 (-1261 *3)) + (-12 (-5 *2 "rest") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *3)) (-4 *3 (-1222)))) ((*1 *2 *1 *3 *2) - (-12 (-5 *3 "first") (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) + (-12 (-5 *3 "first") (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *1 *1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-1160 *3)) (-4 *3 (-1222)))) - ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) + ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1261 *2)) (-4 *2 (-1222))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-551)) (|has| *1 (-6 -4435)) (-4 *1 (-1261 *3)) + (-12 (-5 *2 (-551)) (|has| *1 (-6 -4438)) (-4 *1 (-1261 *3)) (-4 *3 (-1222))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-13 (-1044 (-551)) (-644 (-551)) (-457))) @@ -2592,7 +2592,7 @@ (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-551)))) - (-4 *4 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3573 ($ $ $))))) (-4 *3 (-562)) + (-4 *4 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3576 ($ $ $))))) (-4 *3 (-562)) (-5 *1 (-1252 *3 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-956 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855)) @@ -2604,12 +2604,12 @@ ((*1 *1 *1) (-4 *1 (-1227))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-1252 *3 *2)) - (-4 *2 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3573 ($ $ $)))))))) + (-4 *2 (-13 (-1248 *3) (-562) (-10 -8 (-15 -3576 ($ $ $)))))))) (((*1 *2 *1) (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-131)) - (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4384 *4)))))) + (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))))) ((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4395 *3) (|:| -4379 *4)))) (-5 *1 (-740 *3 *4)) + (-12 (-5 *2 (-646 (-2 (|:| -4398 *3) (|:| -4382 *4)))) (-5 *1 (-740 *3 *4)) (-4 *3 (-1055)) (-4 *4 (-731)))) ((*1 *2 *1) (-12 (-4 *1 (-1251 *3 *4)) (-4 *3 (-1055)) (-4 *4 (-797)) @@ -2678,7 +2678,7 @@ (-12 (-4 *1 (-1074 *2 *3)) (-4 *2 (-13 (-853) (-367))) (-4 *3 (-1248 *2)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-1251 *2 *3)) (-4 *3 (-797)) (|has| *2 (-15 ** (*2 *2 *3))) - (|has| *2 (-15 -4387 (*2 (-1183)))) (-4 *2 (-1055))))) + (|has| *2 (-15 -4390 (*2 (-1183)))) (-4 *2 (-1055))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-175 *3)) (-4 *3 (-310)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2) @@ -2795,13 +2795,13 @@ (|partial| -12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-956 *4 *5 *3)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-956 *4 *5 *3)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-1055)) (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) + (-12 (-4 *3 (-1055)) (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1248 *3))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-776)) (-4 *4 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-1248 *4))))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1248 *4))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-776)) (-4 *1 (-1248 *3)) (-4 *3 (-1055))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-1248 *2)) (-4 *2 (-1055))))) @@ -2842,14 +2842,14 @@ (|partial| -12 (-4 *1 (-1248 *2)) (-4 *2 (-1055)) (-4 *2 (-562))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-1248 *2)) (-4 *2 (-1055)) (-4 *2 (-562))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -4395 *4) (|:| -2161 *3) (|:| -3312 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -4398 *4) (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-1071 *3 *4 *5)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1071 *3 *4 *5)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -4395 *3) (|:| -2161 *1) (|:| -3312 *1))) + (-5 *2 (-2 (|:| -4398 *3) (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1248 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-367)) (-4 *4 (-562)) (-4 *5 (-1248 *4)) @@ -2867,14 +2867,14 @@ (((*1 *2 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-1246 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-1246 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) + (|partial| -12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-1245 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-147))) (-5 *2 (-646 *3)) (-5 *1 (-1244 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-562) (-147))) - (-5 *2 (-2 (|:| -3551 *3) (|:| -3550 *3))) (-5 *1 (-1244 *4 *3)) + (-5 *2 (-2 (|:| -3554 *3) (|:| -3553 *3))) (-5 *1 (-1244 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *2 *2) (|partial| -12 (-4 *3 (-13 (-562) (-147))) (-5 *1 (-1244 *3 *2)) @@ -2898,7 +2898,7 @@ (-5 *2 (-2 (|:| |num| (-694 *4)) (|:| |den| *4))) (-5 *1 (-698 *4 *5)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-2 (|:| -3696 *7) (|:| |rh| (-646 (-412 *6))))) + (-5 *2 (-2 (|:| -3699 *7) (|:| |rh| (-646 (-412 *6))))) (-5 *1 (-812 *5 *6 *7 *3)) (-5 *4 (-646 (-412 *6))) (-4 *7 (-663 *6)) (-4 *3 (-663 (-412 *6))))) ((*1 *2 *3) @@ -2951,13 +2951,13 @@ (-12 (-5 *4 (-112)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) (-5 *1 (-1238 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) (-12 (-4 *4 (-354)) (-5 *2 (-410 *3)) (-5 *1 (-217 *4 *3)) @@ -3023,7 +3023,7 @@ (-12 (-4 *4 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) (-15 -4272 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) (-4 *5 (-798)) (-4 *7 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-461 *4 *5 *6 *7 *3)) (-4 *6 (-562)) (-4 *3 (-956 *7 *5 *4)))) ((*1 *2 *3) @@ -3067,11 +3067,11 @@ (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) (-15 -4272 ((-3 $ "failed") (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ "failed") (-1183)))))) (-4 *6 (-310)) (-5 *2 (-410 *3)) (-5 *1 (-735 *4 *5 *6 *3)) (-4 *3 (-956 (-952 *6) *4 *5)))) ((*1 *2 *3) - (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) (-4 *6 (-562)) (-5 *2 (-410 *3)) (-5 *1 (-737 *4 *5 *6 *3)) (-4 *3 (-956 (-412 (-952 *6)) *4 *5)))) ((*1 *2 *3) @@ -3188,7 +3188,7 @@ ((*1 *2 *1) (-12 (-4 *1 (-1227)) (-5 *2 (-112))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1225))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3657 (-646 (-1183))) (|:| -3658 (-646 (-1183))))) + (-12 (-5 *2 (-2 (|:| -3660 (-646 (-1183))) (|:| -3661 (-646 (-1183))))) (-5 *1 (-1225))))) (((*1 *2 *3) (-12 (-5 *3 (-646 (-1183))) (-5 *2 (-1278)) (-5 *1 (-1225)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-646 (-1183))) (-5 *2 (-1278)) (-5 *1 (-1225))))) @@ -3208,7 +3208,7 @@ (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1107)) (-5 *2 (-112)) (-5 *1 (-1224 *3))))) (((*1 *2) - (-12 (-5 *2 (-2 (|:| -3658 (-646 *3)) (|:| -3657 (-646 *3)))) + (-12 (-5 *2 (-2 (|:| -3661 (-646 *3)) (|:| -3660 (-646 *3)))) (-5 *1 (-1224 *3)) (-4 *3 (-1107))))) (((*1 *2 *3) (-12 (-5 *3 (-646 *4)) (-4 *4 (-1107)) (-5 *2 (-1278)) (-5 *1 (-1224 *4)))) @@ -3224,7 +3224,7 @@ (-12 (-4 *4 (-354)) (-5 *2 (-410 (-1177 (-1177 *4)))) (-5 *1 (-1221 *4)) (-5 *3 (-1177 (-1177 *4)))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4434)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *3 (-1222)) (-5 *1 (-606 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) @@ -3239,10 +3239,10 @@ (((*1 *1 *2) (-12 (-5 *2 (-925)) (-4 *1 (-239 *3 *4)) (-4 *4 (-1055)) (-4 *4 (-1222)))) ((*1 *1 *2) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4398 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4401 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *2) (|:| -2573 *5)) - (-2 (|:| -2572 *2) (|:| -2573 *5)))) + (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *5)) + (-2 (|:| -2575 *2) (|:| -2576 *5)))) (-5 *1 (-466 *3 *4 *2 *5 *6 *7)) (-4 *2 (-855)) (-4 *7 (-956 *4 *5 (-869 *3))))) ((*1 *2 *2) (-12 (-5 *2 (-949 (-226))) (-5 *1 (-1219))))) @@ -3286,12 +3286,12 @@ (((*1 *2 *3 *4 *5) (|partial| -12 (-5 *4 (-1 (-112) *9)) (-5 *5 (-1 (-112) *9 *9)) (-4 *9 (-1071 *6 *7 *8)) (-4 *6 (-562)) (-4 *7 (-798)) (-4 *8 (-855)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3757 (-646 *9)))) (-5 *3 (-646 *9)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3760 (-646 *9)))) (-5 *3 (-646 *9)) (-4 *1 (-1217 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-1 (-112) *8 *8)) (-4 *8 (-1071 *5 *6 *7)) (-4 *5 (-562)) (-4 *6 (-798)) (-4 *7 (-855)) - (-5 *2 (-2 (|:| |bas| *1) (|:| -3757 (-646 *8)))) (-5 *3 (-646 *8)) + (-5 *2 (-2 (|:| |bas| *1) (|:| -3760 (-646 *8)))) (-5 *3 (-646 *8)) (-4 *1 (-1217 *5 *6 *7 *8))))) (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -3299,7 +3299,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1071 *3 *4 *5)) - (-5 *2 (-2 (|:| -4302 (-646 *6)) (|:| -1879 (-646 *6))))))) + (-5 *2 (-2 (|:| -4305 (-646 *6)) (|:| -1879 (-646 *6))))))) (((*1 *2 *1 *3) (-12 (-5 *3 (-646 *1)) (-4 *1 (-1071 *4 *5 *6)) (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *6 (-855)) (-5 *2 (-112)))) @@ -3422,7 +3422,7 @@ (-4 *6 (-855)) (-5 *2 (-646 *1)) (-4 *1 (-1217 *4 *5 *6 *7))))) (((*1 *2 *3) (-12 (-4 *4 (-562)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-1071 *4 *5 *6)) - (-5 *2 (-646 (-2 (|:| -4302 *1) (|:| -1879 (-646 *7))))) (-5 *3 (-646 *7)) + (-5 *2 (-646 (-2 (|:| -4305 *1) (|:| -1879 (-646 *7))))) (-5 *3 (-646 *7)) (-4 *1 (-1217 *4 *5 *6 *7))))) (((*1 *2 *1) (-12 (-4 *1 (-1217 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -3749,7 +3749,7 @@ (-12 (-5 *2 (-1278)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 (*2 $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) (-15 -2152 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-398)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-551)) (-5 *2 (-1278)) (-5 *1 (-398)))) @@ -3794,7 +3794,7 @@ (-12 (-5 *2 (-2 - (|:| -4301 + (|:| -4304 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) @@ -3826,7 +3826,7 @@ (-12 (-5 *2 (-2 - (|:| -4301 + (|:| -4304 (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) @@ -3859,7 +3859,7 @@ (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1200 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1107))))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4301 *3) (|:| -2263 *4)))) (-4 *3 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| -4304 *3) (|:| -2263 *4)))) (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *1 (-1199 *3 *4)))) ((*1 *1) (-12 (-4 *1 (-1199 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-1107))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-1197 *2)) (-4 *2 (-367))))) @@ -3967,13 +3967,13 @@ (-4 *6 (-13 (-310) (-1044 (-551)) (-644 (-551)) (-147))) (-5 *1 (-658 *6 *2 *3)) (-4 *3 (-663 *2)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4435)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4435)))) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2199 (-646 *4)))) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4435)))) - (-4 *7 (-13 (-376 *5) (-10 -7 (-6 -4435)))) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) + (-4 *7 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-646 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2199 (-646 *7))))) (-5 *1 (-672 *5 *6 *7 *3)) (-5 *4 (-646 *7)) (-4 *3 (-691 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -4194,11 +4194,11 @@ (((*1 *2 *1) (|partial| -12 (-5 *2 (-646 (-282))) (-5 *1 (-282)))) ((*1 *2 *1) (-12 (-5 *2 (-646 (-1188))) (-5 *1 (-1188))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1188))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3267)) (-5 *2 (-112)) (-5 *1 (-622)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2398)) (-5 *2 (-112)) (-5 *1 (-622)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3266)) (-5 *2 (-112)) (-5 *1 (-622)))) +(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3270)) (-5 *2 (-112)) (-5 *1 (-622)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2401)) (-5 *2 (-112)) (-5 *1 (-622)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -3269)) (-5 *2 (-112)) (-5 *1 (-622)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -2525)) (-5 *2 (-112)) (-5 *1 (-696 *4)) + (-12 (-5 *3 (|[\|\|]| -2528)) (-5 *2 (-112)) (-5 *1 (-696 *4)) (-4 *4 (-618 (-868))))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| *4)) (-4 *4 (-618 (-868))) (-5 *2 (-112)) @@ -4276,8 +4276,8 @@ (-12 (-5 *3 (-439)) (-5 *2 (-646 - (-3 (|:| -3982 (-1183)) - (|:| -3654 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551))))))))) + (-3 (|:| -3985 (-1183)) + (|:| -3657 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551))))))))) (-5 *1 (-1187))))) (((*1 *2 *1) (-12 (-5 *2 (-646 (-1183))) (-5 *1 (-1187))))) (((*1 *2 *1) @@ -4285,14 +4285,14 @@ (-5 *2 (-646 (-646 - (-3 (|:| -3982 (-1183)) - (|:| -3654 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551)))))))))) + (-3 (|:| -3985 (-1183)) + (|:| -3657 (-646 (-3 (|:| S (-1183)) (|:| P (-952 (-551)))))))))) (-5 *1 (-1187))))) (((*1 *2 *1) (-12 (-5 *2 (-1109)) (-5 *1 (-1187))))) (((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-1187))))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4301 (-1183)) (|:| -2263 (-441))))) + (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 (-441))))) (-5 *1 (-1187))))) (((*1 *1) (-5 *1 (-1186)))) (((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) @@ -4306,19 +4306,19 @@ ((*1 *2 *3 *4 *1) (-12 (-5 *4 (-646 (-1183))) (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-439)) (|:| -4351 #1="void"))) (-5 *2 (-1278)) + (-12 (-5 *3 (-3 (|:| |fst| (-439)) (|:| -4354 #1="void"))) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) + (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) + (-12 (-5 *3 (-1183)) (-5 *4 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1278)) (-5 *1 (-1186))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1183)) (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4351 "void"))) + (-12 (-5 *3 (-1183)) (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 "void"))) (-5 *1 (-1186))))) (((*1 *2 *3 *1) (-12 (-5 *2 (-646 (-1183))) (-5 *1 (-1186)) (-5 *3 (-1183))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1183)) (-5 *2 (-1187)) (-5 *1 (-1186))))) @@ -4344,15 +4344,15 @@ ((*1 *2 *1) (-12 (-5 *2 - (-2 (|:| -2993 (-646 (-868))) (|:| -2814 (-646 (-868))) - (|:| |presup| (-646 (-868))) (|:| -2991 (-646 (-868))) + (-2 (|:| -2996 (-646 (-868))) (|:| -2817 (-646 (-868))) + (|:| |presup| (-646 (-868))) (|:| -2994 (-646 (-868))) (|:| |args| (-646 (-868))))) (-5 *1 (-1183))))) (((*1 *1 *1 *2) (-12 (-5 *2 - (-2 (|:| -2993 (-646 (-868))) (|:| -2814 (-646 (-868))) - (|:| |presup| (-646 (-868))) (|:| -2991 (-646 (-868))) + (-2 (|:| -2996 (-646 (-868))) (|:| -2817 (-646 (-868))) + (|:| |presup| (-646 (-868))) (|:| -2994 (-646 (-868))) (|:| |args| (-646 (-868))))) (-5 *1 (-1183)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-646 (-868)))) (-5 *1 (-1183))))) @@ -4370,50 +4370,50 @@ (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *1 *1) (-5 *1 (-1182))) ((*1 *1 *2) (-12 (-5 *2 - (-3 (|:| I (-317 (-551))) (|:| -3505 (-317 (-382))) + (-3 (|:| I (-317 (-551))) (|:| -3508 (-317 (-382))) (|:| CF (-317 (-169 (-382)))) (|:| |switch| (-1182)))) (-5 *1 (-1182))))) (((*1 *2 *1 *3 *3 *4) @@ -4463,13 +4463,13 @@ ((*1 *2 *1) (-12 (-5 *2 (-1141)) (-5 *1 (-1173))))) (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1222)) (-4 *1 (-151 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -2573 (-776)) (|:| -4213 *4) (|:| |num| *4)))) + (-12 (-5 *2 (-646 (-2 (|:| -2576 (-776)) (|:| -4216 *4) (|:| |num| *4)))) (-4 *4 (-1248 *3)) (-4 *3 (-13 (-367) (-147))) (-5 *1 (-404 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4351 #1="void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 #1="void"))) (-5 *3 (-646 (-952 (-551)))) (-5 *4 (-112)) (-5 *1 (-441)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4351 #1#))) (-5 *3 (-646 (-1183))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 #1#))) (-5 *3 (-646 (-1183))) (-5 *4 (-112)) (-5 *1 (-441)))) ((*1 *2 *1) (-12 (-5 *2 (-1160 *3)) (-5 *1 (-606 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-640 *2)) (-4 *2 (-173)))) @@ -4484,12 +4484,12 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-718 *2 *3 *4)) (-4 *2 (-855)) (-4 *3 (-1107)) (-14 *4 - (-1 (-112) (-2 (|:| -2572 *2) (|:| -2573 *3)) - (-2 (|:| -2572 *2) (|:| -2573 *3)))))) + (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *3)) + (-2 (|:| -2575 *2) (|:| -2576 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-511)) (-5 *3 (-1121)) (-5 *1 (-843)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-878 *2 *3)) (-4 *2 (-1222)) (-4 *3 (-1222)))) ((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| -4301 (-1183)) (|:| -2263 *4)))) (-4 *4 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 *4)))) (-4 *4 (-1107)) (-5 *1 (-894 *3 *4)) (-4 *3 (-1107)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-646 *5)) (-4 *5 (-13 (-1107) (-34))) @@ -4890,11 +4890,11 @@ (-12 (-5 *2 (-1160 *3)) (-4 *3 (-38 (-412 (-551)))) (-5 *1 (-1169 *3))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-412 (-551)))) - (-5 *2 (-2 (|:| -3922 (-1160 *4)) (|:| -3923 (-1160 *4)))) + (-5 *2 (-2 (|:| -3925 (-1160 *4)) (|:| -3926 (-1160 *4)))) (-5 *1 (-1168 *4)) (-5 *3 (-1160 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-38 (-412 (-551)))) - (-5 *2 (-2 (|:| -4079 (-1160 *4)) (|:| -4075 (-1160 *4)))) + (-5 *2 (-2 (|:| -4082 (-1160 *4)) (|:| -4078 (-1160 *4)))) (-5 *1 (-1168 *4)) (-5 *3 (-1160 *4))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-1160 *3)) (-4 *3 (-367)) (-4 *3 (-1055)) (-5 *1 (-1167 *3))))) @@ -4986,7 +4986,7 @@ (-5 *1 (-1160 *4))))) (((*1 *2 *3 *1) (-12 - (-5 *2 (-2 (|:| |cycle?| (-112)) (|:| -3004 (-776)) (|:| |period| (-776)))) + (-5 *2 (-2 (|:| |cycle?| (-112)) (|:| -3007 (-776)) (|:| |period| (-776)))) (-5 *1 (-1160 *4)) (-4 *4 (-1222)) (-5 *3 (-776))))) (((*1 *1 *2) (-12 (-5 *2 (-1 (-1160 *3))) (-5 *1 (-1160 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *1) (-12 (-5 *1 (-646 *2)) (-4 *2 (-1222)))) @@ -5132,17 +5132,17 @@ (-12 (-4 *1 (-340 *3 *4 *5 *6)) (-4 *3 (-367)) (-4 *4 (-1248 *3)) (-4 *5 (-1248 (-412 *4))) (-4 *6 (-346 *3 *4 *5)) (-5 *2 - (-2 (|:| -2496 (-418 *4 (-412 *4) *5 *6)) (|:| |principalPart| *6))))) + (-2 (|:| -2499 (-418 *4 (-412 *4) *5 *6)) (|:| |principalPart| *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| |poly| *6) (|:| -3502 (-412 *6)) (|:| |special| (-412 *6)))) + (-5 *2 (-2 (|:| |poly| *6) (|:| -3505 (-412 *6)) (|:| |special| (-412 *6)))) (-5 *1 (-732 *5 *6)) (-5 *3 (-412 *6)))) ((*1 *2 *3) (-12 (-4 *4 (-367)) (-5 *2 (-646 *3)) (-5 *1 (-902 *3 *4)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *4 *4) (|partial| -12 (-5 *4 (-776)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3551 *3) (|:| -3550 *3))) (-5 *1 (-902 *3 *5)) + (-5 *2 (-2 (|:| -3554 *3) (|:| -3553 *3))) (-5 *1 (-902 *3 *5)) (-4 *3 (-1248 *5)))) ((*1 *2 *3 *2 *4 *4) (-12 (-5 *2 (-646 *9)) (-5 *3 (-646 *8)) (-5 *4 (-112)) @@ -5308,7 +5308,7 @@ (-4 *3 (-13 (-457) (-1044 (-551)) (-644 (-551)))) (-5 *1 (-594 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3502 *3) (|:| |special| *3))) (-5 *1 (-732 *5 *3)))) + (-5 *2 (-2 (|:| -3505 *3) (|:| |special| *3))) (-5 *1 (-732 *5 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) (-5 *2 (-646 (-646 (-694 *5)))) (-5 *1 (-1036 *5)) @@ -5360,10 +5360,10 @@ (-4 *5 (-13 (-1107) (-34))) (-4 *6 (-13 (-1107) (-34))) (-5 *2 (-112)) (-5 *1 (-1147 *5 *6))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4434)) (-4 *1 (-151 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-151 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-679 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1 *3) @@ -5374,9 +5374,9 @@ (-12 (-5 *2 (-1146 *3 *4)) (-4 *3 (-13 (-1107) (-34))) (-4 *4 (-13 (-1107) (-34))) (-5 *1 (-1147 *3 *4))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4434)) (-4 *1 (-236 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-236 *3)) (-4 *3 (-1107)))) - ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4434)) (-4 *1 (-236 *2)) (-4 *2 (-1107)))) + ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4437)) (-4 *1 (-236 *2)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-285 *3)) (-4 *3 (-1222)))) ((*1 *2 *3 *1) @@ -5578,25 +5578,25 @@ (((*1 *2 *1) (-12 (-4 *1 (-1140 *3)) (-4 *3 (-1055)) (-5 *2 - (-2 (|:| -4291 (-776)) (|:| |curves| (-776)) (|:| |polygons| (-776)) + (-2 (|:| -4294 (-776)) (|:| |curves| (-776)) (|:| |polygons| (-776)) (|:| |constructs| (-776))))))) (((*1 *2 *3 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4173 (-1177 *6)) (|:| -2573 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4176 (-1177 *6)) (|:| -2576 (-551))))) (-4 *6 (-310)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-112)) (-5 *1 (-747 *4 *5 *6 *7)) (-4 *7 (-956 *6 *4 *5)))) ((*1 *1 *1) (-12 (-4 *1 (-1140 *2)) (-4 *2 (-1055))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-1138 *4 *2)) - (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4434) (-6 -4435)))))) + (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4437) (-6 -4438)))))) ((*1 *2 *2) (-12 (-4 *3 (-855)) (-4 *3 (-1222)) (-5 *1 (-1138 *3 *2)) - (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4434) (-6 -4435))))))) + (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4437) (-6 -4438))))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-1138 *4 *2)) - (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4434) (-6 -4435)))))) + (-4 *2 (-13 (-609 (-551) *4) (-10 -7 (-6 -4437) (-6 -4438)))))) ((*1 *2 *2) (-12 (-4 *3 (-855)) (-4 *3 (-1222)) (-5 *1 (-1138 *3 *2)) - (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4434) (-6 -4435))))))) + (-4 *2 (-13 (-609 (-551) *3) (-10 -7 (-6 -4437) (-6 -4438))))))) (((*1 *2 *3) (-12 (-5 *3 (-1272 *4)) (-4 *4 (-1055)) (-4 *2 (-1248 *4)) (-5 *1 (-449 *4 *2)))) @@ -5692,8 +5692,8 @@ (|:| |maps| (-646 (-2 (|:| |arg| *5) (|:| |res| *5)))))) (-5 *1 (-1134 *3 *5)) (-4 *3 (-1248 *5))))) (((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-367)) (-4 *5 (-13 (-376 *4) (-10 -7 (-6 -4435)))) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4435)))) (-5 *1 (-672 *4 *5 *2 *3)) + (|partial| -12 (-4 *4 (-367)) (-4 *5 (-13 (-376 *4) (-10 -7 (-6 -4438)))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438)))) (-5 *1 (-672 *4 *5 *2 *3)) (-4 *3 (-691 *4 *5 *2)))) ((*1 *2 *3 *2) (|partial| -12 (-5 *2 (-1272 *4)) (-5 *3 (-694 *4)) (-4 *4 (-367)) @@ -5757,7 +5757,7 @@ (-4 *2 (-1055))))) (((*1 *2 *3) (-12 (-5 *3 (-694 *2)) (-4 *4 (-1248 *2)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-5 *1 (-504 *2 *4 *5)) (-4 *5 (-415 *2 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) @@ -5767,22 +5767,22 @@ (-5 *1 (-526 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-691 *2 *3 *4)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)) - (|has| *2 (-6 (-4436 "*"))) (-4 *2 (-1055)))) + (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055)))) ((*1 *2 *3) (-12 (-4 *4 (-376 *2)) (-4 *5 (-376 *2)) (-4 *2 (-173)) (-5 *1 (-693 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) - (|has| *2 (-6 (-4436 "*"))) (-4 *2 (-1055))))) + (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055))))) (((*1 *2 *1) (-12 (-4 *1 (-691 *2 *3 *4)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)) - (|has| *2 (-6 (-4436 "*"))) (-4 *2 (-1055)))) + (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055)))) ((*1 *2 *3) (-12 (-4 *4 (-376 *2)) (-4 *5 (-376 *2)) (-4 *2 (-173)) (-5 *1 (-693 *2 *4 *5 *3)) (-4 *3 (-691 *2 *4 *5)))) ((*1 *2 *1) (-12 (-4 *1 (-1129 *3 *2 *4 *5)) (-4 *4 (-239 *3 *2)) (-4 *5 (-239 *3 *2)) - (|has| *2 (-6 (-4436 "*"))) (-4 *2 (-1055))))) + (|has| *2 (-6 (-4439 "*"))) (-4 *2 (-1055))))) (((*1 *2 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (-12 (-4 *1 (-1127 *2)) (-4 *2 (-1222))))) @@ -5935,26 +5935,26 @@ (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) - (-5 *2 (-2 (|:| -3696 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) + (-5 *2 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) (-5 *1 (-994 *6 *7 *8 *9 *4)) (-5 *3 (-646 *9)) (-4 *4 (-1077 *6 *7 *8 *9)))) ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| -12 (-5 *5 (-112)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) - (-5 *2 (-2 (|:| -3696 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) + (-5 *2 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *4) (|:| |ineq| (-646 *9)))) (-5 *1 (-1113 *6 *7 *8 *9 *4)) (-5 *3 (-646 *9)) (-4 *4 (-1077 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-646 *10)) (-5 *5 (-112)) (-4 *10 (-1077 *6 *7 *8 *9)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) (-5 *2 - (-646 (-2 (|:| -3696 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) + (-646 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) (-5 *1 (-994 *6 *7 *8 *9 *10)) (-5 *3 (-646 *9)))) ((*1 *2 *3 *4 *5 *5) (-12 (-5 *4 (-646 *10)) (-5 *5 (-112)) (-4 *10 (-1077 *6 *7 *8 *9)) (-4 *6 (-457)) (-4 *7 (-798)) (-4 *8 (-855)) (-4 *9 (-1071 *6 *7 *8)) (-5 *2 - (-646 (-2 (|:| -3696 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) + (-646 (-2 (|:| -3699 (-646 *9)) (|:| -1717 *10) (|:| |ineq| (-646 *9))))) (-5 *1 (-1113 *6 *7 *8 *9 *10)) (-5 *3 (-646 *9))))) (((*1 *2 *2) (-12 (-5 *2 (-646 (-2 (|:| |val| (-646 *6)) (|:| -1717 *7)))) @@ -6102,7 +6102,7 @@ (-12 (-4 *1 (-1110 *3 *4 *5 *6 *7)) (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *5 (-1107)) (-4 *6 (-1107)) (-4 *7 (-1107)) (-5 *2 (-112))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4301 (-1183)) (|:| -2263 *4)))) + (-12 (-5 *2 (-646 (-2 (|:| -4304 (-1183)) (|:| -2263 *4)))) (-5 *1 (-894 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1107)))) ((*1 *2 *1) (-12 (-4 *3 (-1107)) (-4 *4 (-1107)) (-4 *5 (-1107)) (-4 *6 (-1107)) @@ -6143,7 +6143,7 @@ (-12 (-5 *2 (-1272 (-1108 *3 *4))) (-5 *1 (-1108 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112)))) ((*1 *2 *3 *1) (-12 (-5 *3 (-908 *4)) (-4 *4 (-1107)) (-5 *2 (-112)) (-5 *1 (-911 *4)))) @@ -6279,15 +6279,15 @@ (-4 *3 (-1115 *5 *6 *7 *8)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3653 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) (-5 *1 (-1084 *5 *6)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3653 (-646 (-952 *4)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *4)) (|:| -3656 (-646 (-952 *4)))))) (-5 *1 (-1084 *4 *5)) (-5 *3 (-646 (-952 *4))) (-14 *5 (-646 (-1183))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-112)) (-4 *5 (-13 (-310) (-147))) - (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3653 (-646 (-952 *5)))))) + (-5 *2 (-646 (-2 (|:| -1924 (-1177 *5)) (|:| -3656 (-646 (-952 *5)))))) (-5 *1 (-1084 *5 *6)) (-5 *3 (-646 (-952 *5))) (-14 *6 (-646 (-1183)))))) (((*1 *1 *2) (-12 (-5 *2 (-646 (-1081 *3 *4 *5))) (-4 *3 (-1107)) @@ -6530,10 +6530,10 @@ (-14 *4 (-646 (-1183))))) ((*1 *2 *1) (-12 (-4 *1 (-388 *2 *3)) (-4 *3 (-1107)) (-4 *2 (-1055)))) ((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *5 (-239 (-4398 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *5 (-239 (-4401 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *4) (|:| -2573 *5)) - (-2 (|:| -2572 *4) (|:| -2573 *5)))) + (-1 (-112) (-2 (|:| -2575 *4) (|:| -2576 *5)) + (-2 (|:| -2575 *4) (|:| -2576 *5)))) (-4 *2 (-173)) (-5 *1 (-466 *3 *2 *4 *5 *6 *7)) (-4 *4 (-855)) (-4 *7 (-956 *2 *5 (-869 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-514 *2 *3)) (-4 *3 (-855)) (-4 *2 (-1107)))) @@ -6588,36 +6588,36 @@ (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855))))) (((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -4395 *1) (|:| |gap| (-776)) (|:| -3312 *1))) + (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -3315 *1))) (-4 *1 (-1071 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -4395 *1) (|:| |gap| (-776)) (|:| -3312 *1))) + (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -3315 *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -4395 *3) (|:| |gap| (-776)) (|:| -2161 (-786 *3)) - (|:| -3312 (-786 *3)))) + (-2 (|:| -4398 *3) (|:| |gap| (-776)) (|:| -2161 (-786 *3)) + (|:| -3315 (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-1055)))) ((*1 *2 *1 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) - (-5 *2 (-2 (|:| -4395 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3312 *1))) + (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1071 *4 *5 *3)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -4395 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3312 *1))) + (-5 *2 (-2 (|:| -4398 *1) (|:| |gap| (-776)) (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *1 *1 *1) (-12 (-5 *1 (-786 *2)) (-4 *2 (-1055)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1071 *2 *3 *4)) (-4 *2 (-1055)) (-4 *3 (-798)) (-4 *4 (-855))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| |polnum| (-786 *3)) (|:| |polden| *3) (|:| -3913 (-776)))) + (-5 *2 (-2 (|:| |polnum| (-786 *3)) (|:| |polden| *3) (|:| -3916 (-776)))) (-5 *1 (-786 *3)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3913 (-776)))) + (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3916 (-776)))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-51)) (-5 *1 (-52 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) @@ -6681,23 +6681,23 @@ (-4 *4 (-798)) (-4 *5 (-855)) (-4 *1 (-982 *3 *4 *5 *6)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-1044 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) - (|partial| -3969 + (|partial| -3972 (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-38 (-412 (-551))))) (-3755 (-4 *3 (-38 (-551)))) + (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-3758 (-4 *3 (-38 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-550))) (-3755 (-4 *3 (-38 (-412 (-551))))) + (-12 (-3758 (-4 *3 (-550))) (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) + (-12 (-3758 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))))) ((*1 *1 *2) - (|partial| -3969 + (|partial| -3972 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3755 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -6777,11 +6777,11 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) (-5 *1 (-846)))) ((*1 *2 *1) (-12 @@ -6800,23 +6800,23 @@ (-4 *4 (-798)) (-4 *5 (-855)) (-4 *1 (-982 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1044 *2)) (-4 *2 (-1222)))) ((*1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-38 (-412 (-551))))) (-3755 (-4 *3 (-38 (-551)))) + (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-3758 (-4 *3 (-38 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-550))) (-3755 (-4 *3 (-38 (-412 (-551))))) + (-12 (-3758 (-4 *3 (-550))) (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 *3)) - (-12 (-3755 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) + (-12 (-3758 (-4 *3 (-997 (-551)))) (-4 *3 (-38 (-412 (-551)))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *1 (-1071 *3 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855))))) ((*1 *1 *2) - (-3969 + (-3972 (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) - (-12 (-3755 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) + (-12 (-3758 (-4 *3 (-38 (-412 (-551))))) (-4 *3 (-38 (-551))) (-4 *5 (-619 (-1183)))) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855))) (-12 (-5 *2 (-952 (-551))) (-4 *1 (-1071 *3 *4 *5)) @@ -6847,24 +6847,24 @@ (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -3573 (-786 *3)) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) + (-2 (|:| -3576 (-786 *3)) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3573 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-5 *2 (-2 (|:| -3576 *1) (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3573 (-786 *3)) (|:| |coef1| (-786 *3)))) + (-12 (-5 *2 (-2 (|:| -3576 (-786 *3)) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3573 *1) (|:| |coef1| *1))) (-4 *1 (-1071 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3576 *1) (|:| |coef1| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3573 (-786 *3)) (|:| |coef2| (-786 *3)))) + (-12 (-5 *2 (-2 (|:| -3576 (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *2 (-2 (|:| -3573 *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) + (-5 *2 (-2 (|:| -3576 *1) (|:| |coef2| *1))) (-4 *1 (-1071 *3 *4 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-646 *1)) (-4 *1 (-1071 *3 *4 *5))))) @@ -6977,18 +6977,18 @@ ((*1 *1 *1) (-5 *1 (-933))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1095 (-226))) (-5 *1 (-933)))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))) + (-12 (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) (-5 *4 (-412 (-551))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))) + (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))) + (-12 (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) (-5 *4 (-412 (-551))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *2 *2) (|partial| -12 - (-5 *2 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))) + (-5 *2 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))))) ((*1 *1 *1) (-12 (-4 *2 (-13 (-853) (-367))) (-5 *1 (-1067 *2 *3)) (-4 *3 (-1248 *2))))) @@ -7188,8 +7188,8 @@ (-12 (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-5 *2 (-776)) (-5 *1 (-526 *4 *5 *6 *3)) (-4 *3 (-691 *4 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4435)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4435)))) (-5 *2 (-776)) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-776)) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-5 *2 (-776)) @@ -7216,10 +7216,10 @@ (-12 (-4 *1 (-1059 *3 *4 *5 *6 *7)) (-4 *5 (-1055)) (-4 *6 (-239 *4 *5)) (-4 *7 (-239 *3 *5)) (-4 *5 (-562)) (-5 *2 (-776))))) (((*1 *2 *3) - (-12 (|has| *6 (-6 -4435)) (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) + (-12 (|has| *6 (-6 -4438)) (-4 *4 (-367)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-5 *2 (-646 *6)) (-5 *1 (-526 *4 *5 *6 *3)) (-4 *3 (-691 *4 *5 *6)))) ((*1 *2 *3) - (-12 (|has| *9 (-6 -4435)) (-4 *4 (-562)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) + (-12 (|has| *9 (-6 -4438)) (-4 *4 (-562)) (-4 *5 (-376 *4)) (-4 *6 (-376 *4)) (-4 *7 (-997 *4)) (-4 *8 (-376 *7)) (-4 *9 (-376 *7)) (-5 *2 (-646 *6)) (-5 *1 (-527 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-691 *4 *5 *6)) (-4 *10 (-691 *7 *8 *9)))) @@ -7297,7 +7297,7 @@ (-12 (-5 *3 (-412 (-1177 *2))) (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-1055)) (-4 *2 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))) (-5 *1 (-957 *5 *4 *6 *7 *2)) (-4 *7 (-956 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-412 (-1177 (-412 (-952 *5))))) (-5 *4 (-1183)) @@ -7324,12 +7324,12 @@ (-5 *2 (-412 (-1177 *3))) (-5 *1 (-957 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1177 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))) (-4 *7 (-956 *6 *5 *4)) (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-1055)) (-5 *1 (-957 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) @@ -7343,12 +7343,12 @@ (-4 *2 (-855)) (-5 *1 (-957 *4 *2 *5 *6 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *6)) (-15 -3408 (*6 $)) (-15 -3407 (*6 $))))))) + (-10 -8 (-15 -4390 ($ *6)) (-15 -3411 (*6 $)) (-15 -3410 (*6 $))))))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-412 (-952 *4))) (-4 *4 (-562)) (-5 *2 (-1183)) (-5 *1 (-1046 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))) + (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) (-5 *2 (-646 (-1183))) (-5 *1 (-269)))) ((*1 *2 *3) (-12 (-5 *3 (-1177 *7)) (-4 *7 (-956 *6 *4 *5)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -7366,7 +7366,7 @@ (-5 *2 (-646 *5)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-979 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-797)) (-4 *5 (-855)) (-5 *2 (-646 *5)))) @@ -7402,7 +7402,7 @@ (-4 *2 (-13 (-1107) (-10 -8 (-15 * ($ $ $)))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-925)) (-5 *1 (-1037 *2)) - (-4 *2 (-13 (-1107) (-10 -8 (-15 -4280 ($ $ $)))))))) + (-4 *2 (-13 (-1107) (-10 -8 (-15 -4283 ($ $ $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-646 (-1272 *5))) (-5 *4 (-551)) (-5 *2 (-1272 *5)) (-5 *1 (-1036 *5)) (-4 *5 (-367)) (-4 *5 (-372)) (-4 *5 (-1055))))) @@ -7475,10 +7475,10 @@ (-12 (-5 *3 (-776)) (-5 *2 (-694 (-952 *4))) (-5 *1 (-1035 *4)) (-4 *4 (-1055))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-694 *4)) (-5 *3 (-925)) (|has| *4 (-6 (-4436 "*"))) + (-12 (-5 *2 (-694 *4)) (-5 *3 (-925)) (|has| *4 (-6 (-4439 "*"))) (-4 *4 (-1055)) (-5 *1 (-1035 *4)))) ((*1 *2 *2 *3) - (-12 (-5 *2 (-646 (-694 *4))) (-5 *3 (-925)) (|has| *4 (-6 (-4436 "*"))) + (-12 (-5 *2 (-646 (-694 *4))) (-5 *3 (-925)) (|has| *4 (-6 (-4439 "*"))) (-4 *4 (-1055)) (-5 *1 (-1035 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-694 (-412 (-952 (-551))))) (-5 *2 (-646 (-694 (-317 (-551))))) @@ -7511,7 +7511,7 @@ ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1032 *3)) (-4 *3 (-1222))))) (((*1 *2 *2 *3) (-12 (-4 *3 (-367)) (-5 *1 (-1031 *3 *2)) (-4 *2 (-663 *3)))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-5 *2 (-2 (|:| -3696 *3) (|:| -2911 (-646 *5)))) + (-12 (-4 *5 (-367)) (-5 *2 (-2 (|:| -3699 *3) (|:| -2914 (-646 *5)))) (-5 *1 (-1031 *5 *3)) (-5 *4 (-646 *5)) (-4 *3 (-663 *5))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1067 (-1030 *4) (-1177 (-1030 *4)))) (-5 *3 (-868)) @@ -7520,38 +7520,38 @@ (|partial| -12 (-5 *2 (-1067 (-1030 *3) (-1177 (-1030 *3)))) (-5 *1 (-1030 *3)) (-4 *3 (-13 (-853) (-367) (-1026)))))) (((*1 *2 *3) - (-12 (-5 *2 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) - (-5 *4 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))))) + (-5 *4 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) (-5 *4 (-412 (-551))))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3551 *5) (|:| -3550 *5)))) + (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *5) (|:| -3553 *5)))) (-5 *1 (-1027 *3)) (-4 *3 (-1248 (-551))) - (-5 *4 (-2 (|:| -3551 *5) (|:| -3550 *5))))) + (-5 *4 (-2 (|:| -3554 *5) (|:| -3553 *5))))) ((*1 *2 *3) - (-12 (-5 *2 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))))) ((*1 *2 *3 *4) - (-12 (-5 *2 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *2 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 (-412 (-551)))) - (-5 *4 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))))) + (-5 *4 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3551 *4) (|:| -3550 *4)))) + (-12 (-5 *4 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *4) (|:| -3553 *4)))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *4)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3551 *5) (|:| -3550 *5)))) + (-12 (-5 *5 (-412 (-551))) (-5 *2 (-646 (-2 (|:| -3554 *5) (|:| -3553 *5)))) (-5 *1 (-1028 *3)) (-4 *3 (-1248 *5)) - (-5 *4 (-2 (|:| -3551 *5) (|:| -3550 *5)))))) + (-5 *4 (-2 (|:| -3554 *5) (|:| -3553 *5)))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *3 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *2 (-646 (-412 (-551)))) (-5 *1 (-1027 *4)) (-4 *4 (-1248 (-551)))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551))))) + (-12 (-5 *3 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551))))) (-5 *2 (-412 (-551))) (-5 *1 (-1027 *4)) (-4 *4 (-1248 (-551)))))) (((*1 *2 *2) (-12 (-5 *2 (-113)) (-4 *3 (-562)) (-5 *1 (-32 *3 *4)) (-4 *4 (-426 *3)))) @@ -7579,7 +7579,7 @@ (-12 (-5 *3 (-1272 *6)) (-5 *4 (-1272 (-551))) (-5 *5 (-551)) (-4 *6 (-1107)) (-5 *2 (-1 *6)) (-5 *1 (-1023 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3835 *4) (|:| -1628 (-551))))) (-4 *4 (-1107)) + (-12 (-5 *3 (-646 (-2 (|:| -3838 *4) (|:| -1628 (-551))))) (-4 *4 (-1107)) (-5 *2 (-1 *4)) (-5 *1 (-1023 *4))))) (((*1 *2 *3 *3 *3) (|partial| -12 (-4 *4 (-13 (-367) (-147) (-1044 (-551)))) (-4 *5 (-1248 *4)) @@ -7589,14 +7589,14 @@ (-4 *5 (-13 (-367) (-147) (-1044 (-551)))) (-5 *2 (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |h| *6) (|:| |c1| (-412 *6)) - (|:| |c2| (-412 *6)) (|:| -3506 *6))) + (|:| |c2| (-412 *6)) (|:| -3509 *6))) (-5 *1 (-1022 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *3 *3 *3 *4 *5) (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1248 *6)) (-4 *6 (-13 (-367) (-147) (-1044 *4))) (-5 *4 (-551)) (-5 *2 (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) - (|:| -3696 + (|:| -3699 (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) (|:| |beta| *3))))) (-5 *1 (-1021 *6 *3))))) @@ -7608,7 +7608,7 @@ (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)))) (-5 *2 - (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |c| (-412 *6)) (|:| -3506 *6))) + (-2 (|:| |a| *6) (|:| |b| (-412 *6)) (|:| |c| (-412 *6)) (|:| -3509 *6))) (-5 *1 (-1021 *5 *6)) (-5 *3 (-412 *6))))) (((*1 *2 *3 *4 *4 *4 *5 *6 *7) (|partial| -12 (-5 *5 (-1183)) @@ -7635,7 +7635,7 @@ (-5 *7 (-1 (-3 (-2 (|:| -2327 *4) (|:| |coeff| *4)) "failed") *4 *4)) (-4 *4 (-13 (-1208) (-27) (-426 *8))) (-4 *8 (-13 (-457) (-147) (-1044 *3) (-644 *3))) (-5 *3 (-551)) - (-5 *2 (-2 (|:| |ans| *4) (|:| -3550 *4) (|:| |sol?| (-112)))) + (-5 *2 (-2 (|:| |ans| *4) (|:| -3553 *4) (|:| |sol?| (-112)))) (-5 *1 (-1019 *8 *4))))) (((*1 *1 *1) (-12 (-5 *1 (-343 *2 *3 *4)) (-14 *2 (-646 (-1183))) (-14 *3 (-646 (-1183))) @@ -7658,9 +7658,9 @@ (((*1 *2 *1 *1) (-12 (-4 *1 (-1016 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112))))) (((*1 *1 *1 *2) - (-12 (-5 *2 (-646 *1)) (|has| *1 (-6 -4435)) (-4 *1 (-1016 *3)) + (-12 (-5 *2 (-646 *1)) (|has| *1 (-6 -4438)) (-4 *1 (-1016 *3)) (-4 *3 (-1222))))) -(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-1016 *2)) (-4 *2 (-1222))))) +(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-1016 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) (|partial| -12 (-4 *1 (-166 *3)) (-4 *3 (-173)) (-4 *3 (-550)) (-5 *2 (-412 (-551))))) @@ -7725,7 +7725,7 @@ (((*1 *1 *2 *2) (-12 (-5 *2 (-646 (-551))) (-5 *1 (-1010 *3)) (-14 *3 (-551))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-410 *5)) (-4 *5 (-562)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *5) (|:| |radicand| (-646 *5)))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *5) (|:| |radicand| (-646 *5)))) (-5 *1 (-323 *5)) (-5 *4 (-776)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-551))))) (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-1107)) (-5 *1 (-1006 *3))))) @@ -7821,39 +7821,39 @@ (-12 (-4 *3 (-1248 *2)) (-4 *2 (-1248 *4)) (-5 *1 (-991 *4 *2 *3 *5)) (-4 *4 (-354)) (-4 *5 (-729 *2 *3))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) (-4 *5 (-562)) (-5 *1 (-737 *4 *3 *5 *2)) (-4 *2 (-956 (-412 (-952 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) - (-15 -4272 ((-3 $ #1="failed") (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) + (-15 -4275 ((-3 $ #1="failed") (-1183)))))) (-5 *1 (-990 *4 *5 *3 *2)) (-4 *2 (-956 (-952 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-646 *6)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) (-15 -4272 ((-3 $ #1#) (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ #1#) (-1183)))))) (-4 *4 (-1055)) (-4 *5 (-798)) (-5 *1 (-990 *4 *5 *6 *2)) (-4 *2 (-956 (-952 *4) *5 *6))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $))))) + (-12 (-4 *4 (-798)) (-4 *3 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) (-4 *5 (-562)) (-5 *1 (-737 *4 *3 *5 *2)) (-4 *2 (-956 (-412 (-952 *5)) *4 *3)))) ((*1 *2 *2 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) - (-15 -4272 ((-3 $ #1="failed") (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) + (-15 -4275 ((-3 $ #1="failed") (-1183)))))) (-5 *1 (-990 *4 *5 *3 *2)) (-4 *2 (-956 (-952 *4) *5 *3)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-646 *6)) (-4 *6 (-13 (-855) - (-10 -8 (-15 -4411 ((-1183) $)) (-15 -4272 ((-3 $ #1#) (-1183)))))) + (-10 -8 (-15 -4414 ((-1183) $)) (-15 -4275 ((-3 $ #1#) (-1183)))))) (-4 *4 (-1055)) (-4 *5 (-798)) (-5 *1 (-990 *4 *5 *6 *2)) (-4 *2 (-956 (-952 *4) *5 *6))))) (((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) @@ -7953,7 +7953,7 @@ (((*1 *2 *3) (|partial| -12 (-4 *4 (-562)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-1071 *4 *5 *6)) - (-5 *2 (-2 (|:| |bas| (-481 *4 *5 *6 *7)) (|:| -3757 (-646 *7)))) + (-5 *2 (-2 (|:| |bas| (-481 *4 *5 *6 *7)) (|:| -3760 (-646 *7)))) (-5 *1 (-983 *4 *5 *6 *7)) (-5 *3 (-646 *7))))) (((*1 *2 *2) (-12 (-5 *2 (-646 *6)) (-4 *6 (-1071 *3 *4 *5)) (-4 *3 (-562)) (-4 *4 (-798)) @@ -8062,7 +8062,7 @@ ((*1 *2 *2) (-12 (-5 *2 (-646 (-908 *3))) (-5 *1 (-908 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) (-12 (-4 *4 (-1055)) (-4 *5 (-798)) (-4 *3 (-855)) (-4 *6 (-1071 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -3543 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -3546 *1) (|:| |upper| *1))) (-4 *1 (-982 *4 *5 *3 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-982 *3 *4 *5 *6)) (-4 *3 (-1055)) (-4 *4 (-798)) (-4 *5 (-855)) @@ -8106,10 +8106,10 @@ (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1055)) (-4 *3 (-797)))) ((*1 *2 *1) (-12 (-4 *1 (-388 *3 *2)) (-4 *3 (-1055)) (-4 *2 (-1107)))) ((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4398 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *6 (-239 (-4401 *3) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2572 *5) (|:| -2573 *6)) - (-2 (|:| -2572 *5) (|:| -2573 *6)))) + (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) + (-2 (|:| -2575 *5) (|:| -2576 *6)))) (-5 *2 (-718 *5 *6 *7)) (-5 *1 (-466 *3 *4 *5 *6 *7 *8)) (-4 *5 (-855)) (-4 *8 (-956 *4 *6 (-869 *3))))) ((*1 *2 *1) @@ -8121,10 +8121,10 @@ (-12 (-5 *3 (-646 (-925))) (-5 *1 (-152 *4 *2 *5)) (-14 *4 (-925)) (-4 *2 (-367)) (-14 *5 (-999 *4 *2)))) ((*1 *1 *2 *3) - (-12 (-5 *3 (-718 *5 *6 *7)) (-4 *5 (-855)) (-4 *6 (-239 (-4398 *4) (-776))) + (-12 (-5 *3 (-718 *5 *6 *7)) (-4 *5 (-855)) (-4 *6 (-239 (-4401 *4) (-776))) (-14 *7 - (-1 (-112) (-2 (|:| -2572 *5) (|:| -2573 *6)) - (-2 (|:| -2572 *5) (|:| -2573 *6)))) + (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *6)) + (-2 (|:| -2575 *5) (|:| -2576 *6)))) (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-5 *1 (-466 *4 *2 *5 *6 *7 *8)) (-4 *8 (-956 *2 *6 (-869 *4))))) ((*1 *1 *2 *3) (-12 (-4 *1 (-514 *2 *3)) (-4 *2 (-1107)) (-4 *3 (-855)))) @@ -8165,11 +8165,11 @@ (-12 (-5 *2 (-646 (-646 (-551)))) (-5 *1 (-977)) (-5 *3 (-646 (-551)))))) (((*1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-977))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4197 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4200 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4197 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4200 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-562)) (-5 *1 (-975 *2 *3)) (-4 *3 (-1248 *2))))) (((*1 *2 *2 *2 *2 *3) @@ -8179,22 +8179,22 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-776)) (-4 *2 (-562)) (-5 *1 (-975 *2 *4)) (-4 *4 (-1248 *2))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-310)))) + (-12 (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-310)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *3 (-1107)) (-5 *2 (-2 (|:| |lm| *1) (|:| |rm| *1))) (-4 *1 (-390 *3)))) ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -2161 (-776)) (|:| -3312 (-776)))) (-5 *1 (-776)))) + (-12 (-5 *2 (-2 (|:| -2161 (-776)) (|:| -3315 (-776)))) (-5 *1 (-776)))) ((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-457)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| -3288 *4))) (-5 *1 (-975 *4 *3)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| -3291 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-457)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3288 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3291 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *2 (-562)) (-4 *2 (-457)) (-5 *1 (-975 *2 *3)) (-4 *3 (-1248 *2))))) @@ -8205,21 +8205,21 @@ (-12 (-4 *4 (-562)) (-5 *2 (-646 *3)) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4198 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4201 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4198 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4201 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3573 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3576 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3573 *3))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3576 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3573 *3))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3576 *3))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) @@ -8249,18 +8249,18 @@ (((*1 *2 *2 *2 *3) (-12 (-5 *3 (-776)) (-4 *4 (-562)) (-5 *1 (-975 *4 *2)) (-4 *2 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -4197 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -4200 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4197 *4))) + (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4200 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4197 *4))) + (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -4200 *4))) (-5 *1 (-975 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *1) - (-12 (-4 *1 (-409)) (-3755 (|has| *1 (-6 -4425))) - (-3755 (|has| *1 (-6 -4417))))) + (-12 (-4 *1 (-409)) (-3758 (|has| *1 (-6 -4428))) + (-3758 (|has| *1 (-6 -4420))))) ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1107)) (-4 *2 (-855)))) ((*1 *1) (-4 *1 (-849))) ((*1 *1 *1 *1) (-4 *1 (-855))) ((*1 *2 *1) (-12 (-4 *1 (-974 *2)) (-4 *2 (-855))))) @@ -8325,14 +8325,14 @@ (-12 (-5 *3 (-646 (-952 *5))) (-5 *4 (-646 (-1183))) (-4 *5 (-13 (-367) (-147))) (-5 *2 - (-2 (|:| -4395 (-646 (-551))) (|:| |poly| (-646 (-1177 *5))) + (-2 (|:| -4398 (-646 (-551))) (|:| |poly| (-646 (-1177 *5))) (|:| |prim| (-1177 *5)))) (-5 *1 (-967 *5)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-646 (-952 *6))) (-5 *4 (-646 (-1183))) (-5 *5 (-1183)) (-4 *6 (-13 (-367) (-147))) (-5 *2 - (-2 (|:| -4395 (-646 (-551))) (|:| |poly| (-646 (-1177 *6))) + (-2 (|:| -4398 (-646 (-551))) (|:| |poly| (-646 (-1177 *6))) (|:| |prim| (-1177 *6)))) (-5 *1 (-967 *6))))) (((*1 *1 *2 *3) @@ -8352,69 +8352,69 @@ (((*1 *1 *2) (-12 (-5 *2 (-1126)) (-5 *1 (-960))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *3 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *3) (|:| |radicand| (-646 *3)))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| (-646 *3)))) (-5 *1 (-959 *5 *6 *7 *3 *8)) (-5 *4 (-776)) (-4 *8 (-13 (-367) - (-10 -8 (-15 -4387 ($ *3)) (-15 -3408 (*3 $)) (-15 -3407 (*3 $)))))))) + (-10 -8 (-15 -4390 ($ *3)) (-15 -3411 (*3 $)) (-15 -3410 (*3 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *7 (-457)) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *3) (|:| |radicand| *3))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| *3))) (-5 *1 (-959 *5 *6 *7 *8 *3)) (-5 *4 (-776)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *8)) (-15 -3408 (*8 $)) (-15 -3407 (*8 $)))))))) + (-10 -8 (-15 -4390 ($ *8)) (-15 -3411 (*8 $)) (-15 -3410 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-412 (-551))) (-4 *5 (-798)) (-4 *6 (-855)) (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *9) (|:| |radicand| *9))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *9) (|:| |radicand| *9))) (-5 *1 (-959 *5 *6 *7 *8 *9)) (-5 *4 (-776)) (-4 *9 (-13 (-367) - (-10 -8 (-15 -4387 ($ *8)) (-15 -3408 (*8 $)) (-15 -3407 (*8 $)))))))) + (-10 -8 (-15 -4390 ($ *8)) (-15 -3411 (*8 $)) (-15 -3410 (*8 $)))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-798)) (-4 *6 (-855)) (-4 *3 (-562)) (-4 *7 (-956 *3 *5 *6)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *8) (|:| |radicand| *8))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *8) (|:| |radicand| *8))) (-5 *1 (-959 *5 *6 *3 *7 *8)) (-5 *4 (-776)) (-4 *8 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-1055)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| |val| *1) (|:| -2573 (-551)))) (-4 *1 (-426 *3)))) + (-5 *2 (-2 (|:| |val| *1) (|:| -2576 (-551)))) (-4 *1 (-426 *3)))) ((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2573 (-896 *3)))) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2576 (-896 *3)))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *3) (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2573 (-551)))) + (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2576 (-551)))) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-1183)) (-4 *4 (-1055)) (-4 *4 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2573 (-551)))) (-4 *1 (-426 *4)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *4)))) ((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-113)) (-4 *4 (-1055)) (-4 *4 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2573 (-551)))) (-4 *1 (-426 *4)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *4)))) ((*1 *2 *1) (|partial| -12 (-4 *3 (-1118)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2573 (-551)))) (-4 *1 (-426 *3)))) + (-5 *2 (-2 (|:| |var| (-616 *1)) (|:| -2576 (-551)))) (-4 *1 (-426 *3)))) ((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2573 (-776)))) + (|partial| -12 (-5 *2 (-2 (|:| |val| (-896 *3)) (|:| -2576 (-776)))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (|partial| -12 (-4 *1 (-956 *3 *4 *5)) (-4 *3 (-1055)) (-4 *4 (-798)) - (-4 *5 (-855)) (-5 *2 (-2 (|:| |var| *5) (|:| -2573 (-776)))))) + (-4 *5 (-855)) (-5 *2 (-2 (|:| |var| *5) (|:| -2576 (-776)))))) ((*1 *2 *3) (|partial| -12 (-4 *4 (-798)) (-4 *5 (-855)) (-4 *6 (-1055)) - (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2573 (-551)))) + (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2576 (-551)))) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-1118)) (-4 *3 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-426 *3)))) @@ -8428,7 +8428,7 @@ (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-646 *3)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-426 *3)))) @@ -8442,7 +8442,7 @@ (-4 *7 (-956 *6 *4 *5)) (-5 *2 (-646 *3)) (-5 *1 (-957 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1) (-12 (-4 *3 (-1055)) (-4 *4 (-1107)) (-5 *2 (-646 *1)) (-4 *1 (-388 *3 *4)))) ((*1 *2 *1) @@ -8723,7 +8723,7 @@ (-12 (-5 *3 (-646 - (-2 (|:| -3522 (-776)) + (-2 (|:| -3525 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *7) (|:| |rows| (-646 (-551))) @@ -8736,7 +8736,7 @@ (-12 (-5 *3 (-646 - (-2 (|:| -3522 (-776)) + (-2 (|:| -3525 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *7) (|:| |rows| (-646 (-551))) @@ -8753,7 +8753,7 @@ (-12 (-5 *3 (-2 (|:| -1757 (-694 (-412 (-952 *4)))) (|:| |vec| (-646 (-412 (-952 *4)))) - (|:| -3522 (-776)) (|:| |rows| (-646 (-551))) (|:| |cols| (-646 (-551))))) + (|:| -3525 (-776)) (|:| |rows| (-646 (-551))) (|:| |cols| (-646 (-551))))) (-4 *4 (-13 (-310) (-147))) (-4 *5 (-13 (-855) (-619 (-1183)))) (-4 *6 (-798)) (-5 *2 @@ -8773,7 +8773,7 @@ (-4 *6 (-13 (-855) (-619 (-1183)))) (-4 *7 (-798)) (-5 *2 (-646 - (-2 (|:| -3522 (-776)) + (-2 (|:| -3525 (-776)) (|:| |eqns| (-646 (-2 (|:| |det| *8) (|:| |rows| (-646 (-551))) @@ -8946,7 +8946,7 @@ (-12 (-5 *3 (-646 *4)) (-4 *4 (-367)) (-4 *2 (-1248 *4)) (-5 *1 (-929 *4 *2))))) (((*1 *2 *3) - (-12 (-4 *1 (-927)) (-5 *2 (-2 (|:| -4395 (-646 *1)) (|:| -2581 *1))) + (-12 (-4 *1 (-927)) (-5 *2 (-2 (|:| -4398 (-646 *1)) (|:| -2584 *1))) (-5 *3 (-646 *1))))) (((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-646 *1)) (-4 *1 (-927))))) (((*1 *2 *2 *3) @@ -9026,13 +9026,13 @@ (|partial| -12 (-5 *3 (-337 *5 *6 *7 *8)) (-4 *5 (-426 *4)) (-4 *6 (-1248 *5)) (-4 *7 (-1248 (-412 *6))) (-4 *8 (-346 *5 *6 *7)) (-4 *4 (-13 (-562) (-1044 (-551)))) - (-5 *2 (-2 (|:| -4212 (-776)) (|:| -2555 *8))) + (-5 *2 (-2 (|:| -4215 (-776)) (|:| -2558 *8))) (-5 *1 (-917 *4 *5 *6 *7 *8)))) ((*1 *2 *3) (|partial| -12 (-5 *3 (-337 (-412 (-551)) *4 *5 *6)) (-4 *4 (-1248 (-412 (-551)))) (-4 *5 (-1248 (-412 *4))) (-4 *6 (-346 (-412 (-551)) *4 *5)) - (-5 *2 (-2 (|:| -4212 (-776)) (|:| -2555 *6))) (-5 *1 (-918 *4 *5 *6))))) + (-5 *2 (-2 (|:| -4215 (-776)) (|:| -2558 *6))) (-5 *1 (-918 *4 *5 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-337 *5 *6 *7 *8)) (-4 *5 (-426 *4)) (-4 *6 (-1248 *5)) (-4 *7 (-1248 (-412 *6))) (-4 *8 (-346 *5 *6 *7)) @@ -9155,7 +9155,7 @@ (((*1 *1 *2) (-12 (-5 *2 (-646 (-646 *3))) (-4 *3 (-1107)) (-4 *1 (-910 *3))))) (((*1 *2 *3) (-12 (-5 *3 (-1148 *4 *2)) (-14 *4 (-925)) - (-4 *2 (-13 (-1055) (-10 -7 (-6 (-4436 "*"))))) (-5 *1 (-909 *4 *2))))) + (-4 *2 (-13 (-1055) (-10 -7 (-6 (-4439 "*"))))) (-5 *1 (-909 *4 *2))))) (((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |preimage| (-646 *3)) (|:| |image| (-646 *3)))) (-5 *1 (-908 *3)) (-4 *3 (-1107))))) @@ -9194,13 +9194,13 @@ (((*1 *2 *3) (-12 (-5 *3 (-774)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *1 (-570)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-774)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *1 (-570)))) ((*1 *2 *3 *4) @@ -9209,7 +9209,7 @@ (-2 (|:| |fn| (-317 (-226))) (|:| -1612 (-646 (-1095 (-847 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)) + (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)) (|:| |extra| (-1041)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-792)) (-5 *3 (-1069)) @@ -9218,7 +9218,7 @@ (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)) + (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)) (|:| |extra| (-1041)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-805)) (-5 *3 (-1069)) @@ -9227,40 +9227,40 @@ (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (-5 *2 (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-813)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-810)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-813)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-810)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-844)) (-5 *3 (-1069)) - (-5 *4 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))) - (-5 *2 (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)))))) + (-5 *4 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) + (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-844)) (-5 *3 (-1069)) (-5 *4 - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) - (-5 *2 (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-846)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-845)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-846)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-845)))) ((*1 *2 *3 *4) @@ -9274,17 +9274,17 @@ (|:| |dFinish| (-694 (-226)))))) (|:| |f| (-646 (-646 (-317 (-226))))) (|:| |st| (-1165)) (|:| |tol| (-226)))) - (-5 *2 (-2 (|:| -3080 (-382)) (|:| |explanations| (-1165)))))) + (-5 *2 (-2 (|:| -3083 (-382)) (|:| |explanations| (-1165)))))) ((*1 *2 *3) (-12 (-5 *3 (-904)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-903)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-904)) (-5 *4 (-1069)) (-5 *2 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *1 (-903))))) (((*1 *2 *2 *3) @@ -9342,7 +9342,7 @@ (-12 (-5 *3 (-646 *6)) (-5 *4 (-896 *5)) (-4 *5 (-1107)) (-4 *6 (-1222)) (-5 *2 (-112)) (-5 *1 (-897 *5 *6))))) (((*1 *2 *1) - (|partial| -12 (-5 *2 (-2 (|:| -2911 (-113)) (|:| |arg| (-646 (-896 *3))))) + (|partial| -12 (-5 *2 (-2 (|:| -2914 (-113)) (|:| |arg| (-646 (-896 *3))))) (-5 *1 (-896 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) (|partial| -12 (-5 *3 (-113)) (-5 *2 (-646 (-896 *4))) (-5 *1 (-896 *4)) @@ -9400,11 +9400,11 @@ (-4 *3 (-1044 (-1183))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-5 *2 (-646 (-296 (-952 *3)))) (-5 *1 (-893 *5 *3 *4)) - (-4 *3 (-1055)) (-3755 (-4 *3 (-1044 (-1183)))) (-4 *3 (-892 *5)) + (-4 *3 (-1055)) (-3758 (-4 *3 (-1044 (-1183)))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-5 *2 (-894 *5 *3)) (-5 *1 (-893 *5 *3 *4)) - (-3755 (-4 *3 (-1044 (-1183)))) (-3755 (-4 *3 (-1055))) (-4 *3 (-892 *5)) + (-3758 (-4 *3 (-1044 (-1183)))) (-3758 (-4 *3 (-1055))) (-4 *3 (-892 *5)) (-4 *4 (-619 (-896 *5)))))) (((*1 *2 *1 *3) (-12 (-4 *1 (-301)) (-5 *3 (-1183)) (-5 *2 (-112)))) ((*1 *2 *1 *3) (-12 (-4 *1 (-301)) (-5 *3 (-113)) (-5 *2 (-112)))) @@ -9468,7 +9468,7 @@ (-4 *4 (-875 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-408 *3)) (-4 *3 (-409)))) ((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-408 *3)) (-4 *3 (-409)))) - ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4425)) (-4 *1 (-409)))) + ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925)))) ((*1 *2 *1) (-12 (-4 *1 (-875 *3)) (-5 *2 (-1160 (-551)))))) (((*1 *2 *1) @@ -9505,7 +9505,7 @@ (|partial| -12 (-5 *3 (-776)) (-4 *5 (-367)) (-5 *2 (-175 *6)) (-5 *1 (-872 *5 *4 *6)) (-4 *4 (-1265 *5)) (-4 *6 (-1248 *5))))) (((*1 *2 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-5 *2 (-646 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-646 *3)) (-5 *1 (-741 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (-12 (-5 *2 (-646 (-444))) (-5 *1 (-870))))) @@ -9656,34 +9656,34 @@ (((*1 *2 *3 *2) (-12 (-5 *3 (-776)) (-5 *1 (-861 *2)) (-4 *2 (-173))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-367)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) + (-12 (-4 *4 (-367)) (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-771 *3 *4)) (-4 *3 (-713 *4)))) ((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-367)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-562)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| -2161 *1) (|:| -3312 *1))) (-4 *1 (-857 *3)))) + (-5 *2 (-2 (|:| -2161 *1) (|:| -3315 *1))) (-4 *1 (-857 *3)))) ((*1 *2 *3 *3 *4) (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1055)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-858 *5 *3)) + (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-858 *5 *3)) (-4 *3 (-857 *5))))) (((*1 *2 *3 *4 *2) (-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-653 *5)) (-4 *5 (-1055)) @@ -9708,7 +9708,7 @@ ((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2581 *1))) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) (-4 *1 (-857 *3))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) @@ -9718,13 +9718,13 @@ (((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *2 *1 *1) (-12 (-4 *3 (-367)) (-4 *3 (-1055)) - (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2581 *1))) + (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) (-4 *1 (-857 *3))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-367)) (-5 *1 (-771 *2 *3)) (-4 *2 (-713 *3)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-857 *2)) (-4 *2 (-1055)) (-4 *2 (-367))))) (((*1 *1) - (-12 (-4 *1 (-409)) (-3755 (|has| *1 (-6 -4425))) - (-3755 (|has| *1 (-6 -4417))))) + (-12 (-4 *1 (-409)) (-3758 (|has| *1 (-6 -4428))) + (-3758 (|has| *1 (-6 -4420))))) ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1107)) (-4 *2 (-855)))) ((*1 *2 *1) (-12 (-4 *1 (-835 *2)) (-4 *2 (-855)))) ((*1 *1) (-4 *1 (-849))) ((*1 *1 *1 *1) (-4 *1 (-855)))) @@ -9770,13 +9770,13 @@ (((*1 *2 *3) (-12 (-4 *1 (-844)) (-5 *3 - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *2 (-1041)))) ((*1 *2 *3) (-12 (-4 *1 (-844)) - (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))) + (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) (-5 *2 (-1041))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-215 (-507))) (-5 *1 (-842))))) (((*1 *2 *1) (-12 (-4 *1 (-841 *3)) (-4 *3 (-1107)) (-5 *2 (-55))))) @@ -9866,7 +9866,7 @@ (((*1 *1) (-5 *1 (-829)))) (((*1 *2 *1) (-12 (-5 *2 (-1183)) (-5 *1 (-828))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |cd| (-1165)) (|:| -3982 (-1165)))) (-5 *1 (-828))))) + (-12 (-5 *2 (-2 (|:| |cd| (-1165)) (|:| -3985 (-1165)))) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-1165)) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-1183)) (-5 *1 (-828))))) (((*1 *2 *1) (-12 (-5 *2 (-226)) (-5 *1 (-828))))) @@ -9948,7 +9948,7 @@ (-2 (|:| A (-694 *5)) (|:| |eqs| (-646 - (-2 (|:| C (-694 *5)) (|:| |g| (-1272 *5)) (|:| -3696 *6) + (-2 (|:| C (-694 *5)) (|:| |g| (-1272 *5)) (|:| -3699 *6) (|:| |rh| *5)))))) (-5 *1 (-818 *5 *6)) (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *6 (-663 *5)))) @@ -9995,23 +9995,23 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3696 *3)))) + (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3699 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) (-4 *3 (-663 *6)) (-4 *7 (-663 (-412 *6))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3696 (-661 *6 (-412 *6)))))) + (-5 *2 (-646 (-2 (|:| |poly| *6) (|:| -3699 (-661 *6 (-412 *6)))))) (-5 *1 (-817 *5 *6)) (-5 *3 (-661 *6 (-412 *6)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 (-646 *7) *7 (-1177 *7))) (-5 *5 (-1 (-410 *7) *7)) (-4 *7 (-1248 *6)) (-4 *6 (-13 (-367) (-147) (-1044 (-412 (-551))))) - (-5 *2 (-646 (-2 (|:| |frac| (-412 *7)) (|:| -3696 *3)))) + (-5 *2 (-646 (-2 (|:| |frac| (-412 *7)) (|:| -3699 *3)))) (-5 *1 (-814 *6 *7 *3 *8)) (-4 *3 (-663 *7)) (-4 *8 (-663 (-412 *7))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-410 *6) *6)) (-4 *6 (-1248 *5)) (-4 *5 (-13 (-367) (-147) (-1044 (-551)) (-1044 (-412 (-551))))) - (-5 *2 (-646 (-2 (|:| |frac| (-412 *6)) (|:| -3696 (-661 *6 (-412 *6)))))) + (-5 *2 (-646 (-2 (|:| |frac| (-412 *6)) (|:| -3699 (-661 *6 (-412 *6)))))) (-5 *1 (-817 *5 *6)) (-5 *3 (-661 *6 (-412 *6)))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-367)) (-4 *7 (-1248 *5)) (-4 *4 (-729 *5 *7)) @@ -10053,11 +10053,11 @@ (((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-646 *5) *6)) (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *6 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4393 *5) (|:| -3696 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) + (-5 *2 (-646 (-2 (|:| -4396 *5) (|:| -3699 *3)))) (-5 *1 (-814 *5 *6 *3 *7)) (-4 *3 (-663 *6)) (-4 *7 (-663 (-412 *6)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -3696 *5)))) + (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -3699 *5)))) (-5 *1 (-814 *4 *5 *3 *6)) (-4 *3 (-663 *5)) (-4 *6 (-663 (-412 *5)))))) (((*1 *2 *3) (-12 (-4 *2 (-1248 *4)) (-5 *1 (-814 *4 *2 *3 *5)) @@ -10073,19 +10073,19 @@ (-4 *3 (-663 (-412 *2)))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| -4213 *5) (|:| -3655 *5)))) (-5 *1 (-812 *4 *5 *3 *6)) + (-5 *2 (-646 (-2 (|:| -4216 *5) (|:| -3658 *5)))) (-5 *1 (-812 *4 *5 *3 *6)) (-4 *3 (-663 *5)) (-4 *6 (-663 (-412 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *4 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4213 *4) (|:| -3655 *4)))) (-5 *1 (-812 *5 *4 *3 *6)) + (-5 *2 (-646 (-2 (|:| -4216 *4) (|:| -3658 *4)))) (-5 *1 (-812 *5 *4 *3 *6)) (-4 *3 (-663 *4)) (-4 *6 (-663 (-412 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *5 (-1248 *4)) - (-5 *2 (-646 (-2 (|:| -4213 *5) (|:| -3655 *5)))) (-5 *1 (-812 *4 *5 *6 *3)) + (-5 *2 (-646 (-2 (|:| -4216 *5) (|:| -3658 *5)))) (-5 *1 (-812 *4 *5 *6 *3)) (-4 *6 (-663 *5)) (-4 *3 (-663 (-412 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-13 (-367) (-147) (-1044 (-412 (-551))))) (-4 *4 (-1248 *5)) - (-5 *2 (-646 (-2 (|:| -4213 *4) (|:| -3655 *4)))) (-5 *1 (-812 *5 *4 *6 *3)) + (-5 *2 (-646 (-2 (|:| -4216 *4) (|:| -3658 *4)))) (-5 *1 (-812 *5 *4 *6 *3)) (-4 *6 (-663 *4)) (-4 *3 (-663 (-412 *4)))))) (((*1 *2 *3 *4) (|partial| -12 (-5 *4 (-412 *2)) (-4 *2 (-1248 *5)) @@ -10125,7 +10125,7 @@ (-5 *2 (-646 (-2 - (|:| -4301 + (|:| -4304 (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) (|:| |fn| (-1272 (-317 (-226)))) (|:| |yinit| (-646 (-226))) (|:| |intvals| (-646 (-226))) (|:| |g| (-317 (-226))) @@ -10181,7 +10181,7 @@ (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-3969 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) + (-3972 (-12 (-5 *1 (-296 *2)) (-4 *2 (-367)) (-4 *2 (-1222))) (-12 (-5 *1 (-296 *2)) (-4 *2 (-478)) (-4 *2 (-1222))))) ((*1 *1 *1) (-4 *1 (-478))) ((*1 *2 *2) (-12 (-5 *2 (-1272 *3)) (-4 *3 (-354)) (-5 *1 (-533 *3)))) @@ -10195,55 +10195,55 @@ (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) (-12 (-5 *3 (-1 (-382) (-382))) (-5 *4 (-382)) (-5 *2 - (-2 (|:| -3835 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) + (-2 (|:| -3838 *4) (|:| -1713 *4) (|:| |totalpts| (-551)) (|:| |success| (-112)))) (-5 *1 (-794)) (-5 *5 (-551))))) (((*1 *2 *3 *4 *5 *5 *4 *6) @@ -10421,13 +10421,13 @@ (-4 *3 (-1055))))) (((*1 *2 *1 *1) (-12 - (-5 *2 (-2 (|:| -4197 *3) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) + (-5 *2 (-2 (|:| -4200 *3) (|:| |coef1| (-786 *3)) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4197 *3) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) + (-12 (-5 *2 (-2 (|:| -4200 *3) (|:| |coef1| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -4197 *3) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) + (-12 (-5 *2 (-2 (|:| -4200 *3) (|:| |coef2| (-786 *3)))) (-5 *1 (-786 *3)) (-4 *3 (-562)) (-4 *3 (-1055))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-694 (-412 (-551)))) @@ -10471,7 +10471,7 @@ (-4 *10 (-956 *9 *7 *8)) (-5 *2 (-2 (|:| |deter| (-646 (-1177 *10))) - (|:| |dterm| (-646 (-646 (-2 (|:| -3489 (-776)) (|:| |pcoef| *10))))) + (|:| |dterm| (-646 (-646 (-2 (|:| -3492 (-776)) (|:| |pcoef| *10))))) (|:| |nfacts| (-646 *6)) (|:| |nlead| (-646 *10)))) (-5 *1 (-783 *6 *7 *8 *9 *10)) (-5 *3 (-1177 *10)) (-5 *4 (-646 *6)) (-5 *5 (-646 *10))))) @@ -10925,19 +10925,19 @@ (-5 *1 (-753))))) (((*1 *2 *3 *4 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3505)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *4 *5 *3 *3 *4 *4 *4 *6) (-12 (-5 *4 (-551)) (-5 *5 (-694 (-226))) - (-5 *6 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3505)))) (-5 *3 (-226)) + (-5 *6 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *3 (-226)) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3505)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3505)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) (-5 *1 (-753))))) (((*1 *2 *3 *3 *4 *3) (-12 (-5 *3 (-551)) (-5 *4 (-694 (-226))) (-5 *2 (-1041)) (-5 *1 (-752))))) @@ -10977,7 +10977,7 @@ (-5 *1 (-751))))) (((*1 *2 *3 *3 *3 *3 *4 *5) (-12 (-5 *3 (-226)) (-5 *4 (-551)) - (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3505)))) (-5 *2 (-1041)) + (-5 *5 (-3 (|:| |fn| (-393)) (|:| |fp| (-61 -3508)))) (-5 *2 (-1041)) (-5 *1 (-751))))) (((*1 *2 *3 *4 *5 *4) (-12 (-5 *3 (-694 (-226))) (-5 *4 (-551)) (-5 *5 (-112)) (-5 *2 (-1041)) @@ -11001,7 +11001,7 @@ (-4 *7 (-855)) (-4 *8 (-310)) (-4 *9 (-956 *8 *6 *7)) (-4 *6 (-798)) (-5 *2 (-2 (|:| |upol| (-1177 *8)) (|:| |Lval| (-646 *8)) - (|:| |Lfact| (-646 (-2 (|:| -4173 (-1177 *8)) (|:| -2573 (-551))))) + (|:| |Lfact| (-646 (-2 (|:| -4176 (-1177 *8)) (|:| -2576 (-551))))) (|:| |ctpol| *8))) (-5 *1 (-747 *6 *7 *8 *9))))) (((*1 *2 *3 *4 *5) @@ -11009,7 +11009,7 @@ (-4 *6 (-798)) (-4 *9 (-956 *8 *6 *7)) (-5 *2 (-2 (|:| |unitPart| *9) - (|:| |suPart| (-646 (-2 (|:| -4173 (-1177 *9)) (|:| -2573 (-551))))))) + (|:| |suPart| (-646 (-2 (|:| -4176 (-1177 *9)) (|:| -2576 (-551))))))) (-5 *1 (-747 *6 *7 *8 *9)) (-5 *3 (-1177 *9))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-551)) (-4 *6 (-798)) (-4 *7 (-855)) (-4 *8 (-310)) @@ -11020,7 +11020,7 @@ (-12 (-4 *5 (-798)) (-4 *4 (-855)) (-4 *6 (-310)) (-5 *2 (-410 *3)) (-5 *1 (-747 *5 *4 *6 *3)) (-4 *3 (-956 *6 *5 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4173 (-1177 *6)) (|:| -2573 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4176 (-1177 *6)) (|:| -2576 (-551))))) (-4 *6 (-310)) (-4 *4 (-798)) (-4 *5 (-855)) (-5 *2 (-551)) (-5 *1 (-747 *4 *5 *6 *7)) (-4 *7 (-956 *6 *4 *5))))) (((*1 *2 *3) @@ -11040,18 +11040,18 @@ (((*1 *2 *3 *4) (-12 (-4 *6 (-562)) (-4 *2 (-956 *3 *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) (-5 *3 (-412 (-952 *6))) (-4 *5 (-798)) - (-4 *4 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $)))))))) + (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1177 (-952 *6))) (-4 *6 (-562)) (-4 *2 (-956 (-412 (-952 *6)) *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) - (-4 *5 (-798)) (-4 *4 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $)))))))) + (-4 *5 (-798)) (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $)))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1177 *2)) (-4 *2 (-956 (-412 (-952 *6)) *5 *4)) (-5 *1 (-737 *5 *4 *6 *2)) (-4 *5 (-798)) - (-4 *4 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $))))) (-4 *6 (-562))))) + (-4 *4 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) (-4 *6 (-562))))) (((*1 *2 *3) - (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4411 ((-1183) $))))) - (-4 *6 (-562)) (-5 *2 (-2 (|:| -2814 (-952 *6)) (|:| -2245 (-952 *6)))) + (-12 (-4 *4 (-798)) (-4 *5 (-13 (-855) (-10 -8 (-15 -4414 ((-1183) $))))) + (-4 *6 (-562)) (-5 *2 (-2 (|:| -2817 (-952 *6)) (|:| -2245 (-952 *6)))) (-5 *1 (-737 *4 *5 *6 *3)) (-4 *3 (-956 (-412 (-952 *6)) *4 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-646 *8)) (-5 *4 (-135 *5 *6 *7)) (-14 *5 (-551)) @@ -11066,7 +11066,7 @@ (-5 *1 (-732 *5 *2)) (-4 *5 (-367))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1248 *5)) (-4 *5 (-367)) - (-5 *2 (-2 (|:| -3502 (-410 *3)) (|:| |special| (-410 *3)))) + (-5 *2 (-2 (|:| -3505 (-410 *3)) (|:| |special| (-410 *3)))) (-5 *1 (-732 *5 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) ((*1 *2 *1) @@ -11122,16 +11122,16 @@ ((*1 *2 *1) (-12 (-4 *2 (-1107)) (-5 *1 (-718 *3 *2 *4)) (-4 *3 (-855)) (-14 *4 - (-1 (-112) (-2 (|:| -2572 *3) (|:| -2573 *2)) - (-2 (|:| -2572 *3) (|:| -2573 *2))))))) + (-1 (-112) (-2 (|:| -2575 *3) (|:| -2576 *2)) + (-2 (|:| -2575 *3) (|:| -2576 *2))))))) (((*1 *1 *2) (-12 (-5 *2 (-925)) (-4 *1 (-372)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-925)) (-5 *2 (-1272 *4)) (-5 *1 (-533 *4)) (-4 *4 (-354)))) ((*1 *2 *1) (-12 (-4 *2 (-855)) (-5 *1 (-718 *2 *3 *4)) (-4 *3 (-1107)) (-14 *4 - (-1 (-112) (-2 (|:| -2572 *2) (|:| -2573 *3)) - (-2 (|:| -2572 *2) (|:| -2573 *3))))))) + (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *3)) + (-2 (|:| -2575 *2) (|:| -2576 *3))))))) (((*1 *2 *2) (-12 (-4 *3 (-1055)) (-5 *1 (-717 *3 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *1) (-12 (-4 *3 (-1055)) (-5 *2 (-1272 *3)) (-5 *1 (-717 *3 *4)) @@ -11156,7 +11156,7 @@ (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| -12 (-5 *2 (-646 (-1177 *13))) (-5 *3 (-1177 *13)) (-5 *4 (-646 *12)) (-5 *5 (-646 *10)) (-5 *6 (-646 *13)) - (-5 *7 (-646 (-646 (-2 (|:| -3489 (-776)) (|:| |pcoef| *13))))) + (-5 *7 (-646 (-646 (-2 (|:| -3492 (-776)) (|:| |pcoef| *13))))) (-5 *8 (-646 (-776))) (-5 *9 (-1272 (-646 (-1177 *10)))) (-4 *12 (-855)) (-4 *10 (-310)) (-4 *13 (-956 *10 *11 *12)) (-4 *11 (-798)) (-5 *1 (-712 *11 *12 *10 *13))))) @@ -11204,17 +11204,17 @@ ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-706))))) (((*1 *2 *3 *3) (-12 (-4 *3 (-310)) (-4 *3 (-173)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)) - (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-693 *3 *4 *5 *6)) + (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-693 *3 *4 *5 *6)) (-4 *6 (-691 *3 *4 *5)))) ((*1 *2 *3 *3) - (-12 (-5 *2 (-2 (|:| -2161 *3) (|:| -3312 *3))) (-5 *1 (-705 *3)) + (-12 (-5 *2 (-2 (|:| -2161 *3) (|:| -3315 *3))) (-5 *1 (-705 *3)) (-4 *3 (-310))))) (((*1 *2 *2 *3 *3) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-694 *3)) (-4 *3 (-310)) (-5 *1 (-705 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-409)) (-5 *2 (-551)))) ((*1 *2 *1) (-12 (-5 *2 (-551)) (-5 *1 (-704))))) -(((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4425)) (-4 *1 (-409)))) +(((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925)))) ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-704)))) ((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-704))))) @@ -11250,13 +11250,13 @@ ((*1 *2 *2 *3 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-701 *2)) (-4 *2 (-1248 *3))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| |deg| (-776)) (|:| -2984 *5)))) (-4 *5 (-1248 *4)) + (-12 (-5 *3 (-646 (-2 (|:| |deg| (-776)) (|:| -2987 *5)))) (-4 *5 (-1248 *4)) (-4 *4 (-354)) (-5 *2 (-646 *5)) (-5 *1 (-217 *4 *5)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-646 (-2 (|:| -4173 *5) (|:| -4389 (-551))))) (-5 *4 (-551)) + (-12 (-5 *3 (-646 (-2 (|:| -4176 *5) (|:| -4392 (-551))))) (-5 *4 (-551)) (-4 *5 (-1248 *4)) (-5 *2 (-646 *5)) (-5 *1 (-701 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-551)) (-5 *2 (-646 (-2 (|:| -4173 *3) (|:| -4389 *4)))) + (-12 (-5 *4 (-551)) (-5 *2 (-646 (-2 (|:| -4176 *3) (|:| -4392 *4)))) (-5 *1 (-701 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-701 *2)) (-4 *2 (-1248 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-285 *2)) (-4 *2 (-1222)) (-4 *2 (-1107)))) @@ -11267,32 +11267,32 @@ (((*1 *2 *3 *4 *5 *5) (-12 (-5 *5 (-776)) (-4 *6 (-1107)) (-4 *7 (-906 *6)) (-5 *2 (-694 *7)) (-5 *1 (-697 *6 *7 *3 *4)) (-4 *3 (-376 *7)) - (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4434))))))) + (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4437))))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-1272 (-317 (-226)))) (-5 *4 (-646 (-1183))) (-5 *2 (-694 (-317 (-226)))) (-5 *1 (-206)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *6 (-906 *5)) (-5 *2 (-694 *6)) (-5 *1 (-697 *5 *6 *3 *4)) (-4 *3 (-376 *6)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4434))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) (((*1 *2 *3 *4 *5) (-12 (-5 *5 (-776)) (-4 *6 (-1107)) (-4 *3 (-906 *6)) (-5 *2 (-694 *3)) (-5 *1 (-697 *6 *3 *7 *4)) (-4 *7 (-376 *3)) - (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4434))))))) + (-4 *4 (-13 (-376 *6) (-10 -7 (-6 -4437))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *3 (-906 *5)) (-5 *2 (-694 *3)) (-5 *1 (-697 *5 *3 *6 *4)) (-4 *6 (-376 *3)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4434))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) (((*1 *2 *2 *3) (-12 (-4 *4 (-1107)) (-4 *2 (-906 *4)) (-5 *1 (-697 *4 *2 *5 *3)) - (-4 *5 (-376 *2)) (-4 *3 (-13 (-376 *4) (-10 -7 (-6 -4434))))))) + (-4 *5 (-376 *2)) (-4 *3 (-13 (-376 *4) (-10 -7 (-6 -4437))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *2 (-906 *5)) (-5 *1 (-697 *5 *2 *3 *4)) - (-4 *3 (-376 *2)) (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4434))))))) + (-4 *3 (-376 *2)) (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) (((*1 *2 *3 *4) (-12 (-4 *5 (-1107)) (-4 *3 (-906 *5)) (-5 *2 (-1272 *3)) (-5 *1 (-697 *5 *3 *6 *4)) (-4 *6 (-376 *3)) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4434))))))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4437))))))) (((*1 *1 *2) (-12 (-5 *1 (-696 *2)) (-4 *2 (-618 (-868)))))) (((*1 *1) (-12 (-5 *1 (-696 *2)) (-4 *2 (-618 (-868)))))) (((*1 *2 *2 *2 *2 *2 *3) @@ -11426,8 +11426,8 @@ (|:| -2199 (-646 (-1272 (-412 *8)))))) (-5 *1 (-674 *5 *6 *7 *8))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4435)))) - (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4435)))) (-5 *2 (-112)) + (-12 (-4 *5 (-367)) (-4 *6 (-13 (-376 *5) (-10 -7 (-6 -4438)))) + (-4 *4 (-13 (-376 *5) (-10 -7 (-6 -4438)))) (-5 *2 (-112)) (-5 *1 (-672 *5 *6 *4 *3)) (-4 *3 (-691 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-694 *5)) (-5 *4 (-1272 *5)) (-4 *5 (-367)) (-5 *2 (-112)) @@ -11462,12 +11462,12 @@ (((*1 *1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-656 *3)) (-4 *3 (-1222)))) ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-551)) (-4 *1 (-656 *2)) (-4 *2 (-1222))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4384 *4)))) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))) (-5 *1 (-654 *3 *4 *5)) (-4 *3 (-1107)) (-4 *4 (-23)) (-14 *5 *4)))) (((*1 *1 *2 *3) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *2) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4384 *4)))) (-4 *3 (-1107)) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 *4)))) (-4 *3 (-1107)) (-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-654 *3 *4 *5))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-365 *3)) (-4 *3 (-1107)))) ((*1 *2 *1 *3) @@ -11488,7 +11488,7 @@ ((*1 *1 *1) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1 *1) (-12 (-4 *1 (-256 *2)) (-4 *2 (-1222)))) - ((*1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-376 *2)) (-4 *2 (-1222)))) + ((*1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-376 *2)) (-4 *2 (-1222)))) ((*1 *1 *1) (-12 (-5 *1 (-654 *2 *3 *4)) (-4 *2 (-1107)) (-4 *3 (-23)) (-14 *4 *3)))) (((*1 *1) @@ -11531,7 +11531,7 @@ (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-4 *5 (-367)) (-4 *5 (-562)) (-5 *2 (-1272 *5)) (-5 *1 (-643 *5 *4)))) ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-3755 (-4 *5 (-367))) + (|partial| -12 (-5 *3 (-1272 *4)) (-4 *4 (-644 *5)) (-3758 (-4 *5 (-367))) (-4 *5 (-562)) (-5 *2 (-1272 (-412 *5))) (-5 *1 (-643 *5 *4))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-1272 *5)) (-4 *5 (-644 *4)) (-4 *4 (-562)) @@ -11723,7 +11723,7 @@ (|partial| -12 (-5 *5 (-2 (|:| |contp| *3) - (|:| -1963 (-646 (-2 (|:| |irr| *10) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *10) (|:| -2570 (-551))))))) (-5 *6 (-646 *3)) (-5 *7 (-646 *8)) (-4 *8 (-855)) (-4 *3 (-310)) (-4 *10 (-956 *3 *9 *8)) (-4 *9 (-798)) (-5 *2 @@ -11778,7 +11778,7 @@ (-5 *2 (-646 (-2 - (|:| -4301 + (|:| -4304 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) @@ -11813,7 +11813,7 @@ (((*1 *2 *1) (-12 (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1222)) (-5 *2 (-646 *3))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-609 *4 *3)) (-4 *4 (-1107)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-609 *4 *3)) (-4 *4 (-1107)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-112))))) (((*1 *2 *1) (-12 (-4 *1 (-609 *2 *3)) (-4 *3 (-1222)) (-4 *2 (-1107)) (-4 *2 (-855))))) @@ -11823,10 +11823,10 @@ (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1222)) (-4 *3 (-376 *2)) (-4 *4 (-376 *2)))) ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4435)) (-4 *1 (-609 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4438)) (-4 *1 (-609 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222))))) (((*1 *2 *1 *3 *3) - (-12 (|has| *1 (-6 -4435)) (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4438)) (-4 *1 (-609 *3 *4)) (-4 *3 (-1107)) (-4 *4 (-1222)) (-5 *2 (-1278))))) (((*1 *2 *2 *3 *4) (-12 (-5 *3 (-646 (-616 *2))) (-5 *4 (-646 (-1183))) @@ -11845,6 +11845,9 @@ (((*1 *2 *3) (-12 (-5 *3 (-169 *5)) (-4 *5 (-13 (-426 *4) (-1008) (-1208))) (-4 *4 (-562)) (-4 *2 (-13 (-426 (-169 *4)) (-1008) (-1208))) (-5 *1 (-605 *4 *5 *2))))) +(((*1 *1) (-5 *1 (-602)))) +(((*1 *1) (-5 *1 (-602)))) +(((*1 *1) (-5 *1 (-602)))) (((*1 *1 *2 *3) (-12 (-5 *2 (-1032 (-847 (-551)))) (-5 *3 (-1160 (-2 (|:| |k| (-551)) (|:| |c| *4)))) (-4 *4 (-1055)) @@ -11955,7 +11958,7 @@ (((*1 *2 *2 *3) (|partial| -12 (-5 *3 (-776)) (-5 *1 (-592 *2)) (-4 *2 (-550)))) ((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -3106 *3) (|:| -2573 (-776)))) (-5 *1 (-592 *3)) + (-12 (-5 *2 (-2 (|:| -3109 *3) (|:| -2576 (-776)))) (-5 *1 (-592 *3)) (-4 *3 (-550))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-776)) (-5 *2 (-112)) (-5 *1 (-592 *3)) (-4 *3 (-550))))) @@ -12005,7 +12008,7 @@ (((*1 *2 *2 *3) (|partial| -12 (-5 *2 (-628 *4 *5)) (-5 *3 - (-1 (-2 (|:| |ans| *4) (|:| -3550 *4) (|:| |sol?| (-112))) (-551) *4)) + (-1 (-2 (|:| |ans| *4) (|:| -3553 *4) (|:| |sol?| (-112))) (-551) *4)) (-4 *4 (-367)) (-4 *5 (-1248 *4)) (-5 *1 (-579 *4 *5))))) (((*1 *2 *2 *3 *4) (|partial| -12 @@ -12025,7 +12028,7 @@ (((*1 *2 *3 *4 *5 *6) (|partial| -12 (-5 *4 (-1 *8 *8)) (-5 *5 - (-1 (-2 (|:| |ans| *7) (|:| -3550 *7) (|:| |sol?| (-112))) (-551) *7)) + (-1 (-2 (|:| |ans| *7) (|:| -3553 *7) (|:| |sol?| (-112))) (-551) *7)) (-5 *6 (-646 (-412 *8))) (-4 *7 (-367)) (-4 *8 (-1248 *7)) (-5 *3 (-412 *8)) (-5 *2 (-2 @@ -12048,7 +12051,7 @@ (((*1 *2 *3 *4 *5 *3) (-12 (-5 *4 (-1 *7 *7)) (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3550 *6) (|:| |sol?| (-112))) (-551) *6)) + (-1 (-2 (|:| |ans| *6) (|:| -3553 *6) (|:| |sol?| (-112))) (-551) *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-3 (-2 (|:| |answer| (-412 *7)) (|:| |a0| *6)) @@ -12070,7 +12073,7 @@ (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1 *7 *7)) (-5 *5 - (-1 (-2 (|:| |ans| *6) (|:| -3550 *6) (|:| |sol?| (-112))) (-551) *6)) + (-1 (-2 (|:| |ans| *6) (|:| -3553 *6) (|:| |sol?| (-112))) (-551) *6)) (-4 *6 (-367)) (-4 *7 (-1248 *6)) (-5 *2 (-2 (|:| |answer| (-588 (-412 *7))) (|:| |a0| *6))) (-5 *1 (-579 *6 *7)) (-5 *3 (-412 *7))))) @@ -12159,7 +12162,7 @@ (-4 *3 (-635)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1183)) (-4 *5 (-13 (-1044 (-551)) (-457) (-644 (-551)))) - (-5 *2 (-2 (|:| -2498 *3) (|:| |nconst| *3))) (-5 *1 (-572 *5 *3)) + (-5 *2 (-2 (|:| -2501 *3) (|:| |nconst| *3))) (-5 *1 (-572 *5 *3)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *3 *4 *5 *5 *6) (-12 (-5 *5 (-616 *4)) (-5 *6 (-1183)) (-4 *4 (-13 (-426 *7) (-27) (-1208))) @@ -12340,7 +12343,7 @@ (-5 *2 (-646 (-2 - (|:| -4301 + (|:| -4304 (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) @@ -12399,7 +12402,7 @@ (-5 *2 (-2 (|:| -2327 *3) (|:| |coeff| *3))) (-5 *1 (-563 *5 *3)) (-4 *3 (-13 (-27) (-1208) (-426 *5)))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -1956 *1) (|:| -4421 *1) (|:| |associate| *1))) + (-12 (-5 *2 (-2 (|:| -1956 *1) (|:| -4424 *1) (|:| |associate| *1))) (-4 *1 (-562))))) (((*1 *1 *1) (-4 *1 (-562)))) (((*1 *2 *1 *1) (-12 (-4 *1 (-562)) (-5 *2 (-112))))) @@ -12564,7 +12567,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-1272 *4)) (-4 *4 (-354)) (-5 *2 (-1177 *4)) (-5 *1 (-533 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-1278)) (-5 *1 (-533 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-532)) (-5 *2 (-696 (-128)))))) (((*1 *2 *1) (-12 (-4 *1 (-532)) (-5 *2 (-696 (-555)))))) @@ -12707,13 +12710,13 @@ (-12 (-5 *3 (-925)) (-5 *2 (-1278)) (-5 *1 (-215 *4)) (-4 *4 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 (*2 $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) (-15 -2152 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-215 *3)) (-4 *3 (-13 (-855) - (-10 -8 (-15 -4240 ((-1165) $ (-1183))) (-15 -4058 (*2 $)) + (-10 -8 (-15 -4243 ((-1165) $ (-1183))) (-15 -4061 (*2 $)) (-15 -2152 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-507))))) (((*1 *2 *3 *4) @@ -12737,27 +12740,27 @@ (-12 (-5 *2 (-2 (|:| -2199 (-694 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-694 *3)))) - (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) (-4 *4 (-1248 *3)) + (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-5 *2 (-694 *3)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-776)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) + (-12 (-5 *2 (-776)) (-4 *3 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *4 (-1248 *3)) (-5 *1 (-504 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2 *3 *3 *2 *4) (-12 (-5 *3 (-694 *2)) (-5 *4 (-551)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) (-4 *5 (-1248 *2)) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *5 (-1248 *2)) (-5 *1 (-504 *2 *5 *6)) (-4 *6 (-415 *2 *5))))) (((*1 *2 *3 *2 *4) (-12 (-5 *3 (-694 *2)) (-5 *4 (-776)) - (-4 *2 (-13 (-310) (-10 -8 (-15 -4410 ((-410 $) $))))) (-4 *5 (-1248 *2)) + (-4 *2 (-13 (-310) (-10 -8 (-15 -4413 ((-410 $) $))))) (-4 *5 (-1248 *2)) (-5 *1 (-504 *2 *5 *6)) (-4 *6 (-415 *2 *5))))) (((*1 *2 *3 *4 *4) (-12 (-5 *4 (-776)) (-4 *5 (-354)) (-4 *6 (-1248 *5)) @@ -12785,25 +12788,25 @@ (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1222)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4435)) (-4 *1 (-494 *3)) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4438)) (-4 *1 (-494 *3)) (-4 *3 (-1222))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4434)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4434)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-4 *3 (-1107)) (-5 *2 (-776)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4434)) (-4 *1 (-494 *4)) + (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4437)) (-4 *1 (-494 *4)) (-4 *4 (-1222)) (-5 *2 (-776))))) (((*1 *2 *1) (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1222)) (-4 *4 (-376 *3)) (-4 *5 (-376 *3)) (-5 *2 (-646 *3)))) ((*1 *2 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-494 *3)) (-4 *3 (-1222)) (-5 *2 (-646 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-412 (-551))) (-5 *1 (-492))))) (((*1 *2 *3) @@ -12821,7 +12824,7 @@ (-4 *4 (-1055)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-551))) (-14 *3 (-646 (-1183))) (-5 *1 (-459 *3 *4 *5)) - (-4 *4 (-1055)) (-4 *5 (-239 (-4398 *3) (-776))))) + (-4 *4 (-1055)) (-4 *5 (-239 (-4401 *3) (-776))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-646 (-551))) (-5 *1 (-486 *3 *4)) (-14 *3 (-646 (-1183))) (-4 *4 (-1055))))) @@ -12885,33 +12888,33 @@ (-4 *7 (-956 *6 *5 *3)) (-5 *1 (-467 *5 *3 *6 *7 *2)) (-4 *2 (-13 (-1044 (-412 (-551))) (-367) - (-10 -8 (-15 -4387 ($ *7)) (-15 -3408 (*7 $)) (-15 -3407 (*7 $)))))))) + (-10 -8 (-15 -4390 ($ *7)) (-15 -3411 (*7 $)) (-15 -3410 (*7 $)))))))) (((*1 *2 *1) (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *5) (|:| -2573 *2)) - (-2 (|:| -2572 *5) (|:| -2573 *2)))) - (-4 *2 (-239 (-4398 *3) (-776))) (-5 *1 (-466 *3 *4 *5 *2 *6 *7)) + (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *2)) + (-2 (|:| -2575 *5) (|:| -2576 *2)))) + (-4 *2 (-239 (-4401 *3) (-776))) (-5 *1 (-466 *3 *4 *5 *2 *6 *7)) (-4 *5 (-855)) (-4 *7 (-956 *4 *2 (-869 *3)))))) (((*1 *2 *1) - (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4398 *3) (-776))) + (-12 (-14 *3 (-646 (-1183))) (-4 *4 (-173)) (-4 *5 (-239 (-4401 *3) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *2) (|:| -2573 *5)) - (-2 (|:| -2572 *2) (|:| -2573 *5)))) + (-1 (-112) (-2 (|:| -2575 *2) (|:| -2576 *5)) + (-2 (|:| -2575 *2) (|:| -2576 *5)))) (-4 *2 (-855)) (-5 *1 (-466 *3 *4 *2 *5 *6 *7)) (-4 *7 (-956 *4 *5 (-869 *3)))))) (((*1 *1 *2 *3 *4) - (-12 (-14 *5 (-646 (-1183))) (-4 *2 (-173)) (-4 *4 (-239 (-4398 *5) (-776))) + (-12 (-14 *5 (-646 (-1183))) (-4 *2 (-173)) (-4 *4 (-239 (-4401 *5) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *3) (|:| -2573 *4)) - (-2 (|:| -2572 *3) (|:| -2573 *4)))) + (-1 (-112) (-2 (|:| -2575 *3) (|:| -2576 *4)) + (-2 (|:| -2575 *3) (|:| -2576 *4)))) (-5 *1 (-466 *5 *2 *3 *4 *6 *7)) (-4 *3 (-855)) (-4 *7 (-956 *2 *4 (-869 *5)))))) (((*1 *1 *2 *3 *1) - (-12 (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-4 *3 (-239 (-4398 *4) (-776))) + (-12 (-14 *4 (-646 (-1183))) (-4 *2 (-173)) (-4 *3 (-239 (-4401 *4) (-776))) (-14 *6 - (-1 (-112) (-2 (|:| -2572 *5) (|:| -2573 *3)) - (-2 (|:| -2572 *5) (|:| -2573 *3)))) + (-1 (-112) (-2 (|:| -2575 *5) (|:| -2576 *3)) + (-2 (|:| -2575 *5) (|:| -2576 *3)))) (-5 *1 (-466 *4 *2 *5 *3 *6 *7)) (-4 *5 (-855)) (-4 *7 (-956 *2 *3 (-869 *4)))))) (((*1 *2 *3 *2 *4 *5) @@ -13240,7 +13243,7 @@ (-12 (-5 *3 (-925)) (-5 *4 (-410 *2)) (-4 *2 (-1248 *5)) (-5 *1 (-449 *5 *2)) (-4 *5 (-1055))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4173 *4) (|:| -4389 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4176 *4) (|:| -4392 (-551))))) (-4 *4 (-1248 (-551))) (-5 *2 (-741 (-776))) (-5 *1 (-447 *4)))) ((*1 *2 *3) (-12 (-5 *3 (-410 *5)) (-4 *5 (-1248 *4)) (-4 *4 (-1055)) @@ -13276,7 +13279,7 @@ (-12 (-5 *4 (-112)) (-5 *5 (-1103 (-776))) (-5 *6 (-776)) (-5 *2 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) @@ -13286,11 +13289,11 @@ (((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -2987 (-551)) (|:| -1963 (-646 *3)))) (-5 *1 (-447 *3)) + (-12 (-5 *2 (-2 (|:| -2990 (-551)) (|:| -1963 (-646 *3)))) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-410 *3)) (-4 *3 (-562)))) ((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -4173 *4) (|:| -4389 (-551))))) + (-12 (-5 *3 (-646 (-2 (|:| -4176 *4) (|:| -4392 (-551))))) (-4 *4 (-1248 (-551))) (-5 *2 (-776)) (-5 *1 (-447 *4))))) (((*1 *2) (-12 (-5 *2 (-925)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *2) (-12 (-5 *2 (-925)) (-5 *1 (-447 *3)) (-4 *3 (-1248 (-551)))))) @@ -13307,7 +13310,7 @@ (-12 (-5 *3 (-2 (|:| |contp| (-551)) - (|:| -1963 (-646 (-2 (|:| |irr| *4) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *4) (|:| -2570 (-551))))))) (-4 *4 (-1248 (-551))) (-5 *2 (-410 *4)) (-5 *1 (-447 *4))))) (((*1 *2 *2) (-12 (-5 *2 (-393)) (-5 *1 (-442)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-393)) (-5 *1 (-442))))) @@ -13315,7 +13318,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-442))))) (((*1 *2) (-12 (-5 *2 (-1278)) (-5 *1 (-442))))) (((*1 *2 *1) - (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4351 "void"))) (-5 *1 (-441))))) + (-12 (-5 *2 (-3 (|:| |fst| (-439)) (|:| -4354 "void"))) (-5 *1 (-441))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-441))))) (((*1 *1) (-5 *1 (-441)))) (((*1 *1) (-5 *1 (-441)))) @@ -13332,7 +13335,7 @@ (-12 (-4 *4 (-13 (-562) (-1044 (-551)))) (-4 *5 (-426 *4)) (-5 *2 (-3 (|:| |overq| (-1177 (-412 (-551)))) (|:| |overan| (-1177 (-48))) - (|:| -3050 (-112)))) + (|:| -3053 (-112)))) (-5 *1 (-440 *4 *5 *3)) (-4 *3 (-1248 *5))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-13 (-562) (-1044 (-551)))) (-4 *5 (-426 *4)) @@ -13375,19 +13378,19 @@ (-14 *4 (-1183)) (-14 *5 *2))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *2 (-13 (-27) (-1208) (-426 *3) (-10 -8 (-15 -4387 ($ *4))))) + (-4 *2 (-13 (-27) (-1208) (-426 *3) (-10 -8 (-15 -4390 ($ *4))))) (-4 *4 (-853)) (-4 *5 (-13 (-1251 *2 *4) (-367) (-1208) - (-10 -8 (-15 -4251 ($ $)) (-15 -4253 ($ $))))) + (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) (-5 *1 (-429 *3 *2 *4 *5 *6 *7)) (-4 *6 (-989 *5)) (-14 *7 (-1183))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4387 ($ *7))))) + (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4390 ($ *7))))) (-4 *7 (-853)) (-4 *8 (-13 (-1251 *3 *7) (-367) (-1208) - (-10 -8 (-15 -4251 ($ $)) (-15 -4253 ($ $))))) + (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) @@ -13395,11 +13398,11 @@ (-14 *10 (-1183))))) (((*1 *2 *3 *4 *5) (-12 (-5 *4 (-112)) (-4 *6 (-13 (-457) (-1044 (-551)) (-644 (-551)))) - (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4387 ($ *7))))) + (-4 *3 (-13 (-27) (-1208) (-426 *6) (-10 -8 (-15 -4390 ($ *7))))) (-4 *7 (-853)) (-4 *8 (-13 (-1251 *3 *7) (-367) (-1208) - (-10 -8 (-15 -4251 ($ $)) (-15 -4253 ($ $))))) + (-10 -8 (-15 -4254 ($ $)) (-15 -4256 ($ $))))) (-5 *2 (-3 (|:| |%series| *8) (|:| |%problem| (-2 (|:| |func| (-1165)) (|:| |prob| (-1165)))))) @@ -13426,7 +13429,7 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1183)) (-4 *1 (-426 *3)) (-4 *3 (-1107))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1107)) - (-5 *2 (-2 (|:| -4395 (-551)) (|:| |var| (-616 *1)))) (-4 *1 (-426 *3))))) + (-5 *2 (-2 (|:| -4398 (-551)) (|:| |var| (-616 *1)))) (-4 *1 (-426 *3))))) (((*1 *2 *2 *2) (-12 (-5 *2 (-410 *3)) (-4 *3 (-562)) (-5 *1 (-424 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1272 *3)) (-4 *3 (-367)) (-4 *1 (-332 *3)))) ((*1 *1 *2 *3) @@ -13497,13 +13500,13 @@ (-5 *2 (-694 *3))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4384 (-551))))) (-5 *1 (-365 *3)) + (-12 (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 (-551))))) (-5 *1 (-365 *3)) (-4 *3 (-1107)))) ((*1 *2 *1) (-12 (-4 *1 (-390 *3)) (-4 *3 (-1107)) - (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4384 (-776))))))) + (-5 *2 (-646 (-2 (|:| |gen| *3) (|:| -4387 (-776))))))) ((*1 *2 *1) - (-12 (-5 *2 (-646 (-2 (|:| -4173 *3) (|:| -2573 (-551))))) (-5 *1 (-410 *3)) + (-12 (-5 *2 (-646 (-2 (|:| -4176 *3) (|:| -2576 (-551))))) (-5 *1 (-410 *3)) (-4 *3 (-562))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-551)) (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-551)) (-5 *1 (-410 *3)) (-4 *3 (-562))))) @@ -13520,12 +13523,12 @@ ((*1 *2 *1) (-12 (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *1 *1) (-12 (-5 *1 (-410 *2)) (-4 *2 (-562))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-776)) (-5 *3 (-112)) (-5 *1 (-110)))) - ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4425)) (-4 *1 (-409)))) + ((*1 *2 *2) (-12 (-5 *2 (-925)) (|has| *1 (-6 -4428)) (-4 *1 (-409)))) ((*1 *2) (-12 (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-551)) (|has| *1 (-6 -4425)) (-4 *1 (-409)) (-5 *2 (-925))))) + (-12 (-5 *3 (-551)) (|has| *1 (-6 -4428)) (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-551)) (|has| *1 (-6 -4425)) (-4 *1 (-409)) (-5 *2 (-925))))) + (-12 (-5 *3 (-551)) (|has| *1 (-6 -4428)) (-4 *1 (-409)) (-5 *2 (-925))))) (((*1 *2 *1) (-12 (-4 *1 (-354)) (-5 *2 (-776)))) ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-407)) (-5 *2 (-776))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-407)) (-5 *2 (-776)))) @@ -13537,7 +13540,7 @@ (-12 (-4 *2 (-1248 *3)) (-5 *1 (-404 *3 *2)) (-4 *3 (-13 (-367) (-147)))))) (((*1 *2 *1) (-12 (-4 *3 (-13 (-367) (-147))) - (-5 *2 (-646 (-2 (|:| -2573 (-776)) (|:| -4213 *4) (|:| |num| *4)))) + (-5 *2 (-646 (-2 (|:| -2576 (-776)) (|:| -4216 *4) (|:| |num| *4)))) (-5 *1 (-404 *3 *4)) (-4 *4 (-1248 *3))))) (((*1 *2 *2) (-12 (-5 *2 (-646 (-1165))) (-5 *1 (-400))))) (((*1 *2 *3 *4 *5 *6) @@ -13630,13 +13633,13 @@ (((*1 *2 *3) (-12 (-5 *3 (-776)) (-5 *2 (-1278)) (-5 *1 (-382))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4435))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4435))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1222)) (-5 *1 (-379 *4 *2)) - (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4435))))))) + (-4 *2 (-13 (-376 *4) (-10 -7 (-6 -4438))))))) (((*1 *1 *2) (-12 (-5 *2 (-677 *3)) (-4 *3 (-855)) (-4 *1 (-378 *3 *4)) (-4 *4 (-173))))) (((*1 *2 *1) @@ -13645,11 +13648,11 @@ (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-376 *4)) (-4 *4 (-1222)) (-5 *2 (-112))))) (((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-551)) (|has| *1 (-6 -4435)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) + (-12 (-5 *2 (-551)) (|has| *1 (-6 -4438)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4435)) (-4 *1 (-376 *2)) (-4 *2 (-1222)) (-4 *2 (-855)))) + (-12 (|has| *1 (-6 -4438)) (-4 *1 (-376 *2)) (-4 *2 (-1222)) (-4 *2 (-855)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (|has| *1 (-6 -4435)) (-4 *1 (-376 *3)) + (-12 (-5 *2 (-1 (-112) *3 *3)) (|has| *1 (-6 -4438)) (-4 *1 (-376 *3)) (-4 *3 (-1222))))) (((*1 *2) (-12 (-4 *3 (-173)) (-5 *2 (-1272 *1)) (-4 *1 (-371 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-371 *2)) (-4 *2 (-173))))) @@ -13728,8 +13731,8 @@ (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-4 *2 (-13 (-407) - (-10 -7 (-15 -4387 (*2 *4)) (-15 -2197 ((-925) *2)) - (-15 -2199 ((-1272 *2) (-925))) (-15 -4369 (*2 *2))))) + (-10 -7 (-15 -4390 (*2 *4)) (-15 -2197 ((-925) *2)) + (-15 -2199 ((-1272 *2) (-925))) (-15 -4372 (*2 *2))))) (-5 *1 (-361 *2 *4))))) (((*1 *2 *3) (-12 (-4 *4 (-354)) (-5 *2 (-964 (-1177 *4))) (-5 *1 (-360 *4)) @@ -13762,13 +13765,13 @@ ((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-5 *2 (-112)) (-5 *1 (-360 *4))))) (((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3835 (-912 *3)) (|:| -2572 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 (-912 *3)) (|:| -2575 (-1126)))))) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925)))) ((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3835 *3) (|:| -2572 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126)))))) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 (-3 (-1177 *3) *2)))) ((*1 *2) - (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3835 *3) (|:| -2572 (-1126)))))) + (-12 (-5 *2 (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126)))))) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2) (-12 (-5 *2 (-694 (-912 *3))) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) @@ -13776,23 +13779,23 @@ ((*1 *2) (-12 (-5 *2 (-694 *3)) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 - (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3835 *3) (|:| -2572 (-1126))))))))) + (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126))))))))) ((*1 *2) (-12 (-5 *2 (-694 *3)) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2 *3) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-776)) (-5 *1 (-351 *4)))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-356 *3 *4)) (-14 *3 (-925)) (-14 *4 (-925)))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-357 *3 *4)) (-4 *3 (-354)) (-14 *4 - (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3835 *3) (|:| -2572 (-1126))))))))) + (-3 (-1177 *3) (-1272 (-646 (-2 (|:| -3838 *3) (|:| -2575 (-1126))))))))) ((*1 *2) (-12 (-5 *2 (-776)) (-5 *1 (-358 *3 *4)) (-4 *3 (-354)) (-14 *4 (-925))))) (((*1 *2) (-12 (-4 *1 (-354)) - (-5 *2 (-646 (-2 (|:| -4173 (-551)) (|:| -2573 (-551)))))))) + (-5 *2 (-646 (-2 (|:| -4176 (-551)) (|:| -2576 (-551)))))))) (((*1 *2 *3) (-12 (-4 *1 (-354)) (-5 *3 (-551)) (-5 *2 (-1195 (-925) (-776)))))) (((*1 *1) (-4 *1 (-354)))) (((*1 *2) @@ -13800,18 +13803,18 @@ (((*1 *2 *3) (-12 (-5 *3 (-925)) (-5 *2 - (-3 (-1177 *4) (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126))))))) + (-3 (-1177 *4) (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126))))))) (-5 *1 (-351 *4)) (-4 *4 (-354))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-925)) - (-5 *2 (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126)))))) + (-5 *2 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) (-5 *1 (-351 *4)) (-4 *4 (-354))))) (((*1 *2 *3) - (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126)))))) + (-12 (-5 *3 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) (-4 *4 (-354)) (-5 *2 (-694 *4)) (-5 *1 (-351 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) - (-5 *2 (-1272 (-646 (-2 (|:| -3835 *4) (|:| -2572 (-1126)))))) + (-5 *2 (-1272 (-646 (-2 (|:| -3838 *4) (|:| -2575 (-1126)))))) (-5 *1 (-351 *4))))) (((*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-354)) (-5 *2 (-964 (-1126))) @@ -14040,7 +14043,7 @@ (-3 (|:| |nullBranch| "null") (|:| |assignmentBranch| (-2 (|:| |var| (-1183)) (|:| |arrayIndex| (-646 (-952 (-551)))) - (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3683 (-868)))))) + (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3686 (-868)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1183)) (|:| |rand| (-868)) (|:| |ints2Floats?| (-112)))) @@ -14048,17 +14051,17 @@ (-2 (|:| |switch| (-1182)) (|:| |thenClause| (-333)) (|:| |elseClause| (-333)))) (|:| |returnBranch| - (-2 (|:| -3836 (-112)) - (|:| -3835 (-2 (|:| |ints2Floats?| (-112)) (|:| -3683 (-868)))))) + (-2 (|:| -3839 (-112)) + (|:| -3838 (-2 (|:| |ints2Floats?| (-112)) (|:| -3686 (-868)))))) (|:| |blockBranch| (-646 (-333))) (|:| |commentBranch| (-646 (-1165))) (|:| |callBranch| (-1165)) (|:| |forBranch| (-2 (|:| -1612 (-1098 (-952 (-551)))) (|:| |span| (-952 (-551))) - (|:| -3662 (-333)))) + (|:| -3665 (-333)))) (|:| |labelBranch| (-1126)) - (|:| |loopBranch| (-2 (|:| |switch| (-1182)) (|:| -3662 (-333)))) + (|:| |loopBranch| (-2 (|:| |switch| (-1182)) (|:| -3665 (-333)))) (|:| |commonBranch| - (-2 (|:| -3982 (-1183)) (|:| |contents| (-646 (-1183))))) + (-2 (|:| -3985 (-1183)) (|:| |contents| (-646 (-1183))))) (|:| |printBranch| (-646 (-868))))) (-5 *1 (-333))))) (((*1 *2 *1) (-12 (-5 *2 (-1278)) (-5 *1 (-333))))) @@ -14164,7 +14167,7 @@ (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-310)))) ((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2581 *1))) + (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2584 *1))) (-4 *1 (-310))))) (((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-646 *1)) (-4 *1 (-310))))) (((*1 *2 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-853)) (-5 *1 (-307 *3))))) @@ -14207,13 +14210,13 @@ (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))))) (-5 *2 (-1041)) (-5 *1 (-306)))) ((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -3080 (-382)) (|:| -3982 (-1165)) + (-2 (|:| -3083 (-382)) (|:| -3985 (-1165)) (|:| |explanations| (-646 (-1165))) (|:| |extra| (-1041)))) (-5 *2 (-1041)) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-382)) (-5 *2 (-1165)) (-5 *1 (-306))))) @@ -14243,7 +14246,7 @@ (((*1 *2 *3) (-12 (-5 *3 (-646 (-226))) (-5 *2 (-1272 (-704))) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-226)) (-5 *2 (-704)) (-5 *1 (-306))))) (((*1 *2 *3) - (-12 (-5 *3 (-646 (-2 (|:| -3551 (-412 (-551))) (|:| -3550 (-412 (-551)))))) + (-12 (-5 *3 (-646 (-2 (|:| -3554 (-412 (-551))) (|:| -3553 (-412 (-551)))))) (-5 *2 (-646 (-226))) (-5 *1 (-306))))) (((*1 *2 *2) (-12 (-5 *2 (-1095 (-847 (-226)))) (-5 *1 (-306))))) (((*1 *2 *3) @@ -14255,7 +14258,7 @@ (|:| |exponentiations| (-551)) (|:| |functionCalls| (-551)))) (-5 *1 (-306))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))) + (-12 (-5 *3 (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))) (-5 *2 (-382)) (-5 *1 (-269)))) ((*1 *2 *3) (-12 (-5 *3 (-1272 (-317 (-226)))) (-5 *2 (-382)) (-5 *1 (-306))))) (((*1 *2 *3) (-12 (-5 *3 (-317 (-226))) (-5 *2 (-226)) (-5 *1 (-306))))) @@ -14384,7 +14387,7 @@ (-12 (-5 *3 (-551)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1222)) (-4 *4 (-376 *2)) (-4 *5 (-376 *2)))) ((*1 *2 *1 *3 *2) - (-12 (|has| *1 (-6 -4435)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) + (-12 (|has| *1 (-6 -4438)) (-4 *1 (-291 *3 *2)) (-4 *3 (-1107)) (-4 *2 (-1222))))) (((*1 *2 *3 *4) (-12 (-4 *4 (-367)) (-5 *2 (-646 (-1160 *4))) (-5 *1 (-288 *4 *5)) @@ -14395,7 +14398,7 @@ (((*1 *1 *1 *2) (-12 (-5 *2 (-1239 (-551))) (-4 *1 (-285 *3)) (-4 *3 (-1222)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-551)) (-4 *1 (-285 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4434)) (-4 *1 (-236 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4437)) (-4 *1 (-236 *3)) (-4 *3 (-1107)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-285 *3)) (-4 *3 (-1222))))) (((*1 *1 *2 *3 *4) @@ -14498,11 +14501,11 @@ (-5 *3 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (|:| |lsa| - (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3878 (-646 (-226))))))) + (-2 (|:| |lfn| (-646 (-317 (-226)))) (|:| -3881 (-646 (-226))))))) (-5 *2 (-646 (-1165))) (-5 *1 (-269))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-1041)) (-5 *3 (-1183)) (-5 *1 (-269))))) (((*1 *2 *3) (-12 (-5 *3 (-317 (-226))) (-5 *2 (-112)) (-5 *1 (-269))))) @@ -14517,7 +14520,7 @@ (((*1 *2 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-226))) (|:| -3878 (-646 (-226))) + (-2 (|:| |fn| (-317 (-226))) (|:| -3881 (-646 (-226))) (|:| |lb| (-646 (-847 (-226)))) (|:| |cf| (-646 (-317 (-226)))) (|:| |ub| (-646 (-847 (-226)))))) (-5 *1 (-269))))) @@ -14797,8 +14800,8 @@ (((*1 *1 *2) (-12 (-5 *2 (-646 *3)) (-4 *3 (-855)) (-5 *1 (-246 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1222))))) (((*1 *1 *1) (-12 (-4 *1 (-245 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-245 *2)) (-4 *2 (-1222))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-551)) (-5 *1 (-242)))) ((*1 *2 *3) (-12 (-5 *3 (-646 (-1165))) (-5 *2 (-551)) (-5 *1 (-242))))) (((*1 *2 *3) (-12 (-5 *3 (-1165)) (-5 *2 (-1278)) (-5 *1 (-242)))) @@ -14870,13 +14873,13 @@ (((*1 *2 *2 *3 *2) (-12 (-5 *3 (-776)) (-4 *4 (-354)) (-5 *1 (-217 *4 *2)) (-4 *2 (-1248 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-354)) (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -2984 *3)))) + (-12 (-4 *4 (-354)) (-5 *2 (-646 (-2 (|:| |deg| (-776)) (|:| -2987 *3)))) (-5 *1 (-217 *4 *3)) (-4 *3 (-1248 *4))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-112)) (-4 *5 (-354)) (-5 *2 (-2 (|:| |cont| *5) - (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2567 (-551))))))) + (|:| -1963 (-646 (-2 (|:| |irr| *3) (|:| -2570 (-551))))))) (-5 *1 (-217 *5 *3)) (-4 *3 (-1248 *5))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-367)) (-4 *6 (-1248 (-412 *2))) @@ -14967,7 +14970,7 @@ (-2 (|:| |var| (-1183)) (|:| |fn| (-317 (-226))) (|:| -1612 (-1095 (-847 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) - (-5 *2 (-2 (|:| -2911 (-113)) (|:| |w| (-226)))) (-5 *1 (-205))))) + (-5 *2 (-2 (|:| -2914 (-113)) (|:| |w| (-226)))) (-5 *1 (-205))))) (((*1 *2 *3 *3 *2) (-12 (-5 *2 (-1041)) (-5 *3 (-1183)) (-5 *1 (-193))))) (((*1 *2 *3) (-12 @@ -15136,8 +15139,8 @@ (((*1 *2 *1) (-12 (-5 *2 (-1160 *3)) (-5 *1 (-175 *3)) (-4 *3 (-310))))) (((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-172))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-172))))) -(((*1 *2 *2 *3) (-12 (-5 *2 (-1188)) (-5 *3 (-294)) (-5 *1 (-168))))) -(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 -283) (-5 *1 (-168))))) +(((*1 *2 *2 *3) (-12 (-5 *2 (-1141)) (-5 *3 (-294)) (-5 *1 (-168))))) +(((*1 *2 *3) (-12 (-5 *3 (-1141)) (-5 *2 (-696 (-283))) (-5 *1 (-168))))) (((*1 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173))))) (((*1 *1 *2 *2) (-12 (-4 *1 (-166 *2)) (-4 *2 (-173))))) (((*1 *2 *1) @@ -15211,7 +15214,7 @@ (((*1 *2 *3 *1) (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-151 *2)) (-4 *2 (-1222))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4434)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) + (-12 (|has| *1 (-6 -4437)) (-4 *1 (-151 *2)) (-4 *2 (-1222)) (-4 *2 (-1107))))) (((*1 *2 *3 *3) (-12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) @@ -15224,7 +15227,7 @@ (-4 *3 (-1248 (-412 *4)))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-412 *6)) (-4 *5 (-1227)) (-4 *6 (-1248 *5)) - (-5 *2 (-2 (|:| -2573 (-776)) (|:| -4395 *3) (|:| |radicand| *6))) + (-5 *2 (-2 (|:| -2576 (-776)) (|:| -4398 *3) (|:| |radicand| *6))) (-5 *1 (-148 *5 *6 *7)) (-5 *4 (-776)) (-4 *7 (-1248 *3))))) (((*1 *2 *3) (|partial| -12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) @@ -15232,7 +15235,7 @@ (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1248 (-412 *5)))))) (((*1 *2 *3) (-12 (-4 *4 (-1227)) (-4 *5 (-1248 *4)) - (-5 *2 (-2 (|:| -4395 (-412 *5)) (|:| |poly| *3))) (-5 *1 (-148 *4 *5 *3)) + (-5 *2 (-2 (|:| -4398 (-412 *5)) (|:| |poly| *3))) (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1248 (-412 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-776)) (-5 *1 (-144))))) (((*1 *1 *2) (-12 (-5 *2 (-1165)) (-5 *1 (-144)))) @@ -15292,8 +15295,8 @@ ((*1 *2 *2) (-12 (-5 *2 (-776)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551)))))) (((*1 *2 *3) (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551))))) ((*1 *2 *3 *2) (-12 (-5 *2 (-112)) (-5 *1 (-120 *3)) (-4 *3 (-1248 (-551)))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) -(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4435)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) +(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4438)) (-4 *1 (-119 *2)) (-4 *2 (-1222))))) (((*1 *2 *3) (-12 (-4 *4 (-13 (-367) (-1044 (-412 *2)))) (-5 *2 (-551)) (-5 *1 (-115 *4 *3)) (-4 *3 (-1248 *4))))) @@ -15333,11 +15336,11 @@ (|:| |singularities| (-1160 (-226))))) (-5 *1 (-105))))) (((*1 *2 *3) - (-12 (|has| *2 (-6 (-4436 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) + (-12 (|has| *2 (-6 (-4439 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) (-4 *2 (-1055)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1248 *2)) (-4 *4 (-691 *2 *5 *6))))) (((*1 *2 *3 *3) - (-12 (|has| *2 (-6 (-4436 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) + (-12 (|has| *2 (-6 (-4439 "*"))) (-4 *5 (-376 *2)) (-4 *6 (-376 *2)) (-4 *2 (-1055)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1248 *2)) (-4 *4 (-691 *2 *5 *6))))) (((*1 *2 *3 *3) @@ -15377,7 +15380,7 @@ (((*1 *2 *3 *4) (-12 (-4 *5 (-367)) (-4 *5 (-562)) (-5 *2 - (-2 (|:| |minor| (-646 (-925))) (|:| -3696 *3) + (-2 (|:| |minor| (-646 (-925))) (|:| -3699 *3) (|:| |minors| (-646 (-646 (-925)))) (|:| |ops| (-646 *3)))) (-5 *1 (-90 *5 *3)) (-5 *4 (-925)) (-4 *3 (-663 *5))))) (((*1 *2 *3) @@ -15453,84 +15456,84 @@ (-4 *5 (-562)) (-5 *1 (-41 *5 *2)) (-4 *2 (-426 *5)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *5 (-616 $)) $)) - (-15 -3407 ((-1131 *5 (-616 $)) $)) - (-15 -4387 ($ (-1131 *5 (-616 $)))))))))) + (-10 -8 (-15 -3411 ((-1131 *5 (-616 $)) $)) + (-15 -3410 ((-1131 *5 (-616 $)) $)) + (-15 -4390 ($ (-1131 *5 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *3 (-616 $)) $)) - (-15 -3407 ((-1131 *3 (-616 $)) $)) - (-15 -4387 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) + (-15 -3410 ((-1131 *3 (-616 $)) $)) + (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *3 (-616 $)) $)) - (-15 -3407 ((-1131 *3 (-616 $)) $)) - (-15 -4387 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) + (-15 -3410 ((-1131 *3 (-616 $)) $)) + (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-457) (-1044 (-551)))) (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-426 *3)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *3 (-616 $)) $)) - (-15 -3407 ((-1131 *3 (-616 $)) $)) - (-15 -4387 ($ (-1131 *3 (-616 $)))))))))) + (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) + (-15 -3410 ((-1131 *3 (-616 $)) $)) + (-15 -4390 ($ (-1131 *3 (-616 $)))))))))) (((*1 *2 *3) (-12 (-4 *4 (-562)) (-5 *2 (-1177 *3)) (-5 *1 (-41 *4 *3)) (-4 *3 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *4 (-616 $)) $)) - (-15 -3407 ((-1131 *4 (-616 $)) $)) - (-15 -4387 ($ (-1131 *4 (-616 $)))))))))) + (-10 -8 (-15 -3411 ((-1131 *4 (-616 $)) $)) + (-15 -3410 ((-1131 *4 (-616 $)) $)) + (-15 -4390 ($ (-1131 *4 (-616 $)))))))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *3 (-616 $)) $)) - (-15 -3407 ((-1131 *3 (-616 $)) $)) - (-15 -4387 ($ (-1131 *3 (-616 $))))))))) + (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) + (-15 -3410 ((-1131 *3 (-616 $)) $)) + (-15 -4390 ($ (-1131 *3 (-616 $))))))))) ((*1 *2 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-41 *3 *2)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *3 (-616 $)) $)) - (-15 -3407 ((-1131 *3 (-616 $)) $)) - (-15 -4387 ($ (-1131 *3 (-616 $))))))))) + (-10 -8 (-15 -3411 ((-1131 *3 (-616 $)) $)) + (-15 -3410 ((-1131 *3 (-616 $)) $)) + (-15 -4390 ($ (-1131 *3 (-616 $))))))))) ((*1 *2 *2 *3) (-12 (-5 *3 (-646 *2)) (-4 *2 (-13 (-367) (-301) - (-10 -8 (-15 -3408 ((-1131 *4 (-616 $)) $)) - 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\ No newline at end of file |