diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-04-22 09:22:47 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-04-22 09:22:47 +0000 |
| commit | 308aa20f031e73d86801a36eeda29424e65077b2 (patch) | |
| tree | 6f01dd1af6f448e30729748febd2446523255563 /src | |
| parent | 9fac9abefef7f727a59b7861317d148352a43d88 (diff) | |
| download | open-axiom-308aa20f031e73d86801a36eeda29424e65077b2.tar.gz | |
* algebra/young.spad.pamphlet: New.
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 4 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 2 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/young.spad.pamphlet | 85 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1272 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1405 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1319 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9042 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25633 |
10 files changed, 19437 insertions, 19331 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 16bca349..f751bc9a 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,7 @@ +2010-04-22 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/young.spad.pamphlet: New. + 2010-04-21 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/irsn.spad.pamphlet (IrrRepSymNatPackage): Tidy. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 375128d5..346f6ec8 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -944,7 +944,7 @@ axiom_algebra_layer_user = \ ASP78 ASP9 ASP12 ASP55 ASP8 ASP19 \ ASP20 ASP30 ASP31 ASP35 ASP41 ASP42 \ ASP74 ASP77 ASP80 ASP29 IRFORM COMPILER \ - ITFORM ELABOR TALGOP + ITFORM ELABOR TALGOP YDIAGRAM axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 126fc757..e5f1d98f 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -1023,7 +1023,7 @@ axiom_algebra_layer_user = \ ASP78 ASP9 ASP12 ASP55 ASP8 ASP19 \ ASP20 ASP30 ASP31 ASP35 ASP41 ASP42 \ ASP74 ASP77 ASP80 ASP29 IRFORM COMPILER \ - ITFORM ELABOR TALGOP + ITFORM ELABOR TALGOP YDIAGRAM axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index dcc9d64c..f2b3646a 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -277,7 +277,6 @@ (|NumericComplexEigenPackage| . NCEP) (|NumericRealEigenPackage| . NREP) (|NumericContinuedFraction| . NCNTFRAC) - (|Property| . PROPERTY) (|Octonion| . OCT) (|OctonionCategoryFunctions2| . OCTCT2) (|OneDimensionalArray| . ARRAY1) @@ -303,6 +302,7 @@ (|Pair| . PAIR) (|Palette| . PALETTE) (|PartialFraction| . PFR) + (|Partition| . PRTITION) (|PatternFunctions2| . PATTERN2) (|ParameterAst| . PARAMAST) (|ParametricPlaneCurve| . PARPCURV) @@ -339,6 +339,7 @@ (|PrimeField| . PF) (|PrimitiveArrayFunctions2| . PRIMARR2) (|PrintPackage| . PRINT) + (|Property| . PROPERTY) (|PropositionalFormula| . PROPFRML) (|QuadraticForm| . QFORM) (|QuasiComponentPackage| . QCMPACK) @@ -1046,7 +1047,6 @@ (|ParadoxicalCombinatorsForStreams| . YSTREAM) (|ParametricLinearEquations| . PLEQN) (|PartialFractionPackage| . PFRPAC) - (|Partition| . PRTITION) (|Pattern| . PATTERN) (|PatternFunctions1| . PATTERN1) (|PatternMatchFunctionSpace| . PMFS) diff --git a/src/algebra/young.spad.pamphlet b/src/algebra/young.spad.pamphlet new file mode 100644 index 00000000..df84cf01 --- /dev/null +++ b/src/algebra/young.spad.pamphlet @@ -0,0 +1,85 @@ +\documentclass{article} +\usepackage{open-axiom} + +\author{Gabriel Dos~Reis} + +\begin{document} + +\begin{abstract} +\end{abstract} + +\tableofcontents +\eject + + +\section{Young Diagram} + +<<domain YDIAGRAM YoungDiagram>>= +++ Author: Gabriel Dos Reis +++ Date Last Created: April 17, 2010 +++ Date Last Modified: April 17, 2010 +++ Description: +++ This domain provides representations of Young diagrams. +)abbrev domain YDIAGRAM YoungDiagram +YoungDiagram(): Public == Private where + Public == Join(SetCategory,HomotopicTo Partition) with + youngDiagram: List PositiveInteger -> % + ++ \spad{youngDiagram l} returns an object representing a Young + ++ diagram with shape given by the list of integers \spad{l} + shape: % -> Partition + ++ \spad{shape x} returns the partition shaping \spad{x}. + Private == add + macro LP == List PositiveInteger + Rep == Partition + youngDiagram l == per partition l + shape x == rep x + coerce(x: %): Partition == rep x + coerce(p: Partition): % == per p + x = y == rep x = rep y + coerce(x: %): OutputForm == + b := box empty()$OutputForm + pile [blankSeparate [b for i in 1..n] for n in shape(x)::LP] +@ + + + +\section{License} +<<license>>= +--Copyright (C) 2010, Gabriel Dos Reis. +--All rights reserved. +-- +--Redistribution and use in source and binary forms, with or without +--modification, are permitted provided that the following conditions are +--met: +-- +-- - Redistributions of source code must retain the above copyright +-- notice, this list of conditions and the following disclaimer. +-- +-- - Redistributions in binary form must reproduce the above copyright +-- notice, this list of conditions and the following disclaimer in +-- the documentation and/or other materials provided with the +-- distribution. +-- +-- - Neither the name of The Numerical Algorithms Group Ltd. nor the +-- names of its contributors may be used to endorse or promote products +-- derived from this software without specific prior written permission. +-- +--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A +--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER +--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +@ + + +<<*>>= +<<license>> + +<<domain YDIAGRAM YoungDiagram>> +@ diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index bc062c68..d57c53bf 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2268323 . 3480886511) +(2268689 . 3480912610) (-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."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . 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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4446 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4442 . T) (-4447 . T) (-4441 . T)) +((-4449 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4445 . T) (-4450 . T) (-4444 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1708) +(-32 R -1709) ((|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 -1047) (QUOTE (-570))))) (-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 -4449))) +((|HasAttribute| |#1| (QUOTE -4452))) (-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}."))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . 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"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . 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 -1708 UP UPUP -1932) +(-40 -1709 UP UPUP -1574) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) -(-41 R -1708) +((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2895 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2895 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2895 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +(-41 R -1709) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -436) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-311)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) +((-4449 |has| |#1| (-562)) (-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-368))) (|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."))) -((-4449 . T) (-4450 . T)) -((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) +((-4452 . T) (-4453 . T)) +((-2895 (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-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}."))) -((-4446 . T)) +((-4449 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -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 -1708) +(-54 |Base| R -1709) ((|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 @@ -158,7 +158,7 @@ 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"))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-58 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),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-61 -3600) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-61 -3602) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3600) +(-62 -3602) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -3600) +(-63 -3602) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3600) +(-64 -3602) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -3600) +(-65 -3602) ((|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 -3600) +(-66 -3602) ((|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 -3600) +(-67 -3602) ((|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 -3600) +(-68 -3602) ((|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 -3600) +(-69 -3602) ((|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 -3600) +(-70 -3602) ((|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 -3600) +(-71 -3602) ((|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 -3600) +(-72 -3602) ((|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 -3600) +(-73 -3602) ((|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 -3600) +(-74 -3602) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -3600) +(-77 -3602) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -3600) +(-78 -3602) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -3600) +(-79 -3602) ((|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 -3600) +(-80 -3602) ((|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 -3600) +(-81 -3602) ((|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 -3600) +(-82 -3602) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3600) +(-83 -3602) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3600) +(-84 -3602) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3600) +(-85 -3602) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3600) +(-86 -3602) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -3600) +(-87 -3602) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -3600) +(-88 -3602) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -3600) +(-89 -3602) ((|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 (-368)))) (-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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (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\"."))) -((-4449 . T)) +((-4452 . 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."))) -((-4449 . T) ((-4451 "*") . T) (-4450 . T) (-4446 . T) (-4444 . T) (-4443 . T) (-4442 . T) (-4447 . T) (-4441 . T) (-4440 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4445 . T) (-4448 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4436 . T)) +((-4452 . T) ((-4454 "*") . T) (-4453 . T) (-4449 . T) (-4447 . T) (-4446 . T) (-4445 . T) (-4450 . T) (-4444 . T) (-4443 . T) (-4442 . T) (-4441 . T) (-4440 . T) (-4448 . T) (-4451 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4439 . 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}."))) -((-4446 . T)) +((-4449 . 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (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 (-4451 "*")))) +((|HasAttribute| |#1| (QUOTE (-4454 "*")))) (-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"))) -((-4449 . T)) +((-4452 . 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."))) -((-4450 . T)) +((-4453 . 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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -313) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-112) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -619) (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}"))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1708 UP) +(-116 -1709 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 (-117 |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}."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2892 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2895 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4450))) +((|HasAttribute| |#1| (QUOTE -4453))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -418,15 +418,15 @@ NIL NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-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."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2892 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2895 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -470,7 +470,7 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4451 "*") . T)) +(((-4454 "*") . T)) NIL (-136 |minix| -2550 S T$) ((|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}."))) @@ -498,8 +498,8 @@ NIL NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4449 . T) (-4439 . T) (-4450 . T)) -((-2892 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-4452 . T) (-4442 . T) (-4453 . T)) +((-2895 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|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."))) -((-4446 . T)) +((-4449 . T)) NIL (-147 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}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4446 . T)) +((-4449 . T)) NIL -(-149 -1708 UP UPUP) +(-149 -1709 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 @@ -535,14 +535,14 @@ NIL (-151 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 -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasAttribute| |#1| (QUOTE -4449))) +((|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasAttribute| |#1| (QUOTE -4452))) (-152 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 (-153 |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."))) -((-4444 . T) (-4443 . T) (-4446 . T)) +((-4447 . T) (-4446 . T) (-4449 . T)) NIL (-154) ((|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."))) @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -1708) +(-159 R -1709) ((|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 @@ -595,10 +595,10 @@ NIL (-166 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 (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasAttribute| |#2| (QUOTE -4448)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4442 -2892 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3175 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 -2895 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3178 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4442 -2892 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4445 |has| |#1| (-6 -4445)) (-4448 |has| |#1| (-6 -4448)) (-3175 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . 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(QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -626,7 +626,7 @@ NIL NIL (-174) ((|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."))) -(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4451 "*") . T) (-4442 . T) (-4447 . T) (-4441 . T) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") . T) (-4445 . T) (-4450 . T) (-4444 . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-177) ((|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}."))) @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1708) +(-190 R -1709) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1708 UP UPUP R) +(-217 -1709 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -1708 FP) +(-218 -1709 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1708) +(-221 R -1709) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4446 . T)) +((-4449 . T)) NIL -(-226 R -1708) +(-226 R -1709) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -846,15 +846,15 @@ NIL NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-230 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-231 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."))) -((-4450 . T)) +((-4453 . T)) NIL (-232 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -862,7 +862,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (-233 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4446 . T)) +((-4449 . T)) NIL (-234 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -870,15 +870,15 @@ NIL NIL (-235) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4446 . T)) +((-4449 . T)) NIL (-236 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4449))) +((|HasAttribute| |#1| (QUOTE -4452))) (-237 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}."))) -((-4450 . T)) +((-4453 . T)) NIL (-238) ((|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"))) @@ -887,10 +887,10 @@ NIL (-239 S -2550 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 (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4446)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) +((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) (-240 -2550 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"))) -((-4443 |has| |#2| (-1058)) (-4444 |has| |#2| (-1058)) (-4446 |has| |#2| (-6 -4446)) ((-4451 "*") |has| |#2| (-174)) (-4449 . T)) +((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) NIL (-241 -2550 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}."))) @@ -898,8 +898,8 @@ NIL NIL (-242 -2550 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."))) -((-4443 |has| |#2| (-1058)) (-4444 |has| |#2| (-1058)) (-4446 |has| |#2| (-6 -4446)) ((-4451 "*") |has| |#2| (-174)) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST 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(((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -910,7 +910,7 @@ NIL NIL (-245) ((|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}."))) -((-4442 . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-246 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}.")) 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(QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2895 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-2895 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-255 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 (-235)))) (-256 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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL (-257 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}."))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-258) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,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)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,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)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(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)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,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)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,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)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),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)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -998,8 +998,8 @@ NIL NIL (-267 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"))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-268 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 @@ -1044,11 +1044,11 @@ 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 -(-279 R -1708) +(-279 R -1709) ((|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 -(-280 R -1708) +(-280 R -1709) ((|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 @@ -1074,7 +1074,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) (-286 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}."))) -((-4450 . T)) +((-4453 . T)) NIL (-287 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}."))) @@ -1095,18 +1095,18 @@ NIL (-291 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 -4450))) +((|HasAttribute| |#1| (QUOTE -4453))) (-292 |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 -(-293 S R |Mod| -3449 -2024 |exactQuo|) +(-293 S R |Mod| -3547 -3183 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-294) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4442 . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-295) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1122,21 +1122,21 @@ NIL NIL (-298 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-300) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-301 -1708 S) +(-301 -1709 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 -(-302 E -1708) +(-302 E -1709) ((|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 @@ -1174,7 +1174,7 @@ NIL NIL (-311) ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-312 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1184,7 +1184,7 @@ 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 -(-314 -1708) +(-314 -1709) ((|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 @@ -1198,8 +1198,8 @@ NIL NIL (-317 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))}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2892 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2892 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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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 @@ -1210,9 +1210,9 @@ NIL NIL (-320 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4446 -2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 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(-1121)))) (-2895 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) +(-321 R -1709) ((|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 @@ -1222,8 +1222,8 @@ NIL NIL (-323 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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-324 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 @@ -1234,7 +1234,7 @@ NIL NIL (-326 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."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-798)))) (-327 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1250,19 +1250,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) (-330 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-331 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."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) -(-332 S -1708) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +(-332 S -1709) ((|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 (-373)))) -(-333 -1708) +(-333 -1709) ((|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-334) ((|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."))) @@ -1284,15 +1284,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-339 S -1708 UP UPUP R) +(-339 S -1709 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 -1708 UP UPUP R) +(-340 -1709 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 -(-341 -1708 UP UPUP R) +(-341 -1709 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 @@ -1306,32 +1306,32 @@ NIL NIL (-344 |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.}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-384)))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-345 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}."))) NIL NIL -(-346 S -1708 UP UPUP) +(-346 S -1709 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 (-373))) (|HasCategory| |#2| (QUOTE (-368)))) -(-347 -1708 UP UPUP) +(-347 -1709 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."))) -((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-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 @@ -1346,33 +1346,33 @@ 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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-355 R UP -1708) +(-355 R UP -1709) ((|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-359 |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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) (-360 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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) -(-361 -1708 GF) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +(-361 -1709 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 @@ -1380,21 +1380,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-363 -1708 FP FPP) +(-363 -1709 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 (-364 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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 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 (-366 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4446 . T)) +((-4449 . T)) NIL (-367 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1402,7 +1402,7 @@ NIL NIL (-368) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-369 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1418,7 +1418,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-372 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) +((-4449 |has| |#1| (-562)) (-4447 . T) (-4446 . T)) NIL (-373) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1430,7 +1430,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-368)))) (-375 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL (-376 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1439,14 +1439,14 @@ NIL (-377 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109)))) (-378 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4449 . T)) +((-4452 . T)) NIL (-379 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4444 . T) (-4443 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4447 . T) (-4446 . T)) NIL (-380 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."))) @@ -1458,7 +1458,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-382 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}"))) -((-4446 . T)) +((-4449 . 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}."))) @@ -1466,7 +1466,7 @@ NIL NIL (-384) ((|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}."))) -((-4432 . T) (-4440 . T) (-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4435 . T) (-4443 . T) (-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-385 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1474,11 +1474,11 @@ NIL NIL (-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}"))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-387 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}."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-388) ((|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}."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390 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."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-391 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1502,7 +1502,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-856)))) (-393) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-394) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1514,13 +1514,13 @@ NIL NIL (-396 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-397) ((|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 -(-398 -1708 UP UPUP R) +(-398 -1709 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 @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-404 -3600 |returnType| -3928 |symbols|) +(-404 -3602 |returnType| -3931 |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 -(-405 -1708 UP) +(-405 -1709 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1562,15 +1562,15 @@ NIL NIL (-408) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-409 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4432)) (|HasAttribute| |#1| (QUOTE -4440))) +((|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4443))) (-410) ((|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\"."))) -((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-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."))) @@ -1582,15 +1582,15 @@ NIL NIL (-413 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."))) -((-4436 -12 (|has| |#1| (-6 -4447)) (|has| |#1| (-458)) (|has| |#1| (-6 -4436))) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2892 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4436)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4439 -12 (|has| |#1| (-6 -4450)) (|has| |#1| (-458)) (|has| |#1| (-6 -4439))) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2895 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL (-416 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1604,11 +1604,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-419 R -1708 UP A) +(-419 R -1709 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4446 . T)) +((-4449 . T)) NIL -(-420 R -1708 UP A |ibasis|) +(-420 R -1709 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1047) (|devaluate| |#2|)))) @@ -1622,12 +1622,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-423 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4446 |has| |#1| (-562)) (-4444 . T) (-4443 . T)) +((-4449 |has| |#1| (-562)) (-4447 . T) (-4446 . T)) NIL (-424 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) (-425 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1654,17 +1654,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-373)))) (-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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4449 . T) (-4439 . T) (-4450 . T)) +((-4452 . T) (-4442 . T) (-4453 . T)) NIL -(-432 R -1708) +(-432 R -1709) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-433 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4436 -12 (|has| |#1| (-6 -4436)) (|has| |#2| (-6 -4436))) (-4443 . T) (-4444 . T) (-4446 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4436)) (|HasAttribute| |#2| (QUOTE -4436)))) -(-434 R -1708) +((-4439 -12 (|has| |#1| (-6 -4439)) (|has| |#2| (-6 -4439))) (-4446 . T) (-4447 . T) (-4449 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#2| (QUOTE -4439)))) +(-434 R -1709) ((|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 @@ -1674,17 +1674,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-436 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}."))) -((-4446 -2892 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) ((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-562)) (-4441 |has| |#1| (-562))) +((-4449 -2895 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) NIL -(-437 R -1708) +(-437 R -1709) ((|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 -(-438 R -1708) +(-438 R -1709) ((|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)))) -(-439 R -1708) +(-439 R -1709) ((|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 @@ -1692,7 +1692,7 @@ 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 -(-441 R -1708 UP) +(-441 R -1709 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 -1047) (QUOTE (-48))))) @@ -1724,7 +1724,7 @@ 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 -(-449 R UP -1708) +(-449 R UP -1709) ((|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 @@ -1762,16 +1762,16 @@ NIL NIL (-458) ((|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}."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-459 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"))) -((-4446 |has| (-413 (-959 |#1|)) (-562)) (-4444 . T) (-4443 . T)) +((-4449 |has| (-413 (-959 |#1|)) (-562)) (-4447 . T) (-4446 . T)) ((|HasCategory| (-413 (-959 |#1|)) (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-413 (-959 |#1|)) (QUOTE (-562)))) (-460 |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"))) -(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-461 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 @@ -1798,7 +1798,7 @@ NIL NIL (-467 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-468 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1806,7 +1806,7 @@ NIL NIL (-469 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-470 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}."))) @@ -1836,7 +1836,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-477 |lv| -1708 R) +(-477 |lv| -1709 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1846,23 +1846,23 @@ NIL NIL (-479) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4446 . T)) +((-4449 . T)) NIL (-480 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-481 |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."))) -((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) +((-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) (-482 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)}"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-483) ((|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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-484) ((|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'."))) @@ -1870,29 +1870,29 @@ NIL NIL (-485 |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."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-486) ((|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 (-487 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-490 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-491 -1708 UP UPUP R) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +(-491 -1709 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 @@ -1902,12 +1902,12 @@ NIL NIL (-493) ((|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-494 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 -4449)) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) +((|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-495 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1928,33 +1928,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-500 -1708 UP |AlExt| |AlPol|) +(-500 -1709 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-501) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) (-502 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-503 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."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-504 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 -(-505 R UP -1708) +(-505 R UP -1709) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-506 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -313) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-112) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-112) (QUOTE (-1109))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-868))))) (-507 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)}."))) @@ -1968,7 +1968,7 @@ 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 -(-510 -1708 |Expon| |VarSet| |DPoly|) +(-510 -1709 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-1186))))) @@ -2018,36 +2018,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-798)))) (-522 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-523) ((|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 (-524 |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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((-2892 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((-2895 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) (-525 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-526 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."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-527 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 -4450))) +((|HasAttribute| |#3| (QUOTE -4453))) (-528 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 -4450))) +((|HasAttribute| |#7| (QUOTE -4453))) (-529 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."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-530) ((|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 @@ -2080,7 +2080,7 @@ 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 -(-538 K -1708 |Par|) +(-538 K -1709 |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 @@ -2104,7 +2104,7 @@ 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 -(-544 K -1708 |Par|) +(-544 K -1709 |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 @@ -2134,7 +2134,7 @@ NIL NIL (-551) ((|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."))) -((-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4450 . T) (-4451 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) -(-557 R -1708) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +(-557 R -1709) ((|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 -1708 UP UPUP R) +(-558 R0 -1709 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."))) -((-3167 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3170 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . 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."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-563 R -1708) +(-563 R -1709) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2192,7 +2192,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-566 R -1708 L) +(-566 R -1709 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) @@ -2200,31 +2200,31 @@ 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 -1708 UP UPUP R) +(-568 -1709 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 -1708 UP) +(-569 -1709 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 (-570) ((|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."))) -((-4431 . T) (-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4434 . T) (-4440 . T) (-4444 . T) (-4439 . T) (-4450 . T) (-4451 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-571) ((|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 -(-572 R -1708 L) +(-572 R -1709 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -662) (|devaluate| |#2|)))) -(-573 R -1708) +(-573 R -1709) ((|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 -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1148)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-635))))) -(-574 -1708 UP) +(-574 -1709 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 @@ -2232,27 +2232,27 @@ 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 -(-576 -1708) +(-576 -1709) ((|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 (-577 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."))) -((-3167 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3170 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-578) ((|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 -(-579 R -1708) +(-579 R -1709) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-288))) (|HasCategory| |#2| (QUOTE (-635))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-288)))) (|HasCategory| |#1| (QUOTE (-562)))) -(-580 -1708 UP) +(-580 -1709 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-581 R -1708) +(-581 R -1709) ((|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 @@ -2274,21 +2274,21 @@ NIL NIL (-586 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-587 |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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) (-588) ((|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 -(-589 R -1708) +(-589 R -1709) ((|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 -(-590 E -1708) +(-590 E -1709) ((|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 @@ -2296,9 +2296,9 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-592 -1708) +(-592 -1709) ((|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}."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-593 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) @@ -2326,19 +2326,19 @@ NIL NIL (-599 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2892 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2895 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-600 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 (-601 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) (-602 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4451 "*") |has| |#1| (-562)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-562)))) (-603) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2352,7 +2352,7 @@ 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 -(-606 R -1708 FG) +(-606 R -1709 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 @@ -2362,12 +2362,12 @@ NIL NIL (-608 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-609 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 -4450)) (|HasCategory| |#2| (QUOTE (-856))) (|HasAttribute| |#1| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-856))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#3| (QUOTE (-1109)))) (-610 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2382,19 +2382,19 @@ NIL NIL (-613 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4446 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) -((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2895 (-1810 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2895 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-614 |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."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-615 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 (-616 |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}."))) -((-4450 . T)) +((-4453 . T)) NIL (-617 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2412,7 +2412,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-621 -1708 UP) +(-621 -1709 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2434,19 +2434,19 @@ 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."))) -((-4446 . T)) +((-4449 . T)) NIL (-627 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}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-854)))) -(-628 R -1708) +(-628 R -1709) ((|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 (-629 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"))) -((-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4442 . T) (-4446 . T)) +((-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4445 . T) (-4449 . T)) ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-630 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."))) @@ -2462,7 +2462,7 @@ NIL NIL (-633 |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}}."))) -((-4446 . T)) +((-4449 . T)) NIL (-634 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}}."))) @@ -2472,30 +2472,30 @@ 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 R -1708) +(-636 R -1709) ((|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 -(-637 |lv| -1708) +(-637 |lv| -1709) ((|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 (-638) ((|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."))) -((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109)))) +((-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109)))) (-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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-640 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4444 . T) (-4443 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4447 . T) (-4446 . T)) NIL (-641 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4446 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4444 . T) (-4443 . T)) -((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) +((-4449 -2895 (-1810 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) +((-2895 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-642 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2507,10 +2507,10 @@ NIL (-644 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 -((-1795 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) +((-1796 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) (-645 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4446 . T)) +((-4449 . T)) NIL (-646 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2530,8 +2530,8 @@ NIL NIL (-650 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-651 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2542,8 +2542,8 @@ NIL NIL (-653 S) ((|substitute| (($ |#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."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-654 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 @@ -2555,22 +2555,22 @@ NIL (-656 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 -4450))) +((|HasAttribute| |#1| (QUOTE -4453))) (-657 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 -(-658 R -1708 L) +(-658 R -1709 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) ((|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}}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-660 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-661 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2578,15 +2578,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-662 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}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-663 -1708 UP) +(-663 -1709 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)))) -(-664 A -2832) +(-664 A -1444) ((|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}}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) (-665 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} 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}. \\spad{D} is the derivation to use."))) @@ -2602,7 +2602,7 @@ NIL NIL (-668 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}."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) ((|HasCategory| |#1| (QUOTE (-797)))) (-669 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([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 exists."))) @@ -2610,7 +2610,7 @@ NIL NIL (-670 |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) (-4444 . T) (-4443 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4447 . T) (-4446 . T)) ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-174)))) (-671 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}."))) @@ -2618,13 +2618,13 @@ NIL NIL (-672 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}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL -(-673 -1708) +(-673 -1709) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-674 -1708 |Row| |Col| M) +(-674 -1709 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2634,8 +2634,8 @@ NIL NIL (-676 |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."))) -((-4446 . T) (-4449 . T) (-4443 . T) (-4444 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2892 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4449 . T) (-4452 . T) (-4446 . T) (-4447 . T)) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2895 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-677) ((|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 @@ -2655,7 +2655,7 @@ NIL (-681 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 -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-682) ((|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 @@ -2699,10 +2699,10 @@ NIL (-692 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 (-4451 "*"))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562)))) +((|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562)))) (-693 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"))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-694 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|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")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|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}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|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."))) @@ -2710,8 +2710,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562)))) (-695 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."))) -((-4449 . T) (-4450 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4451 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4452 . T) (-4453 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-696 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 @@ -2720,7 +2720,7 @@ 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 -(-698 S -1708 FLAF FLAS) +(-698 S -1709 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 @@ -2730,11 +2730,11 @@ NIL NIL (-700) ((|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"))) -((-4442 . T) (-4447 |has| (-705) (-368)) (-4441 |has| (-705) (-368)) (-3175 . T) (-4448 |has| (-705) (-6 -4448)) (-4445 |has| (-705) (-6 -4445)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2892 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2892 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2892 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4448)) (|HasAttribute| (-705) (QUOTE -4445)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) +((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3178 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2895 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2895 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2895 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) (-701 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}."))) -((-4450 . T)) +((-4453 . T)) NIL (-702 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}."))) @@ -2744,13 +2744,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-704 OV E -1708 PG) +(-704 OV E -1709 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 (-705) ((|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}"))) -((-3167 . T) (-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-706 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."))) @@ -2758,7 +2758,7 @@ NIL NIL (-707) ((|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}"))) -((-4448 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4451 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-708 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"))) @@ -2776,7 +2776,7 @@ 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 -(-712 S -2942 I) +(-712 S -2945 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 @@ -2786,7 +2786,7 @@ NIL NIL (-714 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)}.}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL (-715 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}."))) @@ -2796,25 +2796,25 @@ 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 -(-717 R |Mod| -3449 -2024 |exactQuo|) +(-717 R |Mod| -3547 -3183 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-718 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-719 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-720 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) +((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-721 R |Mod| -3449 -2024 |exactQuo|) +(-721 R |Mod| -3547 -3183 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4446 . T)) +((-4449 . T)) NIL (-722 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2822,11 +2822,11 @@ NIL NIL (-723 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL -(-724 -1708) +(-724 -1709) ((|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]]}."))) -((-4446 . T)) +((-4449 . T)) NIL (-725 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."))) @@ -2850,7 +2850,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373)))) (-730 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."))) -((-4442 |has| |#1| (-368)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-731 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."))) @@ -2860,7 +2860,7 @@ 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 -(-733 -1708 UP) +(-733 -1709 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 @@ -2878,8 +2878,8 @@ NIL NIL (-737 |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."))) -(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4447)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-738 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2894,15 +2894,15 @@ NIL NIL (-741 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) +((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-856)))) (-742 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4439 . T) (-4450 . T)) +((-4442 . T) (-4453 . T)) NIL (-743 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}."))) -((-4449 . T) (-4439 . T) (-4450 . T)) +((-4452 . T) (-4442 . T) (-4453 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-744) ((|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."))) @@ -2914,7 +2914,7 @@ NIL NIL (-746 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL (-747 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"))) @@ -2930,7 +2930,7 @@ NIL NIL (-750 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}."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-751) ((|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}."))) @@ -3012,11 +3012,11 @@ 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 -(-771 -1708) +(-771 -1709) ((|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 -(-772 P -1708) +(-772 P -1709) ((|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 @@ -3024,7 +3024,7 @@ NIL NIL NIL NIL -(-774 UP -1708) +(-774 UP -1709) ((|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 @@ -3038,9 +3038,9 @@ NIL NIL (-777) ((|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."))) -(((-4451 "*") . T)) +(((-4454 "*") . T)) NIL -(-778 R -1708) +(-778 R -1709) ((|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 @@ -3060,7 +3060,7 @@ 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 -(-783 -1708 |ExtF| |SUEx| |ExtP| |n|) +(-783 -1709 |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 @@ -3074,23 +3074,23 @@ NIL NIL (-786 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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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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| (((|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 NIL (-788 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-790 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.}"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-791 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}."))) @@ -3142,25 +3142,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-373)))) (-803 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL -(-804 -2892 R OS S) +(-804 -2895 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-805 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2892 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) +((-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2895 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-806) ((|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 -(-807 R -1708 L) +(-807 R -1709 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 -(-808 R -1708) +(-808 R -1709) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3168,7 +3168,7 @@ 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 -(-810 R -1708) +(-810 R -1709) ((|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 @@ -3176,11 +3176,11 @@ 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 -(-812 -1708 UP UPUP R) +(-812 -1709 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 -(-813 -1708 UP L LQ) +(-813 -1709 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 @@ -3188,41 +3188,41 @@ 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 -(-815 -1708 UP L LQ) +(-815 -1709 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 -(-816 -1708 UP) +(-816 -1709 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-817 -1708 L UP A LO) +(-817 -1709 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 -(-818 -1708 UP) +(-818 -1709 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)))) -(-819 -1708 LO) +(-819 -1709 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 -(-820 -1708 LODO) +(-820 -1709 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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T) (-4444 . T) (-4443 . T)) +(((-4454 "*") |has| |#2| (-368)) (-4445 |has| |#2| (-368)) (-4450 |has| |#2| (-368)) (-4444 |has| |#2| (-368)) (-4449 . T) (-4447 . T) (-4446 . T)) ((|HasCategory| |#2| (QUOTE (-368)))) (-824 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}))."))) @@ -3234,7 +3234,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-856)))) (-826) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-827) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -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}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-235)))) (-834) ((|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."))) @@ -3274,7 +3274,7 @@ NIL NIL (-836 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4449 . T) (-4439 . T) (-4450 . T)) +((-4452 . T) (-4442 . T) (-4453 . T)) NIL (-837) ((|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."))) @@ -3286,8 +3286,8 @@ NIL NIL (-839 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."))) -((-4446 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((-4449 |has| |#1| (-854))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-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}."))) NIL @@ -3298,7 +3298,7 @@ NIL NIL (-842 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) +((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-843) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3326,8 +3326,8 @@ NIL NIL (-849 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4446 |has| |#1| (-854))) -((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) +((-4449 |has| |#1| (-854))) +((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) (-850) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL @@ -3346,7 +3346,7 @@ NIL NIL (-854) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4446 . T)) +((-4449 . T)) NIL (-855 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3362,19 +3362,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) (-858 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL (-859 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 (-368))) (|HasCategory| |#1| (QUOTE (-562)))) -(-860 R |sigma| -3225) +(-860 R |sigma| -3229) ((|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."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) -(-861 |x| R |sigma| -3225) +(-861 |x| R |sigma| -3229) ((|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}."))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) (-862 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..)}."))) @@ -3418,7 +3418,7 @@ NIL NIL (-872 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) +((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (-873 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3430,24 +3430,24 @@ NIL NIL (-875 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-876 |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)."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-877 |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)."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2892 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2895 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) (-878 |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)}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2892 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2895 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) (-879 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 (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-880) ((|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 @@ -3507,7 +3507,7 @@ NIL (-894 |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 (-1795 (|HasCategory| |#2| (QUOTE (-1058)))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) +((-12 (-1796 (|HasCategory| |#2| (QUOTE (-1058)))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-895 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3516,7 +3516,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-897 R -2942) +(-897 R -2945) ((|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 @@ -3540,7 +3540,7 @@ 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 -(-903 UP -1708) +(-903 UP -1709) ((|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 @@ -3558,19 +3558,19 @@ NIL NIL (-907 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}."))) -((-4446 . T)) +((-4449 . T)) NIL (-908 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 (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-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."))) -((-4446 . T)) +((-4449 . 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3578,8 +3578,8 @@ NIL NIL (-912 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4446 . T)) -((-2892 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) +((-4449 . T)) +((-2895 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (-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."))) NIL @@ -3594,13 +3594,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-146)))) (-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}."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-917 |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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-373)))) -(-918 R0 -1708 UP UPUP R) +(-918 R0 -1709 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 @@ -3614,7 +3614,7 @@ NIL NIL (-921 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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-922 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."))) @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-925 -1708) +(-925 -1709) ((|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 @@ -3638,17 +3638,17 @@ 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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-928) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4451 "*") . T)) +(((-4454 "*") . T)) NIL -(-929 -1708 P) +(-929 -1709 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-930 |xx| -1708) +(-930 |xx| -1709) ((|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 @@ -3672,7 +3672,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-936 R -1708) +(-936 R -1709) ((|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 @@ -3684,7 +3684,7 @@ 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 -(-939 S R -1708) +(-939 S R -1709) ((|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 @@ -3704,11 +3704,11 @@ 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 -893) (|devaluate| |#1|)))) -(-944 R -1708 -2942) +(-944 R -1709 -2945) ((|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 -(-945 -2942) +(-945 -2945) ((|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 @@ -3730,8 +3730,8 @@ NIL NIL (-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-951 |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 @@ -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 -4447)) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) +((|HasCategory| |#2| (QUOTE (-916))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#4| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#4| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-957 E V R P -1708) +(-957 E V R P -1709) ((|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 @@ -3766,9 +3766,9 @@ NIL NIL (-959 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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-960 E V R P -1708) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-960 E V R P -1709) ((|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 (-458)))) @@ -3790,13 +3790,13 @@ NIL NIL (-965 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"))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-966) ((|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 -1708) +(-967 -1709) ((|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 @@ -3810,12 +3810,12 @@ NIL NIL (-970 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}"))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4447))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) (-971 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) +((-4449 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-972) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3838,7 +3838,7 @@ NIL NIL (-977 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-978 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}}"))) @@ -3858,7 +3858,7 @@ NIL NIL (-982 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-983) ((|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}."))) @@ -3870,7 +3870,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-562)))) (-985 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."))) -((-4449 . T)) +((-4452 . T)) NIL (-986 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."))) @@ -3886,7 +3886,7 @@ NIL NIL (-989 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}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-990 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) @@ -3904,7 +3904,7 @@ 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 -(-994 K R UP -1708) +(-994 K R UP -1709) ((|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 @@ -3934,7 +3934,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161)))) (-1001 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}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1002 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3946,7 +3946,7 @@ NIL NIL (-1004 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."))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-1005 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}."))) @@ -3954,7 +3954,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-294)))) (-1006 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}."))) -((-4442 |has| |#1| (-294)) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1007 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}."))) @@ -3962,12 +3962,12 @@ NIL NIL (-1008 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.}"))) -((-4442 |has| |#1| (-294)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) +((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) (-1009 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1010 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3976,14 +3976,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1012 -1708 UP UPUP |radicnd| |n|) +(-1012 -1709 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4442 |has| (-413 |#2|) (-368)) (-4447 |has| (-413 |#2|) (-368)) (-4441 |has| (-413 |#2|) (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) +((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2895 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2895 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2895 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) (-1013 |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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) (-1014) ((|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 @@ -4003,7 +4003,7 @@ NIL (-1018 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 -4450)) (|HasCategory| |#2| (QUOTE (-1109)))) +((|HasAttribute| |#1| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-1109)))) (-1019 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 @@ -4014,21 +4014,21 @@ NIL NIL (-1021) ((|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}}"))) -((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) +((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) NIL -(-1022 R -1708) +(-1022 R -1709) ((|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 -(-1023 R -1708) +(-1023 R -1709) ((|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 -(-1024 -1708 UP) +(-1024 -1709 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 -(-1025 -1708 UP) +(-1025 -1709 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 @@ -4062,9 +4062,9 @@ NIL NIL (-1033 |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"))) -((-4442 . T) (-4447 . T) (-4441 . T) (-4444 . T) (-4443 . T) ((-4451 "*") . T) (-4446 . T)) -((-2892 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) -(-1034 -1708 L) +((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) +((-2895 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) +(-1034 -1709 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 @@ -4074,12 +4074,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1109)))) (-1036 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."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-1037 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 (-4451 "*")))) +((|HasAttribute| |#1| (QUOTE (-4454 "*")))) (-1038 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 @@ -4100,14 +4100,14 @@ 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 -(-1043 -1708 |Expon| |VarSet| |FPol| |LFPol|) +(-1043 -1709 |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"))) -(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1044) ((|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.}"))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1045) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4150,7 +4150,7 @@ NIL NIL (-1055 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}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| (-786 |#1| (-870 |#2|)) (QUOTE (-1109))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -786) (|devaluate| |#1|) (LIST (QUOTE -870) (|devaluate| |#2|)))))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-786 |#1| (-870 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-870 |#2|) (QUOTE (-373))) (|HasCategory| (-786 |#1| (-870 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1056) ((|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"))) @@ -4162,9 +4162,9 @@ NIL NIL (-1058) ((|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."))) -((-4446 . T)) +((-4449 . T)) NIL -(-1059 |xx| -1708) +(-1059 |xx| -1709) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4178,12 +4178,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (QUOTE (-562))) (|HasCategory| |#4| (QUOTE (-174)))) (-1062 |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"))) -((-4449 . T) (-4444 . T) (-4443 . T)) +((-4452 . T) (-4447 . T) (-4446 . T)) NIL (-1063 |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}."))) -((-4449 . T) (-4444 . T) (-4443 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2892 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4447 . T) (-4446 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2895 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (-1064 |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 @@ -4206,7 +4206,7 @@ NIL NIL (-1069) ((|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."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1070 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4214,19 +4214,19 @@ NIL NIL (-1071) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4440 . T) (-4444 . T) (-4439 . T) (-4450 . T) (-4451 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1072) ((|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}"))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) (-1073 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1001) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-1186))))) (-1074 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL (-1075) ((|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'."))) @@ -4250,7 +4250,7 @@ NIL NIL (-1080 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}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1081 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."))) @@ -4268,11 +4268,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1085 |Base| R -1708) +(-1085 |Base| R -1709) ((|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 -(-1086 |Base| R -1708) +(-1086 |Base| R -1709) ((|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 @@ -4286,8 +4286,8 @@ NIL NIL (-1089 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."))) -((-4442 |has| |#1| (-368)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) +((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) (-1090 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4314,8 +4314,8 @@ NIL NIL (-1096 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"))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1097 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 @@ -4358,7 +4358,7 @@ NIL NIL (-1107 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}."))) -((-4439 . T)) +((-4442 . T)) NIL (-1108 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}."))) @@ -4374,8 +4374,8 @@ NIL NIL (-1111 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)}}"))) -((-4449 . T) (-4439 . T) (-4450 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4452 . T) (-4442 . T) (-4453 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1112 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4402,7 +4402,7 @@ NIL NIL (-1118 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.}"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1119) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4418,8 +4418,8 @@ NIL NIL (-1122 |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}."))) -((-4443 |has| |#3| (-1058)) (-4444 |has| |#3| (-1058)) (-4446 |has| |#3| (-6 -4446)) ((-4451 "*") |has| |#3| (-174)) (-4449 . 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(LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (-1123 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 @@ -4428,7 +4428,7 @@ 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 -(-1125 R -1708) +(-1125 R -1709) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4446,19 +4446,19 @@ NIL NIL (-1129) ((|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}.")) (|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."))) -((-4437 . T) (-4441 . T) (-4436 . T) (-4447 . T) (-4448 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4440 . T) (-4444 . T) (-4439 . T) (-4450 . T) (-4451 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1130 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4449 . T) (-4450 . T)) +((-4452 . T) (-4453 . T)) NIL (-1131 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-368))) (|HasAttribute| |#3| (QUOTE (-4451 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +((|HasCategory| |#3| (QUOTE (-368))) (|HasAttribute| |#3| (QUOTE (-4454 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) (-1132 |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."))) -((-4449 . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4452 . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1133 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}."))) @@ -4466,17 +4466,17 @@ NIL NIL (-1134 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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1135 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1136 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}"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL -(-1137 UP -1708) +(-1137 UP -1709) ((|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 @@ -4530,19 +4530,19 @@ NIL NIL (-1150 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2892 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2895 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) (-1151 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4446 . T) (-4438 |has| |#2| (-6 (-4451 "*"))) (-4449 . T) (-4443 . T) (-4444 . T)) -((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2892 (|HasAttribute| |#2| (QUOTE (-4451 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4449 . T) (-4441 |has| |#2| (-6 (-4454 "*"))) (-4452 . T) (-4446 . T) (-4447 . T)) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2895 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1152 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1153) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1154 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.}"))) @@ -4550,12 +4550,12 @@ NIL NIL (-1155 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."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-1156 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}."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1157 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 @@ -4566,8 +4566,8 @@ NIL NIL (-1159 |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."))) -((-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) +((-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) (-1160) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4594,20 +4594,20 @@ NIL NIL (-1166 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) -((-4450 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4453 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1167) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1168) NIL -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-1169 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1170 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 @@ -4638,9 +4638,9 @@ NIL NIL (-1177 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4451 "*") -2892 (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4442 -2892 (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . 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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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1184 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1185) ((|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 @@ -4682,8 +4682,8 @@ NIL NIL (-1188 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-6 -4447)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4447))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4450))) (-1189) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4726,8 +4726,8 @@ NIL NIL (-1199 |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}"))) -((-4449 . T) (-4450 . T)) -((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) +((-4452 . T) (-4453 . T)) +((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) (-1200 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4742,7 +4742,7 @@ NIL NIL (-1203 |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})}."))) -((-4450 . T)) +((-4453 . T)) NIL (-1204 |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."))) @@ -4782,8 +4782,8 @@ NIL NIL (-1213 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4450 . T) (-4449 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) +((-4453 . T) (-4452 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (-1214 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4792,7 +4792,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1216 R -1708) +(-1216 R -1709) ((|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 @@ -4800,7 +4800,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1218 R -1708) +(-1218 R -1709) ((|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 -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -893) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -893) (|devaluate| |#1|))))) @@ -4810,12 +4810,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-373)))) (-1220 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1221 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) (-1222 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4828,7 +4828,7 @@ 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 (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) -(-1225 -1708) +(-1225 -1709) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4854,7 +4854,7 @@ NIL NIL (-1231) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1232) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4878,7 +4878,7 @@ NIL NIL (-1237 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1238 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)}."))) @@ -4886,16 +4886,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-368)))) (-1239 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1240 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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the factorization 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 @@ -4930,8 +4930,8 @@ NIL NIL (-1250 |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| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4451 "*") |has| |#2| (-174)) (-4442 |has| |#2| (-562)) (-4445 |has| |#2| (-368)) (-4447 |has| |#2| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4942,15 +4942,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1161)))) (-1253 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4445 |has| |#1| (-368)) (-4447 |has| |#1| (-6 -4447)) (-4444 . T) (-4443 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL (-1254 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 -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3799) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) +((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3802) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) (-1255 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1256 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4962,7 +4962,7 @@ NIL NIL (-1258 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1259 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)}."))) @@ -4970,24 +4970,24 @@ NIL NIL (-1260 |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)}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1261 |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)}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-1262 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4447 |has| |#1| (-368)) (-4441 |has| |#1| (-368)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1263 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))}."))) -(((-4451 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4442 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2892 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) +(((-4454 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4445 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2895 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) (-1264 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4450))) +((|HasAttribute| |#1| (QUOTE -4453))) (-1265 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4999,20 +4999,20 @@ NIL (-1267 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2898) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2023) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-1268 |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."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1269 |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}."))) -(((-4451 "*") |has| |#1| (-174)) (-4442 |has| |#1| (-562)) (-4443 . T) (-4444 . T) (-4446 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3799) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2898) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) +(((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) (-1270 |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 -(-1271 -1708 UP L UTS) +(-1271 -1709 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)))) @@ -5030,7 +5030,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1275 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) NIL (-1276 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -5038,8 +5038,8 @@ NIL NIL (-1277 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4450 . T) (-4449 . T)) -((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) +((-4453 . T) (-4452 . T)) +((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-1278) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5066,13 +5066,13 @@ NIL NIL (-1284 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4444 . T) (-4443 . T)) +((-4447 . T) (-4446 . T)) NIL (-1285 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 -(-1286 K R UP -1708) +(-1286 K R UP -1709) ((|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 @@ -5086,71 +5086,75 @@ NIL NIL (-1289 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)"))) -((-4444 |has| |#1| (-174)) (-4443 |has| |#1| (-174)) (-4446 . T)) +((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (-1290 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}}."))) -((-4450 . T) (-4449 . T)) +((-4453 . T) (-4452 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868))))) (-1291 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})"))) -((-4443 . T) (-4444 . T) (-4446 . T)) +((-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1292 |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."))) -((-4446 . T) (-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4442))) +((-4449 . T) (-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4445))) (-1293 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 (-1294 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) +((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL -(-1295 S -1708) +(-1295 S -1709) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1296 -1708) +(-1296 -1709) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4441 . T) (-4447 . T) (-4442 . T) ((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL (-1297 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -723) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasAttribute| |#2| (QUOTE -4442))) +((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -723) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasAttribute| |#2| (QUOTE -4445))) (-1298 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) +((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) NIL (-1299 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4442 |has| |#1| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4442))) +((-4445 |has| |#1| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4445))) (-1300 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4446 . T) (-4447 |has| |#1| (-6 -4447)) (-4442 |has| |#1| (-6 -4442)) (-4444 . T) (-4443 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4442))) +((-4449 . T) (-4450 |has| |#1| (-6 -4450)) (-4445 |has| |#1| (-6 -4445)) (-4447 . T) (-4446 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4449)) (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4445))) (-1301 |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."))) -((-4442 |has| |#2| (-6 -4442)) (-4444 . T) (-4443 . T) (-4446 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4442))) -(-1302 A) +((-4445 |has| |#2| (-6 -4445)) (-4447 . T) (-4446 . T) (-4449 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4445))) +(-1302) +((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) +NIL +NIL +(-1303 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 NIL -(-1303 R |ls| |ls2|) +(-1304 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} 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{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1304 R) +(-1305 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([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 the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1305 |p|) +(-1306 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4451 "*") . T) (-4443 . T) (-4444 . T) (-4446 . T)) +(((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) NIL NIL NIL @@ -5168,4 +5172,4 @@ NIL NIL NIL NIL -((-3 NIL 2268303 2268308 2268313 2268318) (-2 NIL 2268283 2268288 2268293 2268298) (-1 NIL 2268263 2268268 2268273 2268278) (0 NIL 2268243 2268248 2268253 2268258) (-1305 "ZMOD.spad" 2268052 2268065 2268181 2268238) (-1304 "ZLINDEP.spad" 2267118 2267129 2268042 2268047) (-1303 "ZDSOLVE.spad" 2257063 2257085 2267108 2267113) (-1302 "YSTREAM.spad" 2256558 2256569 2257053 2257058) (-1301 "XRPOLY.spad" 2255778 2255798 2256414 2256483) (-1300 "XPR.spad" 2253573 2253586 2255496 2255595) (-1299 "XPOLY.spad" 2253128 2253139 2253429 2253498) (-1298 "XPOLYC.spad" 2252447 2252463 2253054 2253123) (-1297 "XPBWPOLY.spad" 2250884 2250904 2252227 2252296) (-1296 "XF.spad" 2249347 2249362 2250786 2250879) (-1295 "XF.spad" 2247790 2247807 2249231 2249236) (-1294 "XFALG.spad" 2244838 2244854 2247716 2247785) (-1293 "XEXPPKG.spad" 2244089 2244115 2244828 2244833) (-1292 "XDPOLY.spad" 2243703 2243719 2243945 2244014) (-1291 "XALG.spad" 2243363 2243374 2243659 2243698) (-1290 "WUTSET.spad" 2239202 2239219 2243009 2243036) (-1289 "WP.spad" 2238401 2238445 2239060 2239127) (-1288 "WHILEAST.spad" 2238199 2238208 2238391 2238396) (-1287 "WHEREAST.spad" 2237870 2237879 2238189 2238194) (-1286 "WFFINTBS.spad" 2235533 2235555 2237860 2237865) (-1285 "WEIER.spad" 2233755 2233766 2235523 2235528) (-1284 "VSPACE.spad" 2233428 2233439 2233723 2233750) (-1283 "VSPACE.spad" 2233121 2233134 2233418 2233423) (-1282 "VOID.spad" 2232798 2232807 2233111 2233116) (-1281 "VIEW.spad" 2230478 2230487 2232788 2232793) (-1280 "VIEWDEF.spad" 2225679 2225688 2230468 2230473) (-1279 "VIEW3D.spad" 2209640 2209649 2225669 2225674) (-1278 "VIEW2D.spad" 2197531 2197540 2209630 2209635) (-1277 "VECTOR.spad" 2196205 2196216 2196456 2196483) (-1276 "VECTOR2.spad" 2194844 2194857 2196195 2196200) (-1275 "VECTCAT.spad" 2192748 2192759 2194812 2194839) (-1274 "VECTCAT.spad" 2190459 2190472 2192525 2192530) (-1273 "VARIABLE.spad" 2190239 2190254 2190449 2190454) (-1272 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2147047 2149310 2149315) (-1253 "UPOLYC.spad" 2142061 2142072 2146863 2147016) (-1252 "UPOLYC.spad" 2136993 2137006 2141797 2141802) (-1251 "UPOLYC2.spad" 2136464 2136483 2136983 2136988) (-1250 "UP.spad" 2133663 2133678 2134050 2134203) (-1249 "UPMP.spad" 2132563 2132576 2133653 2133658) (-1248 "UPDIVP.spad" 2132128 2132142 2132553 2132558) (-1247 "UPDECOMP.spad" 2130373 2130387 2132118 2132123) (-1246 "UPCDEN.spad" 2129582 2129598 2130363 2130368) (-1245 "UP2.spad" 2128946 2128967 2129572 2129577) (-1244 "UNISEG.spad" 2128299 2128310 2128865 2128870) (-1243 "UNISEG2.spad" 2127796 2127809 2128255 2128260) (-1242 "UNIFACT.spad" 2126899 2126911 2127786 2127791) (-1241 "ULS.spad" 2117457 2117485 2118544 2118973) (-1240 "ULSCONS.spad" 2109853 2109873 2110223 2110372) (-1239 "ULSCCAT.spad" 2107590 2107610 2109699 2109848) (-1238 "ULSCCAT.spad" 2105435 2105457 2107546 2107551) (-1237 "ULSCAT.spad" 2103667 2103683 2105281 2105430) (-1236 "ULS2.spad" 2103181 2103234 2103657 2103662) (-1235 "UINT8.spad" 2103058 2103067 2103171 2103176) (-1234 "UINT64.spad" 2102934 2102943 2103048 2103053) (-1233 "UINT32.spad" 2102810 2102819 2102924 2102929) (-1232 "UINT16.spad" 2102686 2102695 2102800 2102805) (-1231 "UFD.spad" 2101751 2101760 2102612 2102681) (-1230 "UFD.spad" 2100878 2100889 2101741 2101746) (-1229 "UDVO.spad" 2099759 2099768 2100868 2100873) (-1228 "UDPO.spad" 2097252 2097263 2099715 2099720) (-1227 "TYPE.spad" 2097184 2097193 2097242 2097247) (-1226 "TYPEAST.spad" 2097103 2097112 2097174 2097179) (-1225 "TWOFACT.spad" 2095755 2095770 2097093 2097098) (-1224 "TUPLE.spad" 2095241 2095252 2095654 2095659) (-1223 "TUBETOOL.spad" 2092108 2092117 2095231 2095236) (-1222 "TUBE.spad" 2090755 2090772 2092098 2092103) (-1221 "TS.spad" 2089354 2089370 2090320 2090417) (-1220 "TSETCAT.spad" 2076481 2076498 2089322 2089349) (-1219 "TSETCAT.spad" 2063594 2063613 2076437 2076442) (-1218 "TRMANIP.spad" 2057960 2057977 2063300 2063305) (-1217 "TRIMAT.spad" 2056923 2056948 2057950 2057955) (-1216 "TRIGMNIP.spad" 2055450 2055467 2056913 2056918) (-1215 "TRIGCAT.spad" 2054962 2054971 2055440 2055445) (-1214 "TRIGCAT.spad" 2054472 2054483 2054952 2054957) (-1213 "TREE.spad" 2053047 2053058 2054079 2054106) (-1212 "TRANFUN.spad" 2052886 2052895 2053037 2053042) (-1211 "TRANFUN.spad" 2052723 2052734 2052876 2052881) (-1210 "TOPSP.spad" 2052397 2052406 2052713 2052718) (-1209 "TOOLSIGN.spad" 2052060 2052071 2052387 2052392) (-1208 "TEXTFILE.spad" 2050621 2050630 2052050 2052055) (-1207 "TEX.spad" 2047767 2047776 2050611 2050616) (-1206 "TEX1.spad" 2047323 2047334 2047757 2047762) (-1205 "TEMUTL.spad" 2046878 2046887 2047313 2047318) (-1204 "TBCMPPK.spad" 2044971 2044994 2046868 2046873) (-1203 "TBAGG.spad" 2044021 2044044 2044951 2044966) (-1202 "TBAGG.spad" 2043079 2043104 2044011 2044016) (-1201 "TANEXP.spad" 2042487 2042498 2043069 2043074) (-1200 "TALGOP.spad" 2042211 2042222 2042477 2042482) (-1199 "TABLE.spad" 2040622 2040645 2040892 2040919) (-1198 "TABLEAU.spad" 2040103 2040114 2040612 2040617) (-1197 "TABLBUMP.spad" 2036906 2036917 2040093 2040098) (-1196 "SYSTEM.spad" 2036134 2036143 2036896 2036901) (-1195 "SYSSOLP.spad" 2033617 2033628 2036124 2036129) (-1194 "SYSPTR.spad" 2033516 2033525 2033607 2033612) (-1193 "SYSNNI.spad" 2032698 2032709 2033506 2033511) (-1192 "SYSINT.spad" 2032102 2032113 2032688 2032693) (-1191 "SYNTAX.spad" 2028308 2028317 2032092 2032097) (-1190 "SYMTAB.spad" 2026376 2026385 2028298 2028303) (-1189 "SYMS.spad" 2022399 2022408 2026366 2026371) (-1188 "SYMPOLY.spad" 2021406 2021417 2021488 2021615) (-1187 "SYMFUNC.spad" 2020907 2020918 2021396 2021401) (-1186 "SYMBOL.spad" 2018410 2018419 2020897 2020902) (-1185 "SWITCH.spad" 2015181 2015190 2018400 2018405) (-1184 "SUTS.spad" 2012086 2012114 2013648 2013745) (-1183 "SUPXS.spad" 2009227 2009255 2010218 2010367) (-1182 "SUP.spad" 2006040 2006051 2006813 2006966) (-1181 "SUPFRACF.spad" 2005145 2005163 2006030 2006035) (-1180 "SUP2.spad" 2004537 2004550 2005135 2005140) (-1179 "SUMRF.spad" 2003511 2003522 2004527 2004532) (-1178 "SUMFS.spad" 2003148 2003165 2003501 2003506) (-1177 "SULS.spad" 1993693 1993721 1994793 1995222) (-1176 "SUCHTAST.spad" 1993462 1993471 1993683 1993688) (-1175 "SUCH.spad" 1993144 1993159 1993452 1993457) (-1174 "SUBSPACE.spad" 1985259 1985274 1993134 1993139) (-1173 "SUBRESP.spad" 1984429 1984443 1985215 1985220) (-1172 "STTF.spad" 1980528 1980544 1984419 1984424) (-1171 "STTFNC.spad" 1976996 1977012 1980518 1980523) (-1170 "STTAYLOR.spad" 1969631 1969642 1976877 1976882) (-1169 "STRTBL.spad" 1968136 1968153 1968285 1968312) (-1168 "STRING.spad" 1967545 1967554 1967559 1967586) (-1167 "STRICAT.spad" 1967333 1967342 1967513 1967540) (-1166 "STREAM.spad" 1964251 1964262 1966858 1966873) (-1165 "STREAM3.spad" 1963824 1963839 1964241 1964246) (-1164 "STREAM2.spad" 1962952 1962965 1963814 1963819) (-1163 "STREAM1.spad" 1962658 1962669 1962942 1962947) (-1162 "STINPROD.spad" 1961594 1961610 1962648 1962653) (-1161 "STEP.spad" 1960795 1960804 1961584 1961589) (-1160 "STEPAST.spad" 1960029 1960038 1960785 1960790) (-1159 "STBL.spad" 1958555 1958583 1958722 1958737) (-1158 "STAGG.spad" 1957630 1957641 1958545 1958550) (-1157 "STAGG.spad" 1956703 1956716 1957620 1957625) (-1156 "STACK.spad" 1956060 1956071 1956310 1956337) (-1155 "SREGSET.spad" 1953764 1953781 1955706 1955733) (-1154 "SRDCMPK.spad" 1952325 1952345 1953754 1953759) (-1153 "SRAGG.spad" 1947468 1947477 1952293 1952320) (-1152 "SRAGG.spad" 1942631 1942642 1947458 1947463) (-1151 "SQMATRIX.spad" 1940247 1940265 1941163 1941250) (-1150 "SPLTREE.spad" 1934799 1934812 1939683 1939710) (-1149 "SPLNODE.spad" 1931387 1931400 1934789 1934794) (-1148 "SPFCAT.spad" 1930196 1930205 1931377 1931382) (-1147 "SPECOUT.spad" 1928748 1928757 1930186 1930191) (-1146 "SPADXPT.spad" 1920343 1920352 1928738 1928743) (-1145 "spad-parser.spad" 1919808 1919817 1920333 1920338) (-1144 "SPADAST.spad" 1919509 1919518 1919798 1919803) (-1143 "SPACEC.spad" 1903708 1903719 1919499 1919504) (-1142 "SPACE3.spad" 1903484 1903495 1903698 1903703) (-1141 "SORTPAK.spad" 1903033 1903046 1903440 1903445) (-1140 "SOLVETRA.spad" 1900796 1900807 1903023 1903028) (-1139 "SOLVESER.spad" 1899324 1899335 1900786 1900791) (-1138 "SOLVERAD.spad" 1895350 1895361 1899314 1899319) (-1137 "SOLVEFOR.spad" 1893812 1893830 1895340 1895345) (-1136 "SNTSCAT.spad" 1893412 1893429 1893780 1893807) (-1135 "SMTS.spad" 1891684 1891710 1892977 1893074) (-1134 "SMP.spad" 1889159 1889179 1889549 1889676) (-1133 "SMITH.spad" 1888004 1888029 1889149 1889154) (-1132 "SMATCAT.spad" 1886114 1886144 1887948 1887999) (-1131 "SMATCAT.spad" 1884156 1884188 1885992 1885997) (-1130 "SKAGG.spad" 1883119 1883130 1884124 1884151) (-1129 "SINT.spad" 1882059 1882068 1882985 1883114) (-1128 "SIMPAN.spad" 1881787 1881796 1882049 1882054) (-1127 "SIG.spad" 1881117 1881126 1881777 1881782) (-1126 "SIGNRF.spad" 1880235 1880246 1881107 1881112) (-1125 "SIGNEF.spad" 1879514 1879531 1880225 1880230) (-1124 "SIGAST.spad" 1878899 1878908 1879504 1879509) (-1123 "SHP.spad" 1876827 1876842 1878855 1878860) (-1122 "SHDP.spad" 1866538 1866565 1867047 1867178) (-1121 "SGROUP.spad" 1866146 1866155 1866528 1866533) (-1120 "SGROUP.spad" 1865752 1865763 1866136 1866141) (-1119 "SGCF.spad" 1858891 1858900 1865742 1865747) (-1118 "SFRTCAT.spad" 1857821 1857838 1858859 1858886) (-1117 "SFRGCD.spad" 1856884 1856904 1857811 1857816) (-1116 "SFQCMPK.spad" 1851521 1851541 1856874 1856879) (-1115 "SFORT.spad" 1850960 1850974 1851511 1851516) (-1114 "SEXOF.spad" 1850803 1850843 1850950 1850955) (-1113 "SEX.spad" 1850695 1850704 1850793 1850798) (-1112 "SEXCAT.spad" 1848296 1848336 1850685 1850690) (-1111 "SET.spad" 1846620 1846631 1847717 1847756) (-1110 "SETMN.spad" 1845070 1845087 1846610 1846615) (-1109 "SETCAT.spad" 1844392 1844401 1845060 1845065) (-1108 "SETCAT.spad" 1843712 1843723 1844382 1844387) (-1107 "SETAGG.spad" 1840261 1840272 1843692 1843707) (-1106 "SETAGG.spad" 1836818 1836831 1840251 1840256) (-1105 "SEQAST.spad" 1836521 1836530 1836808 1836813) (-1104 "SEGXCAT.spad" 1835677 1835690 1836511 1836516) (-1103 "SEG.spad" 1835490 1835501 1835596 1835601) (-1102 "SEGCAT.spad" 1834415 1834426 1835480 1835485) (-1101 "SEGBIND.spad" 1834173 1834184 1834362 1834367) (-1100 "SEGBIND2.spad" 1833871 1833884 1834163 1834168) (-1099 "SEGAST.spad" 1833585 1833594 1833861 1833866) (-1098 "SEG2.spad" 1833020 1833033 1833541 1833546) (-1097 "SDVAR.spad" 1832296 1832307 1833010 1833015) (-1096 "SDPOL.spad" 1829722 1829733 1830013 1830140) (-1095 "SCPKG.spad" 1827811 1827822 1829712 1829717) (-1094 "SCOPE.spad" 1826964 1826973 1827801 1827806) (-1093 "SCACHE.spad" 1825660 1825671 1826954 1826959) (-1092 "SASTCAT.spad" 1825569 1825578 1825650 1825655) (-1091 "SAOS.spad" 1825441 1825450 1825559 1825564) (-1090 "SAERFFC.spad" 1825154 1825174 1825431 1825436) (-1089 "SAE.spad" 1823329 1823345 1823940 1824075) (-1088 "SAEFACT.spad" 1823030 1823050 1823319 1823324) (-1087 "RURPK.spad" 1820689 1820705 1823020 1823025) (-1086 "RULESET.spad" 1820142 1820166 1820679 1820684) (-1085 "RULE.spad" 1818382 1818406 1820132 1820137) (-1084 "RULECOLD.spad" 1818234 1818247 1818372 1818377) (-1083 "RTVALUE.spad" 1817969 1817978 1818224 1818229) (-1082 "RSTRCAST.spad" 1817686 1817695 1817959 1817964) (-1081 "RSETGCD.spad" 1814064 1814084 1817676 1817681) (-1080 "RSETCAT.spad" 1804000 1804017 1814032 1814059) (-1079 "RSETCAT.spad" 1793956 1793975 1803990 1803995) (-1078 "RSDCMPK.spad" 1792408 1792428 1793946 1793951) (-1077 "RRCC.spad" 1790792 1790822 1792398 1792403) (-1076 "RRCC.spad" 1789174 1789206 1790782 1790787) (-1075 "RPTAST.spad" 1788876 1788885 1789164 1789169) (-1074 "RPOLCAT.spad" 1768236 1768251 1788744 1788871) (-1073 "RPOLCAT.spad" 1747309 1747326 1767819 1767824) (-1072 "ROUTINE.spad" 1743192 1743201 1745956 1745983) (-1071 "ROMAN.spad" 1742520 1742529 1743058 1743187) (-1070 "ROIRC.spad" 1741600 1741632 1742510 1742515) (-1069 "RNS.spad" 1740503 1740512 1741502 1741595) (-1068 "RNS.spad" 1739492 1739503 1740493 1740498) (-1067 "RNG.spad" 1739227 1739236 1739482 1739487) (-1066 "RNGBIND.spad" 1738387 1738401 1739182 1739187) (-1065 "RMODULE.spad" 1738152 1738163 1738377 1738382) (-1064 "RMCAT2.spad" 1737572 1737629 1738142 1738147) (-1063 "RMATRIX.spad" 1736396 1736415 1736739 1736778) (-1062 "RMATCAT.spad" 1731975 1732006 1736352 1736391) (-1061 "RMATCAT.spad" 1727444 1727477 1731823 1731828) (-1060 "RLINSET.spad" 1726838 1726849 1727434 1727439) (-1059 "RINTERP.spad" 1726726 1726746 1726828 1726833) (-1058 "RING.spad" 1726196 1726205 1726706 1726721) (-1057 "RING.spad" 1725674 1725685 1726186 1726191) (-1056 "RIDIST.spad" 1725066 1725075 1725664 1725669) (-1055 "RGCHAIN.spad" 1723649 1723665 1724551 1724578) (-1054 "RGBCSPC.spad" 1723430 1723442 1723639 1723644) (-1053 "RGBCMDL.spad" 1722960 1722972 1723420 1723425) (-1052 "RF.spad" 1720602 1720613 1722950 1722955) (-1051 "RFFACTOR.spad" 1720064 1720075 1720592 1720597) (-1050 "RFFACT.spad" 1719799 1719811 1720054 1720059) (-1049 "RFDIST.spad" 1718795 1718804 1719789 1719794) (-1048 "RETSOL.spad" 1718214 1718227 1718785 1718790) (-1047 "RETRACT.spad" 1717642 1717653 1718204 1718209) (-1046 "RETRACT.spad" 1717068 1717081 1717632 1717637) (-1045 "RETAST.spad" 1716880 1716889 1717058 1717063) (-1044 "RESULT.spad" 1714940 1714949 1715527 1715554) (-1043 "RESRING.spad" 1714287 1714334 1714878 1714935) (-1042 "RESLATC.spad" 1713611 1713622 1714277 1714282) (-1041 "REPSQ.spad" 1713342 1713353 1713601 1713606) (-1040 "REP.spad" 1710896 1710905 1713332 1713337) (-1039 "REPDB.spad" 1710603 1710614 1710886 1710891) (-1038 "REP2.spad" 1700261 1700272 1710445 1710450) (-1037 "REP1.spad" 1694457 1694468 1700211 1700216) (-1036 "REGSET.spad" 1692254 1692271 1694103 1694130) (-1035 "REF.spad" 1691589 1691600 1692209 1692214) (-1034 "REDORDER.spad" 1690795 1690812 1691579 1691584) (-1033 "RECLOS.spad" 1689578 1689598 1690282 1690375) (-1032 "REALSOLV.spad" 1688718 1688727 1689568 1689573) (-1031 "REAL.spad" 1688590 1688599 1688708 1688713) (-1030 "REAL0Q.spad" 1685888 1685903 1688580 1688585) (-1029 "REAL0.spad" 1682732 1682747 1685878 1685883) (-1028 "RDUCEAST.spad" 1682453 1682462 1682722 1682727) (-1027 "RDIV.spad" 1682108 1682133 1682443 1682448) (-1026 "RDIST.spad" 1681675 1681686 1682098 1682103) (-1025 "RDETRS.spad" 1680539 1680557 1681665 1681670) (-1024 "RDETR.spad" 1678678 1678696 1680529 1680534) (-1023 "RDEEFS.spad" 1677777 1677794 1678668 1678673) (-1022 "RDEEF.spad" 1676787 1676804 1677767 1677772) (-1021 "RCFIELD.spad" 1673973 1673982 1676689 1676782) (-1020 "RCFIELD.spad" 1671245 1671256 1673963 1673968) (-1019 "RCAGG.spad" 1669173 1669184 1671235 1671240) (-1018 "RCAGG.spad" 1667028 1667041 1669092 1669097) (-1017 "RATRET.spad" 1666388 1666399 1667018 1667023) (-1016 "RATFACT.spad" 1666080 1666092 1666378 1666383) (-1015 "RANDSRC.spad" 1665399 1665408 1666070 1666075) (-1014 "RADUTIL.spad" 1665155 1665164 1665389 1665394) (-1013 "RADIX.spad" 1662076 1662090 1663622 1663715) (-1012 "RADFF.spad" 1660489 1660526 1660608 1660764) (-1011 "RADCAT.spad" 1660084 1660093 1660479 1660484) (-1010 "RADCAT.spad" 1659677 1659688 1660074 1660079) (-1009 "QUEUE.spad" 1659025 1659036 1659284 1659311) (-1008 "QUAT.spad" 1657606 1657617 1657949 1658014) (-1007 "QUATCT2.spad" 1657226 1657245 1657596 1657601) (-1006 "QUATCAT.spad" 1655396 1655407 1657156 1657221) (-1005 "QUATCAT.spad" 1653317 1653330 1655079 1655084) (-1004 "QUAGG.spad" 1652144 1652155 1653285 1653312) (-1003 "QQUTAST.spad" 1651912 1651921 1652134 1652139) (-1002 "QFORM.spad" 1651376 1651391 1651902 1651907) (-1001 "QFCAT.spad" 1650078 1650089 1651278 1651371) (-1000 "QFCAT.spad" 1648371 1648384 1649573 1649578) (-999 "QFCAT2.spad" 1648064 1648080 1648361 1648366) (-998 "QEQUAT.spad" 1647623 1647631 1648054 1648059) (-997 "QCMPACK.spad" 1642370 1642389 1647613 1647618) (-996 "QALGSET.spad" 1638449 1638481 1642284 1642289) (-995 "QALGSET2.spad" 1636445 1636463 1638439 1638444) (-994 "PWFFINTB.spad" 1633861 1633882 1636435 1636440) (-993 "PUSHVAR.spad" 1633200 1633219 1633851 1633856) (-992 "PTRANFN.spad" 1629328 1629338 1633190 1633195) (-991 "PTPACK.spad" 1626416 1626426 1629318 1629323) (-990 "PTFUNC2.spad" 1626239 1626253 1626406 1626411) (-989 "PTCAT.spad" 1625494 1625504 1626207 1626234) (-988 "PSQFR.spad" 1624801 1624825 1625484 1625489) (-987 "PSEUDLIN.spad" 1623687 1623697 1624791 1624796) (-986 "PSETPK.spad" 1609120 1609136 1623565 1623570) (-985 "PSETCAT.spad" 1603040 1603063 1609100 1609115) (-984 "PSETCAT.spad" 1596934 1596959 1602996 1603001) (-983 "PSCURVE.spad" 1595917 1595925 1596924 1596929) (-982 "PSCAT.spad" 1594700 1594729 1595815 1595912) (-981 "PSCAT.spad" 1593573 1593604 1594690 1594695) (-980 "PRTITION.spad" 1592658 1592666 1593563 1593568) (-979 "PRTDAST.spad" 1592377 1592385 1592648 1592653) (-978 "PRS.spad" 1581939 1581956 1592333 1592338) (-977 "PRQAGG.spad" 1581374 1581384 1581907 1581934) (-976 "PROPLOG.spad" 1580946 1580954 1581364 1581369) (-975 "PROPFUN2.spad" 1580569 1580582 1580936 1580941) (-974 "PROPFUN1.spad" 1579967 1579978 1580559 1580564) (-973 "PROPFRML.spad" 1578535 1578546 1579957 1579962) (-972 "PROPERTY.spad" 1578023 1578031 1578525 1578530) (-971 "PRODUCT.spad" 1575705 1575717 1575989 1576044) (-970 "PR.spad" 1574097 1574109 1574796 1574923) (-969 "PRINT.spad" 1573849 1573857 1574087 1574092) (-968 "PRIMES.spad" 1572102 1572112 1573839 1573844) (-967 "PRIMELT.spad" 1570183 1570197 1572092 1572097) (-966 "PRIMCAT.spad" 1569810 1569818 1570173 1570178) (-965 "PRIMARR.spad" 1568815 1568825 1568993 1569020) (-964 "PRIMARR2.spad" 1567582 1567594 1568805 1568810) (-963 "PREASSOC.spad" 1566964 1566976 1567572 1567577) (-962 "PPCURVE.spad" 1566101 1566109 1566954 1566959) (-961 "PORTNUM.spad" 1565876 1565884 1566091 1566096) (-960 "POLYROOT.spad" 1564725 1564747 1565832 1565837) (-959 "POLY.spad" 1562060 1562070 1562575 1562702) (-958 "POLYLIFT.spad" 1561325 1561348 1562050 1562055) (-957 "POLYCATQ.spad" 1559443 1559465 1561315 1561320) (-956 "POLYCAT.spad" 1552913 1552934 1559311 1559438) (-955 "POLYCAT.spad" 1545721 1545744 1552121 1552126) (-954 "POLY2UP.spad" 1545173 1545187 1545711 1545716) (-953 "POLY2.spad" 1544770 1544782 1545163 1545168) (-952 "POLUTIL.spad" 1543711 1543740 1544726 1544731) (-951 "POLTOPOL.spad" 1542459 1542474 1543701 1543706) (-950 "POINT.spad" 1541297 1541307 1541384 1541411) (-949 "PNTHEORY.spad" 1537999 1538007 1541287 1541292) (-948 "PMTOOLS.spad" 1536774 1536788 1537989 1537994) (-947 "PMSYM.spad" 1536323 1536333 1536764 1536769) (-946 "PMQFCAT.spad" 1535914 1535928 1536313 1536318) (-945 "PMPRED.spad" 1535393 1535407 1535904 1535909) (-944 "PMPREDFS.spad" 1534847 1534869 1535383 1535388) (-943 "PMPLCAT.spad" 1533927 1533945 1534779 1534784) (-942 "PMLSAGG.spad" 1533512 1533526 1533917 1533922) (-941 "PMKERNEL.spad" 1533091 1533103 1533502 1533507) (-940 "PMINS.spad" 1532671 1532681 1533081 1533086) (-939 "PMFS.spad" 1532248 1532266 1532661 1532666) (-938 "PMDOWN.spad" 1531538 1531552 1532238 1532243) (-937 "PMASS.spad" 1530548 1530556 1531528 1531533) (-936 "PMASSFS.spad" 1529515 1529531 1530538 1530543) (-935 "PLOTTOOL.spad" 1529295 1529303 1529505 1529510) (-934 "PLOT.spad" 1524218 1524226 1529285 1529290) (-933 "PLOT3D.spad" 1520682 1520690 1524208 1524213) (-932 "PLOT1.spad" 1519839 1519849 1520672 1520677) (-931 "PLEQN.spad" 1507129 1507156 1519829 1519834) (-930 "PINTERP.spad" 1506751 1506770 1507119 1507124) (-929 "PINTERPA.spad" 1506535 1506551 1506741 1506746) (-928 "PI.spad" 1506144 1506152 1506509 1506530) (-927 "PID.spad" 1505114 1505122 1506070 1506139) (-926 "PICOERCE.spad" 1504771 1504781 1505104 1505109) (-925 "PGROEB.spad" 1503372 1503386 1504761 1504766) (-924 "PGE.spad" 1494989 1494997 1503362 1503367) (-923 "PGCD.spad" 1493879 1493896 1494979 1494984) (-922 "PFRPAC.spad" 1493028 1493038 1493869 1493874) (-921 "PFR.spad" 1489691 1489701 1492930 1493023) (-920 "PFOTOOLS.spad" 1488949 1488965 1489681 1489686) (-919 "PFOQ.spad" 1488319 1488337 1488939 1488944) (-918 "PFO.spad" 1487738 1487765 1488309 1488314) (-917 "PF.spad" 1487312 1487324 1487543 1487636) (-916 "PFECAT.spad" 1484994 1485002 1487238 1487307) (-915 "PFECAT.spad" 1482704 1482714 1484950 1484955) (-914 "PFBRU.spad" 1480592 1480604 1482694 1482699) (-913 "PFBR.spad" 1478152 1478175 1480582 1480587) (-912 "PERM.spad" 1473837 1473847 1477982 1477997) (-911 "PERMGRP.spad" 1468599 1468609 1473827 1473832) (-910 "PERMCAT.spad" 1467157 1467167 1468579 1468594) (-909 "PERMAN.spad" 1465689 1465703 1467147 1467152) (-908 "PENDTREE.spad" 1465030 1465040 1465318 1465323) (-907 "PDRING.spad" 1463581 1463591 1465010 1465025) (-906 "PDRING.spad" 1462140 1462152 1463571 1463576) (-905 "PDEPROB.spad" 1461155 1461163 1462130 1462135) (-904 "PDEPACK.spad" 1455195 1455203 1461145 1461150) (-903 "PDECOMP.spad" 1454665 1454682 1455185 1455190) (-902 "PDECAT.spad" 1453021 1453029 1454655 1454660) (-901 "PCOMP.spad" 1452874 1452887 1453011 1453016) (-900 "PBWLB.spad" 1451462 1451479 1452864 1452869) (-899 "PATTERN.spad" 1446001 1446011 1451452 1451457) (-898 "PATTERN2.spad" 1445739 1445751 1445991 1445996) (-897 "PATTERN1.spad" 1444075 1444091 1445729 1445734) (-896 "PATRES.spad" 1441650 1441662 1444065 1444070) (-895 "PATRES2.spad" 1441322 1441336 1441640 1441645) (-894 "PATMATCH.spad" 1439519 1439550 1441030 1441035) (-893 "PATMAB.spad" 1438948 1438958 1439509 1439514) (-892 "PATLRES.spad" 1438034 1438048 1438938 1438943) (-891 "PATAB.spad" 1437798 1437808 1438024 1438029) (-890 "PARTPERM.spad" 1435076 1435084 1437788 1437793) (-889 "PARSURF.spad" 1434510 1434538 1435066 1435071) (-888 "PARSU2.spad" 1434307 1434323 1434500 1434505) (-887 "script-parser.spad" 1433827 1433835 1434297 1434302) (-886 "PARSCURV.spad" 1433261 1433289 1433817 1433822) (-885 "PARSC2.spad" 1433052 1433068 1433251 1433256) (-884 "PARPCURV.spad" 1432514 1432542 1433042 1433047) (-883 "PARPC2.spad" 1432305 1432321 1432504 1432509) (-882 "PARAMAST.spad" 1431433 1431441 1432295 1432300) (-881 "PAN2EXPR.spad" 1430845 1430853 1431423 1431428) (-880 "PALETTE.spad" 1429815 1429823 1430835 1430840) (-879 "PAIR.spad" 1428802 1428815 1429403 1429408) (-878 "PADICRC.spad" 1426136 1426154 1427307 1427400) (-877 "PADICRAT.spad" 1424151 1424163 1424372 1424465) (-876 "PADIC.spad" 1423846 1423858 1424077 1424146) (-875 "PADICCT.spad" 1422395 1422407 1423772 1423841) (-874 "PADEPAC.spad" 1421084 1421103 1422385 1422390) (-873 "PADE.spad" 1419836 1419852 1421074 1421079) (-872 "OWP.spad" 1419076 1419106 1419694 1419761) (-871 "OVERSET.spad" 1418649 1418657 1419066 1419071) (-870 "OVAR.spad" 1418430 1418453 1418639 1418644) (-869 "OUT.spad" 1417516 1417524 1418420 1418425) (-868 "OUTFORM.spad" 1406908 1406916 1417506 1417511) (-867 "OUTBFILE.spad" 1406326 1406334 1406898 1406903) (-866 "OUTBCON.spad" 1405332 1405340 1406316 1406321) (-865 "OUTBCON.spad" 1404336 1404346 1405322 1405327) (-864 "OSI.spad" 1403811 1403819 1404326 1404331) (-863 "OSGROUP.spad" 1403729 1403737 1403801 1403806) (-862 "ORTHPOL.spad" 1402214 1402224 1403646 1403651) (-861 "OREUP.spad" 1401667 1401695 1401894 1401933) (-860 "ORESUP.spad" 1400968 1400992 1401347 1401386) (-859 "OREPCTO.spad" 1398825 1398837 1400888 1400893) (-858 "OREPCAT.spad" 1392972 1392982 1398781 1398820) (-857 "OREPCAT.spad" 1387009 1387021 1392820 1392825) (-856 "ORDSET.spad" 1386181 1386189 1386999 1387004) (-855 "ORDSET.spad" 1385351 1385361 1386171 1386176) (-854 "ORDRING.spad" 1384741 1384749 1385331 1385346) (-853 "ORDRING.spad" 1384139 1384149 1384731 1384736) (-852 "ORDMON.spad" 1383994 1384002 1384129 1384134) (-851 "ORDFUNS.spad" 1383126 1383142 1383984 1383989) (-850 "ORDFIN.spad" 1382946 1382954 1383116 1383121) (-849 "ORDCOMP.spad" 1381411 1381421 1382493 1382522) (-848 "ORDCOMP2.spad" 1380704 1380716 1381401 1381406) (-847 "OPTPROB.spad" 1379342 1379350 1380694 1380699) (-846 "OPTPACK.spad" 1371751 1371759 1379332 1379337) (-845 "OPTCAT.spad" 1369430 1369438 1371741 1371746) (-844 "OPSIG.spad" 1369084 1369092 1369420 1369425) (-843 "OPQUERY.spad" 1368633 1368641 1369074 1369079) (-842 "OP.spad" 1368375 1368385 1368455 1368522) (-841 "OPERCAT.spad" 1367841 1367851 1368365 1368370) (-840 "OPERCAT.spad" 1367305 1367317 1367831 1367836) (-839 "ONECOMP.spad" 1366050 1366060 1366852 1366881) (-838 "ONECOMP2.spad" 1365474 1365486 1366040 1366045) (-837 "OMSERVER.spad" 1364480 1364488 1365464 1365469) (-836 "OMSAGG.spad" 1364268 1364278 1364436 1364475) (-835 "OMPKG.spad" 1362884 1362892 1364258 1364263) (-834 "OM.spad" 1361857 1361865 1362874 1362879) (-833 "OMLO.spad" 1361282 1361294 1361743 1361782) (-832 "OMEXPR.spad" 1361116 1361126 1361272 1361277) (-831 "OMERR.spad" 1360661 1360669 1361106 1361111) (-830 "OMERRK.spad" 1359695 1359703 1360651 1360656) (-829 "OMENC.spad" 1359039 1359047 1359685 1359690) (-828 "OMDEV.spad" 1353348 1353356 1359029 1359034) (-827 "OMCONN.spad" 1352757 1352765 1353338 1353343) (-826 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268058 269193 269220) (-228 "DFSFUN.spad" 261688 261696 268038 268043) (-227 "DFLOAT.spad" 258419 258427 261578 261683) (-226 "DFINTTLS.spad" 256650 256666 258409 258414) (-225 "DERHAM.spad" 254564 254596 256630 256645) (-224 "DEQUEUE.spad" 253888 253898 254171 254198) (-223 "DEGRED.spad" 253505 253519 253878 253883) (-222 "DEFINTRF.spad" 251042 251052 253495 253500) (-221 "DEFINTEF.spad" 249552 249568 251032 251037) (-220 "DEFAST.spad" 248920 248928 249542 249547) (-219 "DECIMAL.spad" 247026 247034 247387 247480) (-218 "DDFACT.spad" 244839 244856 247016 247021) (-217 "DBLRESP.spad" 244439 244463 244829 244834) (-216 "DBASE.spad" 243103 243113 244429 244434) (-215 "DATAARY.spad" 242565 242578 243093 243098) (-214 "D03FAFA.spad" 242393 242401 242555 242560) (-213 "D03EEFA.spad" 242213 242221 242383 242388) (-212 "D03AGNT.spad" 241299 241307 242203 242208) (-211 "D02EJFA.spad" 240761 240769 241289 241294) (-210 "D02CJFA.spad" 240239 240247 240751 240756) (-209 "D02BHFA.spad" 239729 239737 240229 240234) (-208 "D02BBFA.spad" 239219 239227 239719 239724) (-207 "D02AGNT.spad" 234033 234041 239209 239214) (-206 "D01WGTS.spad" 232352 232360 234023 234028) (-205 "D01TRNS.spad" 232329 232337 232342 232347) (-204 "D01GBFA.spad" 231851 231859 232319 232324) (-203 "D01FCFA.spad" 231373 231381 231841 231846) (-202 "D01ASFA.spad" 230841 230849 231363 231368) (-201 "D01AQFA.spad" 230287 230295 230831 230836) (-200 "D01APFA.spad" 229711 229719 230277 230282) (-199 "D01ANFA.spad" 229205 229213 229701 229706) (-198 "D01AMFA.spad" 228715 228723 229195 229200) (-197 "D01ALFA.spad" 228255 228263 228705 228710) (-196 "D01AKFA.spad" 227781 227789 228245 228250) (-195 "D01AJFA.spad" 227304 227312 227771 227776) (-194 "D01AGNT.spad" 223371 223379 227294 227299) (-193 "CYCLOTOM.spad" 222877 222885 223361 223366) (-192 "CYCLES.spad" 219669 219677 222867 222872) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2268669 2268674 2268679 2268684) (-2 NIL 2268649 2268654 2268659 2268664) (-1 NIL 2268629 2268634 2268639 2268644) (0 NIL 2268609 2268614 2268619 2268624) (-1306 "ZMOD.spad" 2268418 2268431 2268547 2268604) (-1305 "ZLINDEP.spad" 2267484 2267495 2268408 2268413) (-1304 "ZDSOLVE.spad" 2257429 2257451 2267474 2267479) (-1303 "YSTREAM.spad" 2256924 2256935 2257419 2257424) (-1302 "YDIAGRAM.spad" 2256558 2256567 2256914 2256919) (-1301 "XRPOLY.spad" 2255778 2255798 2256414 2256483) (-1300 "XPR.spad" 2253573 2253586 2255496 2255595) (-1299 "XPOLY.spad" 2253128 2253139 2253429 2253498) (-1298 "XPOLYC.spad" 2252447 2252463 2253054 2253123) (-1297 "XPBWPOLY.spad" 2250884 2250904 2252227 2252296) (-1296 "XF.spad" 2249347 2249362 2250786 2250879) (-1295 "XF.spad" 2247790 2247807 2249231 2249236) (-1294 "XFALG.spad" 2244838 2244854 2247716 2247785) (-1293 "XEXPPKG.spad" 2244089 2244115 2244828 2244833) (-1292 "XDPOLY.spad" 2243703 2243719 2243945 2244014) (-1291 "XALG.spad" 2243363 2243374 2243659 2243698) (-1290 "WUTSET.spad" 2239202 2239219 2243009 2243036) (-1289 "WP.spad" 2238401 2238445 2239060 2239127) (-1288 "WHILEAST.spad" 2238199 2238208 2238391 2238396) (-1287 "WHEREAST.spad" 2237870 2237879 2238189 2238194) (-1286 "WFFINTBS.spad" 2235533 2235555 2237860 2237865) (-1285 "WEIER.spad" 2233755 2233766 2235523 2235528) (-1284 "VSPACE.spad" 2233428 2233439 2233723 2233750) (-1283 "VSPACE.spad" 2233121 2233134 2233418 2233423) (-1282 "VOID.spad" 2232798 2232807 2233111 2233116) (-1281 "VIEW.spad" 2230478 2230487 2232788 2232793) (-1280 "VIEWDEF.spad" 2225679 2225688 2230468 2230473) (-1279 "VIEW3D.spad" 2209640 2209649 2225669 2225674) (-1278 "VIEW2D.spad" 2197531 2197540 2209630 2209635) (-1277 "VECTOR.spad" 2196205 2196216 2196456 2196483) (-1276 "VECTOR2.spad" 2194844 2194857 2196195 2196200) (-1275 "VECTCAT.spad" 2192748 2192759 2194812 2194839) (-1274 "VECTCAT.spad" 2190459 2190472 2192525 2192530) (-1273 "VARIABLE.spad" 2190239 2190254 2190449 2190454) (-1272 "UTYPE.spad" 2189883 2189892 2190229 2190234) (-1271 "UTSODETL.spad" 2189178 2189202 2189839 2189844) (-1270 "UTSODE.spad" 2187394 2187414 2189168 2189173) (-1269 "UTS.spad" 2182198 2182226 2185861 2185958) (-1268 "UTSCAT.spad" 2179677 2179693 2182096 2182193) (-1267 "UTSCAT.spad" 2176800 2176818 2179221 2179226) (-1266 "UTS2.spad" 2176395 2176430 2176790 2176795) (-1265 "URAGG.spad" 2171068 2171079 2176385 2176390) (-1264 "URAGG.spad" 2165705 2165718 2171024 2171029) (-1263 "UPXSSING.spad" 2163350 2163376 2164786 2164919) (-1262 "UPXS.spad" 2160504 2160532 2161482 2161631) (-1261 "UPXSCONS.spad" 2158263 2158283 2158636 2158785) (-1260 "UPXSCCA.spad" 2156834 2156854 2158109 2158258) (-1259 "UPXSCCA.spad" 2155547 2155569 2156824 2156829) (-1258 "UPXSCAT.spad" 2154136 2154152 2155393 2155542) (-1257 "UPXS2.spad" 2153679 2153732 2154126 2154131) (-1256 "UPSQFREE.spad" 2152093 2152107 2153669 2153674) (-1255 "UPSCAT.spad" 2149704 2149728 2151991 2152088) (-1254 "UPSCAT.spad" 2147021 2147047 2149310 2149315) (-1253 "UPOLYC.spad" 2142061 2142072 2146863 2147016) (-1252 "UPOLYC.spad" 2136993 2137006 2141797 2141802) (-1251 "UPOLYC2.spad" 2136464 2136483 2136983 2136988) (-1250 "UP.spad" 2133663 2133678 2134050 2134203) (-1249 "UPMP.spad" 2132563 2132576 2133653 2133658) (-1248 "UPDIVP.spad" 2132128 2132142 2132553 2132558) (-1247 "UPDECOMP.spad" 2130373 2130387 2132118 2132123) (-1246 "UPCDEN.spad" 2129582 2129598 2130363 2130368) (-1245 "UP2.spad" 2128946 2128967 2129572 2129577) (-1244 "UNISEG.spad" 2128299 2128310 2128865 2128870) (-1243 "UNISEG2.spad" 2127796 2127809 2128255 2128260) (-1242 "UNIFACT.spad" 2126899 2126911 2127786 2127791) (-1241 "ULS.spad" 2117457 2117485 2118544 2118973) (-1240 "ULSCONS.spad" 2109853 2109873 2110223 2110372) (-1239 "ULSCCAT.spad" 2107590 2107610 2109699 2109848) (-1238 "ULSCCAT.spad" 2105435 2105457 2107546 2107551) (-1237 "ULSCAT.spad" 2103667 2103683 2105281 2105430) (-1236 "ULS2.spad" 2103181 2103234 2103657 2103662) (-1235 "UINT8.spad" 2103058 2103067 2103171 2103176) (-1234 "UINT64.spad" 2102934 2102943 2103048 2103053) (-1233 "UINT32.spad" 2102810 2102819 2102924 2102929) (-1232 "UINT16.spad" 2102686 2102695 2102800 2102805) (-1231 "UFD.spad" 2101751 2101760 2102612 2102681) (-1230 "UFD.spad" 2100878 2100889 2101741 2101746) (-1229 "UDVO.spad" 2099759 2099768 2100868 2100873) (-1228 "UDPO.spad" 2097252 2097263 2099715 2099720) (-1227 "TYPE.spad" 2097184 2097193 2097242 2097247) (-1226 "TYPEAST.spad" 2097103 2097112 2097174 2097179) (-1225 "TWOFACT.spad" 2095755 2095770 2097093 2097098) (-1224 "TUPLE.spad" 2095241 2095252 2095654 2095659) (-1223 "TUBETOOL.spad" 2092108 2092117 2095231 2095236) (-1222 "TUBE.spad" 2090755 2090772 2092098 2092103) (-1221 "TS.spad" 2089354 2089370 2090320 2090417) (-1220 "TSETCAT.spad" 2076481 2076498 2089322 2089349) (-1219 "TSETCAT.spad" 2063594 2063613 2076437 2076442) (-1218 "TRMANIP.spad" 2057960 2057977 2063300 2063305) (-1217 "TRIMAT.spad" 2056923 2056948 2057950 2057955) (-1216 "TRIGMNIP.spad" 2055450 2055467 2056913 2056918) (-1215 "TRIGCAT.spad" 2054962 2054971 2055440 2055445) (-1214 "TRIGCAT.spad" 2054472 2054483 2054952 2054957) (-1213 "TREE.spad" 2053047 2053058 2054079 2054106) (-1212 "TRANFUN.spad" 2052886 2052895 2053037 2053042) (-1211 "TRANFUN.spad" 2052723 2052734 2052876 2052881) (-1210 "TOPSP.spad" 2052397 2052406 2052713 2052718) (-1209 "TOOLSIGN.spad" 2052060 2052071 2052387 2052392) (-1208 "TEXTFILE.spad" 2050621 2050630 2052050 2052055) (-1207 "TEX.spad" 2047767 2047776 2050611 2050616) (-1206 "TEX1.spad" 2047323 2047334 2047757 2047762) (-1205 "TEMUTL.spad" 2046878 2046887 2047313 2047318) (-1204 "TBCMPPK.spad" 2044971 2044994 2046868 2046873) (-1203 "TBAGG.spad" 2044021 2044044 2044951 2044966) (-1202 "TBAGG.spad" 2043079 2043104 2044011 2044016) (-1201 "TANEXP.spad" 2042487 2042498 2043069 2043074) (-1200 "TALGOP.spad" 2042211 2042222 2042477 2042482) (-1199 "TABLE.spad" 2040622 2040645 2040892 2040919) (-1198 "TABLEAU.spad" 2040103 2040114 2040612 2040617) (-1197 "TABLBUMP.spad" 2036906 2036917 2040093 2040098) (-1196 "SYSTEM.spad" 2036134 2036143 2036896 2036901) (-1195 "SYSSOLP.spad" 2033617 2033628 2036124 2036129) (-1194 "SYSPTR.spad" 2033516 2033525 2033607 2033612) (-1193 "SYSNNI.spad" 2032698 2032709 2033506 2033511) (-1192 "SYSINT.spad" 2032102 2032113 2032688 2032693) (-1191 "SYNTAX.spad" 2028308 2028317 2032092 2032097) (-1190 "SYMTAB.spad" 2026376 2026385 2028298 2028303) (-1189 "SYMS.spad" 2022399 2022408 2026366 2026371) (-1188 "SYMPOLY.spad" 2021406 2021417 2021488 2021615) (-1187 "SYMFUNC.spad" 2020907 2020918 2021396 2021401) (-1186 "SYMBOL.spad" 2018410 2018419 2020897 2020902) (-1185 "SWITCH.spad" 2015181 2015190 2018400 2018405) (-1184 "SUTS.spad" 2012086 2012114 2013648 2013745) (-1183 "SUPXS.spad" 2009227 2009255 2010218 2010367) (-1182 "SUP.spad" 2006040 2006051 2006813 2006966) (-1181 "SUPFRACF.spad" 2005145 2005163 2006030 2006035) (-1180 "SUP2.spad" 2004537 2004550 2005135 2005140) (-1179 "SUMRF.spad" 2003511 2003522 2004527 2004532) (-1178 "SUMFS.spad" 2003148 2003165 2003501 2003506) (-1177 "SULS.spad" 1993693 1993721 1994793 1995222) (-1176 "SUCHTAST.spad" 1993462 1993471 1993683 1993688) (-1175 "SUCH.spad" 1993144 1993159 1993452 1993457) (-1174 "SUBSPACE.spad" 1985259 1985274 1993134 1993139) (-1173 "SUBRESP.spad" 1984429 1984443 1985215 1985220) (-1172 "STTF.spad" 1980528 1980544 1984419 1984424) (-1171 "STTFNC.spad" 1976996 1977012 1980518 1980523) (-1170 "STTAYLOR.spad" 1969631 1969642 1976877 1976882) (-1169 "STRTBL.spad" 1968136 1968153 1968285 1968312) (-1168 "STRING.spad" 1967545 1967554 1967559 1967586) (-1167 "STRICAT.spad" 1967333 1967342 1967513 1967540) (-1166 "STREAM.spad" 1964251 1964262 1966858 1966873) (-1165 "STREAM3.spad" 1963824 1963839 1964241 1964246) (-1164 "STREAM2.spad" 1962952 1962965 1963814 1963819) (-1163 "STREAM1.spad" 1962658 1962669 1962942 1962947) (-1162 "STINPROD.spad" 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1919798 1919803) (-1143 "SPACEC.spad" 1903708 1903719 1919499 1919504) (-1142 "SPACE3.spad" 1903484 1903495 1903698 1903703) (-1141 "SORTPAK.spad" 1903033 1903046 1903440 1903445) (-1140 "SOLVETRA.spad" 1900796 1900807 1903023 1903028) (-1139 "SOLVESER.spad" 1899324 1899335 1900786 1900791) (-1138 "SOLVERAD.spad" 1895350 1895361 1899314 1899319) (-1137 "SOLVEFOR.spad" 1893812 1893830 1895340 1895345) (-1136 "SNTSCAT.spad" 1893412 1893429 1893780 1893807) (-1135 "SMTS.spad" 1891684 1891710 1892977 1893074) (-1134 "SMP.spad" 1889159 1889179 1889549 1889676) (-1133 "SMITH.spad" 1888004 1888029 1889149 1889154) (-1132 "SMATCAT.spad" 1886114 1886144 1887948 1887999) (-1131 "SMATCAT.spad" 1884156 1884188 1885992 1885997) (-1130 "SKAGG.spad" 1883119 1883130 1884124 1884151) (-1129 "SINT.spad" 1882059 1882068 1882985 1883114) (-1128 "SIMPAN.spad" 1881787 1881796 1882049 1882054) (-1127 "SIG.spad" 1881117 1881126 1881777 1881782) (-1126 "SIGNRF.spad" 1880235 1880246 1881107 1881112) (-1125 "SIGNEF.spad" 1879514 1879531 1880225 1880230) (-1124 "SIGAST.spad" 1878899 1878908 1879504 1879509) (-1123 "SHP.spad" 1876827 1876842 1878855 1878860) (-1122 "SHDP.spad" 1866538 1866565 1867047 1867178) (-1121 "SGROUP.spad" 1866146 1866155 1866528 1866533) (-1120 "SGROUP.spad" 1865752 1865763 1866136 1866141) (-1119 "SGCF.spad" 1858891 1858900 1865742 1865747) (-1118 "SFRTCAT.spad" 1857821 1857838 1858859 1858886) (-1117 "SFRGCD.spad" 1856884 1856904 1857811 1857816) (-1116 "SFQCMPK.spad" 1851521 1851541 1856874 1856879) (-1115 "SFORT.spad" 1850960 1850974 1851511 1851516) (-1114 "SEXOF.spad" 1850803 1850843 1850950 1850955) (-1113 "SEX.spad" 1850695 1850704 1850793 1850798) (-1112 "SEXCAT.spad" 1848296 1848336 1850685 1850690) (-1111 "SET.spad" 1846620 1846631 1847717 1847756) (-1110 "SETMN.spad" 1845070 1845087 1846610 1846615) (-1109 "SETCAT.spad" 1844392 1844401 1845060 1845065) (-1108 "SETCAT.spad" 1843712 1843723 1844382 1844387) (-1107 "SETAGG.spad" 1840261 1840272 1843692 1843707) (-1106 "SETAGG.spad" 1836818 1836831 1840251 1840256) (-1105 "SEQAST.spad" 1836521 1836530 1836808 1836813) (-1104 "SEGXCAT.spad" 1835677 1835690 1836511 1836516) (-1103 "SEG.spad" 1835490 1835501 1835596 1835601) (-1102 "SEGCAT.spad" 1834415 1834426 1835480 1835485) (-1101 "SEGBIND.spad" 1834173 1834184 1834362 1834367) (-1100 "SEGBIND2.spad" 1833871 1833884 1834163 1834168) (-1099 "SEGAST.spad" 1833585 1833594 1833861 1833866) (-1098 "SEG2.spad" 1833020 1833033 1833541 1833546) (-1097 "SDVAR.spad" 1832296 1832307 1833010 1833015) (-1096 "SDPOL.spad" 1829722 1829733 1830013 1830140) (-1095 "SCPKG.spad" 1827811 1827822 1829712 1829717) (-1094 "SCOPE.spad" 1826964 1826973 1827801 1827806) (-1093 "SCACHE.spad" 1825660 1825671 1826954 1826959) (-1092 "SASTCAT.spad" 1825569 1825578 1825650 1825655) (-1091 "SAOS.spad" 1825441 1825450 1825559 1825564) (-1090 "SAERFFC.spad" 1825154 1825174 1825431 1825436) (-1089 "SAE.spad" 1823329 1823345 1823940 1824075) (-1088 "SAEFACT.spad" 1823030 1823050 1823319 1823324) (-1087 "RURPK.spad" 1820689 1820705 1823020 1823025) (-1086 "RULESET.spad" 1820142 1820166 1820679 1820684) (-1085 "RULE.spad" 1818382 1818406 1820132 1820137) (-1084 "RULECOLD.spad" 1818234 1818247 1818372 1818377) (-1083 "RTVALUE.spad" 1817969 1817978 1818224 1818229) (-1082 "RSTRCAST.spad" 1817686 1817695 1817959 1817964) (-1081 "RSETGCD.spad" 1814064 1814084 1817676 1817681) (-1080 "RSETCAT.spad" 1804000 1804017 1814032 1814059) (-1079 "RSETCAT.spad" 1793956 1793975 1803990 1803995) (-1078 "RSDCMPK.spad" 1792408 1792428 1793946 1793951) (-1077 "RRCC.spad" 1790792 1790822 1792398 1792403) (-1076 "RRCC.spad" 1789174 1789206 1790782 1790787) (-1075 "RPTAST.spad" 1788876 1788885 1789164 1789169) (-1074 "RPOLCAT.spad" 1768236 1768251 1788744 1788871) (-1073 "RPOLCAT.spad" 1747309 1747326 1767819 1767824) (-1072 "ROUTINE.spad" 1743192 1743201 1745956 1745983) (-1071 "ROMAN.spad" 1742520 1742529 1743058 1743187) (-1070 "ROIRC.spad" 1741600 1741632 1742510 1742515) (-1069 "RNS.spad" 1740503 1740512 1741502 1741595) (-1068 "RNS.spad" 1739492 1739503 1740493 1740498) (-1067 "RNG.spad" 1739227 1739236 1739482 1739487) (-1066 "RNGBIND.spad" 1738387 1738401 1739182 1739187) (-1065 "RMODULE.spad" 1738152 1738163 1738377 1738382) (-1064 "RMCAT2.spad" 1737572 1737629 1738142 1738147) (-1063 "RMATRIX.spad" 1736396 1736415 1736739 1736778) (-1062 "RMATCAT.spad" 1731975 1732006 1736352 1736391) (-1061 "RMATCAT.spad" 1727444 1727477 1731823 1731828) (-1060 "RLINSET.spad" 1726838 1726849 1727434 1727439) (-1059 "RINTERP.spad" 1726726 1726746 1726828 1726833) (-1058 "RING.spad" 1726196 1726205 1726706 1726721) (-1057 "RING.spad" 1725674 1725685 1726186 1726191) (-1056 "RIDIST.spad" 1725066 1725075 1725664 1725669) (-1055 "RGCHAIN.spad" 1723649 1723665 1724551 1724578) (-1054 "RGBCSPC.spad" 1723430 1723442 1723639 1723644) (-1053 "RGBCMDL.spad" 1722960 1722972 1723420 1723425) (-1052 "RF.spad" 1720602 1720613 1722950 1722955) (-1051 "RFFACTOR.spad" 1720064 1720075 1720592 1720597) (-1050 "RFFACT.spad" 1719799 1719811 1720054 1720059) (-1049 "RFDIST.spad" 1718795 1718804 1719789 1719794) (-1048 "RETSOL.spad" 1718214 1718227 1718785 1718790) (-1047 "RETRACT.spad" 1717642 1717653 1718204 1718209) (-1046 "RETRACT.spad" 1717068 1717081 1717632 1717637) (-1045 "RETAST.spad" 1716880 1716889 1717058 1717063) (-1044 "RESULT.spad" 1714940 1714949 1715527 1715554) (-1043 "RESRING.spad" 1714287 1714334 1714878 1714935) (-1042 "RESLATC.spad" 1713611 1713622 1714277 1714282) (-1041 "REPSQ.spad" 1713342 1713353 1713601 1713606) (-1040 "REP.spad" 1710896 1710905 1713332 1713337) (-1039 "REPDB.spad" 1710603 1710614 1710886 1710891) (-1038 "REP2.spad" 1700261 1700272 1710445 1710450) (-1037 "REP1.spad" 1694457 1694468 1700211 1700216) (-1036 "REGSET.spad" 1692254 1692271 1694103 1694130) (-1035 "REF.spad" 1691589 1691600 1692209 1692214) (-1034 "REDORDER.spad" 1690795 1690812 1691579 1691584) (-1033 "RECLOS.spad" 1689578 1689598 1690282 1690375) (-1032 "REALSOLV.spad" 1688718 1688727 1689568 1689573) (-1031 "REAL.spad" 1688590 1688599 1688708 1688713) (-1030 "REAL0Q.spad" 1685888 1685903 1688580 1688585) (-1029 "REAL0.spad" 1682732 1682747 1685878 1685883) (-1028 "RDUCEAST.spad" 1682453 1682462 1682722 1682727) (-1027 "RDIV.spad" 1682108 1682133 1682443 1682448) (-1026 "RDIST.spad" 1681675 1681686 1682098 1682103) (-1025 "RDETRS.spad" 1680539 1680557 1681665 1681670) (-1024 "RDETR.spad" 1678678 1678696 1680529 1680534) (-1023 "RDEEFS.spad" 1677777 1677794 1678668 1678673) (-1022 "RDEEF.spad" 1676787 1676804 1677767 1677772) (-1021 "RCFIELD.spad" 1673973 1673982 1676689 1676782) (-1020 "RCFIELD.spad" 1671245 1671256 1673963 1673968) (-1019 "RCAGG.spad" 1669173 1669184 1671235 1671240) (-1018 "RCAGG.spad" 1667028 1667041 1669092 1669097) (-1017 "RATRET.spad" 1666388 1666399 1667018 1667023) (-1016 "RATFACT.spad" 1666080 1666092 1666378 1666383) (-1015 "RANDSRC.spad" 1665399 1665408 1666070 1666075) (-1014 "RADUTIL.spad" 1665155 1665164 1665389 1665394) (-1013 "RADIX.spad" 1662076 1662090 1663622 1663715) (-1012 "RADFF.spad" 1660489 1660526 1660608 1660764) (-1011 "RADCAT.spad" 1660084 1660093 1660479 1660484) (-1010 "RADCAT.spad" 1659677 1659688 1660074 1660079) (-1009 "QUEUE.spad" 1659025 1659036 1659284 1659311) (-1008 "QUAT.spad" 1657606 1657617 1657949 1658014) (-1007 "QUATCT2.spad" 1657226 1657245 1657596 1657601) (-1006 "QUATCAT.spad" 1655396 1655407 1657156 1657221) (-1005 "QUATCAT.spad" 1653317 1653330 1655079 1655084) (-1004 "QUAGG.spad" 1652144 1652155 1653285 1653312) (-1003 "QQUTAST.spad" 1651912 1651921 1652134 1652139) (-1002 "QFORM.spad" 1651376 1651391 1651902 1651907) (-1001 "QFCAT.spad" 1650078 1650089 1651278 1651371) (-1000 "QFCAT.spad" 1648371 1648384 1649573 1649578) (-999 "QFCAT2.spad" 1648064 1648080 1648361 1648366) (-998 "QEQUAT.spad" 1647623 1647631 1648054 1648059) (-997 "QCMPACK.spad" 1642370 1642389 1647613 1647618) (-996 "QALGSET.spad" 1638449 1638481 1642284 1642289) (-995 "QALGSET2.spad" 1636445 1636463 1638439 1638444) (-994 "PWFFINTB.spad" 1633861 1633882 1636435 1636440) (-993 "PUSHVAR.spad" 1633200 1633219 1633851 1633856) (-992 "PTRANFN.spad" 1629328 1629338 1633190 1633195) (-991 "PTPACK.spad" 1626416 1626426 1629318 1629323) (-990 "PTFUNC2.spad" 1626239 1626253 1626406 1626411) (-989 "PTCAT.spad" 1625494 1625504 1626207 1626234) (-988 "PSQFR.spad" 1624801 1624825 1625484 1625489) (-987 "PSEUDLIN.spad" 1623687 1623697 1624791 1624796) (-986 "PSETPK.spad" 1609120 1609136 1623565 1623570) (-985 "PSETCAT.spad" 1603040 1603063 1609100 1609115) (-984 "PSETCAT.spad" 1596934 1596959 1602996 1603001) (-983 "PSCURVE.spad" 1595917 1595925 1596924 1596929) (-982 "PSCAT.spad" 1594700 1594729 1595815 1595912) (-981 "PSCAT.spad" 1593573 1593604 1594690 1594695) (-980 "PRTITION.spad" 1592658 1592666 1593563 1593568) (-979 "PRTDAST.spad" 1592377 1592385 1592648 1592653) (-978 "PRS.spad" 1581939 1581956 1592333 1592338) (-977 "PRQAGG.spad" 1581374 1581384 1581907 1581934) (-976 "PROPLOG.spad" 1580946 1580954 1581364 1581369) (-975 "PROPFUN2.spad" 1580569 1580582 1580936 1580941) (-974 "PROPFUN1.spad" 1579967 1579978 1580559 1580564) (-973 "PROPFRML.spad" 1578535 1578546 1579957 1579962) (-972 "PROPERTY.spad" 1578023 1578031 1578525 1578530) (-971 "PRODUCT.spad" 1575705 1575717 1575989 1576044) (-970 "PR.spad" 1574097 1574109 1574796 1574923) (-969 "PRINT.spad" 1573849 1573857 1574087 1574092) (-968 "PRIMES.spad" 1572102 1572112 1573839 1573844) (-967 "PRIMELT.spad" 1570183 1570197 1572092 1572097) (-966 "PRIMCAT.spad" 1569810 1569818 1570173 1570178) (-965 "PRIMARR.spad" 1568815 1568825 1568993 1569020) (-964 "PRIMARR2.spad" 1567582 1567594 1568805 1568810) (-963 "PREASSOC.spad" 1566964 1566976 1567572 1567577) (-962 "PPCURVE.spad" 1566101 1566109 1566954 1566959) (-961 "PORTNUM.spad" 1565876 1565884 1566091 1566096) (-960 "POLYROOT.spad" 1564725 1564747 1565832 1565837) (-959 "POLY.spad" 1562060 1562070 1562575 1562702) (-958 "POLYLIFT.spad" 1561325 1561348 1562050 1562055) (-957 "POLYCATQ.spad" 1559443 1559465 1561315 1561320) (-956 "POLYCAT.spad" 1552913 1552934 1559311 1559438) (-955 "POLYCAT.spad" 1545721 1545744 1552121 1552126) (-954 "POLY2UP.spad" 1545173 1545187 1545711 1545716) (-953 "POLY2.spad" 1544770 1544782 1545163 1545168) (-952 "POLUTIL.spad" 1543711 1543740 1544726 1544731) (-951 "POLTOPOL.spad" 1542459 1542474 1543701 1543706) (-950 "POINT.spad" 1541297 1541307 1541384 1541411) (-949 "PNTHEORY.spad" 1537999 1538007 1541287 1541292) (-948 "PMTOOLS.spad" 1536774 1536788 1537989 1537994) (-947 "PMSYM.spad" 1536323 1536333 1536764 1536769) (-946 "PMQFCAT.spad" 1535914 1535928 1536313 1536318) (-945 "PMPRED.spad" 1535393 1535407 1535904 1535909) (-944 "PMPREDFS.spad" 1534847 1534869 1535383 1535388) (-943 "PMPLCAT.spad" 1533927 1533945 1534779 1534784) (-942 "PMLSAGG.spad" 1533512 1533526 1533917 1533922) (-941 "PMKERNEL.spad" 1533091 1533103 1533502 1533507) (-940 "PMINS.spad" 1532671 1532681 1533081 1533086) (-939 "PMFS.spad" 1532248 1532266 1532661 1532666) (-938 "PMDOWN.spad" 1531538 1531552 1532238 1532243) (-937 "PMASS.spad" 1530548 1530556 1531528 1531533) (-936 "PMASSFS.spad" 1529515 1529531 1530538 1530543) (-935 "PLOTTOOL.spad" 1529295 1529303 1529505 1529510) (-934 "PLOT.spad" 1524218 1524226 1529285 1529290) (-933 "PLOT3D.spad" 1520682 1520690 1524208 1524213) (-932 "PLOT1.spad" 1519839 1519849 1520672 1520677) (-931 "PLEQN.spad" 1507129 1507156 1519829 1519834) (-930 "PINTERP.spad" 1506751 1506770 1507119 1507124) (-929 "PINTERPA.spad" 1506535 1506551 1506741 1506746) (-928 "PI.spad" 1506144 1506152 1506509 1506530) (-927 "PID.spad" 1505114 1505122 1506070 1506139) (-926 "PICOERCE.spad" 1504771 1504781 1505104 1505109) (-925 "PGROEB.spad" 1503372 1503386 1504761 1504766) (-924 "PGE.spad" 1494989 1494997 1503362 1503367) (-923 "PGCD.spad" 1493879 1493896 1494979 1494984) (-922 "PFRPAC.spad" 1493028 1493038 1493869 1493874) (-921 "PFR.spad" 1489691 1489701 1492930 1493023) (-920 "PFOTOOLS.spad" 1488949 1488965 1489681 1489686) (-919 "PFOQ.spad" 1488319 1488337 1488939 1488944) (-918 "PFO.spad" 1487738 1487765 1488309 1488314) (-917 "PF.spad" 1487312 1487324 1487543 1487636) (-916 "PFECAT.spad" 1484994 1485002 1487238 1487307) (-915 "PFECAT.spad" 1482704 1482714 1484950 1484955) (-914 "PFBRU.spad" 1480592 1480604 1482694 1482699) (-913 "PFBR.spad" 1478152 1478175 1480582 1480587) (-912 "PERM.spad" 1473837 1473847 1477982 1477997) (-911 "PERMGRP.spad" 1468599 1468609 1473827 1473832) (-910 "PERMCAT.spad" 1467157 1467167 1468579 1468594) (-909 "PERMAN.spad" 1465689 1465703 1467147 1467152) (-908 "PENDTREE.spad" 1465030 1465040 1465318 1465323) (-907 "PDRING.spad" 1463581 1463591 1465010 1465025) (-906 "PDRING.spad" 1462140 1462152 1463571 1463576) (-905 "PDEPROB.spad" 1461155 1461163 1462130 1462135) (-904 "PDEPACK.spad" 1455195 1455203 1461145 1461150) (-903 "PDECOMP.spad" 1454665 1454682 1455185 1455190) (-902 "PDECAT.spad" 1453021 1453029 1454655 1454660) (-901 "PCOMP.spad" 1452874 1452887 1453011 1453016) (-900 "PBWLB.spad" 1451462 1451479 1452864 1452869) (-899 "PATTERN.spad" 1446001 1446011 1451452 1451457) (-898 "PATTERN2.spad" 1445739 1445751 1445991 1445996) (-897 "PATTERN1.spad" 1444075 1444091 1445729 1445734) (-896 "PATRES.spad" 1441650 1441662 1444065 1444070) (-895 "PATRES2.spad" 1441322 1441336 1441640 1441645) (-894 "PATMATCH.spad" 1439519 1439550 1441030 1441035) (-893 "PATMAB.spad" 1438948 1438958 1439509 1439514) (-892 "PATLRES.spad" 1438034 1438048 1438938 1438943) (-891 "PATAB.spad" 1437798 1437808 1438024 1438029) (-890 "PARTPERM.spad" 1435076 1435084 1437788 1437793) (-889 "PARSURF.spad" 1434510 1434538 1435066 1435071) (-888 "PARSU2.spad" 1434307 1434323 1434500 1434505) (-887 "script-parser.spad" 1433827 1433835 1434297 1434302) (-886 "PARSCURV.spad" 1433261 1433289 1433817 1433822) (-885 "PARSC2.spad" 1433052 1433068 1433251 1433256) (-884 "PARPCURV.spad" 1432514 1432542 1433042 1433047) (-883 "PARPC2.spad" 1432305 1432321 1432504 1432509) (-882 "PARAMAST.spad" 1431433 1431441 1432295 1432300) (-881 "PAN2EXPR.spad" 1430845 1430853 1431423 1431428) (-880 "PALETTE.spad" 1429815 1429823 1430835 1430840) (-879 "PAIR.spad" 1428802 1428815 1429403 1429408) (-878 "PADICRC.spad" 1426136 1426154 1427307 1427400) (-877 "PADICRAT.spad" 1424151 1424163 1424372 1424465) (-876 "PADIC.spad" 1423846 1423858 1424077 1424146) (-875 "PADICCT.spad" 1422395 1422407 1423772 1423841) (-874 "PADEPAC.spad" 1421084 1421103 1422385 1422390) (-873 "PADE.spad" 1419836 1419852 1421074 1421079) (-872 "OWP.spad" 1419076 1419106 1419694 1419761) (-871 "OVERSET.spad" 1418649 1418657 1419066 1419071) (-870 "OVAR.spad" 1418430 1418453 1418639 1418644) (-869 "OUT.spad" 1417516 1417524 1418420 1418425) (-868 "OUTFORM.spad" 1406908 1406916 1417506 1417511) (-867 "OUTBFILE.spad" 1406326 1406334 1406898 1406903) (-866 "OUTBCON.spad" 1405332 1405340 1406316 1406321) (-865 "OUTBCON.spad" 1404336 1404346 1405322 1405327) (-864 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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 c980c8be..dafdedee 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188571 . 3480886518) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) -((((-570)) . T) (($) -2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) +(188640 . 3480912616) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2107 |#1|) (|:| -2340 |#2|))))) +((((-570)) . T) (($) -2895 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-1047 (-413 (-570))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-570)) . T)) -((($ $) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) +((($ $) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2| |#2|) . T) ((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) -((($) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) +((($) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570))))) (|has| |#1| (-916)) ((((-868)) . T)) ((((-868)) . T)) @@ -24,19 +24,19 @@ ((((-227)) . T) (((-868)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -(-2892 (|has| |#1| (-826)) (|has| |#1| (-856))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-854))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +(-2895 (|has| |#1| (-826)) (|has| |#1| (-856))) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-854)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-320 |#1|)) . T) (((-570)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-570)) . T) (((-876 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-868)) . T)) ((((-1191)) . T)) @@ -49,14 +49,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1191)) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(((|#2| (-488 (-2569 |#1|) (-777))) . T)) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2| (-488 (-2570 |#1|) (-777))) . T)) (((|#1| (-537 (-1186))) . T)) (((#0=(-876 |#1|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) ((((-1168)) . T) (((-965 (-130))) . T) (((-868)) . T)) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#4| (-373)) (|has| |#3| (-373)) (((|#1|) . T)) @@ -71,13 +71,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-562)) -((((-570)) . T) (((-413 (-570))) -2892 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) -((((-2 (|:| -2268 |#1|) (|:| -3357 |#2|))) . 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T)) (-12 (|has| |#4| (-235)) (|has| |#4| (-1058))) (-12 (|has| |#3| (-235)) (|has| |#3| (-1058))) -(-2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2895 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2895 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) @@ -270,14 +270,14 @@ (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . 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T)) (|has| |#1| (-562)) (|has| |#1| (-562)) @@ -290,21 +290,21 @@ ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))) ((($) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) (($) . 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T)) ((((-542)) |has| |#1| (-620 (-542))) (((-899 (-384))) |has| |#1| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#1| (-620 (-899 (-570))))) -(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) -((((-2 (|:| -2268 |#1|) (|:| -3357 |#2|))) . T)) +(((|#4|) -2895 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2895 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +((((-2 (|:| -2267 |#1|) (|:| -3994 |#2|))) . T)) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) @@ -312,14 +312,14 @@ (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-413 $) (-413 $)) |has| |#2| (-562)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-916)) ((((-1168) (-52)) . T)) ((((-570)) |has| #0=(-413 |#2|) (-645 (-570))) ((#0#) . T)) ((((-542)) . T) (((-227)) . T) (((-384)) . T) (((-899 (-384))) . T)) ((((-868)) . T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-868)) . T)) @@ -333,15 +333,15 @@ (|has| |#1| (-1109)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-542)) |has| |#1| (-620 (-542)))) ((((-868)) . T) (((-1191)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) ((((-1191)) . T)) -((($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| |#1| (-235)) -((($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1| (-537 (-824 (-1186)))) . T)) (((|#1| (-980)) . T)) ((((-570)) . T) ((|#2|) . T)) @@ -351,7 +351,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1161)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-146)) (|has| (-1263 |#1| |#2| |#3| |#4|) (-148)) (|has| |#1| (-146)) @@ -363,27 +363,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) -((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-824 (-1186))) . T) (($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . 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T)) +(((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) ((#0=(-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) #0#) |has| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))))) ((((-868)) . T)) ((((-570) |#1|) . T)) ((((-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#2| (-620 (-542)))) (((-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#2| (-620 (-899 (-384))))) (((-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#2| (-620 (-899 (-570)))))) ((($) . T)) ((((-868)) . T)) -((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2895 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-868)) . T)) (|has| (-1262 |#2| |#3| |#4|) (-148)) @@ -394,16 +394,16 @@ ((((-868)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((|#1|) . T)) ((((-570) |#1|) . T)) (((|#2|) |has| |#2| (-174))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-854))) ((((-868)) |has| |#1| (-1109))) -(-2892 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-917 |#1|)) . T)) ((((-413 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-570) |#1|))) @@ -414,7 +414,7 @@ ((((-868)) . T)) ((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562))) (|has| |#1| (-368)) -(-2892 (-12 (|has| (-1269 |#1| |#2| |#3|) (-235)) (|has| |#1| (-368))) (|has| |#1| (-15 * (|#1| (-570) |#1|)))) +(-2895 (-12 (|has| (-1269 |#1| |#2| |#3|) (-235)) (|has| |#1| (-368))) (|has| |#1| (-15 * (|#1| (-570) |#1|)))) (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-368)) (|has| |#1| (-15 * (|#1| (-777) |#1|))) @@ -428,21 +428,21 @@ ((((-570) |#1|) . T)) ((((-868)) . T)) (((|#2|) . T)) -(-2892 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-562))) ((($) |has| |#1| (-562)) (((-570)) . T)) -(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) -(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) -((((-1269 |#1| |#2| |#3|)) . 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T) (((-1277 |#3|)) . T)) ((((-587 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) ((($) . T) (((-413 (-570))) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2892 (|has| |#1| (-174)) (|has| |#1| (-562)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T) (($) -2895 (|has| |#1| (-174)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) . T)) ((((-868)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((($) . T)) -((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((#1=(-1269 |#1| |#2| |#3|) #1#) |has| |#1| (-368)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . 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T) (($ $) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((#0=(-413 (-570)) #0#) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) +((($) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) . T)) +(((|#1|) . T) (($) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368)))) (((|#3|) |has| |#3| (-1058))) -((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2895 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) (((|#2| (-825 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -470,20 +470,20 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2|) . T) ((|#6|) . T)) (|has| |#1| (-368)) ((((-570)) . T) ((|#2|) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . 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T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-854))) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) (|has| |#2| (-826)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-854)) -(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2895 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-542)) |has| |#1| (-620 (-542)))) (((|#1| |#2|) . T)) ((((-1186)) -12 (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))))) ((((-1168) |#1|) . T)) (((|#1| |#2| |#3| (-537 |#3|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-373)) (|has| |#1| (-373)) (|has| |#1| (-373)) ((((-868)) . T)) ((((-413 (-570))) . T)) (((|#1|) . T)) -(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-413 (-570))) . T)) (|has| |#1| (-373)) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-570)) . T)) ((((-570)) . T)) (((|#1|) . T) (((-570)) . T)) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) @@ -538,10 +538,10 @@ ((((-570) |#4|) . T)) ((((-570) |#3|) . T)) (((|#1|) . T) (((-570)) |has| |#1| (-645 (-570)))) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1263 |#1| |#2| |#3| |#4|)) . T)) ((((-413 (-570))) . T) (((-570)) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -550,9 +550,9 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) ((((-570)) . T)) ((((-570)) . T)) -((($) . T) (((-570)) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-570)) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . 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T)) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-174)) (|has| |#1| (-562))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-1277 |#1|) (-1277 |#1|)) . T)) ((((-570) (-145)) . T)) ((($) . T)) -(-2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2895 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2895 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1191)) . T) (((-868)) . T)) ((((-1191)) . T)) ((((-868)) . T)) @@ -982,20 +982,20 @@ (((|#1| (-980)) . T)) (((|#1| |#1|) . T)) ((($) . 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T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (|has| |#2| (-854)) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) -(-2892 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2895 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-174)) ((|#4|) . T) (((-570)) . T)) (((|#2|) |has| |#2| (-174))) @@ -1007,7 +1007,7 @@ (((|#1|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-413 (-570))) . T)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) (|has| |#1| (-834)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) (((-570)) |has| |#1| (-1047 (-570))) ((|#1|) . T)) (|has| |#1| (-1109)) @@ -1018,13 +1018,13 @@ (((|#4|) |has| |#4| (-1109))) (((|#3|) |has| |#3| (-1109))) (|has| |#3| (-373)) -((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +((($) |has| |#1| (-562)) ((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) ((((-868)) . T)) ((((-868)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562)))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2895 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1| |#1|) |has| |#1| (-174))) (|has| |#2| (-368)) @@ -1032,19 +1032,19 @@ (((|#1|) |has| |#1| (-174))) ((((-413 (-570))) . T) (((-570)) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) -((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) +((($ $) -2895 (|has| |#1| (-174)) (|has| |#1| (-562))) ((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570))))) ((($) . T) (((-570)) . 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T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) (((|#1|) |has| |#1| (-174))) (|has| $ (-148)) (|has| $ (-148)) @@ -1054,15 +1054,15 @@ ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-479)) (|has| |#1| (-562)) (|has| |#1| (-1058)) (|has| |#1| (-1121))) ((($ $) |has| |#1| (-290 $ $)) ((|#1| $) |has| |#1| (-290 |#1| |#1|))) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-1186)) . T)) (|has| |#1| (-562)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-562)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) @@ -1073,7 +1073,7 @@ (|has| |#1| (-148)) (|has| |#1| (-146)) (|has| |#4| (-854)) -(((|#2| (-242 (-2569 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-242 (-2570 |#1|) (-777)) (-870 |#1|)) . T)) (|has| |#3| (-854)) (((|#1| (-537 |#3|) |#3|) . T)) (|has| |#1| (-148)) @@ -1087,21 +1087,21 @@ (|has| |#1| (-148)) ((((-413 (-570))) |has| |#2| (-368)) (($) . 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T)) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-562)) (((|#1|) . T)) (((|#1|) . T)) @@ -1125,11 +1125,11 @@ (((|#1| (-413 (-570))) . T)) (((|#3|) . T) (((-618 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) -((((-570)) -2892 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) +((((-570)) -2895 (|has| |#2| (-174)) (|has| |#2| (-854)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-1058))) ((|#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-1109))) (((-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1137,8 +1137,8 @@ ((((-868)) . T)) ((((-868)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) -(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) |has| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))))) +(((|#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) (((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) |has| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2107 |#1|) (|:| -2340 |#2|))))) +(((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109))) (((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) |has| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (-313 (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))))) ((((-868)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1152,10 +1152,10 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) ((((-570)) . T) (($) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| (-1103 |#1|) (-1109)) -(((|#2| |#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) -(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)))) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2| |#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($ $) |has| |#2| (-174))) +(((|#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)))) +((((-570) (-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) ((((-570)) . T)) ((((-1191)) . T)) ((((-777)) . T)) @@ -1173,39 +1173,39 @@ ((((-117 |#1|)) . T)) (((|#1|) . T)) ((((-413 (-570))) . T) (($) . 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T)) (((|#1|) |has| |#1| (-313 |#1|))) @@ -1257,11 +1257,11 @@ (|has| |#1| (-373)) ((((-1186) $) |has| |#1| (-520 (-1186) $)) (($ $) |has| |#1| (-313 $)) ((|#1| |#1|) |has| |#1| (-313 |#1|)) (((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|))) ((((-1186)) |has| |#1| (-907 (-1186)))) -(-2892 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) +(-2895 (-12 (|has| |#1| (-235)) (|has| |#1| (-368))) (|has| |#1| (-354))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-394) |#1|) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-1109)) (((|#2|) . T) (((-868)) . T)) ((((-868)) . T)) @@ -1269,8 +1269,8 @@ ((((-917 |#1|)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) |has| |#2| (-174)) (($) -2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1279,16 +1279,16 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (((|#1| |#1|) . T)) (((#0=(-876 |#1|)) |has| #0# (-313 #0#))) -((((-570)) . 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T)) (|has| |#1| (-1212)) (((#0=(-570) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) @@ -1300,8 +1300,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (|has| |#1| (-368)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) . T) ((#0=(-413 (-570)) #0#) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((($ $) . T) ((#0=(-413 (-570)) #0#) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1| |#1|) . T)) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -1316,29 +1316,29 @@ (((|#1| |#2|) . T)) (|has| |#1| (-854)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-562))) +((($) . T) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . 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T)) -((((-570) (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) +((((-570) (-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T) ((|#1| |#2|) . T)) ((((-413 (-570))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) ((((-917 |#1|)) . T)) (|has| |#1| (-368)) @@ -1346,11 +1346,11 @@ (|has| |#1| (-368)) (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-854)) -((($) -2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -2895 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (|has| |#1| (-368)) (((|#1|) . T) (($) . T)) (|has| |#1| (-854)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . 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T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-413 (-570))) . T) (((-413 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1182 |#1|)) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) @@ -1536,8 +1536,8 @@ (((|#1|) . T) (((-570)) . T) (($) . T)) (((|#2|) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#2|) . T)) (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T)) @@ -1550,7 +1550,7 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2106 |#1|) (|:| -2340 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((#0=(-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) #0#) |has| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (-313 (-2 (|:| -2107 |#1|) (|:| -2340 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1109)) (|has| |#2| (-368)) @@ -1560,16 +1560,16 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (((|#1|) |has| |#1| (-174))) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) -((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) |has| |#1| (-174)) (($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916)))) +((($) -2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T)) (((|#1|) . T)) ((((-1168) (-52)) . T)) (((|#1|) . T)) -((((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . 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T)) -(-2892 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) -(-2892 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) +(-2895 (|has| |#1| (-148)) (-12 (|has| |#1| (-368)) (|has| |#2| (-148)))) +(-2895 (|has| |#1| (-146)) (-12 (|has| |#1| (-368)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1168) |#1|) . T)) @@ -1621,24 +1621,24 @@ (((|#3|) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((|#1|) . T)) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-570)) . T) (($) . T)) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (((-1184 |#1| |#2| |#3|)) |has| |#1| (-368)) (((-570)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)))) -(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#4|) -2895 (|has| |#4| (-174)) (|has| |#4| (-368)))) +(((|#3|) -2895 (|has| |#3| (-174)) (|has| |#3| (-368)))) (|has| |#2| (-368)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) -(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) +(((|#4|) -2895 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058))) (($) |has| |#4| (-174))) +(((|#3|) -2895 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058))) (($) |has| |#3| (-174))) (((|#2|) |has| |#2| (-1058))) ((((-1168) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) @@ -1647,8 +1647,8 @@ ((($) . T) (((-570)) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) ((((-394) (-1168)) . T)) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((((-868)) -2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 #0#))) . T)) +((((-868)) -2895 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-619 (-868))) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-373)) (|has| |#2| (-732)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058)) (|has| |#2| (-1109))) (((-1277 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2107 (-1168)) (|:| -2340 #0#))) . T)) (((|#1|) . T)) ((((-868)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) @@ -1657,7 +1657,7 @@ ((((-570)) . T)) (|has| |#2| (-148)) (|has| |#1| (-479)) -(-2892 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2895 (|has| |#1| (-479)) (|has| |#1| (-732)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (|has| |#1| (-368)) ((((-868)) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -1668,8 +1668,8 @@ (|has| |#1| (-854)) ((((-868)) . T)) (((|#2|) . T)) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-562)))) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (((-1269 |#1| |#2| |#3|)) |has| |#1| (-368)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2895 (|has| |#1| (-368)) (|has| |#1| (-562)))) ((($) |has| |#1| (-562)) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#2|) . T) (((-570)) . T) (((-825 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1678,7 +1678,7 @@ ((((-868)) . T)) ((((-868)) . T)) (|has| |#1| (-1109)) -(((|#2| (-488 (-2569 |#1|) (-777)) (-870 |#1|)) . T)) +(((|#2| (-488 (-2570 |#1|) (-777)) (-870 |#1|)) . T)) ((((-413 (-570))) . #0=(|has| |#2| (-368))) (($) . #0#)) (((|#1| (-537 (-1186)) (-1186)) . T)) (((|#1|) . T)) @@ -1699,17 +1699,17 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-1186) (-52)) . T)) ((($ $) . T)) (((|#1| (-570)) . T)) ((((-917 |#1|)) . T)) -(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2895 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) (|has| |#1| (-856)) (|has| |#1| (-856)) @@ -1723,17 +1723,18 @@ ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-413 (-959 |#1|))) . T)) +((((-980)) . 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T)) -(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-854)) (|has| |#1| (-854)) (|has| |#1| (-854)) @@ -1751,14 +1752,14 @@ ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-1186)) |has| |#1| (-907 (-1186))) (((-1091)) . T)) (((|#1|) . 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T)) ((((-570) |#1|) . T)) ((((-1186)) |has| (-413 |#2|) (-907 (-1186)))) -(((|#1|) . T) (($) -2892 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) +(((|#1|) . T) (($) -2895 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) ((((-542)) |has| |#2| (-620 (-542)))) ((((-695 |#2|)) . T) (((-868)) . T)) (((|#1|) . T)) @@ -2348,22 +2351,22 @@ (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-876 |#1|)) . T)) (((|#1|) |has| |#1| (-174))) -(-2892 (|has| |#4| (-799)) (|has| |#4| (-854))) -(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2895 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2895 (|has| |#3| (-799)) (|has| |#3| (-854))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) (((|#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) -(((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)))) +(((|#3|) -2895 (|has| |#3| (-174)) (|has| |#3| (-368)))) (((|#2|) |has| |#2| (-1058))) (((|#3|) . T)) (((|#1|) . T)) ((((-413 |#2|)) . T)) -(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)))) +(((|#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)))) (((|#1|) . T)) -(((|#2|) -2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) +(((|#2|) -2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-1058))) (($) |has| |#2| (-174))) (((|#3|) -12 (|has| |#3| (-313 |#3|)) (|has| |#3| (-1109)))) ((((-570) |#1|) . T)) (((|#1|) . T)) @@ -2372,17 +2375,17 @@ ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) ((((-413 (-570))) . T) (($) . T)) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-1231))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-1231))) ((($) . 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T)) @@ -2473,10 +2476,10 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-570)) . T) (($) . T) (((-413 (-570))) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) @@ -2486,10 +2489,10 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-368))) -((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-413 (-570))) -2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((#0=(-786 |#1| (-870 |#2|)) #0#) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) ((((-570)) . T) (($) . T)) @@ -2508,13 +2511,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . 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T)) -(((|#2|) |has| |#2| (-6 (-4451 "*")))) +(((|#2|) |has| |#2| (-6 (-4454 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((($) . T)) @@ -2534,7 +2537,7 @@ (((|#1|) . T)) (((|#3|) . T) (((-570)) . T)) ((((-1262 |#2| |#3| |#4|)) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-413 (-570))) . T)) -((((-48)) -12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (((-570)) -2892 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1047 (-570))) (|has| |#1| (-1058))) ((|#1|) . T) (((-618 $)) . T) (($) |has| |#1| (-562)) (((-413 (-570))) -2892 (|has| |#1| (-562)) (|has| |#1| (-1047 (-413 (-570))))) (((-413 (-959 |#1|))) |has| |#1| (-562)) (((-959 |#1|)) |has| |#1| (-1058)) (((-1186)) . T)) +((((-48)) -12 (|has| |#1| (-562)) (|has| |#1| (-1047 (-570)))) (((-570)) -2895 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1047 (-570))) (|has| |#1| (-1058))) ((|#1|) . T) (((-618 $)) . 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T)) (((|#1| $) |has| |#1| (-290 |#1| |#1|))) ((((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-562)) (($) |has| |#1| (-562))) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-562))) ((|#1|) . T)) (|has| |#1| (-368)) -((($) |has| |#1| (-854)) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) |has| |#1| (-854)) (((-570)) -2895 (|has| |#1| (-21)) (|has| |#1| (-854)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-148)) @@ -2575,17 +2578,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109)))) (((|#2| |#3|) . 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T)) ((($) . T)) -(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-368)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1262 |#2| |#3| |#4|)) . T) (((-413 (-570))) |has| #0# (-38 (-413 (-570))))) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(-2892 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) +(-2895 (-12 (|has| |#1| (-311)) (|has| |#1| (-916))) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) ((((-570)) |has| |#1| (-645 (-570))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-868)) . T)) @@ -2645,28 +2648,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) (((|#2|) . T)) -(((|#2|) -2892 (|has| |#2| (-6 (-4451 "*"))) (|has| |#2| (-174)))) -(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(((|#2|) -2895 (|has| |#2| (-6 (-4454 "*"))) (|has| |#2| (-174)))) +(-2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#2| (-916)) (|has| |#1| (-916)) (((|#2|) |has| |#2| (-174))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-1269 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-868)) . T)) ((((-868)) . T)) ((((-542)) . T) (((-570)) . T) (((-899 (-570))) . T) (((-384)) . T) (((-227)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-570)) . T)) (((|#1| (-413 (-570))) . T)) (((|#1|) . T)) -(-2892 (|has| |#1| (-294)) (|has| |#1| (-368))) +(-2895 (|has| |#1| (-294)) (|has| |#1| (-368))) ((((-145)) . T)) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) (|has| |#1| (-854)) @@ -2682,7 +2685,7 @@ ((((-868)) . T)) ((((-868)) . T)) ((((-189)) . T) (((-868)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -2695,7 +2698,7 @@ ((((-868)) . T)) ((((-1168)) . T)) ((((-1186) |#1|) |has| |#1| (-520 (-1186) |#1|)) ((|#1| |#1|) |has| |#1| (-313 |#1|))) -((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) (|has| |#1| (-856)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) @@ -2707,16 +2710,16 @@ (((|#2|) . T)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) ((($) . T) (((-570)) . T) (((-413 (-570))) . T) (((-618 $)) . T)) -(-2892 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2892 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2895 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2895 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-1186) (-52)) . T)) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (|has| |#1| (-916)) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) (|has| |#1| (-916)) @@ -2733,12 +2736,12 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (|has| |#1| (-826)) (((#0=(-917 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((((-413 |#2|)) . T)) (|has| |#1| (-854)) -((((-1213 |#1|)) . T) (((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-1213 |#1|)) . T) (((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1| |#1|) . T) ((#0=(-413 (-570)) #0#) . T) ((#1=(-570) #1#) . T) (($ $) . T)) ((((-917 |#1|)) . T) (($) . T) (((-413 (-570))) . T)) (((|#2|) |has| |#2| (-1058)) (((-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) @@ -2754,28 +2757,28 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) -((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2106 (-1186)) (|:| -2340 #0#))) . T)) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) +((((-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2107 (-1186)) (|:| -2340 #0#))) . T)) (|has| |#1| (-354)) ((((-570)) . T)) ((((-868)) . T)) (((|#1|) . T)) (((#0=(-1263 |#1| |#2| |#3| |#4|) $) |has| #0# (-290 #0# #0#))) (|has| |#1| (-368)) -(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2892 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) +(((|#1|) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058))) (($) -2895 (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058))) (((-570)) -2895 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-907 (-1186))) (|has| |#1| (-1058)))) (((#0=(-1091) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) (((#0=(-413 (-570)) #0#) . T) ((#1=(-705) #1#) . T) (($ $) . T)) ((((-320 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-868)) . T)) (|has| |#1| (-1109)) (((|#1|) . T)) -(((|#1|) -2892 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) -(((|#1|) -2892 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2895 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) +(((|#1|) -2895 (|has| |#2| (-372 |#1|)) (|has| |#2| (-423 |#1|)))) (((|#2|) . T)) ((((-413 (-570))) . T) (((-705)) . T) (($) . T)) ((((-585)) . T)) @@ -2800,7 +2803,7 @@ (((|#1|) . T)) ((((-570)) . T)) (((|#2|) . T) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (($) . T) (((-570)) . T)) -(-2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((|#2|) . T) (((-570)) |has| |#2| (-645 (-570)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2844,7 +2847,7 @@ (|has| |#2| (-1031)) ((($) . T)) (|has| |#1| (-916)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2853,10 +2856,10 @@ (|has| |#1| (-368)) ((((-917 |#1|)) . T)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) . T)) -((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) -((($) |has| |#1| (-854)) (((-570)) -2892 (|has| |#1| (-21)) (|has| |#1| (-854)))) +((($) -2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) |has| |#1| (-854)) (((-570)) -2895 (|has| |#1| (-21)) (|has| |#1| (-854)))) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) -(-2892 (|has| |#1| (-373)) (|has| |#1| (-856))) +(-2895 (|has| |#1| (-373)) (|has| |#1| (-856))) (((|#1|) . T)) ((((-777)) . T)) ((((-868)) . T)) @@ -2867,17 +2870,17 @@ ((((-570)) . T) (($) . T)) ((((-570)) . T) (($) . T)) ((((-777) |#1|) . T)) -(((|#2| (-242 (-2569 |#1|) (-777))) . T)) +(((|#2| (-242 (-2570 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) ((((-413 (-570))) . T)) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((((-1168)) . T) (((-868)) . T)) -(((#0=(-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) #0#) |has| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))))) +(((#0=(-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) #0#) |has| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (-313 (-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))))) ((((-1168)) . T)) (|has| |#1| (-916)) (|has| |#2| (-368)) (((|#1|) . T) (($) . T) (((-570)) . T)) -(-2892 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) (((|#1|) . T)) @@ -2894,11 +2897,11 @@ (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570)))) -(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) (|has| |#1| (-38 (-413 (-570)))) (-12 (|has| |#1| (-551)) (|has| |#1| (-834))) ((((-868)) . T)) -((((-1186)) -2892 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) +((((-1186)) -2895 (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))) (-12 (|has| |#1| (-368)) (|has| |#2| (-907 (-1186)))))) (|has| |#1| (-368)) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) (|has| |#1| (-368)) @@ -2910,7 +2913,7 @@ (((|#2|) |has| |#1| (-368))) (((|#2|) |has| |#1| (-368))) ((((-570)) . T) (($) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2940,11 +2943,11 @@ (((|#2|) |has| |#1| (-368))) ((((-384)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-384)))) (((-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-893 (-570))))) (|has| |#1| (-368)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#1|) . T)) ((($) . T) (((-570)) . T) ((|#2|) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (((|#3|) . T)) ((((-1168)) . T) (((-512)) . T) (((-227)) . T) (((-570)) . T)) @@ -2952,23 +2955,23 @@ (|has| |#1| (-562)) (((|#4| |#4|) -12 (|has| |#4| (-313 |#4|)) (|has| |#4| (-1109)))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) -(-2892 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#2|) . T)) (((|#2|) . T)) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-38 (-413 (-570)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-413 (-570)))) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) ((((-1168) |#1|) . T)) (|has| |#1| (-148)) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) (|has| |#1| (-148)) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-373))) ((($) . T)) (|has| |#1| (-148)) ((((-587 |#1|)) . T)) @@ -2982,7 +2985,7 @@ ((((-413 (-570))) |has| |#2| (-1047 (-570))) (((-570)) |has| |#2| (-1047 (-570))) (((-1186)) |has| |#2| (-1047 (-1186))) ((|#2|) . T)) (((#0=(-413 |#2|) #0#) . T) ((#1=(-413 (-570)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2892 (|has| |#1| (-146)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-354))) (|has| |#1| (-148)) ((((-868)) . T)) ((($) . T)) @@ -3008,7 +3011,7 @@ ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-868)) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3030,7 +3033,7 @@ ((((-570)) . T)) ((((-868)) . T)) ((((-570)) . T)) -(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2895 (|has| |#2| (-799)) (|has| |#2| (-854))) ((((-171 (-384))) . T) (((-227)) . T) (((-384)) . T)) ((((-868)) . T)) ((((-868)) . T)) @@ -3042,9 +3045,9 @@ (((|#1|) . T) (($) . T) (((-413 (-570))) . 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T)) -(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)))) +(((|#1|) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)))) (((|#1|) . T)) -(((|#1|) -2892 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) +(((|#1|) -2895 (|has| |#1| (-174)) (|has| |#1| (-368)) (|has| |#1| (-1058)))) ((((-570)) . T) (((-413 (-570))) . T)) (((|#1|) . T)) (|has| |#1| (-562)) ((($) . T) (((-570)) . T) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-368))) ((((-413 |#2|)) . T) (((-413 (-570))) . T) (($) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) ((((-384)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-368)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) (|has| |#1| (-368)) (|has| |#1| (-562)) (|has| |#1| (-1109)) ((((-786 |#1| (-870 |#2|))) |has| (-786 |#1| (-870 |#2|)) (-313 (-786 |#1| (-870 |#2|))))) -(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3091,13 +3094,13 @@ (|has| |#2| (-368)) ((((-587 |#1|)) . T) (((-413 (-570))) . T) (($) . T) (((-570)) . T)) ((((-570)) . T) (((-413 (-570))) . T) (($) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-570)) . T)) (((|#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) ((((-868)) . T)) ((((-868)) . T)) -(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2895 (|has| |#3| (-799)) (|has| |#3| (-854))) ((((-868)) . T)) ((((-1129)) . T) (((-868)) . T)) ((((-542)) . T) (((-868)) . T)) @@ -3108,12 +3111,12 @@ ((((-570)) . T)) (((|#3|) . T)) ((((-868)) . T)) -(-2892 (|has| |#1| (-311)) (|has| |#1| (-368)) (|has| |#1| (-354))) -((((-570)) . T) (((-413 (-570))) -2892 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570))))) ((|#2|) . T) (($) -2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-870 |#1|)) . T)) -((((-1134 |#1| |#2|)) . T) ((|#2|) . T) (($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-570)) . T)) -((((-1182 |#1|)) . T) (((-570)) . T) (($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . 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T)) +((((-1182 |#1|)) . T) (((-570)) . T) (($) -2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) (((-1091)) . T) ((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +(-2895 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-562)) (|has| |#1| (-1058))) +((((-1134 |#1| (-1186))) . T) (((-570)) . T) (((-1097 (-1186))) . T) (($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570))))) (((-1186)) . T)) (((#0=(-587 |#1|) #0#) . T) (($ $) . T) ((#1=(-413 (-570)) #1#) . T)) ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) (((|#1|) |has| |#1| (-174))) @@ -3125,13 +3128,13 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) . T)) -(((|#2|) |has| |#2| (-6 (-4451 "*")))) +(((|#2|) |has| |#2| (-6 (-4454 "*")))) (((|#1|) . T)) ((((-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((|#1|) . T) (((-570)) . T)) (((|#1|) . T)) ((((-868)) . T)) ((((-298 |#3|)) . T)) -(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2892 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +(((#0=(-413 (-570)) #0#) |has| |#2| (-38 (-413 (-570)))) ((|#2| |#2|) . T) (($ $) -2895 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-413 (-570))) |has| |#2| (-38 (-413 (-570)))) ((|#2|) . T)) @@ -3139,21 +3142,21 @@ (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) (((|#1|) . T) (((-413 (-570))) . T) (($) . T)) -((($ $) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1| |#1|) . 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T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (|has| |#2| (-916)) (|has| |#1| (-916)) -((($) -2892 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) (((|#1|) . T)) -((((-2 (|:| -2106 (-1168)) (|:| -2340 |#1|))) . T)) +((((-2 (|:| -2107 (-1168)) (|:| -2340 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3172,10 +3175,10 @@ (((#0=(-413 (-570)) #0#) . T)) ((((-413 (-570))) . T)) (((|#1|) |has| |#1| (-174))) -(-2892 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) (((|#1|) . T)) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1|) . T)) ((((-413 (-570))) . T) (((-570)) . T) (($) . T)) ((((-542)) . T)) @@ -3194,14 +3197,14 @@ ((($ $) . T) ((#0=(-413 (-570)) #0#) . T)) ((((-1186)) |has| |#1| (-907 (-1186)))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) -((($) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#1|) . T)) -(((#0=(-413 (-570)) #0#) |has| |#1| (-38 (-413 (-570)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-826)) (|has| |#2| (-826)) -((((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-413 (-570))) -2892 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) +((((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) ((|#2|) |has| |#1| (-368)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-413 (-570))) -2895 (|has| |#1| (-38 (-413 (-570)))) (|has| |#1| (-368))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1|) . T) (((-570)) |has| |#1| (-1047 (-570))) (((-413 (-570))) |has| |#1| (-1047 (-413 (-570))))) ((((-570)) |has| |#1| (-893 (-570))) (((-384)) |has| |#1| (-893 (-384)))) @@ -3238,7 +3241,7 @@ (((|#1|) . 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T)) -(-2892 (|has| |#2| (-799)) (|has| |#2| (-854))) -(-2892 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) +(-2895 (|has| |#2| (-799)) (|has| |#2| (-854))) +(-2895 (-12 (|has| |#1| (-799)) (|has| |#2| (-799))) (-12 (|has| |#1| (-856)) (|has| |#2| (-856)))) ((((-876 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-373)) @@ -3284,7 +3287,7 @@ (((|#1|) . T)) ((((-868)) . T)) (|has| |#2| (-916)) -((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570))))) ((((-868)) . T)) ((((-868)) . T)) @@ -3311,7 +3314,7 @@ ((((-1191)) . T)) ((((-650 |#1|)) . T)) ((($) . T) (((-570)) . T) (((-1263 |#1| |#2| |#3| |#4|)) . T) (((-413 (-570))) . 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T)) -(-2892 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-570)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3344,9 +3347,9 @@ ((($) . T) (((-413 (-570))) . T)) ((($) . T)) ((($) . T)) -(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2895 (|has| |#1| (-856)) (|has| |#1| (-1109))) (((|#1|) . T)) -((($) -2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((((-868)) . T)) ((((-145)) . T)) (((|#1|) . T) (((-413 (-570))) . T)) @@ -3378,7 +3381,7 @@ (|has| |#1| (-1109)) (|has| |#1| (-1109)) (|has| |#2| (-368)) -(((|#1|) . T) (($) -2892 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) +(((|#1|) . T) (($) -2895 (|has| |#1| (-294)) (|has| |#1| (-368))) (((-413 (-570))) |has| |#1| (-368))) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570)))) @@ -3387,32 +3390,32 @@ ((((-1186)) -12 (|has| |#3| (-907 (-1186))) (|has| |#3| (-1058)))) (((|#1|) . T)) (|has| |#1| (-235)) -(((|#2| (-242 (-2569 |#1|) (-777))) . T)) +(((|#2| (-242 (-2570 |#1|) (-777))) . T)) (((|#1| (-537 |#3|)) . T)) (|has| |#1| (-373)) (|has| |#1| (-373)) (|has| |#1| (-373)) (((|#1|) . T) (($) . T)) (((|#1| (-537 |#2|)) . T)) -(-2892 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-368)) (|has| |#2| (-799)) (|has| |#2| (-854)) (|has| |#2| (-1058))) (((|#1| (-777)) . 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T) (($) -2895 (|has| |#2| (-174)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916)))) +((($) -2895 (|has| |#1| (-174)) (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) . T) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) (((|#1|) . T) (($) . T) (((-413 (-570))) . T)) @@ -3452,12 +3455,12 @@ (((|#1|) . 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T)) -((($) -2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) +((($) -2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((|#1|) |has| |#1| (-174)) (((-413 (-570))) |has| |#1| (-38 (-413 (-570))))) ((($ $) . T) (((-1186) $) . T)) ((((-1269 |#1| |#2| |#3|)) . T)) (|has| |#2| (-916)) @@ -3650,7 +3653,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-174))) ((((-705)) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-1191)) . T)) (((|#1|) |has| |#1| (-174))) ((((-1191)) . T)) @@ -3667,13 +3670,13 @@ ((((-1191)) . T)) ((((-1191)) . T)) ((((-1191)) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1191)) . T)) ((((-1191)) . 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T)) ((((-570)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2892 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) +(-2895 (|has| |#2| (-174)) (|has| |#2| (-732)) (|has| |#2| (-854)) (|has| |#2| (-1058))) ((((-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) -(-2892 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-2895 (-12 (|has| |#1| (-479)) (|has| |#2| (-479))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-368)) @@ -3728,7 +3731,7 @@ (((|#1| |#2|) . T)) ((((-570)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-570)) . T)) -(-2892 (|has| |#1| (-354)) (|has| |#1| (-373))) +(-2895 (|has| |#1| (-354)) (|has| |#1| (-373))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-413 (-570))) . T) (($) . T) (((-570)) . T)) @@ -3740,7 +3743,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-542)) |has| |#1| (-620 (-542)))) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-856)) (|has| |#1| (-1109)))) ((($) . T) (((-413 (-570))) . T)) (|has| |#1| (-916)) (|has| |#1| (-916)) @@ -3751,14 +3754,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-570)) . T)) ((((-1191)) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-562))) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-562))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#2|) . T)) -(-2892 (|has| |#1| (-21)) (|has| |#1| (-854))) +(-2895 (|has| |#1| (-21)) (|has| |#1| (-854))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-868)) -2892 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) +((((-868)) -2895 (-12 (|has| |#1| (-619 (-868))) (|has| |#2| (-619 (-868)))) (-12 (|has| |#1| (-1109)) (|has| |#2| (-1109))))) ((((-413 |#2|) |#3|) . T)) ((((-413 (-570))) . T) (($) . T)) (|has| |#1| (-38 (-413 (-570)))) @@ -3772,19 +3775,19 @@ (((|#1|) . T) (((-413 (-570))) . T) (((-570)) . T) (($) . T)) (((#0=(-570) #0#) . T)) ((($) . T) (((-413 (-570))) . T)) -(-2892 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) -(-2892 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) +(-2895 (|has| |#4| (-174)) (|has| |#4| (-732)) (|has| |#4| (-854)) (|has| |#4| (-1058))) +(-2895 (|has| |#3| (-174)) (|has| |#3| (-732)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((((-868)) . T) (((-1191)) . T)) (|has| |#4| (-799)) -(-2892 (|has| |#4| (-799)) (|has| |#4| (-854))) +(-2895 (|has| |#4| (-799)) (|has| |#4| (-854))) (|has| |#4| (-854)) (|has| |#3| (-799)) ((((-1191)) . T)) -(-2892 (|has| |#3| (-799)) (|has| |#3| (-854))) +(-2895 (|has| |#3| (-799)) (|has| |#3| (-854))) (|has| |#3| (-854)) ((((-570)) . T)) (((|#2|) . T)) -((((-1186)) -2892 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) +((((-1186)) -2895 (-12 (|has| (-1184 |#1| |#2| |#3|) (-907 (-1186))) (|has| |#1| (-368))) (-12 (|has| |#1| (-15 * (|#1| (-570) |#1|))) (|has| |#1| (-907 (-1186)))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-413 (-570)) |#1|))) (|has| |#1| (-907 (-1186))))) ((((-1186)) -12 (|has| |#1| (-15 * (|#1| (-777) |#1|))) (|has| |#1| (-907 (-1186))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3799,11 +3802,11 @@ ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) ((((-1149 |#1| |#2|)) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1031)) -(((|#2|) . T) (((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) ((((-868)) . T)) ((((-542)) |has| |#2| (-620 (-542))) (((-899 (-570))) |has| |#2| (-620 (-899 (-570)))) (((-899 (-384))) |has| |#2| (-620 (-899 (-384)))) (((-384)) . #0=(|has| |#2| (-1031))) (((-227)) . #0#)) ((((-298 |#3|)) . T)) @@ -3820,15 +3823,15 @@ ((((-1184 |#1| |#2| |#3|)) . T)) ((((-1184 |#1| |#2| |#3|)) . T) (((-1177 |#1| |#2| |#3|)) . T)) ((((-868)) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-570) |#1|) . T)) ((((-1184 |#1| |#2| |#3|)) |has| |#1| (-368))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-368)) -(((|#3|) . T) ((|#2|) . T) (($) -2892 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2892 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) -(((|#2|) . T) (($) -2892 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2892 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) +(((|#3|) . T) ((|#2|) . T) (($) -2895 (|has| |#4| (-174)) (|has| |#4| (-854)) (|has| |#4| (-1058))) ((|#4|) -2895 (|has| |#4| (-174)) (|has| |#4| (-368)) (|has| |#4| (-1058)))) +(((|#2|) . T) (($) -2895 (|has| |#3| (-174)) (|has| |#3| (-854)) (|has| |#3| (-1058))) ((|#3|) -2895 (|has| |#3| (-174)) (|has| |#3| (-368)) (|has| |#3| (-1058)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-368)) @@ -3843,7 +3846,7 @@ ((((-189)) . T) (((-868)) . T)) ((((-868)) . T)) (((|#1|) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) ((((-130)) . T) (((-868)) . T)) ((((-570) |#1|) . T)) ((((-130)) . T)) @@ -3852,13 +3855,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-368)) (|has| |#2| (-290 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) -(-2892 (|has| |#1| (-856)) (|has| |#1| (-1109))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-458)) (|has| |#1| (-916))) +(-2895 (|has| |#1| (-856)) (|has| |#1| (-1109))) ((((-868)) . T)) ((((-868)) . T)) ((((-868)) . T)) (((|#1| (-537 |#2|)) . T)) -((((-2 (|:| -2106 (-1186)) (|:| -2340 (-52)))) . T)) +((((-2 (|:| -2107 (-1186)) (|:| -2340 (-52)))) . T)) ((((-570) (-130)) . T)) (((|#1| (-570)) . T)) (((|#1| (-413 (-570))) . T)) @@ -3873,8 +3876,8 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) -(-2892 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) -(-2892 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) +(-2895 (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) +(-2895 (|has| |#1| (-458)) (|has| |#1| (-562)) (|has| |#1| (-916))) ((($) . T)) (((|#2| (-537 (-870 |#1|))) . T)) ((((-1191)) . T)) @@ -3889,13 +3892,13 @@ ((((-1191)) . T)) ((((-868)) . T) (((-1191)) . T)) ((((-1191)) . T)) -((((-868)) -2892 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) +((((-868)) -2895 (|has| |#1| (-619 (-868))) (|has| |#1| (-1109)))) (((|#1|) . T)) (((|#2| (-777)) . T)) (((|#1| |#2|) . T)) ((((-1168) |#1|) . T)) ((((-413 |#2|)) . T)) -((((-2 (|:| -2106 |#1|) (|:| -2340 |#2|))) . T)) +((((-2 (|:| -2107 |#1|) (|:| -2340 |#2|))) . T)) (|has| |#1| (-562)) (|has| |#1| (-562)) ((($) . T) ((|#2|) . T)) @@ -3906,14 +3909,14 @@ ((((-570)) . T) (($) . T)) (((|#2| $) |has| |#2| (-290 |#2| |#2|))) (((|#1| (-650 |#1|)) |has| |#1| (-854))) -(-2892 (|has| |#1| (-235)) (|has| |#1| (-354))) -(-2892 (|has| |#1| (-368)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-235)) (|has| |#1| (-354))) +(-2895 (|has| |#1| (-368)) (|has| |#1| (-354))) ((((-1273 |#1|)) . T) (((-570)) . T) ((|#2|) . T) (((-413 (-570))) |has| |#2| (-1047 (-413 (-570))))) (|has| |#1| (-1109)) (((|#1|) . T)) -((((-1273 |#1|)) . T) (((-570)) . T) (($) -2892 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2892 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) +((((-1273 |#1|)) . T) (((-570)) . T) (($) -2895 (|has| |#2| (-368)) (|has| |#2| (-458)) (|has| |#2| (-562)) (|has| |#2| (-916))) (((-1091)) . T) ((|#2|) . T) (((-413 (-570))) -2895 (|has| |#2| (-38 (-413 (-570)))) (|has| |#2| (-1047 (-413 (-570)))))) ((((-413 (-570))) . T) (($) . T)) -((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2892 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2892 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) +((((-1008 |#1|)) . T) ((|#1|) . T) (((-570)) -2895 (|has| (-1008 |#1|) (-1047 (-570))) (|has| |#1| (-1047 (-570)))) (((-413 (-570))) -2895 (|has| (-1008 |#1|) (-1047 (-413 (-570)))) (|has| |#1| (-1047 (-413 (-570)))))) ((((-917 |#1|)) . T) (((-413 (-570))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) (((|#1| |#1|) -12 (|has| |#1| (-313 |#1|)) (|has| |#1| (-1109)))) @@ -3929,10 +3932,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1149 |#1| |#2|) #0#) |has| (-1149 |#1| |#2|) (-313 (-1149 |#1| |#2|)))) (((|#1|) . 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T) ((-651 . -93) T) ((-326 . -1065) 182008) ((-254 . -797) 181987) ((-254 . -800) 181938) ((-31 . -496) 181919) ((-254 . -799) 181898) ((-253 . -797) 181877) ((-253 . -800) 181828) ((-253 . -799) 181807) ((-31 . -619) 181773) ((-50 . -1067) T) ((-254 . -732) 181683) ((-253 . -732) 181593) ((-1221 . -1109) T) ((-676 . -23) T) ((-587 . -1067) T) ((-524 . -1067) T) ((-384 . -1065) 181558) ((-326 . -111) 181533) ((-73 . -388) T) ((-73 . -401) T) ((-1033 . -38) 181470) ((-700 . -406) 181452) ((-99 . -102) T) ((-717 . -1109) T) ((-1305 . -1060) 181439) ((-1012 . -146) 181411) ((-1012 . -148) 181383) ((-876 . -652) 181355) ((-384 . -111) 181311) ((-323 . -1231) 181290) ((-480 . -1011) 181256) ((-359 . -38) 181221) ((-40 . -375) 181193) ((-879 . -619) 181065) ((-128 . -126) 181049) ((-122 . -126) 181033) ((-842 . -1065) 181003) ((-839 . -21) 180955) ((-833 . -1065) 180939) ((-839 . -25) 180891) ((-323 . -562) 180842) ((-523 . -622) 180823) ((-570 . -834) T) ((-242 . -1227) T) ((-1043 . -622) 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T) ((-570 . -1109) T) ((-501 . -1109) T) ((-247 . -292) 160906) ((-317 . -233) 160867) ((-1182 . -893) NIL) ((-55 . -1109) T) ((-1134 . -893) 160726) ((-130 . -856) T) ((-1182 . -1047) 160606) ((-1134 . -1047) 160489) ((-185 . -619) 160471) ((-860 . -1047) 160367) ((-788 . -290) 160294) ((-823 . -1121) T) ((-1043 . -732) T) ((-608 . -657) 160278) ((-1055 . -985) 160207) ((-1008 . -102) T) ((-823 . -23) T) ((-718 . -1161) 160185) ((-700 . -1067) T) ((-608 . -378) 160169) ((-356 . -458) T) ((-348 . -294) T) ((-1278 . -1109) T) ((-250 . -1109) T) ((-405 . -102) T) ((-293 . -21) T) ((-293 . -25) T) ((-366 . -732) T) ((-716 . -1109) T) ((-705 . -1109) T) ((-366 . -479) T) ((-1221 . -619) 160151) ((-1182 . -382) 160135) ((-1134 . -382) 160119) ((-1033 . -417) 160081) ((-142 . -231) 160063) ((-384 . -800) T) ((-384 . -797) T) ((-876 . -174) T) ((-384 . -732) T) ((-717 . -619) 160045) ((-718 . -38) 159874) ((-1277 . -1275) 159858) ((-356 . -408) T) ((-1277 . -1109) 159808) ((-1200 . -1109) T) 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. -1231) T) ((-1008 . -313) 158953) ((-882 . -622) 158934) ((-720 . -654) 158894) ((-219 . -1231) T) ((-687 . -622) 158875) ((-227 . -1047) 158835) ((-40 . -294) T) ((-682 . -622) 158816) ((-493 . -562) T) ((-484 . -622) 158797) ((-320 . -652) 158481) ((-317 . -652) 158395) ((-364 . -25) T) ((-364 . -21) T) ((-358 . -25) T) ((-219 . -562) T) ((-358 . -21) T) ((-350 . -25) T) ((-350 . -21) T) ((-247 . -622) 158372) ((-139 . -622) 158353) ((-138 . -622) 158334) ((-134 . -622) 158315) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1067) T) ((-586 . -174) T) ((-570 . -174) T) ((-501 . -174) T) ((-664 . -619) 158297) ((-743 . -742) 158281) ((-341 . -619) 158263) ((-68 . -388) T) ((-68 . -401) T) ((-1111 . -107) 158247) ((-1071 . -893) 158229) ((-959 . -893) 158154) ((-659 . -1121) T) ((-629 . -723) 158141) ((-487 . -893) NIL) ((-1155 . -102) T) ((-1103 . -624) 158125) ((-1071 . -1047) 158107) ((-97 . -619) 158089) ((-483 . -148) T) ((-959 . -1047) 157969) ((-118 . -723) 157914) ((-659 . -23) T) 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. -152) 144158) ((-348 . -235) T) ((-348 . -245) T) ((-40 . -1065) 144103) ((-878 . -891) 144087) ((-878 . -893) 144012) ((-718 . -1067) T) ((-700 . -1011) NIL) ((-1261 . -47) 143982) ((-1240 . -47) 143959) ((-1150 . -1019) 143930) ((-3 . |UnionCategory|) T) ((-1129 . -723) 143917) ((-1114 . -619) 143899) ((-1089 . -148) 143878) ((-1089 . -146) 143829) ((-973 . -622) 143813) ((-227 . -927) T) ((-40 . -111) 143742) ((-878 . -1047) 143606) ((-1013 . -368) T) ((-1012 . -233) 143583) ((-707 . -1060) 143570) ((-921 . -368) T) ((-707 . -646) 143557) ((-323 . -1215) 143523) ((-384 . -311) T) ((-323 . -1212) 143489) ((-320 . -174) 143468) ((-317 . -174) T) ((-587 . -1296) 143455) ((-524 . -1296) 143432) ((-364 . -148) 143411) ((-117 . -1060) 143398) ((-364 . -146) 143349) ((-358 . -148) 143328) ((-358 . -146) 143279) ((-350 . -148) 143258) ((-614 . -1203) 143234) ((-117 . -646) 143221) ((-350 . -146) 143172) ((-323 . -35) 143138) ((-481 . -1203) 143117) ((0 . |EnumerationCategory|) T) ((-323 . 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139739) ((-48 . -620) 139684) ((-242 . -132) 139554) ((-1300 . -652) 139513) ((-1250 . -927) 139492) ((-822 . -1231) 139471) ((-394 . -496) 139452) ((-1044 . -520) 139296) ((-394 . -619) 139262) ((-822 . -562) 139193) ((-592 . -654) 139168) ((-267 . -47) 139140) ((-249 . -47) 139097) ((-537 . -515) 139074) ((-586 . -622) 139046) ((-570 . -622) 139018) ((-501 . -622) 138951) ((-1083 . -1227) T) ((-1009 . -1227) T) ((-1269 . -23) T) ((-705 . -1065) 138916) ((-1269 . -1121) T) ((-1262 . -1121) T) ((-1262 . -23) T) ((-1241 . -1121) T) ((-1241 . -23) T) ((-1012 . -375) 138888) ((-112 . -373) T) ((-480 . -907) 138794) ((-1221 . -732) T) ((-911 . -619) 138776) ((-55 . -622) 138758) ((-91 . -107) 138742) ((-1129 . -294) T) ((-912 . -856) 138693) ((-707 . -1161) T) ((-705 . -111) 138649) ((-849 . -652) 138566) ((-602 . -1121) T) ((-601 . -1121) T) ((-718 . -723) 138395) ((-717 . -732) T) ((-1013 . -132) T) ((-980 . -132) T) ((-493 . -856) T) ((-921 . -132) T) ((-805 . -25) T) ((-805 . -21) T) 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. -619) 131929) ((-805 . -856) 131908) ((-1169 . -152) 131855) ((-1008 . -520) 131767) ((-359 . -235) T) ((-359 . -245) T) ((-394 . -622) 131748) ((-1013 . -25) T) ((-142 . -619) 131730) ((-142 . -620) 131689) ((-917 . -311) T) ((-1013 . -21) T) ((-980 . -25) T) ((-921 . -21) T) ((-921 . -25) T) ((-433 . -21) T) ((-433 . -25) T) ((-849 . -417) 131673) ((-48 . -1058) T) ((-1299 . -1291) 131657) ((-1297 . -1291) 131641) ((-1044 . -610) 131616) ((-320 . -620) 131477) ((-320 . -619) 131459) ((-317 . -620) NIL) ((-317 . -619) 131441) ((-48 . -245) T) ((-48 . -235) T) ((-660 . -290) 131402) ((-556 . -237) 131352) ((-140 . -619) 131319) ((-137 . -619) 131301) ((-115 . -619) 131283) ((-483 . -38) 131248) ((-1301 . -1298) 131227) ((-1292 . -132) T) ((-1300 . -1067) T) ((-1091 . -102) T) ((-88 . -1227) T) ((-506 . -313) NIL) ((-1009 . -107) 131211) ((-896 . -1109) T) ((-892 . -1109) T) ((-1277 . -657) 131195) ((-1277 . -378) 131179) ((-331 . -1227) T) ((-599 . -856) T) ((-1151 . -1109) T) 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. -23) T) ((-1160 . -1092) T) ((-1134 . -23) T) ((-860 . -23) T) ((-487 . -562) 130162) ((-1151 . -723) 130094) ((-676 . -1060) 130078) ((-1155 . -520) 130011) ((-676 . -646) 129995) ((-1044 . -620) NIL) ((-1044 . -619) 129977) ((-96 . -1092) T) ((-872 . -723) 129947) ((-1221 . -47) 129916) ((-254 . -132) T) ((-253 . -132) T) ((-1113 . -1109) T) ((-1012 . -1109) T) ((-62 . -619) 129898) ((-1177 . -856) NIL) ((-1033 . -798) T) ((-1033 . -801) T) ((-1305 . -1065) 129885) ((-1305 . -111) 129870) ((-1269 . -25) T) ((-1269 . -21) T) ((-876 . -654) 129857) ((-1262 . -21) T) ((-1262 . -25) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1036 . -152) 129841) ((-878 . -826) 129820) ((-878 . -927) T) ((-718 . -290) 129747) ((-602 . -21) T) ((-344 . -652) 129706) ((-602 . -25) T) ((-601 . -21) T) ((-176 . -652) 129623) ((-40 . -732) T) ((-224 . -520) 129556) ((-601 . -25) T) ((-482 . -152) 129540) ((-469 . -152) 129524) ((-928 . -800) T) ((-928 . -732) T) ((-777 . -799) T) ((-777 . -800) T) ((-512 . 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. -1121) T) ((-118 . -916) NIL) ((-1299 . -1298) 125863) ((-1297 . -1298) 125842) ((-788 . -893) NIL) ((-786 . -893) 125701) ((-1292 . -25) T) ((-1292 . -21) T) ((-1224 . -102) 125679) ((-1115 . -401) T) ((-629 . -654) 125666) ((-460 . -893) NIL) ((-681 . -102) 125644) ((-1096 . -1047) 125471) ((-877 . -23) T) ((-788 . -1047) 125330) ((-786 . -1047) 125187) ((-118 . -654) 125132) ((-460 . -1047) 125008) ((-320 . -622) 124572) ((-317 . -622) 124455) ((-396 . -652) 124424) ((-655 . -1047) 124408) ((-633 . -102) T) ((-224 . -495) 124392) ((-1277 . -34) T) ((-627 . -652) 124351) ((-293 . -1060) 124338) ((-137 . -622) 124322) ((-293 . -646) 124309) ((-641 . -723) 124293) ((-613 . -723) 124277) ((-676 . -38) 124237) ((-323 . -102) T) ((-85 . -619) 124219) ((-50 . -1047) 124203) ((-1129 . -1065) 124190) ((-1096 . -382) 124174) ((-788 . -382) 124158) ((-705 . -732) T) ((-705 . -800) T) ((-705 . -797) T) ((-587 . -1047) 124145) ((-524 . -1047) 124122) ((-60 . -57) 124084) ((-328 . -132) T) 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NIL) ((-118 . -732) T) ((-700 . -916) NIL) ((-1055 . -520) 122829) ((-487 . -132) T) ((-577 . -23) T) ((-681 . -313) 122767) ((-641 . -767) T) ((-613 . -767) T) ((-1241 . -856) NIL) ((-1089 . -1060) 122677) ((-1012 . -294) T) ((-700 . -654) 122627) ((-254 . -21) T) ((-356 . -1109) T) ((-254 . -25) T) ((-253 . -21) T) ((-253 . -25) T) ((-153 . -38) 122611) ((-2 . -102) T) ((-917 . -927) T) ((-1089 . -646) 122479) ((-488 . -1284) 122449) ((-1129 . -1058) T) ((-717 . -311) T) ((-364 . -1060) 122401) ((-358 . -1060) 122353) ((-350 . -1060) 122305) ((-364 . -646) 122257) ((-225 . -1047) 122234) ((-358 . -646) 122186) ((-108 . -1060) 122136) ((-350 . -646) 122088) ((-298 . -723) 122030) ((-707 . -1067) T) ((-493 . -458) T) ((-413 . -520) 121942) ((-108 . -646) 121892) ((-219 . -458) T) ((-1129 . -235) T) ((-299 . -152) 121842) ((-1008 . -620) 121803) ((-1008 . -619) 121785) ((-998 . -619) 121767) ((-117 . -1067) T) ((-660 . -1065) 121751) ((-227 . -499) T) ((-405 . -619) 121733) ((-405 . 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. -235) T) ((-707 . -723) 117208) ((-344 . -1109) T) ((-176 . -1109) T) ((-335 . -856) T) ((-424 . -458) 117158) ((-384 . -23) T) ((-364 . -38) 117123) ((-358 . -38) 117088) ((-350 . -38) 117053) ((-80 . -447) T) ((-80 . -401) T) ((-227 . -25) T) ((-227 . -21) T) ((-842 . -1121) T) ((-108 . -38) 117003) ((-833 . -1121) T) ((-780 . -1109) T) ((-117 . -723) 116990) ((-678 . -1047) 116974) ((-618 . -102) T) ((-842 . -23) T) ((-833 . -23) T) ((-1166 . -290) 116951) ((-1122 . -313) 116889) ((-488 . -1060) 116786) ((-1111 . -237) 116770) ((-64 . -402) T) ((-64 . -401) T) ((-1160 . -102) T) ((-110 . -102) T) ((-488 . -646) 116712) ((-40 . -382) 116689) ((-96 . -102) T) ((-659 . -858) 116673) ((-1144 . -1092) T) ((-1071 . -21) T) ((-1071 . -25) T) ((-1063 . -1060) 116657) ((-821 . -233) 116626) ((-959 . -25) T) ((-959 . -21) T) ((-1063 . -646) 116568) ((-627 . -1067) T) ((-1129 . -373) T) ((-1036 . -313) 116506) ((-676 . -652) 116465) ((-487 . -25) T) ((-487 . -21) T) ((-390 . -1060) 116449) 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. -1047) 111486) ((-650 . -856) 111465) ((-1289 . -102) T) ((-299 . -102) T) ((-718 . -373) 111444) ((-118 . -1047) 111421) ((-396 . -723) 111405) ((-627 . -723) 111389) ((-45 . -313) 111193) ((-822 . -146) 111172) ((-822 . -148) 111151) ((-293 . -652) 111123) ((-1300 . -387) 111102) ((-825 . -856) T) ((-1279 . -1109) T) ((-1169 . -231) 111049) ((-392 . -856) 111028) ((-1269 . -1215) 110994) ((-1269 . -1212) 110960) ((-1262 . -1212) 110926) ((-521 . -132) T) ((-1262 . -1215) 110892) ((-1241 . -1212) 110858) ((-1241 . -1215) 110824) ((-1269 . -35) 110790) ((-1269 . -95) 110756) ((-641 . -619) 110725) ((-613 . -619) 110694) ((-227 . -856) T) ((-1262 . -95) 110660) ((-1262 . -35) 110626) ((-1261 . -1121) T) ((-1129 . -654) 110613) ((-1241 . -95) 110579) ((-1240 . -1121) T) ((-599 . -152) 110561) ((-1089 . -354) 110540) ((-176 . -294) T) ((-118 . -382) 110517) ((-118 . -343) 110494) ((-1241 . -35) 110460) ((-876 . -311) T) ((-317 . -800) NIL) ((-317 . -797) NIL) ((-320 . -732) 110309) 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. -622) 108092) ((-877 . -856) NIL) ((-570 . -1031) T) ((-501 . -1031) T) ((-1142 . -619) 108074) ((-1122 . -240) 108053) ((-216 . -102) T) ((-1159 . -102) T) ((-71 . -619) 108035) ((-1151 . -1058) T) ((-1188 . -38) 107932) ((-864 . -619) 107914) ((-570 . -551) T) ((-676 . -1067) T) ((-737 . -956) 107867) ((-1151 . -235) 107846) ((-1091 . -1109) T) ((-1043 . -25) T) ((-1043 . -21) T) ((-1012 . -1065) 107791) ((-912 . -102) T) ((-872 . -1058) T) ((-700 . -907) NIL) ((-360 . -333) 107775) ((-360 . -368) T) ((-357 . -333) 107759) ((-357 . -368) T) ((-349 . -333) 107743) ((-349 . -368) T) ((-493 . -102) T) ((-1289 . -38) 107713) ((-552 . -856) T) ((-529 . -693) 107663) ((-219 . -102) T) ((-1033 . -1047) 107543) ((-1012 . -111) 107472) ((-1184 . -982) 107441) ((-526 . -152) 107425) ((-1089 . -375) 107404) ((-356 . -619) 107386) ((-326 . -21) T) ((-359 . -1047) 107363) ((-326 . -25) T) ((-1183 . -982) 107325) ((-1177 . -982) 107294) ((-76 . -619) 107276) ((-1135 . -982) 107243) ((-705 . 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. -619) 78007) ((-358 . -619) 77989) ((-350 . -619) 77971) ((-66 . -402) T) ((-66 . -401) T) ((-108 . -620) 77901) ((-108 . -619) 77843) ((-213 . -902) T) ((-965 . -152) 77827) ((-777 . -132) T) ((-676 . -622) 77745) ((-135 . -732) T) ((-117 . -732) T) ((-1261 . -35) 77711) ((-1063 . -495) 77695) ((-586 . -23) T) ((-570 . -23) T) ((-501 . -23) T) ((-1240 . -95) 77661) ((-1240 . -35) 77627) ((-1182 . -102) T) ((-1134 . -102) T) ((-860 . -102) T) ((-229 . -495) 77611) ((-1299 . -111) 77590) ((-1297 . -111) 77569) ((-44 . -1065) 77553) ((-1299 . -622) 77499) ((-1250 . -1253) 77483) ((-861 . -858) 77467) ((-1299 . -1058) T) ((-1188 . -294) 77446) ((-110 . -290) 77421) ((-1297 . -622) 77350) ((-129 . -152) 77332) ((-1151 . -907) 77291) ((-44 . -111) 77270) ((-1232 . -1109) T) ((-1191 . -1272) T) ((-1176 . -496) 77251) ((-1176 . -619) 77217) ((-676 . -1058) T) ((-1168 . -620) NIL) ((-1168 . -619) 77199) ((-1072 . -616) 77174) ((-1072 . -1109) T) ((-1003 . -496) 77155) ((-74 . -447) T) ((-74 . -401) T) ((-1003 . -619) 77121) ((-153 . -1065) 77105) ((-676 . -235) 77084) ((-577 . -560) 77068) ((-360 . -148) 77047) ((-360 . -146) 76998) ((-357 . -148) 76977) ((-357 . -146) 76928) ((-349 . -148) 76907) ((-349 . -146) 76858) ((-267 . -146) 76837) ((-267 . -148) 76816) ((-254 . -38) 76786) ((-249 . -148) 76765) ((-118 . -368) T) ((-249 . -146) 76744) ((-253 . -38) 76714) ((-153 . -111) 76693) ((-1012 . -1047) 76581) ((-1177 . -854) NIL) ((-700 . -1231) T) ((-805 . -1067) T) ((-705 . -1121) T) ((-1297 . -1058) T) ((-1166 . -1227) T) ((-1012 . -382) 76558) ((-917 . -146) T) ((-917 . -148) 76540) ((-876 . -132) T) ((-821 . -1065) 76437) ((-705 . -23) T) ((-700 . -562) T) ((-227 . -1060) 76402) ((-653 . -619) 76334) ((-653 . -620) 76295) ((-638 . -620) NIL) ((-638 . -619) 76277) ((-493 . -174) T) ((-227 . -646) 76242) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-480 . -1215) 76208) ((-480 . -1212) 76174) ((-277 . -619) 76156) ((-276 . -619) 76138) ((-275 . -619) 76120) 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. -25) T) ((-487 . -21) T) ((-390 . -1060) 116518) ((-896 . -619) 116500) ((-892 . -619) 116482) ((-529 . -520) 116415) ((-254 . -856) 116366) ((-253 . -856) 116317) ((-390 . -646) 116287) ((-877 . -645) 116264) ((-482 . -313) 116202) ((-469 . -313) 116140) ((-356 . -294) T) ((-1166 . -1265) 116124) ((-1151 . -619) 116086) ((-1151 . -620) 116047) ((-1149 . -102) T) ((-1008 . -1065) 115943) ((-40 . -907) 115895) ((-1166 . -610) 115872) ((-1306 . -654) 115859) ((-872 . -496) 115836) ((-1072 . -152) 115782) ((-878 . -1231) T) ((-1008 . -111) 115664) ((-344 . -723) 115648) ((-872 . -619) 115610) ((-176 . -723) 115542) ((-413 . -290) 115500) ((-878 . -562) T) ((-108 . -406) 115482) ((-84 . -389) T) ((-84 . -401) T) ((-707 . -174) T) ((-623 . -619) 115464) ((-99 . -732) T) ((-488 . -102) 115254) ((-99 . -479) T) ((-117 . -174) T) ((-1299 . -652) 115213) ((-1297 . -652) 115172) ((-1122 . -38) 115142) ((-171 . -645) 115090) ((-1063 . -102) T) ((-1008 . -622) 114980) ((-877 . -25) T) ((-821 . 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. -388) T) ((-70 . -401) T) ((-1175 . -102) T) ((-676 . -520) 101196) ((-1289 . -652) 101141) ((-695 . -313) 101079) ((-970 . -38) 100976) ((-1190 . -619) 100958) ((-741 . -38) 100928) ((-556 . -313) 100732) ((-1184 . -1060) 100615) ((-320 . -1227) T) ((-356 . -235) T) ((-356 . -245) T) ((-317 . -1227) T) ((-293 . -1109) T) ((-1183 . -1060) 100450) ((-1177 . -1060) 100240) ((-1135 . -1060) 100123) ((-1184 . -646) 100020) ((-1183 . -646) 99861) ((-717 . -1231) T) ((-1177 . -646) 99657) ((-1166 . -657) 99641) ((-1135 . -646) 99538) ((-1221 . -562) 99517) ((-825 . -391) 99501) ((-717 . -562) T) ((-320 . -891) 99485) ((-320 . -893) 99410) ((-317 . -891) 99371) ((-317 . -893) NIL) ((-805 . -313) 99336) ((-323 . -723) 99177) ((-392 . -391) 99161) ((-328 . -327) 99138) ((-491 . -102) T) ((-480 . -25) T) ((-480 . -21) T) ((-424 . -38) 99112) ((-320 . -1047) 98775) ((-227 . -1212) T) ((-227 . -1215) T) ((-3 . -619) 98757) ((-317 . -1047) 98687) ((-2 . -1109) T) ((-2 . |RecordCategory|) T) 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90593) ((-1177 . -406) 90545) ((-1013 . -313) NIL) ((-821 . -495) 90529) ((-602 . -646) 90502) ((-359 . -927) T) ((-601 . -646) 90399) ((-1166 . -34) T) ((-413 . -654) 90351) ((-50 . -23) T) ((-717 . -132) T) ((-718 . -1047) 90231) ((-587 . -23) T) ((-108 . -520) NIL) ((-524 . -23) T) ((-171 . -415) 90202) ((-1149 . -1109) T) ((-1292 . -1291) 90186) ((-707 . -801) T) ((-707 . -798) T) ((-1129 . -311) T) ((-384 . -148) T) ((-284 . -619) 90168) ((-283 . -619) 90150) ((-1240 . -1001) 90120) ((-48 . -927) T) ((-681 . -495) 90104) ((-254 . -1284) 90074) ((-253 . -1284) 90044) ((-1186 . -856) T) ((-1122 . -174) 90023) ((-1129 . -1031) T) ((-1055 . -34) T) ((-842 . -148) 90002) ((-842 . -146) 89981) ((-743 . -107) 89965) ((-618 . -133) T) ((-488 . -1109) 89755) ((-1188 . -1067) T) ((-877 . -458) T) ((-85 . -1227) T) ((-242 . -38) 89725) ((-142 . -107) 89707) ((-718 . -382) 89691) ((-839 . -622) 89559) ((-1300 . -732) T) ((-1289 . -1067) T) ((-1129 . -551) T) ((-585 . -102) T) ((-130 . -496) 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. -288) 88377) ((-1221 . -499) 88343) ((-1013 . -38) 88293) ((-219 . -854) T) ((-424 . -652) 88252) ((-921 . -38) 88204) ((-849 . -800) 88183) ((-849 . -797) 88162) ((-849 . -732) 88141) ((-364 . -294) T) ((-358 . -294) T) ((-350 . -294) T) ((-171 . -458) 88072) ((-433 . -38) 88056) ((-108 . -294) T) ((-225 . -23) T) ((-413 . -800) 88035) ((-413 . -797) 88014) ((-413 . -732) T) ((-506 . -292) 87989) ((-483 . -1065) 87954) ((-664 . -132) T) ((-627 . -622) 87923) ((-1122 . -520) 87856) ((-341 . -132) T) ((-171 . -408) 87835) ((-488 . -723) 87777) ((-821 . -290) 87754) ((-483 . -111) 87710) ((-659 . -1067) T) ((-822 . -1060) 87553) ((-1288 . -1092) T) ((-1250 . -458) 87484) ((-822 . -646) 87333) ((-1287 . -1092) T) ((-1096 . -132) T) ((-1063 . -723) 87275) ((-788 . -132) T) ((-786 . -132) T) ((-577 . -458) T) ((-1036 . -520) 87208) ((-627 . -1058) T) ((-598 . -1109) T) ((-539 . -175) T) ((-467 . -132) T) ((-460 . -132) T) ((-45 . -1109) T) ((-390 . -723) 87178) ((-823 . -1109) T) ((-482 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index ed019478..131d383c 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3480886509) -(4452 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3480912608) +(4455 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -481,664 +481,667 @@ |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| - |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| + |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |sncndn| |head| |seriesToOutputForm| |ceiling| - |e02aef| |pi| |solveLinear| |OMsend| |tanh2trigh| |fmecg| |OMputFloat| - |integralLastSubResultant| |elaborate| |constantIfCan| |infinity| - |OMgetAttr| |comparison| |removeCoshSq| |doubleDisc| - |subResultantGcdEuclidean| |numerator| |internalDecompose| - |atrapezoidal| |region| |highCommonTerms| |rectangularMatrix| |cond| - |sechIfCan| |fracPart| |newReduc| |deepestTail| |argumentListOf| - |copy!| |tanSum| |minGbasis| |contract| |subResultantsChain| - |generate| |bumptab1| |applyRules| |log10| |accuracyIF| |sinIfCan| - |kovacic| |complexNumericIfCan| |length| |map| |sturmVariationsOf| - |countRealRoots| |imports| |OMgetString| |integerIfCan| - |getVariableOrder| |bitand| |iisech| |kernel| |complexSolve| |cycle| - |pointPlot| |scripts| |ramifiedAtInfinity?| |scripted?| |isQuotient| - |graeffe| |incrementBy| |PDESolve| |clikeUniv| |getBadValues| - |outerProduct| |bitior| |isEquiv| |draw| |backOldPos| |perfectSqrt| - |decomposeFunc| |insert!| |hspace| |OMputBind| |belong?| |secIfCan| - |qualifier| |zCoord| |expand| |createGenericMatrix| |pleskenSplit| - |rombergo| |f02ajf| |f04maf| |OMgetType| |resultantEuclidean| - |currentEnv| |refine| |OMgetInteger| |sub| |filterWhile| |basicSet| - |crest| |tubeRadius| |pdf2df| |build| |ratDsolve| |inputBinaryFile| - |complexElementary| |arbitrary| |exactQuotient| |SturmHabicht| - |triangular?| |filterUntil| |symbol| |getCode| |quadraticNorm| - |s19acf| |realEigenvectors| |mainVariables| |radix| |convert| |tanAn| - |maxdeg| |previous| |s14aaf| |setPrologue!| |select| - |mainCoefficients| |viewWriteAvailable| |expression| |slex| - |makeObject| |yCoordinates| |musserTrials| |OMcloseConn| |errorKind| - |addMatchRestricted| |moduloP| |pToDmp| |height| |OMencodingBinary| - |maxPoints3D| |truncate| |sqfree| |integer| |realSolve| |curve?| - |coef| |pquo| |setValue!| |point?| |sts2stst| |rationalPower| |high| - |minimize| |maxIndex| |var1Steps| |coth2trigh| |weakBiRank| - |zeroSquareMatrix| |makeUnit| |recur| |minPoints3D| - |numberOfFractionalTerms| |subResultantChain| |mesh?| |palgextint0| - |tanhIfCan| |coerceListOfPairs| |outputAsScript| |bringDown| - |tubeRadiusDefault| |yRange| |completeHermite| |negative?| - |removeSinhSq| ** |deepCopy| |replace| |radPoly| |leftFactor| - |complement| |mathieu22| |poisson| |zRange| |inspect| - |initiallyReduced?| |repSq| |mkAnswer| |meshPar1Var| |writeInt8!| - |approxNthRoot| |critMTonD1| |screenResolution| |rightRank| |setTex!| - |imaginary| |map!| |rootOfIrreduciblePoly| |exprToXXP| |compdegd| - |discriminantEuclidean| |hMonic| |column| |df2st| |logpart| - |makeRecord| |imagi| |repeating| |lo| |zeroSetSplit| |cCsc| |qsetelt!| - |coerceP| |leadingExponent| |submod| |power| |conjug| |extractIfCan| - |schwerpunkt| |totalGroebner| |unitsColorDefault| |socf2socdf| |incr| - |round| |dualSignature| |ranges| |label| |getZechTable| - |clipPointsDefault| |matrixConcat3D| |adaptive?| |initial| |rootsOf| - |times!| |monomRDE| |resetNew| |leftCharacteristicPolynomial| - |totalDifferential| |reduceByQuasiMonic| |localReal?| |rowEch| - |laurentIfCan| |tRange| |integralRepresents| |OMgetEndError| - |completeEchelonBasis| |maxRowIndex| |removeSquaresIfCan| - |limitedIntegrate| |rst| |UnVectorise| |possiblyNewVariety?| - |perspective| |lazyPquo| |factorials| |distdfact| |divisor| - |processTemplate| |screenResolution3D| |physicalLength| |s17aff| - |getDatabase| |singRicDE| |subNode?| |makeop| Y |printStatement| - |asimpson| |youngGroup| |leftPower| |shiftRight| |nullary| |acsch| - |findConstructor| |genericLeftDiscriminant| |consnewpol| - |selectPolynomials| |iterationVar| |zag| |fixedPoints| |s21bcf| - |continuedFraction| |choosemon| |preprocess| |extendedEuclidean| - |ratDenom| |dAndcExp| |SFunction| |bernoulliB| |cyclic| |checkForZero| - |irreducible?| |semiDegreeSubResultantEuclidean| |failed?| - |cyclicEntries| |midpoints| |tail| |integralBasisAtInfinity| - |virtualDegree| |imagK| |makeYoungTableau| |readByte!| |startTable!| - |constructor| |rules| |LiePoly| |front| |addmod| |solveRetract| - |collect| |topFortranOutputStack| |numberOfChildren| |setClosed| - |mainExpression| |dmpToHdmp| |evenInfiniteProduct| |perfectNthPower?| - |nothing| |mainPrimitivePart| |ramified?| |cLog| |cschIfCan| |option| - |interactiveEnv| |f04atf| |ode| |getPickedPoints| |ridHack1| - |prepareSubResAlgo| |showSummary| |mergeFactors| |explicitlyEmpty?| - |cAcosh| |cubic| |e02dcf| |multiEuclidean| |lllp| |axes| - |bezoutDiscriminant| |pair?| |s18dcf| |graphCurves| |divisors| - |splitSquarefree| |iicos| |rightFactorCandidate| |squareFree| |trigs| - |changeWeightLevel| |e02baf| |getExplanations| |showAttributes| - |bitCoef| |factorSquareFreePolynomial| |bits| |optional?| - |setprevious!| |genus| |unknown| |OMbindTCP| - |rightRegularRepresentation| |imagk| |f2st| |symmetricPower| |iroot| - |macroExpand| |rootSimp| |headAst| |zeroMatrix| |rightTrim| |s15adf| - |intcompBasis| |radicalEigenvector| |sumSquares| - |genericRightMinimalPolynomial| |d01anf| |lowerBound| - |prolateSpheroidal| |rightDiscriminant| |bernoulli| - |semiResultantEuclidean2| |leftTrim| |increment| |nlde| |extendIfCan| - |f02awf| |light| |simpson| |normal01| |iitan| |listOfMonoms| |iibinom| - |halfExtendedResultant2| |antisymmetricTensors| |leftFactorIfCan| - |relativeApprox| |nextPrimitivePoly| |enumerate| |solid| |sample| - |say| |moduleSum| F |cyclicEqual?| |createIrreduciblePoly| - |denomRicDE| |multiplyCoefficients| |checkRur| |setelt!| |functorData| - |d01amf| |explogs2trigs| |aromberg| |algSplitSimple| |symmetricGroup| - |factorsOfDegree| |cAsin| |linGenPos| |mvar| |f01bsf| - |reduceBasisAtInfinity| |newSubProgram| |selectOptimizationRoutines| - |tab| |cycles| |mainMonomials| |maxColIndex| |wholePart| - |basisOfRightAnnihilator| |symmetric?| |charClass| |rootRadius| - |leftRegularRepresentation| |function| |push!| |remove| |multivariate| - |invertible?| |e01baf| |rquo| |nextIrreduciblePoly| |extendedint| - |heapSort| |minus!| |splitConstant| |fortran| - |tryFunctionalDecomposition| |mpsode| |symmetricProduct| |variables| - |currentScope| |result| |fortranCompilerName| |lastSubResultant| - |tableau| |lquo| |open| |rightAlternative?| |alternative?| |middle| - |useEisensteinCriterion?| |nextsousResultant2| |c05adf| |last| |eval| - |compound?| |reset| |swapColumns!| |mainDefiningPolynomial| - |simpleBounds?| |polygon?| |updatF| |assoc| |linearAssociatedOrder| - |fillPascalTriangle| |eof?| |null| |vconcat| |basisOfNucleus| |f04faf| - |f04asf| |transcendent?| |charpol| |diagonalProduct| |find| |bottom!| - |infieldIntegrate| |pattern| |outputAsTex| |not| |bracket| |qPot| - |outputBinaryFile| |write| |oneDimensionalArray| |outputArgs| - |OMgetEndAtp| |atanhIfCan| |s01eaf| |indices| |traceMatrix| |addiag| - |OMgetBind| |and| |surface| |midpoint| |save| |c06gcf| - |algebraicDecompose| |tanIfCan| |selectIntegrationRoutines| - |operations| |se2rfi| |forLoop| |hue| |cAcot| |lagrange| |or| - |resetBadValues| |taylor| |halfExtendedSubResultantGcd2| |scaleRoots| - |rdHack1| |deleteProperty!| |leftAlternative?| |bivariateSLPEBR| - |rotatex| |e02daf| |log2| |arity| |internalSubQuasiComponent?| |xor| - |laurent| |cycleEntry| |packageCall| |OMputSymbol| |outputGeneral| - |inverseColeman| |stirling1| |weighted| |message| |usingTable?| - |content| |wronskianMatrix| |subPolSet?| |case| |puiseux| |initTable!| - |toroidal| |f04mbf| |quickSort| |groebner| |btwFact| |f01rcf| - |cylindrical| |Zero| |updateStatus!| |pointSizeDefault| - |complexIntegrate| |asinhIfCan| |iiacot| |interval| |entry?| - |cycleRagits| |hi| |OMputEndError| |solveInField| - |showFortranOutputStack| |d02gaf| |One| |roughBase?| |inv| |medialSet| - |whitePoint| |SturmHabichtMultiple| |nand| |getStream| |OMread| - |lookup| |squareTop| |ground?| |transform| |reducedDiscriminant| - |f01qcf| |monicCompleteDecompose| |groebner?| |expandLog| |makeCos| - |mathieu11| |isExpt| |s17dlf| |legendreP| |ground| |lcm| |parseString| - |limitPlus| |expextendedint| |movedPoints| |rootBound| |argument| - |halfExtendedResultant1| |lieAdmissible?| |closedCurve| |lexico| - |printTypes| |positiveSolve| |beauzamyBound| |perfectSquare?| - |shuffle| |leadingMonomial| |clearDenominator| |matrixGcd| - |mapExponents| |singleFactorBound| |integers| - |numberOfIrreduciblePoly| |dual| |basisOfCommutingElements| |append| - |hessian| |tan2cot| |leadingCoefficient| |symbol?| |binaryTournament| - |leadingIndex| |drawComplexVectorField| |modulus| |rename!| |iiasinh| - |iflist2Result| |fortranReal| |pointLists| |primitiveMonomials| - |stopTableInvSet!| |completeSmith| |elt| |gcd| |output| |meshFun2Var| - |hdmpToP| |euclideanNormalForm| |gensym| |unrankImproperPartitions1| - |acotIfCan| |lieAlgebra?| |getOperands| |cSec| - |solveLinearPolynomialEquationByFractions| |false| |fintegrate| - |reductum| |univariatePolynomials| |c05pbf| |rk4a| - |functionIsContinuousAtEndPoints| |internalSubPolSet?| |algebraicOf| - |lowerPolynomial| |removeZeroes| |computeCycleEntry| |squareMatrix| - |numFunEvals| |var2StepsDefault| |logGamma| - |primPartElseUnitCanonical| |lowerCase| |basis| |radicalEigenvalues| - |makeCrit| |internalLastSubResultant| |iidsum| - |factorSquareFreeByRecursion| |genericPosition| |rootOf| - |sortConstraints| |points| |closed?| |over| - |removeRoughlyRedundantFactorsInContents| |binaryTree| |aCubic| - |conditionsForIdempotents| |latex| |readUInt16!| |cyclicSubmodule| - |completeEval| |integralAtInfinity?| |rangePascalTriangle| |shellSort| - |linearDependenceOverZ| |reflect| |generic| |derivationCoordinates| - |mindegTerm| |moebiusMu| |cyclicParents| |degreePartition| |hcrf| - |fractionFreeGauss!| |binarySearchTree| |cCsch| |parabolic| |isOp| - |integer?| |upperCase!| |df2ef| |setFormula!| |genericLeftNorm| - |internalIntegrate0| |writeUInt8!| |lprop| |empty?| - |leftMinimalPolynomial| |categories| |conjugate| |putColorInfo| - |subResultantGcd| |hasPredicate?| |merge| |iiatan| |presub| - |companionBlocks| |sylvesterMatrix| |associates?| |seriesSolve| - |atoms| |pointColorPalette| |flexibleArray| |unitNormal| - |headReduced?| |rightMinimalPolynomial| |countable?| |cAsinh| - |numberOfVariables| |divideIfCan| |cAsech| |inconsistent?| - |leadingIdeal| |selectOrPolynomials| |adaptive| |cPower| |c02agf| - |s17dhf| |pastel| |torsion?| |SturmHabichtCoefficients| - |recoverAfterFail| |createThreeSpace| |rightRecip| |makeViewport2D| - |HermiteIntegrate| |exponents| |startTableGcd!| - |fortranCarriageReturn| |e02ahf| |simplifyLog| |putGraph| - |primeFrobenius| |characteristicSerie| |tablePow| |prod| - |plusInfinity| |rational| |commutativeEquality| |lazyEvaluate| - |OMencodingUnknown| |Lazard2| |jokerMode| |semiResultantEuclideannaif| - |changeBase| |quotedOperators| |symmetricSquare| |ODESolve| - |minusInfinity| |read!| |lexGroebner| |bag| |s15aef| |rotate!| - |stripCommentsAndBlanks| |bothWays| - |removeRoughlyRedundantFactorsInPols| |cartesian| |solve1| |multiset| - |linkToFortran| |getMatch| |lfunc| |primlimintfrac| |extractClosed| - |closeComponent| |Ei| |superHeight| |rootNormalize| |laguerre| - |monicModulo| |setImagSteps| |thenBranch| |blankSeparate| |composite| - |key| |iisinh| |host| |realEigenvalues| |odd?| |escape| - |cyclotomicFactorization| |iicsch| |cot2trig| |optpair| - |createLowComplexityTable| |reopen!| |readInt8!| |factorset| |mulmod| - |componentUpperBound| |s13aaf| |nullSpace| |largest| |bfEntry| - |specialTrigs| |filename| |removeZero| |OMclose| |degree| |mapGen| - |An| |vertConcat| |leftExactQuotient| |type| |duplicates| - |determinant| |rowEchelonLocal| |OMconnInDevice| |brillhartTrials| - |reducedContinuedFraction| |euclideanSize| |scanOneDimSubspaces| - |ricDsolve| |extendedSubResultantGcd| |traverse| |fill!| |equiv| - |radicalSolve| |parse| |leftZero| |endOfFile?| |cCot| |twoFactor| - |ptFunc| |solveLinearPolynomialEquationByRecursion| |froot| |next| - |hermite| |upperCase| |printStats!| |setchildren!| |getMeasure| - |relerror| |interReduce| |SturmHabichtSequence| |subscript| |merge!| - |sin?| |e02ajf| |commonDenominator| |d02kef| |diagonalMatrix| - |powerSum| |e02zaf| |fullDisplay| |delay| |dictionary| |multinomial| - |shrinkable| |f02aaf| |iCompose| |setMinPoints| |setleft!| - |elementary| |coefficients| |checkPrecision| |fixPredicate| |jacobian| - |crushedSet| |trailingCoefficient| |part?| |singularitiesOf| |sec2cos| - |elaborateFile| |nthr| |queue| |elRow2!| EQ - |standardBasisOfCyclicSubmodule| |irreducibleFactor| |lfextendedint| - |nextPrime| |inRadical?| |e04gcf| |nullity| |returnTypeOf| - |deepExpand| |isTimes| |sumOfSquares| |rangeIsFinite| |integral| |lhs| - |revert| |ScanFloatIgnoreSpaces| |tanh2coth| |insertBottom!| - |cyclicCopy| |row| |nextColeman| |pushdterm| |d02gbf| |e01bff| - |factorPolynomial| |rhs| |simplifyPower| |lambert| |chebyshevU| - |isAnd| |padicFraction| |internalAugment| |lex| |OMputApp| - |OMmakeConn| |prinpolINFO| |f02adf| |rootKerSimp| |safeFloor| - |cyclotomicDecomposition| |firstSubsetGray| |commaSeparate| - |fibonacci| |csubst| |domainTemplate| |absolutelyIrreducible?| - |mainSquareFreePart| |laurentRep| |quasiMonic?| |coefficient| |f02agf| - |rarrow| |doubleResultant| |wordsForStrongGenerators| |deref| |rule| - |Gamma| |plot| |pointData| |OMencodingSGML| |qroot| |hermiteH| - |withPredicates| |s18adf| |cycleLength| |setsubMatrix!| |innerSolve1| - |partition| |index| |oddlambert| |quote| |typeList| |bandedHessian| - |stoseInvertibleSet| |ipow| |makeViewport3D| |invertIfCan| |vectorise| - |iiexp| |numberOfComponents| |increasePrecision| |mainValue| |bit?| - |e02dff| |getProperties| |HenselLift| |useNagFunctions| - |identification| |center| |discreteLog| |modularFactor| |systemSizeIF| - |mainMonomial| |pureLex| |externalList| GF2FG |hitherPlane| - |viewThetaDefault| |denominators| |makeSin| |pair| |noKaratsuba| - |e01daf| |e02akf| |sayLength| |monomialIntPoly| |startStats!| - 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|problemPoints| - |createMultiplicationMatrix| |tab1| |e02ddf| |t| |yellow| |entries| - |reify| |root?| |lepol| |tanNa| LODO2FUN |nextSubsetGray| |direction| - |loadNativeModule| |viewport3D| |collectUpper| |clearTable!| - |bivariate?| |intermediateResultsIF| |coefChoose| |knownInfBasis| - |algebraicVariables| |palgRDE0| |unaryFunction| - |generalizedContinuumHypothesisAssumed| |pomopo!| |gcdPrimitive| |hex| - |printInfo!| |s19adf| |constant| |nextSublist| |monicRightFactorIfCan| - |critM| |complexNumeric| |fortranLogical| |infiniteProduct| - |leviCivitaSymbol| |showAllElements| |pointColor| |space| |iiasin| - |roughUnitIdeal?| |byte| |predicate| |wholeRagits| |quasiRegular| - |conjugates| |padicallyExpand| |sup| |unknownEndian| |child?| - |changeNameToObjf| |kernels| |numberOfPrimitivePoly| |thetaCoord| - |getGoodPrime| |associatedSystem| |select!| - |createPrimitiveNormalPoly| |swap| |operator| |singularAtInfinity?| - |cons| |e02bdf| |idealSimplify| |iiacsch| |setAdaptive3D| |prevPrime| - |associator| |semiResultantReduitEuclidean| - |stoseIntegralLastSubResultant| |iomode| |mathieu24| |critB| |step| - |taylorQuoByVar| |yCoord| |besselI| |split| |univariate| |zeroDim?| - |viewDeltaYDefault| |listBranches| |makeMulti| |complexNormalize| - |clearTheSymbolTable| |comment| |chiSquare1| |palgLODE0| - |univariateSolve| |element?| |extendedResultant| |rootSplit| - |mkIntegral| |userOrdered?| |subresultantSequence| |iiacos| - |complexLimit| |iifact| |commutative?| |integralDerivationMatrix| - |ode2| |fixedPoint| |coerce| |identityMatrix| |factor| |algint| - |lazyResidueClass| |Nul| |completeHensel| |stoseInvertible?sqfreg| - |int| |fortranLinkerArgs| |firstNumer| |acschIfCan| |construct| - |float?| |overlap| |sqrt| |OMconnectTCP| |source| |cyclic?| |mkcomm| - |OMgetEndObject| |qelt| |controlPanel| |parameters| |real| |cCos| - |purelyAlgebraicLeadingMonomial?| |frst| |c06eaf| |lazyVariations| - |f02abf| |setref| |qsetelt| |flexible?| |imag| |vspace| - |zeroSetSplitIntoTriangularSystems| |compiledFunction| |child| - |meatAxe| |hypergeometric0F1| |Vectorise| |xRange| - |expandTrigProducts| |directProduct| |palgextint| |oddInfiniteProduct| - |curveColor| |outputMeasure| |exteriorDifferential| |rroot| |create| - |swap!| |indiceSubResultant| |OMgetApp| |hostByteOrder| |totolex| - |chainSubResultants| |scopes| |antiCommutator| |groebnerFactorize| - |complexEigenvectors| |brace| |OMputEndObject| |target| |ptree| - |integralMatrixAtInfinity| |generators| |argumentList!| - |rewriteSetWithReduction| |rowEchLocal| |e01sef| - |associatorDependence| |qinterval| |destruct| |internalIntegrate| - |makeprod| |genericRightTrace| |evenlambert| |e02bcf| |rightDivide| - |nodes| |stoseInvertible?| |generalizedContinuumHypothesisAssumed?| - |curveColorPalette| |whatInfinity| |s19abf| |symmetricDifference| - |kind| |internalInfRittWu?| |stoseInvertibleSetreg| |besselK| - |expenseOfEvaluation| |polCase| |s17ajf| |dioSolve| |generalTwoFactor| - |nthExponent| |op| |cRationalPower| |acosIfCan| |makeSUP| |cAtan| - |useEisensteinCriterion| |positive?| |separant| |f02aff| |mappingMode| - |mainVariable?| |mkPrim| |open?| |oblateSpheroidal| |ravel| |monomial| - |simplifyExp| |quoByVar| |OMencodingXML| |nextPartition| |coerceL| - |iicoth| |rightTraceMatrix| |infix| |ran| |sumOfKthPowerDivisors| - |reshape| |squareFreePolynomial| |rename| |cosSinInfo| - |toseLastSubResultant| |arguments| |assign| |coordinate| |isList| - |setelt| |whileLoop| |triangulate| |constant?| |retractable?| - |buildSyntax| |fglmIfCan| |index?| |setPosition| |schema| |rischDEsys| - |alphabetic| |Frobenius| |limitedint| |linearlyDependentOverZ?| - |addMatch| |purelyTranscendental?| |OMopenString| |stFunc1| |copy| - |mapmult| |tValues| |Aleph| |selectFiniteRoutines| |euclideanGroebner| - |setTopPredicate| |reciprocalPolynomial| |union| |mapMatrixIfCan| - |putProperties| |infinityNorm| |setEmpty!| |selectfirst| |bigEndian| - |mindeg| |d02cjf| |semiIndiceSubResultantEuclidean| |mathieu23| - |dihedral| |graphImage| |fractRagits| |numerators| |doublyTransitive?| - |idealiser| |isImplies| |update| |modifyPointData| |adjoint| - |multMonom| |wordInStrongGenerators| |polygon| |autoCoerce| |opeval| - |unmakeSUP| |setrest!| |setLength!| |primitivePart| |trim| - |subtractIfCan| |implies| |readLineIfCan!| |composites| |alphabetic?| - |sinhcosh| |multiEuclideanTree| |rightMult| |number?| |just| - |hexDigit?| |leftRemainder| |bfKeys| |createPrimitiveElement| |sort!| - |drawStyle| |rank| |psolve| |monomials| |unary?| |OMreadFile| - |changeMeasure| |imagE| |jordanAlgebra?| |split!| |GospersMethod| - |legendre| |loopPoints| |startPolynomial| |normal?| |prefixRagits| - |digit?| |rightRemainder| |appendPoint| |lyndon?| |s17dgf| - |cyclePartition| |position| |contours| |lowerCase?| |randnum| - |difference| |minPoly| |tracePowMod| |powerAssociative?| |match?| - |in?| |e02def| |leadingSupport| |variable?| |linearPart| - |repeatUntilLoop| |lyndonIfCan| |fortranLiteral| |monic?| |zeroOf| - |exQuo| |roughEqualIdeals?| |OMlistSymbols| |curry| - |lazyPseudoQuotient| |outlineRender| |uniform01| |aQuadratic| |polar| - |move| |numberOfHues| |product| |rk4| |rewriteIdealWithHeadRemainder| - |s19aaf| |capacity| |declare| |cycleSplit!| |inGroundField?| |trunc| - |parametersOf| |janko2| |findCycle| |viewSizeDefault| |inrootof| - |permutation| |leftScalarTimes!| |iisqrt3| |infieldint| |setOfMinN| - |selectNonFiniteRoutines| |categoryFrame| |showTheSymbolTable| - |primes| |basisOfMiddleNucleus| |voidMode| |denomLODE| |polygamma| - |univcase| |collectQuasiMonic| |basisOfLeftNucloid| |minrank| - |swapRows!| |rowEchelon| |invertibleElseSplit?| |listexp| |simplify| - |writeByte!| |polarCoordinates| |arg1| |iiasec| |reducedQPowers| - |f02bbf| |tanQ| |lazyIntegrate| |basisOfLeftAnnihilator| - |balancedFactorisation| |stFuncN| |useSingleFactorBound| |palgint| - |arg2| |sech| |member?| |boundOfCauchy| |blue| |rur| |rightLcm| - |radicalRoots| |diag| |ignore?| |airyAi| |csch| |leftQuotient| - |acscIfCan| |putProperty| |e02gaf| |close| - |semiSubResultantGcdEuclidean2| |cscIfCan| |genericLeftTrace| - |innerEigenvectors| |conditions| |bumptab| |asinh| |connect| - |coshIfCan| |kmax| |minRowIndex| |palginfieldint| |monomialIntegrate| - |diophantineSystem| |setAttributeButtonStep| |inverseIntegralMatrix| - |match| |acosh| |ListOfTerms| |colorDef| |mainKernel| |stop| |e02bef| - |abelianGroup| |display| |autoReduced?| |bright| |ord| - |rationalApproximation| |precision| |cosIfCan| |atanh| - |LagrangeInterpolation| |mapDown!| |integerBound| |octon| |cAcos| - |OMserve| |presuper| |li| |acoth| |mapSolve| |subset?| |henselFact| - |mightHaveRoots| |genericLeftMinimalPolynomial| |lazyGintegrate| - |setleaves!| |linearAssociatedExp| |leadingCoefficientRicDE| - |basisOfCenter| |s18aff| |goto| |asech| |transcendentalDecompose| - |extractBottom!| |listConjugateBases| |simpsono| |badValues| |s18def| - |xn| |elseBranch| |palgintegrate| |ef2edf| |character?| |deriv| - |rootPoly| |BumInSepFFE| |plus!| |multiple| |generalLambert| - |trapezoidalo| |subspace| |reducedSystem| |input| |minPoints| - |currentSubProgram| |realElementary| |headReduce| |magnitude| - |environment| |f07aef| |applyQuote| |constantKernel| |sn| |infinite?| - |library| |s17akf| |radicalEigenvectors| |differentialVariables| - |dimensionOfIrreducibleRepresentation| |separateDegrees| |hasoln| - |totalLex| |gcdPolynomial| |skewSFunction| |alphanumeric| - |mapUnivariate| |someBasis| |nil?| |sumOfDivisors| |collectUnder| - |subscriptedVariables| |decompose| |idealiserMatrix| |powmod| |cAsec| - |explicitEntries?| |besselY| |numericIfCan| |lookupFunction| |d02bbf| - |ruleset| |removeRoughlyRedundantFactorsInPol| |copies| |f01qef| - |OMreceive| |LyndonWordsList1| |tubePointsDefault| |baseRDE| |c06gbf| - |box| |plotPolar| |orthonormalBasis| |binomThmExpt| |s20acf| |set| - |Beta| |partitions| |generalSqFr| |square?| |clearTheFTable| - |stoseInternalLastSubResultant| |nativeModuleExtension| |elliptic?| - |test| |createLowComplexityNormalBasis| |id| |numFunEvals3D| - |insertTop!| |factorAndSplit| |palgRDE| |edf2df| |d03faf| - |exprToGenUPS| |suchThat| |testModulus| |normDeriv2| |compose| - |OMReadError?| |eigenMatrix| |s17acf| |finiteBound| |iilog| - |palglimint0| |c06fqf| |table| |RittWuCompare| |var1StepsDefault| - |component| |setCondition!| |showRegion| |any| |clip| |module| - |polyPart| |expintegrate| |insert| |new| |hdmpToDmp| |branchIfCan| - |generalInfiniteProduct| |createMultiplicationTable| |torsionIfCan| - |obj| |lfinfieldint| |structuralConstants| |f02wef| |addPointLast| - |size?| |showTheRoutinesTable| |solveLinearlyOverQ| |eq| |readLine!| - |OMgetBVar| |c06fuf| |prefix| |zeroDimPrimary?| |cache| - |selectMultiDimensionalRoutines| |callForm?| |iipow| |iter| |f01brf| - |subMatrix| |c06gqf| |sparsityIF| |startTableInvSet!| - |setScreenResolution3D| |resultant| |order| |OMgetSymbol| - |setProperty| |delete| |OMputError| |signature| |exponential1| - |OMputAttr| |signAround| |extractSplittingLeaf| |connectTo| - |quasiComponent| |subst| |double?| |normalise| |exp1| |OMlistCDs| - |sech2cosh| |zeroVector| |cSinh| |LiePolyIfCan| |calcRanges| - |fortranInteger| |one?| |exprHasLogarithmicWeights| |OMgetError| - |areEquivalent?| |fortranCharacter| |s17def| |csch2sinh| |normalDeriv| - |principal?| |drawCurves| |fractRadix| |LazardQuotient| |conjunction| - |e04fdf| |expandPower| |directory| |script| |antiAssociative?| - |squareFreePart| |factorial| |cycleTail| |lazyIrreducibleFactors| - |setMaxPoints3D| |directSum| |radicalSimplify| |any?| |central?| - |readUInt8!| |sorted?| |headRemainder| |weierstrass| - |exponentialOrder| |setOrder| |ref| |retractIfCan| |rk4qc| - |rightExactQuotient| |exactQuotient!| |flatten| |aspFilename| - |selectPDERoutines| |exp| |equality| |removeRedundantFactors| |c06ekf| - |commutator| |coHeight| |objects| |tex| |sign| |localIntegralBasis| - |left| |s18aef| |numer| |particularSolution| |ddFact| |factorFraction| - |leadingBasisTerm| |rightRankPolynomial| |genericRightTraceForm| - |base| |/\\| |f01rdf| |pushNewContour| |right| |setnext!| |outputList| - |denom| |droot| |setPredicates| |semiDiscriminantEuclidean| - |resultantReduitEuclidean| |viewWriteDefault| |setRow!| |\\/| |redmat| - |minimumExponent| |reduceLODE| F2FG |separate| |createNormalElement| - |universe| |conditionP| |jacobi| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |hyperelliptic| |lexico| |contains?| + |viewDeltaXDefault| |pi| |weierstrass| |choosemon| |e04gcf| |concat!| + |triangular?| |s14abf| |printTypes| |clipParametric| |addBadValue| + |exponentialOrder| |infinity| |hexDigit| |preprocess| |getCode| + |nullity| |f01ref| |buildSyntax| |rightExtendedGcd| |positiveSolve| + |ldf2vmf| |prime?| |cond| |setOrder| |extendedEuclidean| + |quadraticNorm| |relationsIdeal| |returnTypeOf| |fglmIfCan| |f02bjf| + |branchPoint?| |beauzamyBound| |numericalIntegration| |overset?| + |generate| |ratDenom| |log10| |antiCommutative?| |ref| |deepExpand| + |c02aff| |length| |map| |index?| |s19acf| |perfectSquare?| |c06ecf| + |e02agf| |badNum| |bitand| |setPosition| |kernel| |dAndcExp| |e04ycf| + |isTimes| |scripts| |flagFactor| |realEigenvectors| |isQuotient| + |iidprod| |incrementBy| |nsqfree| |shuffle| |finite?| |outerProduct| + |bitior| |partitions| |draw| |SFunction| |sumOfSquares| |dmp2rfi| + |listYoungTableaus| |schema| |mainVariables| |palgLODE| + |mainCharacterization| |clearDenominator| |s13adf| |expand| + |generalSqFr| |rangeIsFinite| |bernoulliB| |qfactor| |showArrayValues| + |rischDEsys| |radix| |currentEnv| |matrixGcd| |lifting1| |Hausdorff| + |permanent| |filterWhile| |square?| |setright!| |cyclic| + |setClipValue| |integral| |alphabetic| |tanAn| |mapExponents| |e04dgf| + |semiSubResultantGcdEuclidean1| |findBinding| |filterUntil| |symbol| + |clearTheFTable| |checkForZero| |ratDsolve| |OMwrite| |diagonal?| + |revert| |convert| |Frobenius| |maxdeg| |previous| |singleFactorBound| + |setPoly| |lowerCase!| |infRittWu?| |select| |expression| + |stoseInternalLastSubResultant| |irreducible?| |makeObject| + |inputBinaryFile| |limitedint| |ScanFloatIgnoreSpaces| |chebyshevT| + |s14aaf| |diff| |height| |cSin| |OMputEndAttr| |integers| |mesh| + |integer| |nativeModuleExtension| |adaptive3D?| |coef| + |semiDegreeSubResultantEuclidean| |complexElementary| + |toseInvertibleSet| |tanh2coth| |linearlyDependentOverZ?| + |setPrologue!| |getMultiplicationTable| |numberOfIrreduciblePoly| + |hasSolution?| |transcendenceDegree| |elliptic?| |arbitrary| + |insertBottom!| |failed?| |notelem| |leftGcd| |addMatch| + |mainCoefficients| |safeCeiling| |dual| |showTheIFTable| + |nextsubResultant2| |createLowComplexityNormalBasis| |f02akf| |yRange| + |cyclicEntries| |selectODEIVPRoutines| |cyclicCopy| ** + |purelyTranscendental?| |viewWriteAvailable| + |basisOfCommutingElements| |debug3D| |OMreadStr| |parent| + |numFunEvals3D| |zRange| |principalAncestors| |midpoints| + |setRealSteps| |row| |OMopenString| |slex| |rombergo| |hessian| + |elements| |functionIsOscillatory| |resultantnaif| |insertTop!| |map!| + |yCoordinates| |integralBasisAtInfinity| |nextColeman| RF2UTS + |rightQuotient| |stFunc1| |power!| |makeRecord| |f02ajf| |quartic| + |tan2cot| |lo| |hostPlatform| |factorAndSplit| |qsetelt!| + |paraboloidal| |virtualDegree| |musserTrials| |pushdterm| |s18acf| + |mapmult| |getIdentifier| |denominator| |symbol?| |extension| |incr| + |palgRDE| |uncouplingMatrices| |label| |imagK| |byteBuffer| |d02gbf| + |tValues| |OMcloseConn| |initial| |binaryTournament| |mapCoef| + |listRepresentation| |airyBi| |edf2df| |Aleph| |makeYoungTableau| + |normalDenom| |e01bff| |antisymmetric?| |errorKind| |leadingIndex| + |signatureAst| |pop!| |csc2sin| |d03faf| + |stiffnessAndStabilityOfODEIF| |readByte!| |patternMatch| + |factorPolynomial| |selectFiniteRoutines| |addMatchRestricted| + |drawComplexVectorField| |iiacsc| |rightNorm| |nthExpon| + |exprToGenUPS| |simplifyPower| |euclideanGroebner| |startTable!| + |symFunc| |viewDefaults| |moduloP| Y |sncndn| |modulus| + |halfExtendedSubResultantGcd1| |s17agf| |monomRDEsys| |testModulus| + |acsch| |shanksDiscLogAlgorithm| |LiePoly| |reverse!| |lambert| + |setTopPredicate| |pToDmp| |head| |rightUnits| |rename!| + |certainlySubVariety?| |initiallyReduce| |normDeriv2| |ratPoly| + |front| |chvar| |chebyshevU| |reciprocalPolynomial| |OMencodingBinary| + |iiasinh| |irDef| |range| |pseudoDivide| |compose| |tail| |rotatez| + |addmod| |mix| |isAnd| |mapMatrixIfCan| |maxPoints3D| |constructor| + |rules| |edf2efi| |iflist2Result| |randomLC| |partialFraction| + |OMReadError?| |putProperties| |solveRetract| |padicFraction| |curve| + |rCoord| |truncate| |fortranReal| |nothing| |stronglyReduced?| + |zerosOf| |every?| |eigenMatrix| |option| |primeFactor| |collect| + |insertMatch| |internalAugment| |infinityNorm| |sqfree| |showSummary| + |innerint| |pointLists| |primextendedint| |dequeue!| |s17acf| + |topFortranOutputStack| |extractPoint| |lex| |getConstant| |setEmpty!| + |setvalue!| |stopTableInvSet!| |factorSFBRlcUnit| |splitDenominator| + |finiteBound| |e02aef| |numberOfChildren| |OMputApp| |bat1| |pdf2ef| + |selectfirst| |showAttributes| |noValueMode| |completeSmith| + |intChoose| |divideExponents| |iilog| |unknown| |solveLinear| + |setClosed| |morphism| |OMmakeConn| |bigEndian| |eigenvalues| + |macroExpand| |linearAssociatedLog| |returns| |meshFun2Var| |coerceS| + |rightTrim| |palglimint0| |OMsend| |mainExpression| |prinpolINFO| + |e01saf| |complete| |mindeg| |extract!| |iiatanh| |hdmpToP| + |unrankImproperPartitions0| |leftTrim| |c06fqf| |tanh2trigh| + |dmpToHdmp| |f02adf| |squareFreeFactors| |d02cjf| |f04axf| |option?| + |euclideanNormalForm| |extractTop!| |constantLeft| |RittWuCompare| + |fmecg| |evenInfiniteProduct| |rootKerSimp| |OMputString| |operators| + |semiIndiceSubResultantEuclidean| |say| |gensym| F |list?| + |tanintegrate| |laguerreL| |var1StepsDefault| |OMputFloat| + |perfectNthPower?| |safeFloor| |cAtanh| |expint| |mathieu23| + |localAbs| |unrankImproperPartitions1| |bitTruth| |c05nbf| |component| + |integralLastSubResultant| |mainPrimitivePart| + |cyclotomicDecomposition| |removeSuperfluousQuasiComponents| + |dihedral| |binomial| |d03eef| |acotIfCan| |rspace| |extractProperty| + |has?| |setCondition!| |elaborate| |ramified?| |firstSubsetGray| + |graphImage| |llprop| |remove| |function| |multivariate| |lieAlgebra?| + |minPol| |nonSingularModel| |credPol| |createNormalPrimitivePoly| + |showRegion| |constantIfCan| |fortran| |approxSqrt| |cLog| |variables| + |commaSeparate| |fractRagits| |result| |identitySquareMatrix| + |getOperands| |univariatePolynomialsGcds| |showClipRegion| + |numerators| |clip| |open| |OMgetAttr| |fibonacci| |cschIfCan| + |linSolve| |last| |eval| |reduced?| |reset| |cSec| |alternatingGroup| + |var2Steps| |isPlus| |module| |assoc| |comparison| |interactiveEnv| + |null| |OMUnknownCD?| |csubst| |doublyTransitive?| |perfectNthRoot| + |solveLinearPolynomialEquationByFractions| |OMputInteger| |iiGamma| + |OMParseError?| |polyPart| |domainTemplate| |removeCoshSq| |f04atf| + |pattern| |not| |subNodeOf?| |idealiser| |OMgetFloat| |write| + |upperCase?| |fintegrate| |edf2ef| |OMputAtp| |expintegrate| + |doubleDisc| |absolutelyIrreducible?| |ode| |clearFortranOutputStack| + |and| |isImplies| |hasHi| |save| |d01aqf| |univariatePolynomials| + |permutations| |nthFractionalTerm| |operations| |hdmpToDmp| + |pmintegrate| |subResultantGcdEuclidean| |taylor| |getPickedPoints| + |or| |mainSquareFreePart| |indicialEquation| |modifyPointData| + |c05pbf| |s17ahf| |reducedForm| |inverseIntegralMatrixAtInfinity| + |branchIfCan| |iiperm| |numerator| |leftOne| |ridHack1| |xor| + |laurentRep| |laurent| |adjoint| |bombieriNorm| |rk4a| |primitive?| + |bounds| |multMonom| |generalInfiniteProduct| |message| + |internalDecompose| |prepareSubResAlgo| |quasiMonic?| |case| + |pointColorDefault| |puiseux| |setfirst!| + |functionIsContinuousAtEndPoints| |s17adf| |clipBoolean| |duplicates?| + |createMultiplicationTable| |atrapezoidal| |mergeFactors| |Zero| + |coth2tanh| |coefficient| |bandedJacobian| |wordInStrongGenerators| + |numberOfOperations| |internalSubPolSet?| |green| |hi| |null?| + |torsionIfCan| |region| |normalizeAtInfinity| |f02agf| |One| |atom?| + |inv| |polygon| |s21baf| |algebraicOf| |unitNormalize| FG2F + |lfinfieldint| |highCommonTerms| |imagi| |ground?| |supersub| |rarrow| + |opeval| |shade| |lowerPolynomial| |setScreenResolution| |prindINFO| + |quoted?| |structuralConstants| |repeating| |rectangularMatrix| + |doubleResultant| |ground| |lcm| |sinhIfCan| |cAcsc| |unmakeSUP| + |seriesToOutputForm| |s20adf| |removeZeroes| |figureUnits| |scale| + |f02wef| |zeroSetSplit| |sechIfCan| |generalizedEigenvector| + |leadingMonomial| |wordsForStrongGenerators| |birth| |setrest!| + |ceiling| |ScanFloatIgnoreSpacesIfCan| |floor| |addPointLast| + |fracPart| |cCsc| |setLength!| |palglimint| |append| |deref| + |leadingCoefficient| |recip| |rotatex| |f2df| |size?| + |patternMatchTimes| |reseed| |coerceP| |newReduc| |FormatArabic| + |primitiveMonomials| |gcd| |output| |Gamma| |elt| |minColIndex| + |primitivePart| |df2mf| |e02daf| |build| |gcdcofact| |cos2sec| + |showTheRoutinesTable| |leadingExponent| |deepestTail| |false| + |reductum| |hconcat| |plot| |minset| |trim| |log2| |irCtor| |conical| + |polyRDE| |solveLinearlyOverQ| |submod| |argumentListOf| + |subtractIfCan| |changeThreshhold| |arity| |shallowCopy| + |setLabelValue| |eyeDistance| |readLine!| |copy!| |power| + |isConnected?| |OMconnInDevice| |normalElement| |implies| |printCode| + |internalSubQuasiComponent?| |iprint| |characteristicSet| |OMgetBVar| + |conjug| |tanSum| |brillhartTrials| |rationalFunction| |nthCoef| + |readLineIfCan!| |mathieu12| |cycleEntry| |singular?| |c06fpf| + |c06fuf| |minGbasis| |extractIfCan| |reducedContinuedFraction| + |ellipticCylindrical| |primintegrate| |composites| |packageCall| + |OMputEndAtp| |zeroDimPrimary?| |schwerpunkt| |contract| + |euclideanSize| |reorder| |alphabetic?| |e01sff| |OMputSymbol| + |subresultantVector| |rootProduct| |factorList| + |selectMultiDimensionalRoutines| |subResultantsChain| |totalGroebner| + |f02fjf| |scanOneDimSubspaces| |categories| |sinhcosh| |unexpand| + |outputGeneral| |integrate| |OMgetEndBVar| |fortranTypeOf| |callForm?| + |unitsColorDefault| |bumptab1| |normalizedDivide| |ricDsolve| + |multiEuclideanTree| |printHeader| |nextNormalPoly| |inverseColeman| + |slash| |returnType!| |iipow| |applyRules| |socf2socdf| + |extendedSubResultantGcd| |karatsubaDivide| |stirling1| |prinb| + |normFactors| |node?| |f01brf| |accuracyIF| |round| |asinIfCan| + |traverse| |internalIntegrate| |members| |groebgen| |weighted| + |lazyPseudoRemainder| |stoseInvertibleSetsqfreg| |subMatrix| + |dualSignature| |sinIfCan| |iicot| |fill!| |makeprod| |real?| + |decreasePrecision| |usingTable?| |eulerE| |OMopenFile| |plusInfinity| + |c06gqf| |ranges| |kovacic| |ParCond| |equiv| |genericRightTrace| + |definingPolynomial| |complexEigenvalues| |content| |chineseRemainder| + |isAtom| |minusInfinity| |getZechTable| |complexNumericIfCan| + |bezoutMatrix| |radicalSolve| |internal?| |evenlambert| |copyInto!| + |wronskianMatrix| |bezoutResultant| |numberOfNormalPoly| |character?| + |clipPointsDefault| |sturmVariationsOf| |modTree| |leftZero| |e02bcf| + |numberOfComposites| |OMgetEndApp| |subPolSet?| |getRef| + |clearTheIFTable| |deriv| |tubePlot| |matrixConcat3D| |countRealRoots| + |endOfFile?| |key| |changeName| |rightDivide| |linears| |initTable!| + |alternating| |complex?| |rootPoly| |imports| |adaptive?| |weight| + |cCot| |nodes| |subTriSet?| |toroidal| |OMgetAtp| |f02aef| + |characteristicPolynomial| |BumInSepFFE| |rootsOf| + |getMultiplicationMatrix| |filename| |twoFactor| |stoseInvertible?| + |intensity| |df2fi| |f04mbf| |attributeData| |components| |type| + |plus!| |times!| |ptFunc| |imagj| |basisOfCentroid| + |generalizedContinuumHypothesisAssumed?| |quickSort| + |indiceSubResultantEuclidean| |UP2ifCan| |evaluate| |generalLambert| + |solveLinearPolynomialEquationByRecursion| |monomRDE| |parse| + |typeLists| |curveColorPalette| |low| |groebner| |resize| |romberg| + |indicialEquations| |trapezoidalo| |next| |resetNew| |froot| + |rightFactorIfCan| |whatInfinity| |doubleFloatFormat| |btwFact| + |d01gbf| |rewriteIdealWithRemainder| + |removeIrreducibleRedundantFactors| |subspace| + |leftCharacteristicPolynomial| |restorePrecision| |hermite| |s19abf| + |geometric| |elliptic| |f01rcf| |computeInt| |maxrow| |reducedSystem| + |totalDifferential| |modularGcd| |upperCase| |e01bgf| + |symmetricDifference| |cylindrical| |iiasech| |karatsubaOnce| + |checkPrecision| |imagI| |minPoints| |reduceByQuasiMonic| + |printStats!| |less?| |factor1| |internalInfRittWu?| |mapExpon| + |primitivePart!| |updateStatus!| |pow| EQ |currentSubProgram| + |localReal?| |groebnerIdeal| |setchildren!| |expenseOfEvaluationIF| + |stoseInvertibleSetreg| |currentCategoryFrame| |pointSizeDefault| + |dark| |besselJ| |realElementary| |palgint0| |rowEch| |getMeasure| + |lhs| |quadratic| |besselK| |complexIntegrate| |repeating?| + |definingInequation| |nonQsign| |headReduce| |relerror| |laurentIfCan| + |incrementKthElement| |rhs| |expenseOfEvaluation| |writeBytes!| |Ci| + |asinhIfCan| |newTypeLists| |getVariableOrder| |fixedPointExquo| + |magnitude| |tRange| |root| |interReduce| |partialDenominators| + |polCase| |iiacot| |iisech| |unprotectedRemoveRedundantFactors| + |realRoots| |univariatePolynomial| |environment| |integralRepresents| + |SturmHabichtSequence| |getCurve| |s17ajf| |B1solve| |interval| + |nthRoot| |testDim| |cExp| |f07aef| |rule| |OMgetEndError| |subscript| + |viewport2D| |dioSolve| |sdf2lst| |entry?| |lazyPrem| |showAll?| + |discriminant| |constantKernel| |index| |completeEchelonBasis| + |firstUncouplingMatrix| |merge!| |leftLcm| |generalTwoFactor| + |cycleRagits| |lastSubResultantElseSplit| |weights| |addPoint2| + |infinite?| |maxRowIndex| |sin?| |pseudoRemainder| |nthExponent| + UTS2UP |solveid| |OMputEndError| |partialNumerators| |inf| |s17akf| + |removeSquaresIfCan| |center| |splitLinear| |e02ajf| |isMult| + |cRationalPower| |solveInField| |nextLatticePermutation| + |fortranDoubleComplex| |s21bdf| |radicalEigenvectors| + |limitedIntegrate| |pair| |resultantEuclideannaif| |commonDenominator| + |prinshINFO| |acosIfCan| |showFortranOutputStack| |cotIfCan| |polyred| + |value| |listOfLists| |differentialVariables| |rst| |d02kef| + |rational?| |regime| |makeSUP| |d02gaf| |more?| |logical?| + |bubbleSort!| |dimensionOfIrreducibleRepresentation| |UnVectorise| + |represents| |diagonalMatrix| |cAtan| |graphStates| |factorOfDegree| + |roughBase?| |f04jgf| |rdregime| |separateDegrees| + |possiblyNewVariety?| |powerSum| |transpose| |nor| + |useEisensteinCriterion| |replaceKthElement| |medialSet| |binding| + |roughSubIdeal?| |entry| |hasoln| |perspective| |key?| |e02zaf| + |invmod| |positive?| |whitePoint| |contractSolve| |lintgcd| |iExquo| + |totalLex| |lazyPquo| |fullDisplay| |quadraticForm| |separant| |red| + |SturmHabichtMultiple| |lighting| |linearPolynomials| |sincos| + |gcdPolynomial| |factorials| |delay| |makingStats?| |f02aff| + |RemainderList| |nand| |topPredicate| |maxint| |pade| |skewSFunction| + |distdfact| |decimal| |dictionary| |mappingMode| |oddintegers| + |kroneckerDelta| |intPatternMatch| |getStream| |reverse| |phiCoord| + |alphanumeric| |divisor| |multinomial| |remove!| |laplacian| + |mainVariable?| |generalizedInverse| |OMread| |iitanh| |normalized?| + |mapUnivariate| |call| |processTemplate| |shrinkable| |s21bbf| + |rationalPoint?| |mkPrim| |alphanumeric?| |lookup| |LyndonCoordinates| + |setAdaptive| |someBasis| |leaves| |tree| |screenResolution3D| + |f02aaf| |sin2csc| |innerSolve| |open?| |squareTop| |sequences| + |leftRank| |countRealRootsMultiple| |nil?| |physicalLength| |sequence| + |iCompose| |oblateSpheroidal| |primPartElseUnitCanonical!| + |fortranComplex| |transform| |irreducibleRepresentation| |atanIfCan| + |sumOfDivisors| |s17aff| |linearDependence| |setMinPoints| |bytes| + |simplifyExp| |factorByRecursion| |reducedDiscriminant| |top!| + |rightUnit| |collectUnder| |setleft!| |getDatabase| |viewZoomDefault| + |init| |constantRight| |quoByVar| |f01qcf| |lazyPseudoDivide| + |squareFreeLexTriangular| |prime| |subscriptedVariables| |singRicDE| + |elementary| |stFunc2| |OMencodingXML| |unitVector| |gcdprim| + |monicCompleteDecompose| |normalize| |LowTriBddDenomInv| |decompose| + |subNode?| |wreath| |coefficients| |parametric?| |nextPartition| + |nthFlag| |groebner?| |algintegrate| |po| |idealiserMatrix| + |generator| |makeop| |f04adf| |fixPredicate| |coerceL| |max| + |finiteBasis| |expandLog| |integral?| |rightCharacteristicPolynomial| + |powmod| |printStatement| |jacobian| |leftRecip| |iicoth| |ScanRoman| + |makeCos| |generateIrredPoly| |writable?| |paren| |cAsec| |asimpson| + |crushedSet| |invertibleSet| |rightTraceMatrix| |makeFloatFunction| + |showTheFTable| |OMputEndBVar| |mathieu11| |search| |lazy?| + |explicitEntries?| |trailingCoefficient| |exprex| |infix| + |rationalIfCan| |stack| |rem| |isExpt| |algebraicCoefficients?| + |permutationGroup| |endSubProgram| |besselY| |realSolve| |part?| + |insertionSort!| |setErrorBound| |ran| |gethi| |s17dlf| |dimension| + |measure2Result| |quo| |numericIfCan| |curve?| |singularitiesOf| + |mirror| |solid?| |sumOfKthPowerDivisors| |condition| |dflist| + |legendreP| |bipolar| |deepestInitial| |lookupFunction| |pquo| + |e02bbf| |sec2cos| |anfactor| |squareFreePolynomial| + |numericalOptimization| |div| |mainForm| |d02bbf| |setValue!| + |elaborateFile| |dn| |heap| |rename| |rightAlternative?| + |goodnessOfFit| |exquo| |ode1| |dim| + |removeRoughlyRedundantFactorsInPol| |point?| |leftTraceMatrix| |nthr| + |cyclotomic| |cosSinInfo| |alternative?| |rischNormalize| |laplace| ~= + |copies| |sts2stst| |edf2fi| |queue| |powers| |toseLastSubResultant| + |middle| |explicitlyFinite?| |taylorRep| |#| |f01qef| |matrix| + |rationalPower| |dec| |assign| |deleteRoutine!| + |useEisensteinCriterion?| |shallowExpand| |pascalTriangle| ~ + |OMreceive| |read!| |high| |fullPartialFraction| |concat| + |computeCycleLength| |coordinate| |nextsousResultant2| |zeroDimPrime?| + |irVar| |LyndonWordsList1| |minimize| |cardinality| |lexGroebner| + |regularRepresentation| |isList| |c05adf| |leadingTerm| |frobenius| + |printInfo| |tubePointsDefault| |maxIndex| |bag| |lfintegrate| + |whileLoop| |clearCache| |purelyAlgebraic?| |compound?| |level| + |baseRDE| |var1Steps| |s15aef| |symmetricTensors| + |exprHasWeightCosWXorSinWX| |triangulate| |swapColumns!| |unit?| + |stosePrepareSubResAlgo| |c06gbf| |coth2trigh| |overlabel| |rotate!| + |enterPointData| |constant?| |cycleElt| |mainDefiningPolynomial| + |solve| |substring?| |plotPolar| |weakBiRank| |OMsupportsSymbol?| + |stripCommentsAndBlanks| |char| |squareFreePrim| |retractable?| + |simpleBounds?| |failed| |factors| |monicRightDivide| + |orthonormalBasis| |zeroSquareMatrix| |bothWays| |bumprow| + |insertRoot!| |polygon?| |pole?| |suffix?| |binomThmExpt| |makeUnit| + |curryRight| |removeRoughlyRedundantFactorsInPols| |lazyResidueClass| + |aQuartic| |updatF| |fi2df| |empty| |s20acf| |recur| |cartesian| + |cAcsch| |Nul| |block| |compile| |nary?| |linearAssociatedOrder| + |OMsetEncoding| |prefix?| |status| |Beta| |minPoints3D| |solve1| + |uniform| |completeHensel| |dominantTerm| |fillPascalTriangle| + |lyndon| |scan| |numberOfFractionalTerms| |multiset| |expt| + |fortranLiteralLine| |stoseInvertible?sqfreg| |parabolicCylindrical| + |eof?| |minIndex| |youngDiagram| |leftQuotient| |second| + |linkToFortran| |subResultantChain| |erf| |elColumn2!| |e01bef| + |fortranLinkerArgs| |float| |divide| |vconcat| |stronglyReduce| + |shape| |acscIfCan| |third| |mesh?| |getMatch| |multiple?| + |firstNumer| |redpps| |basisOfNucleus| |coerceImages| |string?| + |putProperty| |palgextint0| |lfunc| |subSet| |messagePrint| + |acschIfCan| |void| |f04faf| |argscript| |interpretString| |e02gaf| + |primlimintfrac| |tanhIfCan| |dilog| |asechIfCan| + |permutationRepresentation| |float?| |sPol| |f04asf| |ScanArabic| + |infix?| |semiSubResultantGcdEuclidean2| |overlap| |coerceListOfPairs| + |numberOfImproperPartitions| |extractClosed| |sin| |modifyPoint| + |mask| |transcendent?| |indicialEquationAtInfinity| |errorInfo| + |cscIfCan| |cos| |outputAsScript| |infLex?| |closeComponent| + |OMconnectTCP| |pr2dmp| |charpol| |makeFR| |inverse| + |genericLeftTrace| |bringDown| |Ei| |tan| |expr| |multisect| + |reverseLex| |cyclic?| |diagonalProduct| |bipolarCylindrical| + |symbolTableOf| |innerEigenvectors| |mkcomm| |tubeRadiusDefault| + |evaluateInverse| |superHeight| |cot| |quotientByP| |find| |write!| + |moreAlgebraic?| |bumptab| |rootPower| |completeHermite| + |rootNormalize| |sec| |OMgetEndObject| |triangularSystems| GE + |bottom!| |s13acf| |dmpToP| |double| |connect| |basisOfLeftNucleus| + |positiveRemainder| |negative?| |controlPanel| |laguerre| |csc| |log| + GT |infieldIntegrate| |expPot| |elRow1!| |coshIfCan| |cCos| + |removeSinhSq| |variable| |monicModulo| |prem| |iteratedInitials| + |asin| LE |outputAsTex| |const| |OMgetVariable| |kmax| + |basisOfRightNucloid| |setImagSteps| |mapUnivariateIfCan| |deepCopy| + |iterators| BY |purelyAlgebraicLeadingMonomial?| |acos| LT |bracket| + |iiacosh| |constantToUnaryFunction| |minRowIndex| |thenBranch| + |replace| |frst| |fixedDivisor| |rightPower| |atan| |qPot| |hclf| + |strongGenerators| |palginfieldint| |radPoly| |c06eaf| |blankSeparate| + |sylvesterSequence| |rootDirectory| |acot| |outputBinaryFile| |biRank| + |redPo| |monomialIntegrate| |integralMatrix| |leftFactor| + |stoseLastSubResultant| |composite| |lazyVariations| |asec| + |oneDimensionalArray| |raisePolynomial| |characteristic| + |diophantineSystem| |iisinh| |complement| |f02abf| |powern| + |OMconnOutDevice| |acsc| |divisorCascade| |outputArgs| |trueEqual| + |declare!| |setAttributeButtonStep| |complementaryBasis| |mathieu22| + |host| |numberOfMonomials| |setref| |sinh| |OMgetEndAtp| |makeEq| + |augment| |inverseIntegralMatrix| |nonLinearPart| |poisson| + |flexible?| |realEigenvalues| |outputForm| |cosh| |dfRange| + |atanhIfCan| |curryLeft| NOT |ListOfTerms| |inspect| |OMgetEndAttr| + |OMputVariable| |odd?| |vspace| |tanh| |getButtonValue| |s01eaf| + |lists| |d01fcf| OR |colorDef| |escape| |initiallyReduced?| + |UpTriBddDenomInv| |removeCosSq| |zeroSetSplitIntoTriangularSystems| + |coth| |indices| |pushuconst| |d01apf| AND |mainKernel| |repSq| + |cyclotomicFactorization| |readInt32!| |LyndonWordsList| + |compiledFunction| |traceMatrix| |keys| |resultantReduit| |coleman| + |e02bef| |iicsch| |mkAnswer| |univariate?| |depth| |semicolonSeparate| + |child| |addiag| |genericRightDiscriminant| |cothIfCan| |abelianGroup| + |meshPar1Var| |color| |cot2trig| |meatAxe| |clipSurface| |stopTable!| + |OMgetBind| |debug| |segment| |getGraph| |autoReduced?| |writeInt8!| + |spherical| |optpair| |hypergeometric0F1| |d01alf| |surface| D + |harmonic| |OMUnknownSymbol?| |ord| |approxNthRoot| + |createLowComplexityTable| |lfextlimint| |critpOrder| |Vectorise| + |midpoint| |trace2PowMod| |cyclicGroup| |rationalApproximation| + |critMTonD1| |irForm| |reopen!| |expandTrigProducts| + |axesColorDefault| |c06gcf| |resetAttributeButtons| |stirling2| + |cosIfCan| |screenResolution| |compBound| |readInt8!| |palgextint| + |complexExpand| |algebraicDecompose| |rubiksGroup| |htrigs| + |LagrangeInterpolation| |rightRank| |integralCoordinates| |factorset| + |horizConcat| |oddInfiniteProduct| |tanIfCan| |style| + |semiResultantEuclidean1| |mapDown!| |setTex!| |mulmod| |sinh2csch| + |curveColor| |f01mcf| |mat| |selectIntegrationRoutines| + |makeGraphImage| * |integerBound| |imaginary| |gbasis| + |componentUpperBound| |eigenvector| |outputMeasure| |se2rfi| |unparse| + |explimitedint| |octon| |rootOfIrreduciblePoly| |s13aaf| |is?| + |exteriorDifferential| |c06frf| |properties| |forLoop| |optimize| + |d01bbf| |maxrank| |cAcos| |exprToXXP| |limit| |nullSpace| |rroot| + |roughBasicSet| |translate| |hue| |rightGcd| + |initializeGroupForWordProblem| |OMserve| = |compdegd| + |stoseSquareFreePart| |largest| |overbar| |create| |cAcot| |print| + |algebraicSort| |untab| |presuper| |discriminantEuclidean| |bfEntry| + |dimensions| |exportedOperators| |swap!| |resolve| |lagrange| + |minimalPolynomial| |trapezoidal| < |mapSolve| |hMonic| |specialTrigs| + |constantCoefficientRicDE| |indiceSubResultant| |intersect| + |resetBadValues| |cSech| |shufflein| > |subset?| |column| + |jordanAdmissible?| |removeZero| |OMgetApp| + |rewriteSetByReducingWithParticularGenerators| + |halfExtendedSubResultantGcd2| |rightScalarTimes!| |orbits| <= + |henselFact| |df2st| |doubleComplex?| |OMclose| |hostByteOrder| + |readIfCan!| |scaleRoots| |elem?| |sturmSequence| >= |mightHaveRoots| + |logpart| |primextintfrac| |degree| |totolex| |viewpoint| |rdHack1| + |setProperties| |lexTriangular| |operation| + |genericLeftMinimalPolynomial| |arrayStack| |mapGen| + |chainSubResultants| |monicDecomposeIfCan| |deleteProperty!| |reindex| + |leastPower| |lazyGintegrate| |linearlyDependent?| |An| |scopes| + |digits| |interpret| |leftAlternative?| |npcoef| |enqueue!| + |setleaves!| + |vertConcat| |f01qdf| |antiCommutator| |distance| + |true| |bivariateSLPEBR| |algDsolve| |selectsecond| + |linearAssociatedExp| - |cn| |backOldPos| |leastAffineMultiple| + |leftExactQuotient| |groebnerFactorize| |wordInGenerators| + |polynomialZeros| |sizeMultiplication| |mantissa| + |leadingCoefficientRicDE| / |perfectSqrt| |duplicates| |OMputEndBind| + |complexEigenvectors| |scalarMatrix| |halfExtendedResultant2| + |charthRoot| |chiSquare| |basisOfCenter| |maximumExponent| + |determinant| |OMputEndObject| |normalForm| |category| + |antisymmetricTensors| |nil| |postfix| |makeResult| |s18aff| + |complexRoots| |rowEchelonLocal| |integralMatrixAtInfinity| + |toseInvertible?| |domain| |leftFactorIfCan| |initials| |extend| + |goto| |generators| |compactFraction| |package| |relativeApprox| + |factorsOfCyclicGroupSize| |tensorProduct| |transcendentalDecompose| + |setEpilogue!| |subResultantGcd| |shift| |KrullNumber| |argumentList!| + |pointPlot| |nextPrimitivePoly| |decrease| |associative?| + |approximate| |extractBottom!| |readInt16!| |hasPredicate?| |c06gsf| + |rewriteSetWithReduction| |ramifiedAtInfinity?| |enumerate| |complex| + |OMputBVar| |enterInCache| |listConjugateBases| |varList| |merge| + |quasiRegular?| |iisec| |rowEchLocal| |solid| |simpsono| |iiatan| + |prepareDecompose| |show| |e01sef| |diagonal| |mappingAst| |sample| + UP2UTS |property| |badValues| |brillhartIrreducible?| |belong?| + |presub| |att2Result| |associatorDependence| |moduleSum| + |hasTopPredicate?| |closedCurve?| |s18def| |outputSpacing| + |companionBlocks| |secIfCan| |trace| |qinterval| |f04qaf| + |cyclicEqual?| |ip4Address| |cTan| |xn| |sylvesterMatrix| |vark| + |retract| |leader| |unravel| |createIrreduciblePoly| |optAttributes| + |units| |elseBranch| |mapUp!| |associates?| |delta| |roughUnitIdeal?| + |abs| |denomRicDE| |symbolIfCan| |karatsuba| |palgintegrate| + |seriesSolve| |PollardSmallFactor| |wholeRagits| |cfirst| + |multiplyCoefficients| |pushucoef| |possiblyInfinite?| |ef2edf| + |atoms| |expIfCan| |makeSketch| |quasiRegular| |checkRur| + |totalDegree| |qqq| |pointColorPalette| |setStatus| |conjugates| + |graphState| |setelt!| |divergence| |terms| |product| + |radicalOfLeftTraceForm| |typeForm| |flexibleArray| |padicallyExpand| + |interpolate| |functorData| |code| |digamma| |listLoops| |rk4| + |leftUnit| |unitNormal| |sup| |mainContent| |d01amf| + |numberOfDivisors| |prologue| |rewriteIdealWithHeadRemainder| + |formula| |trigs2explogs| |headReduced?| |unknownEndian| |elaboration| + |explogs2trigs| |OMgetEndBind| |epilogue| |s19aaf| + |rightMinimalPolynomial| |lambda| |acothIfCan| |ParCondList| |child?| + |rk4qc| |aromberg| |cCosh| |OMunhandledSymbol| |capacity| |plus| + |countable?| |useSingleFactorBound?| |changeNameToObjf| |monicDivide| + |rightExactQuotient| |algSplitSimple| |pol| |coord| |cycleSplit!| + |cAsinh| |inR?| |numberOfPrimitivePoly| |makeSeries| |exactQuotient!| + |dom| |symmetricGroup| |littleEndian| |coordinates| |inGroundField?| + |varselect| |f04mcf| |nrows| |numberOfVariables| |thetaCoord| |sum| + |aspFilename| |datalist| |factorsOfDegree| |fortranDouble| |cot2tan| + |trunc| |hspace| |removeRedundantFactorsInContents| |ncols| + |divideIfCan| |expintfldpoly| |getGoodPrime| |selectPDERoutines| + |cAsin| |iicsc| |inHallBasis?| |parametersOf| |times| |fprindINFO| + |cAsech| |basisOfRightNucleus| |associatedSystem| |equality| + |distFact| |linGenPos| |computePowers| |symbolTable| |janko2| |linear| + |encodingDirectory| |inconsistent?| |select!| |critT| + |removeRedundantFactors| |top| |mvar| |lazyPremWithDefault| |before?| + |findCycle| |lp| |systemCommand| |leadingIdeal| |pdct| + |createPrimitiveNormalPoly| |stopTableGcd!| |c06ekf| |linearMatrix| + |pushFortranOutputStack| |f01bsf| |setStatus!| |title| |comp| + |viewSizeDefault| |polynomial| |associatedEquations| |swap| + |selectOrPolynomials| |tableForDiscreteLogarithm| |point| |commutator| + |ldf2lst| |reduceBasisAtInfinity| |popFortranOutputStack| |cross| + |inrootof| |monom| |node| |options| |critMonD1| |adaptive| + |singularAtInfinity?| |bsolve| |coHeight| |continue| |sort| |d01ajf| + |newSubProgram| |quatern| |outputAsFortran| |permutation| |normal| + |drawToScale| |cPower| |e02bdf| |PDESolve| |defineProperty| |sign| |e| + |complexSolve| |selectOptimizationRoutines| |leftTrace| |wrregime| + |leftScalarTimes!| |eq?| |c02agf| |dimensionsOf| |clikeUniv| + |qualifier| |idealSimplify| |series| |localIntegralBasis| |list| + |cycle| |tab| |isobaric?| |predicates| |iisqrt3| |common| |s17dhf| + |string| |zCoord| |imagJ| |iiacsch| |check| |s18aef| |car| |scripted?| + |cycles| |convergents| |drawComplex| |infieldint| |close!| |pastel| + |inverseLaplace| |setAdaptive3D| |graeffe| |particularSolution| + |random| |cdr| |mainMonomials| |exists?| |pushdown| |setOfMinN| |pile| + |torsion?| |position!| |prevPrime| |ddFact| |setDifference| + |maxColIndex| |binary| |fTable| |selectNonFiniteRoutines| + |nextNormalPrimitivePoly| |bivariatePolynomials| + |SturmHabichtCoefficients| |associator| |min| |factorFraction| + |setIntersection| |wholePart| |ksec| |e01sbf| |categoryFrame| + |removeDuplicates!| |recoverAfterFail| |semiResultantReduitEuclidean| + |baseRDEsys| |leadingBasisTerm| |setUnion| |basisOfRightAnnihilator| + |OMputEndApp| |unvectorise| |showTheSymbolTable| |approximants| + |createThreeSpace| |stoseIntegralLastSubResultant| |superscript| + |rightRankPolynomial| |decomposeFunc| |apply| |symmetric?| + |quadratic?| |shiftLeft| |primes| |matrixDimensions| |rightRecip| + |iomode| |meshPar2Var| |genericRightTraceForm| |insert!| |charClass| + |divideIfCan!| |e04ucf| |basisOfMiddleNucleus| |zero| |lllip| + |makeViewport2D| |mathieu24| |primitiveElement| |f01rdf| |size| + |rootRadius| |distribute| |modularGcdPrimitive| |voidMode| |critB| + |HermiteIntegrate| |OMgetObject| |pack!| |width| |pushNewContour| + |leftRegularRepresentation| |primintfldpoly| |f04arf| |denomLODE| + |And| |exponents| |taylorQuoByVar| |writeLine!| |s14baf| |equation| + |setnext!| |normalizedAssociate| |push!| |extractIndex| |vector| + |polygamma| |Or| |iiacoth| |startTableGcd!| |yCoord| |viewPhiDefault| + |droot| |first| |reduction| |invertible?| |irreducibleFactors| + |differentiate| |univcase| |Not| |fortranCarriageReturn| |updatD| + |d02ejf| |besselI| |setPredicates| |rest| |e01baf| |normalizeIfCan| + |splitNodeOf!| |parents| |collectQuasiMonic| |numeric| |e02ahf| + |selectSumOfSquaresRoutines| |f02axf| |split| + |semiDiscriminantEuclidean| |substitute| |rquo| |OMputObject| + |supDimElseRittWu?| |basisOfLeftNucloid| |radical| |partialQuotients| + |lifting| |simplifyLog| |zeroDim?| |hash| |resultantReduitEuclidean| + |removeDuplicates| |nextIrreduciblePoly| |d02raf| + |solveLinearPolynomialEquation| |minrank| |count| |primaryDecomp| + |putGraph| |d01gaf| |viewDeltaYDefault| |viewWriteDefault| + |extendedint| |FormatRoman| |mr| |tube| |swapRows!| |recolor| + |primeFrobenius| |super| |leftExtendedGcd| |name| |optional| + |listBranches| |setRow!| |heapSort| |leftRankPolynomial| + |resetVariableOrder| |OMgetString| |rowEchelon| |eigenvectors| + |genericRightNorm| |makeMulti| |characteristicSerie| |lift| |body| + |redmat| |inc| |minus!| |computeBasis| |degreeSubResultantEuclidean| + |integerIfCan| |invertibleElseSplit?| |cup| |tablePow| + |lineColorDefault| |reduce| |complexNormalize| |minimumExponent| + |parts| |splitConstant| |functionIsFracPolynomial?| |monomial?| + |listexp| |unit| |prod| |exprHasAlgebraicWeight| |clearTheSymbolTable| + |reduceLODE| |tryFunctionalDecomposition| |e04mbf| + |showIntensityFunctions| |simplify| |branchPointAtInfinity?| + |rational| |asecIfCan| |chiSquare1| F2FG |mpsode| |setColumn!| + |delete!| |writeByte!| |commutativeEquality| |setMaxPoints| + |palgLODE0| |subCase?| |separate| |symmetricProduct| |cCoth| + |multiplyExponents| |polarCoordinates| |createGenericMatrix| + |exprToUPS| |lazyEvaluate| |zeroDimensional?| |univariateSolve| + |createNormalElement| |currentScope| |isAbsolutelyIrreducible?| + SEGMENT |setlast!| |iiasec| |error| |pleskenSplit| |gcdcofactprim| + |OMencodingUnknown| |expressIdealMember| |element?| |port| |pdf2df| + |universe| |fortranCompilerName| |createPrimitivePoly| |leftDivide| + |reducedQPowers| |assert| |tower| |Lazard| |Lazard2| + |extendedResultant| |roman| |conditionP| |lastSubResultant| + |subHeight| |randomR| |f02bbf| |rootSplit| |jokerMode| + |quasiMonicPolynomials| |f02xef| |t| |jacobi| |tableau| + |representationType| |definingEquations| |tanQ| + |semiResultantEuclideannaif| |rischDE| |mkIntegral| |integralBasis| + |loadNativeModule| |lquo| |f07fef| |OMsupportsCD?| |lazyIntegrate| + |changeBase| |printingInfo?| |categoryMode| |userOrdered?| |e01bhf| + |zero?| |basisOfLeftAnnihilator| |closed| |quotedOperators| + |homogeneous?| |subresultantSequence| |explicitlyEmpty?| |constant| + |quasiAlgebraicSet| |smith| |balancedFactorisation| |complexNumeric| + |symmetricSquare| |mapdiv| |iiacos| |Is| |cAcosh| |constantOpIfCan| + |readBytes!| |stFuncN| |byte| |predicate| |ODESolve| |create3Space| + |complexLimit| |pseudoQuotient| |cubic| |digit| |c06ebf| + |useSingleFactorBound| |kernels| |iifact| |ffactor| |e02dcf| + |derivative| |createZechTable| |palgint| |computeCycleEntry| + |operator| |vedf2vef| |cons| |commutative?| |diagonals| + |multiEuclidean| |sizeLess?| |groebSolve| |member?| |bitLength| + |squareMatrix| |integralDerivationMatrix| |getBadValues| + |noncommutativeJordanAlgebra?| |step| |lllp| |leftDiscriminant| + |e04jaf| |boundOfCauchy| |univariate| |numFunEvals| |LazardQuotient2| + |isEquiv| |logIfCan| |ode2| |axes| |comment| |blue| |identity| + |var2StepsDefault| |fixedPoint| |variationOfParameters| + |bezoutDiscriminant| |increase| |pointData| |rur| |logGamma| + |gradient| |balancedBinaryTree| |identityMatrix| |rotatey| |pair?| + |OMencodingSGML| |coerce| |rightLcm| |factor| |readUInt32!| + |primPartElseUnitCanonical| |algint| |cAcoth| |OMputBind| |int| + |s18dcf| |qroot| |xCoord| |construct| |radicalRoots| |Si| |sqrt| + |source| |lowerCase| |graphCurves| |iicosh| |hermiteH| |diag| |qelt| + |parameters| |real| |basis| |mergeDifference| |extendedIntegrate| + |twist| |divisors| |BasicMethod| |withPredicates| |qsetelt| |ignore?| + |imag| |padecf| |radicalEigenvalues| |safetyMargin| + |getSyntaxFormsFromFile| |splitSquarefree| |setButtonValue| |s18adf| + |xRange| |airyAi| |directProduct| |makeCrit| |isNot| |iisin| + |rightTrace| |iicos| |noLinearFactor?| |cycleLength| |polyRicDE| + |internalLastSubResultant| |d01asf| |algebraic?| |f04maf| + |rightFactorCandidate| |tubePoints| |setsubMatrix!| |rightMult| + |iidsum| |brace| |isOr| |target| |ptree| |createNormalPoly| |critBonD| + |OMgetType| |squareFree| |ocf2ocdf| |innerSolve1| |number?| |destruct| + |factorSquareFreeByRecursion| |dihedralGroup| |crest| |leftNorm| + |createRandomElement| |trigs| |setMinPoints3D| |partition| |just| + |tubeRadius| |genericPosition| |bat| |d02bhf| |fractionPart| |kind| + |changeWeightLevel| |s17dcf| |oddlambert| |hexDigit?| |lflimitedint| + |rootOf| |rightOne| |zoom| |sparsityIF| |op| |e02baf| + |separateFactors| |quote| |leftRemainder| |sortConstraints| |s17aef| + |totalfract| |toseSquareFreePart| |startTableInvSet!| + |getExplanations| |removeConstantTerm| |typeList| |bfKeys| |ravel| + |monomial| |pToHdmp| |points| |e04naf| |leastMonomial| + |setScreenResolution3D| |bitCoef| |LyndonBasis| |bandedHessian| + |createPrimitiveElement| |symmetricRemainder| |closed?| |sh| |reshape| + |degreeSubResultant| |resultant| |arguments| |constantOperator| + |factorSquareFreePolynomial| |stoseInvertibleSet| |setelt| |sort!| + |over| |viewPosDefault| |lastSubResultantEuclidean| + |removeRedundantFactorsInPols| |order| |bits| |ipow| |corrPoly| + |drawStyle| |bindings| |removeRoughlyRedundantFactorsInContents| + |patternVariable| |minordet| |OMgetSymbol| |resultantEuclidean| + |isPower| |optional?| |copy| |makeViewport3D| |psolve| |binaryTree| + |principalIdeal| |quotient| |inputOutputBinaryFile| |setProperty| + |union| |refine| |setprevious!| |invertIfCan| |gramschmidt| + |monomials| |goodPoint| |aCubic| |minimumDegree| |remainder| + |OMputError| |genus| |coercePreimagesImages| |vectorise| |unary?| + |outputFloating| |conditionsForIdempotents| |f07adf| |nodeOf?| + |update| |exponential1| |iiexp| |OMbindTCP| |autoCoerce| |complexForm| + |OMreadFile| |measure| |latex| |validExponential| |mapBivariate| + |OMputAttr| |rightRegularRepresentation| |exponent| + |numberOfComponents| |changeMeasure| |rationalPoints| |readUInt16!| + |rightZero| |problemPoints| |signAround| |imagk| |complexZeros| + |increasePrecision| |imagE| |createMultiplicationMatrix| + |binaryFunction| |cyclicSubmodule| |rank| |seed| + |extractSplittingLeaf| |f2st| |mainValue| |factorSquareFree| + |jordanAlgebra?| |completeEval| |allRootsOf| |getProperty| |tab1| + |connectTo| |symmetricPower| |bit?| |mainVariable| |digit?| |split!| + |integralAtInfinity?| |numberOfFactors| |e02ddf| |position| |addPoint| + |quasiComponent| |iroot| |e02dff| |invmultisect| |GospersMethod| |cap| + |rangePascalTriangle| |match?| |yellow| |shiftRoots| |double?| + |rootSimp| |summation| |getProperties| |legendre| |shellSort| + |eulerPhi| |combineFeatureCompatibility| |entries| |normalise| + |headAst| |scalarTypeOf| |HenselLift| |loopPoints| |ReduceOrder| + |linearDependenceOverZ| |reify| |maxPoints| |exp1| |zeroMatrix| + |useNagFunctions| |numberOfComputedEntries| |startPolynomial| + |reflect| |declare| |cosh2sech| |root?| |extensionDegree| |OMlistCDs| + |s15adf| |identification| |stoseInvertible?reg| |normal?| |generic| + |f07fdf| |stopMusserTrials| |lepol| |sech2cosh| |intcompBasis| + |discreteLog| |getOrder| |prefixRagits| |derivationCoordinates| + |omError| |saturate| |tanNa| |zeroVector| |radicalEigenvector| + |clipWithRanges| |modularFactor| |rightRemainder| |trivialIdeal?| + |mindegTerm| |doubleRank| LODO2FUN |cSinh| |sumSquares| |arg1| + |stiffnessAndStabilityFactor| |systemSizeIF| |appendPoint| |moebiusMu| + |disjunction| |lSpaceBasis| |nextSubsetGray| |LiePolyIfCan| + |genericRightMinimalPolynomial| |arg2| |sech| |linear?| |mainMonomial| + |lyndon?| |cyclicParents| |tan2trig| |leftMult| |direction| + |calcRanges| |factorGroebnerBasis| |d01anf| |csch| |pureLex| |s17dgf| + |localUnquote| |degreePartition| |close| |nthRootIfCan| |viewport3D| + |fortranInteger| |asinh| |conditions| |lowerBound| + |selectAndPolynomials| |externalList| |cyclePartition| |hcrf| + |getOperator| |neglist| |collectUpper| |one?| |prolateSpheroidal| + |toScale| |match| GF2FG |acosh| |contours| |dequeue| |stop| + |fractionFreeGauss!| |clearTable!| |display| |removeSinSq| |bright| + |exprHasLogarithmicWeights| |rightDiscriminant| + |eisensteinIrreducible?| |precision| |atanh| |hitherPlane| + |lowerCase?| |binarySearchTree| |e02adf| |iFTable| |bivariate?| + |OMgetError| |li| |acoth| |bernoulli| |monicLeftDivide| + |viewThetaDefault| |randnum| |cCsch| |upDateBranches| + |intermediateResultsIF| |readable?| |areEquivalent?| |denominators| + |semiResultantEuclidean2| |external?| |asech| |difference| |parabolic| + |setFieldInfo| |cTanh| |coefChoose| |fortranCharacter| |increment| + |nextPrimitiveNormalPoly| |makeSin| |minPoly| |isOp| |acoshIfCan| + |knownInfBasis| |taylorIfCan| |s17def| |nilFactor| |nlde| |multiple| + |noKaratsuba| |tracePowMod| |input| |integer?| |internalZeroSetSplit| + |jacobiIdentity?| |algebraicVariables| |csch2sinh| |applyQuote| + |extendIfCan| |generalPosition| |e01daf| |sn| |powerAssociative?| + |makeVariable| |library| |upperCase!| |newLine| |palgRDE0| + |normalDeriv| |f02awf| |e02akf| |exponential| |in?| |push| |df2ef| + |freeOf?| |unaryFunction| |principal?| |light| |sayLength| |satisfy?| + |e02def| |setFormula!| |anticoord| + |generalizedContinuumHypothesisAssumed| |plenaryPower| |drawCurves| + |monomialIntPoly| |simpson| |ruleset| |semiLastSubResultantEuclidean| + |leadingSupport| |genericLeftNorm| |routines| |pomopo!| |leaf?| + |fractRadix| |box| |normal01| |orbit| |startStats!| |variable?| + |internalIntegrate0| |supRittWu?| |set| |gcdPrimitive| |aLinear| + |LazardQuotient| |iitan| |wholeRadix| |children| |linearPart| |test| + |setLegalFortranSourceExtensions| |id| |writeUInt8!| |hex| |dot| + |conjunction| |iisqrt2| |listOfMonoms| |generalizedEigenvectors| + |suchThat| |repeatUntilLoop| |rk4f| |lprop| |nthFactor| |printInfo!| + |e04fdf| |iibinom| |iiabs| |f01maf| |lyndonIfCan| |table| |empty?| + |gderiv| |s19adf| |numberOfCycles| |expandPower| |any| |sqfrFactor| + |redPol| |fortranLiteral| |leftMinimalPolynomial| |insert| |new| + |back| |nextSublist| |mdeg| |antiAssociative?| |youngGroup| |obj| + |primlimitedint| |normInvertible?| |OMgetInteger| |monic?| + |outputFixed| |unitCanonical| |conjugate| |eq| |monicRightFactorIfCan| + |squareFreePart| |leftPower| |prefix| |myDegree| |cache| |constDsolve| + |zeroOf| |critM| |putColorInfo| |changeVar| |iter| |d01akf| + |factorial| |shiftRight| |showScalarValues| |graphs| |exQuo| |sub| + |fortranLogical| |leftUnits| |delete| |signature| |cycleTail| + |nullary| |generic?| |rewriteIdealWithQuasiMonicGenerators| |basicSet| + |roughEqualIdeals?| |subst| |parseString| |euler| |ratpart| + |infiniteProduct| |lazyIrreducibleFactors| |findConstructor| + |makeTerm| |setVariableOrder| |OMlistSymbols| |nullary?| |limitPlus| + |leviCivitaSymbol| |rotate| |setMaxPoints3D| |genericLeftDiscriminant| + |sizePascalTriangle| |moebius| |curry| |colorFunction| + |expextendedint| |isOpen?| |showAllElements| |directSum| |consnewpol| + |lazyPseudoQuotient| |directory| |script| |ideal| |movedPoints| + |pointColor| |nextItem| |radicalSimplify| |selectPolynomials| + |physicalLength!| |elRow2!| |outlineRender| |rootBound| |firstDenom| + |space| |pushup| |any?| |realZeros| |iterationVar| + |standardBasisOfCyclicSubmodule| |retractIfCan| |uniform01| |argument| + |exptMod| |iiasin| |flatten| |exp| |triangSolve| |central?| |zag| + |irreducibleFactor| |tryFunctionalDecomposition?| |aQuadratic| + |objects| |tex| |halfExtendedResultant1| |norm| |left| |readUInt8!| + |numer| |fixedPoints| |lfextendedint| |upperBound| |polar| + |lieAdmissible?| |genericLeftTraceForm| |base| |/\\| + |removeSuperfluousCases| |d03edf| |right| |sorted?| |outputList| + |denom| |s21bcf| |even?| |nextPrime| |exactQuotient| |move| |getlo| + |\\/| |closedCurve| |probablyZeroDim?| |subQuasiComponent?| + |headRemainder| |continuedFraction| |inRadical?| |pmComplexintegrate| + |SturmHabicht| |numberOfHues| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase 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T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) |has| |#1| (-893 (-384))) ((-893 (-570)) |has| |#1| (-893 (-570))) ((-891 |#1|) . T) ((-916) -12 (|has| |#1| (-311)) (|has| |#1| (-916))) ((-927) -2895 (|has| |#1| (-354)) (|has| |#1| (-368)) (|has| |#1| (-311))) ((-1011) -12 (|has| |#1| (-1011)) (|has| |#1| (-1212))) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1060 #0#) -2895 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1060 |#1|) . T) ((-1060 $) . T) ((-1065 #0#) -2895 (|has| |#1| (-354)) (|has| |#1| (-368))) ((-1065 |#1|) . T) ((-1065 $) . T) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1161) |has| |#1| (-354)) ((-1212) |has| |#1| (-1212)) ((-1215) |has| |#1| (-1212)) ((-1227) . 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T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2892 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2892 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2892 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2892 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2892 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . T) ((-1284 |#2|) |has| |#2| (-368))) -((-3482 (((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 21)) (-3624 ((|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|) 23)) (-1356 (((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)) 18))) -(((-241 |#1| |#2| |#3|) (-10 -7 (-15 -3482 ((-242 |#1| |#3|) (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -3624 (|#3| (-1 |#3| |#2| |#3|) (-242 |#1| |#2|) |#3|)) (-15 -1356 ((-242 |#1| |#3|) (-1 |#3| |#2|) (-242 |#1| |#2|)))) (-777) (-1227) (-1227)) (T -241)) -((-1356 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *7 (-1227)) (-5 *2 (-242 *5 *7)) (-5 *1 (-241 *5 *6 *7)))) (-3624 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-242 *5 *6)) (-14 *5 (-777)) (-4 *6 (-1227)) (-4 *2 (-1227)) (-5 *1 (-241 *5 *6 *2)))) (-3482 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-242 *6 *7)) (-14 *6 (-777)) (-4 *7 (-1227)) (-4 *5 (-1227)) (-5 *2 (-242 *6 *5)) (-5 *1 (-241 *6 *7 *5))))) -(-10 -7 (-15 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|#2| (-1109)))) (((-413 (-570)) $) NIL (-12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109)))) ((|#2| $) 29 (|has| |#2| (-1109)))) (-4196 (((-695 (-570)) (-695 $)) NIL (-12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) (((-2 (|:| -2415 (-695 (-570))) (|:| |vec| (-1277 (-570)))) (-695 $) (-1277 $)) NIL (-12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058)))) (((-2 (|:| -2415 (-695 |#2|)) (|:| |vec| (-1277 |#2|))) (-695 $) (-1277 $)) NIL (|has| |#2| (-1058))) (((-695 |#2|) (-695 $)) NIL (|has| |#2| (-1058)))) (-2875 (((-3 $ "failed") $) 59 (|has| |#2| (-732)))) (-3446 (($) NIL (|has| |#2| (-373)))) (-1517 ((|#2| $ (-570) |#2|) NIL (|has| $ (-6 -4450)))) (-3820 ((|#2| $ (-570)) 57)) (-3903 (((-112) $) NIL (|has| |#2| (-854)))) (-3627 (((-650 |#2|) $) 15 (|has| $ (-6 -4449)))) (-4346 (((-112) $) NIL (|has| |#2| (-732)))) (-1479 (((-112) $) NIL (|has| |#2| (-854)))) (-2929 (((-112) $ (-777)) NIL)) (-2383 (((-570) $) 20 (|has| (-570) (-856)))) (-3466 (($ $ $) NIL (-2892 (|has| |#2| 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(-1058)))) (($ $ (-650 (-1186))) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-1186) (-777)) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-650 (-1186)) (-650 (-777))) NIL (-12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058)))) (($ $ (-1 |#2| |#2|) (-777)) NIL (|has| |#2| (-1058))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1058)))) (-3072 (((-112) $ $) NIL (-2892 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3052 (((-112) $ $) NIL (-2892 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3022 (((-112) $ $) 28 (|has| |#2| (-1109)))) (-3062 (((-112) $ $) NIL (-2892 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3042 (((-112) $ $) 66 (-2892 (|has| |#2| (-799)) (|has| |#2| (-854))))) (-3122 (($ $ |#2|) NIL (|has| |#2| (-368)))) (-3111 (($ $ $) NIL (|has| |#2| (-1058))) (($ $) NIL (|has| |#2| (-1058)))) (-3101 (($ $ $) 35 (|has| |#2| (-25)))) (** (($ $ (-777)) NIL (|has| |#2| (-732))) (($ $ (-928)) NIL (|has| |#2| (-732)))) (* (($ (-570) $) NIL (|has| |#2| (-1058))) (($ $ $) 48 (|has| |#2| (-732))) (($ $ |#2|) 46 (|has| |#2| (-732))) (($ |#2| $) 47 (|has| |#2| (-732))) (($ (-777) $) NIL (|has| |#2| (-132))) (($ (-928) $) NIL (|has| |#2| (-25)))) (-2569 (((-777) $) NIL (|has| $ (-6 -4449))))) +((-3846 (*1 *1 *2) (-12 (-5 *2 (-1277 *4)) (-4 *4 (-1227)) (-4 *1 (-240 *3 *4)))) (-2451 (*1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-240 *3 *4)) (-4 *4 (-1058)) (-4 *4 (-1227)))) (-4266 (*1 *2 *1 *1) (-12 (-4 *1 (-240 *3 *2)) (-4 *2 (-1227)) (-4 *2 (-1058)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-240 *3 *2)) (-4 *2 (-1227)) (-4 *2 (-732)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-240 *3 *2)) (-4 *2 (-1227)) (-4 *2 (-732))))) +(-13 (-610 (-570) |t#2|) (-619 (-1277 |t#2|)) (-10 -8 (-6 -4452) (-15 -3846 ($ (-1277 |t#2|))) (IF (|has| |t#2| (-1109)) (-6 (-417 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1058)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-233 |t#2|)) (-6 (-382 |t#2|)) (-15 -2451 ($ (-928))) (-15 -4266 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-732)) (PROGN (-6 (-732)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-373)) (-6 (-373)) |%noBranch|) (IF (|has| |t#2| (-174)) (PROGN (-6 (-38 |t#2|)) (-6 (-174))) |%noBranch|) (IF (|has| |t#2| (-6 -4449)) (-6 -4449) |%noBranch|) (IF (|has| |t#2| (-854)) (-6 (-854)) |%noBranch|) (IF (|has| |t#2| (-799)) (-6 (-799)) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-1284 |t#2|)) |%noBranch|))) +(((-21) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-23) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-25) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-174)) ((-102) -2895 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2895 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-111 $ $) |has| |#2| (-174)) ((-132) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132))) ((-622 #0=(-413 (-570))) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-622 (-570)) -2895 (|has| |#2| (-1058)) (-12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-622 |#2|) -2895 (|has| |#2| (-1109)) (|has| |#2| (-174))) ((-619 (-868)) -2895 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-619 (-868))) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-619 (-1277 |#2|)) . T) ((-174) |has| |#2| (-174)) ((-233 |#2|) |has| |#2| (-1058)) ((-235) -12 (|has| |#2| (-235)) (|has| |#2| (-1058))) ((-290 #1=(-570) |#2|) . T) ((-292 #1# |#2|) . T) ((-313 |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-373) |has| |#2| (-373)) ((-382 |#2|) |has| |#2| (-1058)) ((-417 |#2|) |has| |#2| (-1109)) ((-495 |#2|) . T) ((-610 #1# |#2|) . T) ((-520 |#2| |#2|) -12 (|has| |#2| (-313 |#2|)) (|has| |#2| (-1109))) ((-652 (-570)) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 |#2|) -2895 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-652 $) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-654 |#2|) -2895 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-654 $) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-646 |#2|) -2895 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-645 (-570)) -12 (|has| |#2| (-645 (-570))) (|has| |#2| (-1058))) ((-645 |#2|) |has| |#2| (-1058)) ((-723 |#2|) -2895 (|has| |#2| (-368)) (|has| |#2| (-174))) ((-732) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-797) |has| |#2| (-854)) ((-798) -2895 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-799) |has| |#2| (-799)) ((-800) -2895 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-801) -2895 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-854) |has| |#2| (-854)) ((-856) -2895 (|has| |#2| (-854)) (|has| |#2| (-799))) ((-907 (-1186)) -12 (|has| |#2| (-907 (-1186))) (|has| |#2| (-1058))) ((-1047 #0#) -12 (|has| |#2| (-1047 (-413 (-570)))) (|has| |#2| (-1109))) ((-1047 (-570)) -12 (|has| |#2| (-1047 (-570))) (|has| |#2| (-1109))) ((-1047 |#2|) |has| |#2| (-1109)) ((-1060 |#2|) -2895 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1060 $) |has| |#2| (-174)) ((-1065 |#2|) -2895 (|has| |#2| (-1058)) (|has| |#2| (-368)) (|has| |#2| (-174))) ((-1065 $) |has| |#2| (-174)) ((-1058) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1067) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-174))) ((-1121) -2895 (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-732)) (|has| |#2| (-174))) ((-1109) -2895 (|has| |#2| (-1109)) (|has| |#2| (-1058)) (|has| |#2| (-854)) (|has| |#2| (-799)) (|has| |#2| (-732)) (|has| |#2| (-373)) (|has| |#2| (-368)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25))) ((-1227) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #0#) -2895 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 |#1|) . T) ((-622 |#2|) . T) ((-622 |#3|) . T) ((-622 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-619 (-868)) . T) ((-174) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| |#1| (-620 (-542))) (|has| |#3| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| |#1| (-620 (-899 (-384)))) (|has| |#3| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| |#1| (-620 (-899 (-570)))) (|has| |#3| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) |has| |#1| (-235)) ((-294) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-313 $) . T) ((-330 |#1| |#4|) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2895 (|has| |#1| (-916)) (|has| |#1| (-458))) ((-520 |#2| |#1|) |has| |#1| (-235)) ((-520 |#2| $) |has| |#1| (-235)) ((-520 |#3| |#1|) . T) ((-520 |#3| $) . T) ((-520 $ $) . T) ((-562) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-652 #0#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#4| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#2|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . 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T) ((-654 #0#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #0#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #0#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458))) ((-732) . T) ((-907 |#3|) . T) ((-893 (-384)) -12 (|has| |#1| (-893 (-384))) (|has| |#3| (-893 (-384)))) ((-893 (-570)) -12 (|has| |#1| (-893 (-570))) (|has| |#3| (-893 (-570)))) ((-956 |#1| |#2| |#3|) . T) ((-916) |has| |#1| (-916)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 |#1|) . T) ((-1047 |#3|) . T) ((-1060 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1065 #0#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . T) ((-1231) |has| |#1| (-916))) +((-2560 (((-112) $ $) NIL)) (-3989 (((-1168) $) NIL)) (-2814 (((-650 (-1144)) $) 18)) (-3580 (((-1129) $) NIL)) (-3802 (((-868) $) 27) (($ (-1191)) NIL) (((-1191) $) NIL)) (-3616 (((-1144) $) 20)) (-3359 (((-112) $ $) NIL)) (-3025 (((-112) $ $) NIL))) +(((-1075) (-13 (-1092) (-10 -8 (-15 -2814 ((-650 (-1144)) $)) (-15 -3616 ((-1144) $))))) (T -1075)) +((-2814 (*1 *2 *1) (-12 (-5 *2 (-650 (-1144))) (-5 *1 (-1075)))) (-3616 (*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1075))))) +(-13 (-1092) (-10 -8 (-15 -2814 ((-650 (-1144)) $)) (-15 -3616 ((-1144) $)))) +((-3721 (((-112) |#3| $) 15)) (-3896 (((-3 $ "failed") |#3| (-928)) 29)) (-1929 (((-3 |#3| "failed") |#3| $) 45)) (-2346 (((-112) |#3| $) 19)) (-2788 (((-112) |#3| $) 17))) +(((-1076 |#1| |#2| |#3|) (-10 -8 (-15 -3896 ((-3 |#1| "failed") |#3| (-928))) (-15 -1929 ((-3 |#3| "failed") |#3| |#1|)) (-15 -2346 ((-112) |#3| |#1|)) (-15 -2788 ((-112) |#3| |#1|)) (-15 -3721 ((-112) |#3| |#1|))) (-1077 |#2| |#3|) (-13 (-854) (-368)) (-1253 |#2|)) (T -1076)) +NIL +(-10 -8 (-15 -3896 ((-3 |#1| "failed") |#3| (-928))) (-15 -1929 ((-3 |#3| "failed") |#3| |#1|)) (-15 -2346 ((-112) |#3| |#1|)) (-15 -2788 ((-112) |#3| |#1|)) (-15 -3721 ((-112) |#3| |#1|))) +((-2560 (((-112) $ $) 7)) (-3721 (((-112) |#2| $) 22)) (-3408 (((-570) |#2| $) 23)) (-3896 (((-3 $ "failed") |#2| (-928)) 16)) (-3157 ((|#1| |#2| $ |#1|) 14)) (-1929 (((-3 |#2| "failed") |#2| $) 19)) (-2346 (((-112) |#2| $) 20)) (-2788 (((-112) |#2| $) 21)) (-3989 (((-1168) $) 10)) (-3580 (((-1129) $) 11)) (-2075 ((|#2| $) 18)) (-3802 (((-868) $) 12)) (-3359 (((-112) $ $) 9)) (-3170 ((|#1| |#2| $ |#1|) 15)) (-4017 (((-650 $) |#2|) 17)) (-3025 (((-112) $ $) 6))) (((-1077 |#1| |#2|) (-141) (-13 (-854) (-368)) (-1253 |t#1|)) (T -1077)) -((-4395 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-570)))) (-3467 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-1479 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-3903 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-2875 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) (-4 *2 (-1253 *3)))) (-2755 (*1 *2 *1) (-12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) (-4 *2 (-1253 *3)))) (-3043 (*1 *2 *3) (-12 (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-650 *1)) (-4 *1 (-1077 *4 *3)))) (-1979 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-928)) (-4 *4 (-13 (-854) (-368))) (-4 *1 (-1077 *4 *2)) (-4 *2 (-1253 *4)))) (-3167 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1077 *2 *3)) (-4 *2 (-13 (-854) (-368))) (-4 *3 (-1253 *2)))) (-1701 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1077 *2 *3)) (-4 *2 (-13 (-854) (-368))) (-4 *3 (-1253 *2))))) -(-13 (-1109) (-10 -8 (-15 -4395 ((-570) |t#2| $)) (-15 -3467 ((-112) |t#2| $)) (-15 -1479 ((-112) |t#2| $)) (-15 -3903 ((-112) |t#2| $)) (-15 -2875 ((-3 |t#2| "failed") |t#2| $)) (-15 -2755 (|t#2| $)) (-15 -3043 ((-650 $) |t#2|)) (-15 -1979 ((-3 $ "failed") |t#2| (-928))) (-15 -3167 (|t#1| |t#2| $ |t#1|)) (-15 -1701 (|t#1| |t#2| $ |t#1|)))) +((-3408 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-570)))) (-3721 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-2788 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-2346 (*1 *2 *3 *1) (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-112)))) (-1929 (*1 *2 *2 *1) (|partial| -12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) (-4 *2 (-1253 *3)))) (-2075 (*1 *2 *1) (-12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) (-4 *2 (-1253 *3)))) (-4017 (*1 *2 *3) (-12 (-4 *4 (-13 (-854) (-368))) (-4 *3 (-1253 *4)) (-5 *2 (-650 *1)) (-4 *1 (-1077 *4 *3)))) (-3896 (*1 *1 *2 *3) (|partial| -12 (-5 *3 (-928)) (-4 *4 (-13 (-854) (-368))) (-4 *1 (-1077 *4 *2)) (-4 *2 (-1253 *4)))) (-3170 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1077 *2 *3)) (-4 *2 (-13 (-854) (-368))) (-4 *3 (-1253 *2)))) (-3157 (*1 *2 *3 *1 *2) (-12 (-4 *1 (-1077 *2 *3)) (-4 *2 (-13 (-854) (-368))) (-4 *3 (-1253 *2))))) +(-13 (-1109) (-10 -8 (-15 -3408 ((-570) |t#2| $)) (-15 -3721 ((-112) |t#2| $)) (-15 -2788 ((-112) |t#2| $)) (-15 -2346 ((-112) |t#2| $)) (-15 -1929 ((-3 |t#2| "failed") |t#2| $)) (-15 -2075 (|t#2| $)) (-15 -4017 ((-650 $) |t#2|)) (-15 -3896 ((-3 $ "failed") |t#2| (-928))) (-15 -3170 (|t#1| |t#2| $ |t#1|)) (-15 -3157 (|t#1| |t#2| $ |t#1|)))) (((-102) . 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T) ((-652 |#1|) . T) ((-652 |#2|) |has| |#1| (-368)) ((-652 $) . T) ((-654 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-654 |#1|) . T) ((-654 |#2|) |has| |#1| (-368)) ((-654 $) . T) ((-646 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-646 |#1|) |has| |#1| (-174)) ((-646 |#2|) |has| |#1| (-368)) ((-646 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-645 (-570)) -12 (|has| |#1| (-368)) (|has| |#2| (-645 (-570)))) ((-645 |#2|) |has| |#1| (-368)) ((-723 #1#) -2892 (|has| |#1| (-368)) (|has| |#1| (-38 (-413 (-570))))) ((-723 |#1|) |has| |#1| (-174)) ((-723 |#2|) |has| |#1| (-368)) ((-723 $) -2892 (|has| |#1| (-562)) (|has| |#1| (-368))) ((-732) . 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T) ((-23) . T) ((-47 |#1| #0=(-777)) . T) ((-25) . T) ((-38 #1=(-413 (-570))) |has| |#1| (-38 (-413 (-570)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-413 (-570)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-622 #1#) -2895 (|has| |#1| (-1047 (-413 (-570)))) (|has| |#1| (-38 (-413 (-570))))) ((-622 (-570)) . T) ((-622 #2=(-1091)) . T) ((-622 |#1|) . T) ((-622 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-619 (-868)) . T) ((-174) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-620 (-542)) -12 (|has| (-1091) (-620 (-542))) (|has| |#1| (-620 (-542)))) ((-620 (-899 (-384))) -12 (|has| (-1091) (-620 (-899 (-384)))) (|has| |#1| (-620 (-899 (-384))))) ((-620 (-899 (-570))) -12 (|has| (-1091) (-620 (-899 (-570)))) (|has| |#1| (-620 (-899 (-570))))) ((-233 |#1|) . T) ((-235) . T) ((-290 (-413 $) (-413 $)) |has| |#1| (-562)) ((-290 |#1| |#1|) . T) ((-290 $ $) . T) ((-294) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-311) |has| |#1| (-368)) ((-313 $) . T) ((-330 |#1| #0#) . T) ((-382 |#1|) . T) ((-417 |#1|) . T) ((-458) -2895 (|has| |#1| (-916)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-520 #2# |#1|) . T) ((-520 #2# $) . T) ((-520 $ $) . T) ((-562) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-652 #1#) |has| |#1| (-38 (-413 (-570)))) ((-652 (-570)) . T) ((-652 |#1|) . T) ((-652 $) . T) ((-654 #1#) |has| |#1| (-38 (-413 (-570)))) ((-654 |#1|) . T) ((-654 $) . T) ((-646 #1#) |has| |#1| (-38 (-413 (-570)))) ((-646 |#1|) |has| |#1| (-174)) ((-646 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-645 (-570)) |has| |#1| (-645 (-570))) ((-645 |#1|) . T) ((-723 #1#) |has| |#1| (-38 (-413 (-570)))) ((-723 |#1|) |has| |#1| (-174)) ((-723 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368))) ((-732) . T) ((-907 #2#) . T) ((-907 (-1186)) |has| |#1| (-907 (-1186))) ((-893 (-384)) -12 (|has| (-1091) (-893 (-384))) (|has| |#1| (-893 (-384)))) ((-893 (-570)) -12 (|has| (-1091) (-893 (-570))) (|has| |#1| (-893 (-570)))) ((-956 |#1| #0# #2#) . T) ((-916) |has| |#1| (-916)) ((-927) |has| |#1| (-368)) ((-1047 (-413 (-570))) |has| |#1| (-1047 (-413 (-570)))) ((-1047 (-570)) |has| |#1| (-1047 (-570))) ((-1047 #2#) . T) ((-1047 |#1|) . T) ((-1060 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1060 |#1|) . T) ((-1060 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1065 #1#) |has| |#1| (-38 (-413 (-570)))) ((-1065 |#1|) . T) ((-1065 $) -2895 (|has| |#1| (-916)) (|has| |#1| (-562)) (|has| |#1| (-458)) (|has| |#1| (-368)) (|has| |#1| (-174))) ((-1058) . T) ((-1067) . T) ((-1121) . T) ((-1109) . 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2911994 2912135 "TRIGCAT-" 2912140 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908760 2910773 2911054 "TREE" 2911669 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908034 2908562 2908592 "TRANFUN" 2908627 T TRANFUN (NIL) -9 NIL 2908693 NIL) (-1211 2907313 2907504 2907784 "TRANFUN-" 2907789 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907117 2907149 2907210 "TOPSP" 2907274 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906465 2906580 2906734 "TOOLSIGN" 2906998 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905099 2905642 2905881 "TEXTFILE" 2906248 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903011 2903552 2903981 "TEX" 2904692 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902792 2902823 2902895 "TEX1" 2902974 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902440 2902503 2902593 "TEMUTL" 2902724 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900594 2900874 2901199 "TBCMPPK" 2902163 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892371 2898754 2898810 "TBAGG" 2899210 NIL TBAGG (NIL T T) -9 NIL 2899421 NIL) (-1202 2887441 2888929 2890683 "TBAGG-" 2890688 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886825 2886932 2887077 "TANEXP" 2887330 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886336 2886600 2886690 "TALGOP" 2886770 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879726 2886193 2886286 "TABLE" 2886291 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879138 2879237 2879375 "TABLEAU" 2879623 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873746 2874966 2876214 "TABLBUMP" 2877924 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872968 2873115 2873296 "SYSTEM" 2873587 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869427 2870126 2870909 "SYSSOLP" 2872219 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869225 2869382 2869413 "SYSPTR" 2869418 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868269 2868774 2868893 "SYSNNI" 2869079 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869164) (-1192 2867576 2868035 2868114 "SYSINT" 2868174 NIL SYSINT (NIL NIL) -8 NIL NIL 2868219) (-1191 2863908 2864854 2865564 "SYNTAX" 2866888 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861066 2861668 2862300 "SYMTAB" 2863298 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856315 2857217 2858200 "SYMS" 2860105 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853550 2855773 2856003 "SYMPOLY" 2856120 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853067 2853142 2853265 "SYMFUNC" 2853462 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849087 2850379 2851192 "SYMBOL" 2852276 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842626 2844315 2846035 "SWITCH" 2847389 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835860 2841447 2841750 "SUTS" 2842381 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827926 2835107 2835380 "SUPXS" 2835645 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819685 2827544 2827670 "SUP" 2827835 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818844 2818971 2819188 "SUPFRACF" 2819553 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818465 2818524 2818637 "SUP2" 2818779 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816913 2817187 2817543 "SUMRF" 2818164 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816248 2816314 2816506 "SUMFS" 2816834 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800215 2815425 2815676 "SULS" 2816055 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799817 2800037 2800107 "SUCHTAST" 2800167 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799112 2799342 2799482 "SUCH" 2799725 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792979 2794018 2794977 "SUBSPACE" 2798200 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792409 2792499 2792663 "SUBRESP" 2792867 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785777 2787074 2788385 "STTF" 2791145 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779950 2781070 2782217 "STTFNC" 2784677 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771263 2773132 2774926 "STTAYLOR" 2778191 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764393 2771127 2771210 "STRTBL" 2771215 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759757 2764348 2764379 "STRING" 2764384 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754618 2759130 2759160 "STRICAT" 2759219 T STRICAT (NIL) -9 NIL 2759281 NIL) (-1166 2747371 2752237 2752848 "STREAM" 2754042 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746881 2746958 2747102 "STREAM3" 2747288 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745863 2746046 2746281 "STREAM2" 2746694 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745551 2745603 2745696 "STREAM1" 2745805 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744567 2744748 2744979 "STINPROD" 2745367 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744119 2744329 2744359 "STEP" 2744439 T STEP (NIL) -9 NIL 2744517 NIL) (-1160 2743306 2743608 2743756 "STEPAST" 2743993 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736738 2743205 2743282 "STBL" 2743287 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731864 2735959 2736002 "STAGG" 2736155 NIL STAGG (NIL T) -9 NIL 2736244 NIL) (-1157 2729566 2730168 2731040 "STAGG-" 2731045 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727713 2729336 2729428 "STACK" 2729509 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720408 2725854 2726310 "SREGSET" 2727343 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712833 2714202 2715715 "SRDCMPK" 2719014 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705750 2710273 2710303 "SRAGG" 2711606 T SRAGG (NIL) -9 NIL 2712214 NIL) (-1152 2704767 2705022 2705401 "SRAGG-" 2705406 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699227 2703714 2704135 "SQMATRIX" 2704393 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692912 2695945 2696672 "SPLTREE" 2698572 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688875 2689568 2690214 "SPLNODE" 2692338 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687922 2688155 2688185 "SPFCAT" 2688629 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686659 2686869 2687133 "SPECOUT" 2687680 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677769 2679641 2679671 "SPADXPT" 2684347 T SPADXPT (NIL) -9 NIL 2686511 NIL) (-1145 2677530 2677570 2677639 "SPADPRSR" 2677722 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675579 2677485 2677516 "SPADAST" 2677521 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667524 2669297 2669340 "SPACEC" 2673713 NIL SPACEC (NIL T) -9 NIL 2675529 NIL) (-1142 2665654 2667456 2667505 "SPACE3" 2667510 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664406 2664577 2664868 "SORTPAK" 2665459 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662498 2662801 2663213 "SOLVETRA" 2664070 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661548 2661770 2662031 "SOLVESER" 2662271 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656852 2657740 2658735 "SOLVERAD" 2660600 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652667 2653276 2654005 "SOLVEFOR" 2656219 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646937 2652016 2652113 "SNTSCAT" 2652118 NIL SNTSCAT (NIL T T T T) -9 NIL 2652188 NIL) (-1135 2641043 2645260 2645651 "SMTS" 2646627 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635728 2640931 2641008 "SMP" 2641013 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633887 2634188 2634586 "SMITH" 2635425 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626600 2630796 2630899 "SMATCAT" 2632250 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632800 NIL) (-1131 2623540 2624363 2625541 "SMATCAT-" 2625546 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621206 2622776 2622819 "SKAGG" 2623080 NIL SKAGG (NIL T) -9 NIL 2623215 NIL) (-1129 2617532 2620679 2620863 "SINT" 2621015 T SINT (NIL) -8 NIL NIL 2621177) (-1128 2617304 2617342 2617408 "SIMPAN" 2617488 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616583 2616839 2616979 "SIG" 2617186 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615421 2615642 2615917 "SIGNRF" 2616342 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614254 2614405 2614689 "SIGNEF" 2615250 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613560 2613837 2613961 "SIGAST" 2614152 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611250 2611704 2612210 "SHP" 2613101 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605102 2611151 2611227 "SHDP" 2611232 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604675 2604867 2604897 "SGROUP" 2604990 T SGROUP (NIL) -9 NIL 2605052 NIL) (-1120 2604533 2604559 2604632 "SGROUP-" 2604637 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601324 2602022 2602745 "SGCF" 2603832 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595692 2600771 2600868 "SFRTCAT" 2600873 NIL SFRTCAT (NIL T T T T) -9 NIL 2600912 NIL) (-1117 2589113 2590131 2591267 "SFRGCD" 2594675 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582239 2583312 2584498 "SFQCMPK" 2588046 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581859 2581948 2582059 "SFORT" 2582180 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580977 2581699 2581820 "SEXOF" 2581825 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580084 2580858 2580926 "SEX" 2580931 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575597 2576312 2576407 "SEXCAT" 2579344 NIL SEXCAT (NIL T T T T T) -9 NIL 2579922 NIL) (-1111 2572750 2575531 2575579 "SET" 2575584 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570974 2571463 2571768 "SETMN" 2572491 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570470 2570622 2570652 "SETCAT" 2570828 T SETCAT (NIL) -9 NIL 2570938 NIL) (-1108 2570162 2570240 2570370 "SETCAT-" 2570375 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566523 2568623 2568666 "SETAGG" 2569536 NIL SETAGG (NIL T) -9 NIL 2569876 NIL) (-1106 2565981 2566097 2566334 "SETAGG-" 2566339 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565424 2565677 2565778 "SEQAST" 2565902 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564623 2564917 2564978 "SEGXCAT" 2565264 NIL SEGXCAT (NIL T T) -9 NIL 2565384 NIL) (-1103 2563629 2564289 2564471 "SEG" 2564476 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562608 2562822 2562865 "SEGCAT" 2563387 NIL SEGCAT (NIL T) -9 NIL 2563608 NIL) (-1101 2561540 2561971 2562179 "SEGBIND" 2562435 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561161 2561220 2561333 "SEGBIND2" 2561475 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560734 2560962 2561039 "SEGAST" 2561106 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559953 2560079 2560283 "SEG2" 2560578 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559363 2559888 2559935 "SDVAR" 2559940 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551890 2559133 2559263 "SDPOL" 2559268 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550483 2550749 2551068 "SCPKG" 2551605 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549647 2549819 2550011 "SCOPE" 2550313 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548867 2549001 2549180 "SCACHE" 2549502 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548513 2548699 2548729 "SASTCAT" 2548734 T SASTCAT (NIL) -9 NIL 2548747 NIL) (-1091 2548000 2548348 2548424 "SAOS" 2548459 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547565 2547600 2547773 "SAERFFC" 2547959 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541504 2547462 2547542 "SAE" 2547547 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541097 2541132 2541291 "SAEFACT" 2541463 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539418 2539732 2540133 "RURPK" 2540763 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538055 2538361 2538666 "RULESET" 2539252 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535278 2535808 2536266 "RULE" 2537736 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534890 2535072 2535155 "RULECOLD" 2535230 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534680 2534708 2534779 "RTVALUE" 2534841 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534151 2534397 2534491 "RSTRCAST" 2534608 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528999 2529794 2530714 "RSETGCD" 2533350 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518229 2523308 2523405 "RSETCAT" 2527524 NIL RSETCAT (NIL T T T T) -9 NIL 2528621 NIL) (-1079 2516156 2516695 2517519 "RSETCAT-" 2517524 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508542 2509918 2511438 "RSDCMPK" 2514755 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506521 2506988 2507062 "RRCC" 2508148 NIL RRCC (NIL T T) -9 NIL 2508492 NIL) (-1076 2505872 2506046 2506325 "RRCC-" 2506330 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505315 2505568 2505669 "RPTAST" 2505793 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479161 2488520 2488587 "RPOLCAT" 2499253 NIL RPOLCAT (NIL T T T) -9 NIL 2502413 NIL) (-1073 2470659 2472999 2476121 "RPOLCAT-" 2476126 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461590 2468870 2469352 "ROUTINE" 2470199 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458388 2461216 2461356 "ROMAN" 2461472 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456632 2457248 2457508 "ROIRC" 2458193 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452864 2455148 2455178 "RNS" 2455482 T RNS (NIL) -9 NIL 2455756 NIL) (-1068 2451373 2451756 2452290 "RNS-" 2452365 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450776 2451184 2451214 "RNG" 2451219 T RNG (NIL) -9 NIL 2451240 NIL) (-1066 2449779 2450141 2450343 "RNGBIND" 2450627 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449178 2449566 2449609 "RMODULE" 2449614 NIL RMODULE (NIL T) -9 NIL 2449641 NIL) (-1064 2448014 2448108 2448444 "RMCAT2" 2449079 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444864 2447360 2447657 "RMATRIX" 2447776 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437691 2439951 2440066 "RMATCAT" 2443425 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444407 NIL) (-1061 2437066 2437213 2437520 "RMATCAT-" 2437525 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436467 2436688 2436731 "RLINSET" 2436925 NIL RLINSET (NIL T) -9 NIL 2437016 NIL) (-1059 2436034 2436109 2436237 "RINTERP" 2436386 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435092 2435646 2435676 "RING" 2435732 T RING (NIL) -9 NIL 2435824 NIL) (-1057 2434884 2434928 2435025 "RING-" 2435030 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433725 2433962 2434220 "RIDIST" 2434648 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425014 2433193 2433399 "RGCHAIN" 2433573 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424364 2424770 2424811 "RGBCSPC" 2424869 NIL RGBCSPC (NIL T) -9 NIL 2424921 NIL) (-1053 2423522 2423903 2423944 "RGBCMDL" 2424176 NIL RGBCMDL (NIL T) -9 NIL 2424290 NIL) (-1052 2420516 2421130 2421800 "RF" 2422886 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420162 2420225 2420328 "RFFACTOR" 2420447 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419887 2419922 2420019 "RFFACT" 2420121 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418004 2418368 2418750 "RFDIST" 2419527 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417457 2417549 2417712 "RETSOL" 2417906 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417093 2417173 2417216 "RETRACT" 2417349 NIL RETRACT (NIL T) -9 NIL 2417436 NIL) (-1046 2416942 2416967 2417054 "RETRACT-" 2417059 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416544 2416764 2416834 "RETAST" 2416894 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409282 2416197 2416324 "RESULT" 2416439 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407873 2408551 2408750 "RESRING" 2409185 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407509 2407558 2407656 "RESLATC" 2407810 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407214 2407249 2407356 "REPSQ" 2407468 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404636 2405216 2405818 "REP" 2406634 T REP (NIL) -7 NIL NIL NIL) (-1039 2404333 2404368 2404479 "REPDB" 2404595 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398233 2399622 2400845 "REP2" 2403145 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394610 2395291 2396099 "REP1" 2397460 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387306 2392751 2393207 "REGSET" 2394240 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386071 2386454 2386704 "REF" 2387091 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385448 2385551 2385718 "REDORDER" 2385955 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381416 2384661 2384888 "RECLOS" 2385276 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380468 2380649 2380864 "REALSOLV" 2381223 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380314 2380355 2380385 "REAL" 2380390 T REAL (NIL) -9 NIL 2380425 NIL) (-1030 2376797 2377599 2378483 "REAL0Q" 2379479 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372398 2373386 2374447 "REAL0" 2375778 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371869 2372115 2372209 "RDUCEAST" 2372326 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 2371274 2371346 2371553 "RDIV" 2371791 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1026 2370342 2370516 2370729 "RDIST" 2371096 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1025 2368939 2369226 2369598 "RDETRS" 2370050 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1024 2366751 2367205 2367743 "RDETR" 2368481 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1023 2365376 2365654 2366051 "RDEEFS" 2366467 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1022 2363885 2364191 2364616 "RDEEF" 2365064 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1021 2357946 2360866 2360896 "RCFIELD" 2362191 T RCFIELD (NIL) -9 NIL 2362922 NIL) (-1020 2356010 2356514 2357210 "RCFIELD-" 2357285 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1019 2352279 2354111 2354154 "RCAGG" 2355238 NIL RCAGG (NIL T) -9 NIL 2355703 NIL) (-1018 2351907 2352001 2352164 "RCAGG-" 2352169 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1017 2351242 2351354 2351519 "RATRET" 2351791 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1016 2350795 2350862 2350983 "RATFACT" 2351170 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1015 2350103 2350223 2350375 "RANDSRC" 2350665 T RANDSRC (NIL) -7 NIL NIL NIL) (-1014 2349837 2349881 2349954 "RADUTIL" 2350052 T RADUTIL (NIL) -7 NIL NIL NIL) (-1013 2342951 2348668 2348979 "RADIX" 2349560 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1012 2334570 2342793 2342923 "RADFF" 2342928 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1011 2334217 2334292 2334322 "RADCAT" 2334482 T RADCAT (NIL) -9 NIL NIL NIL) (-1010 2333999 2334047 2334147 "RADCAT-" 2334152 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1009 2332097 2333769 2333861 "QUEUE" 2333942 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1008 2328634 2332030 2332078 "QUAT" 2332083 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1007 2328265 2328308 2328439 "QUATCT2" 2328585 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2321714 2325059 2325101 "QUATCAT" 2325892 NIL QUATCAT (NIL T) -9 NIL 2326658 NIL) (-1005 2317853 2318890 2320280 "QUATCAT-" 2320376 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1004 2315318 2316929 2316972 "QUAGG" 2317353 NIL QUAGG (NIL T) -9 NIL 2317528 NIL) (-1003 2314920 2315140 2315210 "QQUTAST" 2315270 T QQUTAST (NIL) -8 NIL NIL NIL) (-1002 2313813 2314313 2314487 "QFORM" 2314792 NIL QFORM (NIL NIL T) -8 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NIL NIL NIL) (-859 1990860 1991360 1991921 "OREPCTO" 1992821 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984546 1986747 1986788 "OREPCAT" 1989136 NIL OREPCAT (NIL T) -9 NIL 1990240 NIL) (-857 1981693 1982475 1983533 "OREPCAT-" 1983538 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980844 1981142 1981170 "ORDSET" 1981479 T ORDSET (NIL) -9 NIL 1981643 NIL) (-855 1980275 1980423 1980647 "ORDSET-" 1980652 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978840 1979631 1979659 "ORDRING" 1979861 T ORDRING (NIL) -9 NIL 1979986 NIL) (-853 1978485 1978579 1978723 "ORDRING-" 1978728 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977865 1978328 1978356 "ORDMON" 1978361 T ORDMON (NIL) -9 NIL 1978382 NIL) (-851 1977027 1977174 1977369 "ORDFUNS" 1977714 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976365 1976784 1976812 "ORDFIN" 1976877 T ORDFIN (NIL) -9 NIL 1976951 NIL) (-849 1972924 1974951 1975360 "ORDCOMP" 1975989 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972190 1972317 1972503 "ORDCOMP2" 1972784 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968771 1969681 1970495 "OPTPROB" 1971396 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965573 1966212 1966916 "OPTPACK" 1968087 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963260 1964026 1964054 "OPTCAT" 1964873 T OPTCAT (NIL) -9 NIL 1965523 NIL) (-844 1962644 1962937 1963042 "OPSIG" 1963175 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962412 1962451 1962517 "OPQUERY" 1962598 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959543 1960723 1961227 "OP" 1961941 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958917 1959143 1959184 "OPERCAT" 1959396 NIL OPERCAT (NIL T) -9 NIL 1959493 NIL) (-840 1958672 1958728 1958845 "OPERCAT-" 1958850 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955485 1957469 1957838 "ONECOMP" 1958336 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954790 1954905 1955079 "ONECOMP2" 1955357 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954209 1954315 1954445 "OMSERVER" 1954680 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951071 1953649 1953689 "OMSAGG" 1953750 NIL OMSAGG (NIL T) -9 NIL 1953814 NIL) (-835 1949694 1949957 1950239 "OMPKG" 1950809 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949124 1949227 1949255 "OM" 1949554 T OM (NIL) -9 NIL NIL NIL) (-833 1947671 1948673 1948842 "OMLO" 1949005 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946631 1946778 1946998 "OMEXPR" 1947497 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945922 1946177 1946313 "OMERR" 1946515 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945073 1945343 1945503 "OMERRK" 1945782 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944524 1944750 1944858 "OMENC" 1944985 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938419 1939604 1940775 "OMDEV" 1943373 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937488 1937659 1937853 "OMCONN" 1938245 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936009 1936985 1937013 "OINTDOM" 1937018 T OINTDOM (NIL) -9 NIL 1937039 NIL) (-825 1933347 1934697 1935034 "OFMONOID" 1935704 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932758 1933284 1933329 "ODVAR" 1933334 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930181 1932503 1932658 "ODR" 1932663 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922762 1929957 1930083 "ODPOL" 1930088 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916584 1922634 1922739 "ODP" 1922744 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915350 1915565 1915840 "ODETOOLS" 1916358 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912317 1912975 1913691 "ODESYS" 1914683 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907199 1908107 1909132 "ODERTRIC" 1911392 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906625 1906707 1906901 "ODERED" 1907111 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903513 1904061 1904738 "ODERAT" 1906048 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900472 1900937 1901534 "ODEPRRIC" 1903042 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898415 1899011 1899497 "ODEPROB" 1900006 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894935 1895420 1896067 "ODEPRIM" 1897894 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894184 1894286 1894546 "ODEPAL" 1894827 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890346 1891137 1892001 "ODEPACK" 1893340 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889407 1889514 1889736 "ODEINT" 1890235 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883508 1884933 1886380 "ODEIFTBL" 1887980 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878906 1879692 1880644 "ODEEF" 1882667 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878255 1878344 1878567 "ODECONST" 1878811 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876380 1877041 1877069 "ODECAT" 1877674 T ODECAT (NIL) -9 NIL 1878205 NIL) (-805 1873235 1876085 1876207 "OCT" 1876290 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872873 1872916 1873043 "OCTCT2" 1873186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867522 1869957 1869997 "OC" 1871094 NIL OC (NIL T) -9 NIL 1871952 NIL) (-802 1864749 1865497 1866487 "OC-" 1866581 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864101 1864569 1864597 "OCAMON" 1864602 T OCAMON (NIL) -9 NIL 1864623 NIL) (-800 1863632 1863973 1864001 "OASGP" 1864006 T OASGP (NIL) -9 NIL 1864026 NIL) (-799 1862893 1863382 1863410 "OAMONS" 1863450 T OAMONS (NIL) -9 NIL 1863493 NIL) (-798 1862307 1862740 1862768 "OAMON" 1862773 T OAMON (NIL) -9 NIL 1862793 NIL) (-797 1861565 1862083 1862111 "OAGROUP" 1862116 T OAGROUP (NIL) -9 NIL 1862136 NIL) (-796 1861255 1861305 1861393 "NUMTUBE" 1861509 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854828 1856346 1857882 "NUMQUAD" 1859739 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850584 1851572 1852597 "NUMODE" 1853823 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847939 1848819 1848847 "NUMINT" 1849770 T NUMINT (NIL) -9 NIL 1850534 NIL) (-792 1846887 1847084 1847302 "NUMFMT" 1847741 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833246 1836191 1838723 "NUMERIC" 1844394 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827616 1832695 1832790 "NTSCAT" 1832795 NIL NTSCAT (NIL T T T T) -9 NIL 1832834 NIL) (-789 1826810 1826975 1827168 "NTPOLFN" 1827455 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814887 1823635 1824447 "NSUP" 1826031 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814519 1814576 1814685 "NSUP2" 1814824 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804745 1814293 1814426 "NSMP" 1814431 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803177 1803478 1803835 "NREP" 1804433 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801768 1802020 1802378 "NPCOEF" 1802920 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800834 1800949 1801165 "NORMRETR" 1801649 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798875 1799165 1799574 "NORMPK" 1800542 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798560 1798588 1798712 "NORMMA" 1798841 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798360 1798517 1798546 "NONE" 1798551 T NONE (NIL) -8 NIL NIL NIL) (-779 1798149 1798178 1798247 "NONE1" 1798324 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797646 1797708 1797887 "NODE1" 1798081 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795931 1796782 1797037 "NNI" 1797384 T NNI (NIL) -8 NIL NIL 1797619) (-776 1794351 1794664 1795028 "NLINSOL" 1795599 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790592 1791587 1792486 "NIPROB" 1793472 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789349 1789583 1789885 "NFINTBAS" 1790354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788523 1788999 1789040 "NETCLT" 1789212 NIL NETCLT (NIL T) -9 NIL 1789294 NIL) (-772 1787231 1787462 1787743 "NCODIV" 1788291 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786993 1787030 1787105 "NCNTFRAC" 1787188 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785173 1785537 1785957 "NCEP" 1786618 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784024 1784797 1784825 "NASRING" 1784935 T NASRING (NIL) -9 NIL 1785015 NIL) (-768 1783819 1783863 1783957 "NASRING-" 1783962 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782926 1783451 1783479 "NARNG" 1783596 T NARNG (NIL) -9 NIL 1783687 NIL) (-766 1782618 1782685 1782819 "NARNG-" 1782824 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781497 1781704 1781939 "NAGSP" 1782403 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772769 1774453 1776126 "NAGS" 1779844 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771317 1771625 1771956 "NAGF07" 1772458 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765855 1767146 1768453 "NAGF04" 1770030 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758823 1760437 1762070 "NAGF02" 1764242 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754047 1755147 1756264 "NAGF01" 1757726 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747675 1749241 1750826 "NAGE04" 1752482 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738844 1740965 1743095 "NAGE02" 1745565 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734797 1735744 1736708 "NAGE01" 1737900 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732592 1733126 1733684 "NAGD03" 1734259 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724342 1726270 1728224 "NAGD02" 1730658 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718153 1719578 1721018 "NAGD01" 1722922 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714362 1715184 1716021 "NAGC06" 1717336 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712827 1713159 1713515 "NAGC05" 1714026 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712203 1712322 1712466 "NAGC02" 1712703 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711162 1711745 1711785 "NAALG" 1711864 NIL NAALG (NIL T) -9 NIL 1711925 NIL) (-749 1710997 1711026 1711116 "NAALG-" 1711121 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704947 1706055 1707242 "MULTSQFR" 1709893 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704266 1704341 1704525 "MULTFACT" 1704859 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696990 1700903 1700956 "MTSCAT" 1702026 NIL MTSCAT (NIL T T) -9 NIL 1702541 NIL) (-745 1696702 1696756 1696848 "MTHING" 1696930 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696494 1696527 1696587 "MSYSCMD" 1696662 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692576 1695249 1695569 "MSET" 1696207 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689645 1692137 1692178 "MSETAGG" 1692183 NIL MSETAGG (NIL T) -9 NIL 1692217 NIL) (-741 1685487 1687024 1687769 "MRING" 1688945 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685053 1685120 1685251 "MRF2" 1685414 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684671 1684706 1684850 "MRATFAC" 1685012 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682283 1682578 1683009 "MPRFF" 1684376 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676580 1682137 1682234 "MPOLY" 1682239 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676070 1676105 1676313 "MPCPF" 1676539 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675584 1675627 1675811 "MPC3" 1676021 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674779 1674860 1675081 "MPC2" 1675499 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673080 1673417 1673807 "MONOTOOL" 1674439 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672305 1672622 1672650 "MONOID" 1672869 T MONOID (NIL) -9 NIL 1673016 NIL) (-731 1671851 1671970 1672151 "MONOID-" 1672156 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662326 1668277 1668336 "MONOGEN" 1669010 NIL MONOGEN (NIL T T) -9 NIL 1669466 NIL) (-729 1659544 1660279 1661279 "MONOGEN-" 1661398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658377 1658823 1658851 "MONADWU" 1659243 T MONADWU (NIL) -9 NIL 1659481 NIL) (-727 1657749 1657908 1658156 "MONADWU-" 1658161 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657108 1657352 1657380 "MONAD" 1657587 T MONAD (NIL) -9 NIL 1657699 NIL) (-725 1656793 1656871 1657003 "MONAD-" 1657008 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655082 1655706 1655985 "MOEBIUS" 1656546 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654360 1654764 1654804 "MODULE" 1654809 NIL MODULE (NIL T) -9 NIL 1654848 NIL) (-722 1653928 1654024 1654214 "MODULE-" 1654219 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651608 1652292 1652619 "MODRING" 1653752 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648552 1649713 1650234 "MODOP" 1651137 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647140 1647619 1647896 "MODMONOM" 1648415 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637184 1645431 1645845 "MODMON" 1646777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634340 1636028 1636304 "MODFIELD" 1637059 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633317 1633621 1633811 "MMLFORM" 1634170 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632843 1632886 1633065 "MMAP" 1633268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630922 1631689 1631730 "MLO" 1632153 NIL MLO (NIL T) -9 NIL 1632395 NIL) (-713 1628288 1628804 1629406 "MLIFT" 1630403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627679 1627763 1627917 "MKUCFUNC" 1628199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627278 1627348 1627471 "MKRECORD" 1627602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626325 1626487 1626715 "MKFUNC" 1627089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625713 1625817 1625973 "MKFLCFN" 1626208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624990 1625092 1625277 "MKBCFUNC" 1625606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621697 1624544 1624680 "MINT" 1624874 T MINT (NIL) -8 NIL NIL NIL) (-706 1620509 1620752 1621029 "MHROWRED" 1621452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615889 1619044 1619449 "MFLOAT" 1620124 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615246 1615322 1615493 "MFINFACT" 1615801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611561 1612409 1613293 "MESH" 1614382 T MESH (NIL) -7 NIL NIL NIL) (-702 1609951 1610263 1610616 "MDDFACT" 1611248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606746 1609110 1609151 "MDAGG" 1609406 NIL MDAGG (NIL T) -9 NIL 1609549 NIL) (-700 1596486 1606039 1606246 "MCMPLX" 1606559 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595623 1595769 1595970 "MCDEN" 1596335 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593513 1593783 1594163 "MCALCFN" 1595353 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592438 1592678 1592911 "MAYBE" 1593319 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590050 1590573 1591135 "MATSTOR" 1591909 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586007 1589422 1589670 "MATRIX" 1589835 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581773 1582480 1583216 "MATLIN" 1585364 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571879 1575065 1575142 "MATCAT" 1580022 NIL MATCAT (NIL T T T) -9 NIL 1581439 NIL) (-692 1568235 1569256 1570612 "MATCAT-" 1570617 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566829 1566982 1567315 "MATCAT2" 1568070 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564941 1565265 1565649 "MAPPKG3" 1566504 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563922 1564095 1564317 "MAPPKG2" 1564765 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562421 1562705 1563032 "MAPPKG1" 1563628 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561500 1561827 1562004 "MAPPAST" 1562264 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561111 1561169 1561292 "MAPHACK3" 1561436 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560703 1560764 1560878 "MAPHACK2" 1561043 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560141 1560244 1560386 "MAPHACK1" 1560594 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558220 1558841 1559145 "MAGMA" 1559869 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557699 1557944 1558035 "MACROAST" 1558149 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554117 1555938 1556399 "M3D" 1557271 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548223 1552486 1552527 "LZSTAGG" 1553309 NIL LZSTAGG (NIL T) -9 NIL 1553604 NIL) (-679 1544181 1545354 1546811 "LZSTAGG-" 1546816 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541268 1542072 1542559 "LWORD" 1543726 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540844 1541072 1541147 "LSTAST" 1541213 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534010 1540615 1540749 "LSQM" 1540754 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533234 1533373 1533601 "LSPP" 1533865 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531046 1531347 1531803 "LSMP" 1532923 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527825 1528499 1529229 "LSMP1" 1530348 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521702 1526992 1527033 "LSAGG" 1527095 NIL LSAGG (NIL T) -9 NIL 1527173 NIL) (-671 1518397 1519321 1520534 "LSAGG-" 1520539 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515996 1517541 1517790 "LPOLY" 1518192 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515578 1515663 1515786 "LPEFRAC" 1515905 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513899 1514672 1514925 "LO" 1515410 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513551 1513663 1513691 "LOGIC" 1513802 T LOGIC (NIL) -9 NIL 1513883 NIL) (-666 1513413 1513436 1513507 "LOGIC-" 1513512 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512606 1512746 1512939 "LODOOPS" 1513269 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510029 1512522 1512588 "LODO" 1512593 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508567 1508802 1509155 "LODOF" 1509776 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504785 1507216 1507257 "LODOCAT" 1507695 NIL LODOCAT (NIL T) -9 NIL 1507906 NIL) (-661 1504518 1504576 1504703 "LODOCAT-" 1504708 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501838 1504359 1504477 "LODO2" 1504482 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499273 1501775 1501820 "LODO1" 1501825 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498154 1498319 1498624 "LODEEF" 1499096 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493393 1496284 1496325 "LNAGG" 1497272 NIL LNAGG (NIL T) -9 NIL 1497716 NIL) (-656 1492540 1492754 1493096 "LNAGG-" 1493101 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488676 1489465 1490104 "LMOPS" 1491955 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488079 1488467 1488508 "LMODULE" 1488513 NIL LMODULE (NIL T) -9 NIL 1488539 NIL) (-653 1485277 1487724 1487847 "LMDICT" 1487989 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484683 1484904 1484945 "LLINSET" 1485136 NIL LLINSET (NIL T) -9 NIL 1485227 NIL) (-651 1484382 1484591 1484651 "LITERAL" 1484656 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477545 1483316 1483620 "LIST" 1484111 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477070 1477144 1477283 "LIST3" 1477465 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476077 1476255 1476483 "LIST2" 1476888 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474211 1474523 1474922 "LIST2MAP" 1475724 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473807 1474044 1474085 "LINSET" 1474090 NIL LINSET (NIL T) -9 NIL 1474124 NIL) (-645 1472468 1473138 1473179 "LINEXP" 1473434 NIL LINEXP (NIL T) -9 NIL 1473583 NIL) (-644 1471115 1471375 1471672 "LINDEP" 1472220 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467882 1468601 1469378 "LIMITRF" 1470370 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466185 1466481 1466890 "LIMITPS" 1467577 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460613 1465696 1465924 "LIE" 1466006 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459561 1460030 1460070 "LIECAT" 1460210 NIL LIECAT (NIL T) -9 NIL 1460361 NIL) (-639 1459402 1459429 1459517 "LIECAT-" 1459522 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451898 1458851 1459016 "LIB" 1459257 T LIB (NIL) -8 NIL NIL NIL) (-637 1447533 1448416 1449351 "LGROBP" 1451015 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445531 1445805 1446155 "LF" 1447254 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444371 1445063 1445091 "LFCAT" 1445298 T LFCAT (NIL) -9 NIL 1445437 NIL) (-634 1441273 1441903 1442591 "LEXTRIPK" 1443735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438017 1438843 1439346 "LEXP" 1440853 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437493 1437738 1437830 "LETAST" 1437945 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435891 1436204 1436605 "LEADCDET" 1437175 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435081 1435155 1435384 "LAZM3PK" 1435812 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429998 1433158 1433696 "LAUPOL" 1434593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429577 1429621 1429782 "LAPLACE" 1429948 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427516 1428678 1428929 "LA" 1429410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426510 1427094 1427135 "LALG" 1427197 NIL LALG (NIL T) -9 NIL 1427256 NIL) (-625 1426224 1426283 1426419 "LALG-" 1426424 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426059 1426083 1426124 "KVTFROM" 1426186 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424982 1425426 1425611 "KTVLOGIC" 1425894 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424817 1424841 1424882 "KRCFROM" 1424944 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423721 1423908 1424207 "KOVACIC" 1424617 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423556 1423580 1423621 "KONVERT" 1423683 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423391 1423415 1423456 "KOERCE" 1423518 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421221 1421984 1422361 "KERNEL" 1423047 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420717 1420798 1420930 "KERNEL2" 1421135 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414487 1419256 1419310 "KDAGG" 1419687 NIL KDAGG (NIL T T) -9 NIL 1419893 NIL) (-615 1414016 1414140 1414345 "KDAGG-" 1414350 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407164 1413677 1413832 "KAFILE" 1413894 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401592 1406675 1406903 "JORDAN" 1406985 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400971 1401241 1401362 "JOINAST" 1401491 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400817 1400876 1400931 "JAVACODE" 1400936 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397069 1399022 1399076 "IXAGG" 1400005 NIL IXAGG (NIL T T) -9 NIL 1400464 NIL) (-609 1395988 1396294 1396713 "IXAGG-" 1396718 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391518 1395910 1395969 "IVECTOR" 1395974 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390284 1390521 1390787 "ITUPLE" 1391285 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388786 1388963 1389258 "ITRIGMNP" 1390106 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387531 1387735 1388018 "ITFUN3" 1388562 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387163 1387220 1387329 "ITFUN2" 1387468 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386322 1386643 1386817 "ITFORM" 1387009 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384283 1385342 1385620 "ITAYLOR" 1386077 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373228 1378420 1379583 "ISUPS" 1383153 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372332 1372472 1372708 "ISUMP" 1373075 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367707 1372277 1372318 "ISTRING" 1372323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367183 1367428 1367520 "ISAST" 1367635 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366392 1366474 1366690 "IRURPK" 1367097 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365328 1365529 1365769 "IRSN" 1366172 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363399 1363754 1364183 "IRRF2F" 1364966 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363146 1363184 1363260 "IRREDFFX" 1363355 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361761 1362020 1362319 "IROOT" 1362879 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358365 1359445 1360137 "IR" 1361101 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357570 1357858 1358009 "IRFORM" 1358234 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355183 1355678 1356244 "IR2" 1357048 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354283 1354396 1354610 "IR2F" 1355066 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354074 1354108 1354168 "IPRNTPK" 1354243 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350655 1353963 1354032 "IPF" 1354037 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348982 1350580 1350637 "IPADIC" 1350642 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348294 1348542 1348672 "IP4ADDR" 1348872 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347668 1347923 1348055 "IOMODE" 1348182 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346741 1347265 1347392 "IOBFILE" 1347561 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346229 1346645 1346673 "IOBCON" 1346678 T IOBCON (NIL) -9 NIL 1346699 NIL) (-581 1345740 1345798 1345981 "INVLAPLA" 1346165 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335388 1337742 1340128 "INTTR" 1343404 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331723 1332465 1333330 "INTTOOLS" 1334573 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331309 1331400 1331517 "INTSLPE" 1331626 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329262 1331232 1331291 "INTRVL" 1331296 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326864 1327376 1327951 "INTRF" 1328747 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326275 1326372 1326514 "INTRET" 1326762 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324272 1324661 1325131 "INTRAT" 1325883 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321535 1322118 1322737 "INTPM" 1323757 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318280 1318879 1319617 "INTPAF" 1320921 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313459 1314421 1315472 "INTPACK" 1317249 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310407 1313256 1313365 "INT" 1313370 T INT (NIL) -8 NIL NIL NIL) (-569 1309659 1309811 1310019 "INTHERTR" 1310249 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309098 1309178 1309366 "INTHERAL" 1309573 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306944 1307387 1307844 "INTHEORY" 1308661 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298350 1299971 1301743 "INTG0" 1305296 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278923 1283713 1288523 "INTFTBL" 1293560 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278172 1278310 1278483 "INTFACT" 1278782 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275599 1276045 1276602 "INTEF" 1277726 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273966 1274705 1274733 "INTDOM" 1275034 T INTDOM (NIL) -9 NIL 1275241 NIL) (-561 1273335 1273509 1273751 "INTDOM-" 1273756 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269723 1271651 1271705 "INTCAT" 1272504 NIL INTCAT (NIL T) -9 NIL 1272825 NIL) (-559 1269195 1269298 1269426 "INTBIT" 1269615 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267894 1268048 1268355 "INTALG" 1269040 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267377 1267467 1267624 "INTAF" 1267798 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260720 1267187 1267327 "INTABL" 1267332 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260061 1260527 1260592 "INT8" 1260626 T INT8 (NIL) -8 NIL NIL 1260671) (-554 1259401 1259867 1259932 "INT64" 1259966 T INT64 (NIL) -8 NIL NIL 1260011) (-553 1258741 1259207 1259272 "INT32" 1259306 T INT32 (NIL) -8 NIL NIL 1259351) (-552 1258081 1258547 1258612 "INT16" 1258646 T INT16 (NIL) -8 NIL NIL 1258691) (-551 1252991 1255704 1255732 "INS" 1256666 T INS (NIL) -9 NIL 1257331 NIL) (-550 1250231 1251002 1251976 "INS-" 1252049 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249006 1249233 1249531 "INPSIGN" 1249984 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248124 1248241 1248438 "INPRODPF" 1248886 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247018 1247135 1247372 "INPRODFF" 1248004 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246018 1246170 1246430 "INNMFACT" 1246854 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245215 1245312 1245500 "INMODGCD" 1245917 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243723 1243968 1244292 "INFSP" 1244960 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242907 1243024 1243207 "INFPROD0" 1243603 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239762 1240972 1241487 "INFORM" 1242400 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239372 1239432 1239530 "INFORM1" 1239697 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238895 1238984 1239098 "INFINITY" 1239278 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238071 1238615 1238716 "INETCLTS" 1238814 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236687 1236937 1237258 "INEP" 1237819 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235936 1236584 1236649 "INDE" 1236654 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235500 1235568 1235685 "INCRMAPS" 1235863 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234318 1234769 1234975 "INBFILE" 1235314 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229617 1230554 1231498 "INBFF" 1233406 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228525 1228794 1228822 "INBCON" 1229335 T INBCON (NIL) -9 NIL 1229601 NIL) (-532 1227777 1228000 1228276 "INBCON-" 1228281 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227256 1227501 1227592 "INAST" 1227706 T INAST (NIL) -8 NIL NIL NIL) (-530 1226683 1226935 1227041 "IMPTAST" 1227170 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223129 1226527 1226631 "IMATRIX" 1226636 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221837 1221960 1222276 "IMATQF" 1222985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220057 1220284 1220621 "IMATLIN" 1221593 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214635 1219981 1220039 "ILIST" 1220044 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212540 1214495 1214608 "IIARRAY2" 1214613 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207938 1212451 1212515 "IFF" 1212520 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207285 1207555 1207671 "IFAST" 1207842 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202280 1206577 1206765 "IFARRAY" 1207142 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201460 1202184 1202257 "IFAMON" 1202262 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201044 1201109 1201163 "IEVALAB" 1201370 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200719 1200787 1200947 "IEVALAB-" 1200952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200350 1200633 1200696 "IDPO" 1200701 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199600 1200239 1200314 "IDPOAMS" 1200319 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198907 1199489 1199564 "IDPOAM" 1199569 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197966 1198242 1198295 "IDPC" 1198708 NIL IDPC (NIL T T) -9 NIL 1198857 NIL) (-514 1197435 1197858 1197931 "IDPAM" 1197936 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196811 1197327 1197400 "IDPAG" 1197405 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196456 1196647 1196722 "IDENT" 1196756 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192711 1193559 1194454 "IDECOMP" 1195613 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185549 1186634 1187681 "IDEAL" 1191747 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184709 1184821 1185021 "ICDEN" 1185433 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183780 1184189 1184336 "ICARD" 1184582 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181840 1182153 1182558 "IBPTOOLS" 1183457 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177447 1181460 1181573 "IBITS" 1181759 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174170 1174746 1175441 "IBATOOL" 1176864 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171949 1172411 1172944 "IBACHIN" 1173705 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169778 1171795 1171898 "IARRAY2" 1171903 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165884 1169704 1169761 "IARRAY1" 1169766 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159993 1164296 1164777 "IAN" 1165423 T IAN (NIL) -8 NIL NIL NIL) (-500 1159504 1159561 1159734 "IALGFACT" 1159930 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159032 1159145 1159173 "HYPCAT" 1159380 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158570 1158687 1158873 "HYPCAT-" 1158878 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158165 1158365 1158448 "HOSTNAME" 1158507 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158010 1158047 1158088 "HOMOTOP" 1158093 NIL HOMOTOP (NIL T) -9 NIL 1158126 NIL) (-495 1154642 1156020 1156061 "HOAGG" 1157042 NIL HOAGG (NIL T) -9 NIL 1157721 NIL) (-494 1153236 1153635 1154161 "HOAGG-" 1154166 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147238 1152829 1152979 "HEXADEC" 1153106 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145986 1146208 1146471 "HEUGCD" 1147015 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145062 1145823 1145953 "HELLFDIV" 1145958 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143241 1144839 1144927 "HEAP" 1145006 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142504 1142793 1142927 "HEADAST" 1143127 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136370 1142419 1142481 "HDP" 1142486 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130358 1136005 1136157 "HDMP" 1136271 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129682 1129822 1129986 "HB" 1130214 T HB (NIL) -7 NIL NIL NIL) (-485 1123068 1129528 1129632 "HASHTBL" 1129637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122544 1122789 1122881 "HASAST" 1122996 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120322 1122166 1122348 "HACKPI" 1122382 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115990 1120175 1120288 "GTSET" 1120293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109405 1115868 1115966 "GSTBL" 1115971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101683 1108436 1108701 "GSERIES" 1109196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100824 1101241 1101269 "GROUP" 1101472 T GROUP (NIL) -9 NIL 1101606 NIL) (-478 1100190 1100349 1100600 "GROUP-" 1100605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098557 1098878 1099265 "GROEBSOL" 1099867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097471 1097759 1097810 "GRMOD" 1098339 NIL GRMOD (NIL T T) -9 NIL 1098507 NIL) (-475 1097239 1097275 1097403 "GRMOD-" 1097408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092529 1093593 1094593 "GRIMAGE" 1096259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090995 1091256 1091580 "GRDEF" 1092225 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090439 1090555 1090696 "GRAY" 1090874 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089626 1090032 1090083 "GRALG" 1090236 NIL GRALG (NIL T T) -9 NIL 1090329 NIL) (-470 1089287 1089360 1089523 "GRALG-" 1089528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086064 1088872 1089050 "GPOLSET" 1089194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085418 1085475 1085733 "GOSPER" 1086001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081150 1081856 1082382 "GMODPOL" 1085117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080155 1080339 1080577 "GHENSEL" 1080962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074311 1075154 1076174 "GENUPS" 1079239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074008 1074059 1074148 "GENUFACT" 1074254 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073420 1073497 1073662 "GENPGCD" 1073926 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072894 1072929 1073142 "GENMFACT" 1073379 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071460 1071717 1072024 "GENEEZ" 1072637 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065608 1071071 1071233 "GDMP" 1071383 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054951 1059379 1060485 "GCNAALG" 1064591 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053278 1054140 1054168 "GCDDOM" 1054423 T GCDDOM (NIL) -9 NIL 1054580 NIL) (-457 1052748 1052875 1053090 "GCDDOM-" 1053095 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051420 1051605 1051909 "GB" 1052527 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040036 1042366 1044758 "GBINTERN" 1049111 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037873 1038165 1038586 "GBF" 1039711 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036654 1036819 1037086 "GBEUCLID" 1037689 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036003 1036128 1036277 "GAUSSFAC" 1036525 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034370 1034672 1034986 "GALUTIL" 1035722 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032678 1032952 1033276 "GALPOLYU" 1034097 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030043 1030333 1030740 "GALFACTU" 1032375 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021849 1023348 1024956 "GALFACT" 1028475 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019237 1019895 1019923 "FVFUN" 1021079 T FVFUN (NIL) -9 NIL 1021799 NIL) (-446 1018503 1018685 1018713 "FVC" 1019004 T FVC (NIL) -9 NIL 1019187 NIL) (-445 1018146 1018328 1018396 "FUNDESC" 1018455 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017761 1017943 1018024 "FUNCTION" 1018098 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015505 1016083 1016549 "FT" 1017315 T FT (NIL) -8 NIL NIL NIL) (-442 1014296 1014806 1015009 "FTEM" 1015322 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012587 1012876 1013273 "FSUPFACT" 1013987 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010984 1011273 1011605 "FST" 1012275 T FST (NIL) -8 NIL NIL NIL) (-439 1010183 1010289 1010477 "FSRED" 1010866 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008882 1009138 1009485 "FSPRMELT" 1009898 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006188 1006626 1007112 "FSPECF" 1008445 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987826 996157 996198 "FS" 1000082 NIL FS (NIL T) -9 NIL 1002371 NIL) (-435 976469 979462 983519 "FS-" 983819 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975997 976051 976221 "FSINT" 976410 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974289 974990 975293 "FSERIES" 975776 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973331 973447 973671 "FSCINT" 974169 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969539 972275 972316 "FSAGG" 972686 NIL FSAGG (NIL T) -9 NIL 972945 NIL) (-430 967301 967902 968698 "FSAGG-" 968793 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966343 966486 966713 "FSAGG2" 967154 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964025 964305 964852 "FS2UPS" 966061 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963659 963702 963831 "FS2" 963976 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962537 962708 963010 "FS2EXPXP" 963484 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961963 962078 962230 "FRUTIL" 962417 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953376 957458 958816 "FR" 960637 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948345 951019 951059 "FRNAALG" 952455 NIL FRNAALG (NIL T) -9 NIL 953062 NIL) (-422 944018 945094 946369 "FRNAALG-" 947119 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943656 943699 943826 "FRNAAF2" 943969 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942031 942505 942801 "FRMOD" 943468 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939774 940406 940724 "FRIDEAL" 941822 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938965 939052 939343 "FRIDEAL2" 939681 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938098 938512 938553 "FRETRCT" 938558 NIL FRETRCT (NIL T) -9 NIL 938734 NIL) (-416 937210 937441 937792 "FRETRCT-" 937797 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934298 935508 935567 "FRAMALG" 936449 NIL FRAMALG (NIL T T) -9 NIL 936741 NIL) (-414 932432 932887 933517 "FRAMALG-" 933740 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926351 931905 932182 "FRAC" 932187 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925987 926044 926151 "FRAC2" 926288 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925623 925680 925787 "FR2" 925924 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920136 923029 923057 "FPS" 924176 T FPS (NIL) -9 NIL 924733 NIL) (-409 919585 919694 919858 "FPS-" 920004 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916887 918556 918584 "FPC" 918809 T FPC (NIL) -9 NIL 918951 NIL) (-407 916680 916720 916817 "FPC-" 916822 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915470 916168 916209 "FPATMAB" 916214 NIL FPATMAB (NIL T) -9 NIL 916366 NIL) (-405 913143 913646 914072 "FPARFRAC" 915107 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908537 909035 909717 "FORTRAN" 912575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906253 906753 907292 "FORT" 908018 T FORT (NIL) -7 NIL NIL NIL) (-402 903929 904491 904519 "FORTFN" 905579 T FORTFN (NIL) -9 NIL 906203 NIL) (-401 903693 903743 903771 "FORTCAT" 903830 T FORTCAT (NIL) -9 NIL 903892 NIL) (-400 901799 902309 902699 "FORMULA" 903323 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901587 901617 901686 "FORMULA1" 901763 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901110 901162 901335 "FORDER" 901529 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900206 900370 900563 "FOP" 900937 T FOP (NIL) -7 NIL NIL NIL) (-396 898787 899486 899660 "FNLA" 900088 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897516 897931 897959 "FNCAT" 898419 T FNCAT (NIL) -9 NIL 898679 NIL) (-394 897055 897475 897503 "FNAME" 897508 T FNAME (NIL) -8 NIL NIL NIL) (-393 895618 896581 896609 "FMTC" 896614 T FMTC (NIL) -9 NIL 896650 NIL) (-392 894364 895554 895600 "FMONOID" 895605 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891192 892360 892401 "FMONCAT" 893618 NIL FMONCAT (NIL T) -9 NIL 894223 NIL) (-390 890384 890934 891083 "FM" 891088 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887808 888454 888482 "FMFUN" 889626 T FMFUN (NIL) -9 NIL 890334 NIL) (-388 887077 887258 887286 "FMC" 887576 T FMC (NIL) -9 NIL 887758 NIL) (-387 884156 885016 885070 "FMCAT" 886265 NIL FMCAT (NIL T T) -9 NIL 886760 NIL) (-386 883022 883922 884022 "FM1" 884101 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880796 881212 881706 "FLOATRP" 882573 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874374 878525 879146 "FLOAT" 880195 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871812 872312 872890 "FLOATCP" 873841 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870552 871390 871431 "FLINEXP" 871436 NIL FLINEXP (NIL T) -9 NIL 871529 NIL) (-381 869706 869941 870269 "FLINEXP-" 870274 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868782 868926 869150 "FLASORT" 869558 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865898 866766 866818 "FLALG" 868045 NIL FLALG (NIL T T) -9 NIL 868512 NIL) (-378 859634 863384 863425 "FLAGG" 864687 NIL FLAGG (NIL T) -9 NIL 865339 NIL) (-377 858360 858699 859189 "FLAGG-" 859194 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857402 857545 857772 "FLAGG2" 858213 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854253 855261 855320 "FINRALG" 856448 NIL FINRALG (NIL T T) -9 NIL 856956 NIL) (-374 853413 853642 853981 "FINRALG-" 853986 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852793 853032 853060 "FINITE" 853256 T FINITE (NIL) -9 NIL 853363 NIL) (-372 845150 847337 847377 "FINAALG" 851044 NIL FINAALG (NIL T) -9 NIL 852497 NIL) (-371 840482 841532 842676 "FINAALG-" 844055 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839850 840237 840340 "FILE" 840412 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838508 838846 838900 "FILECAT" 839584 NIL FILECAT (NIL T T) -9 NIL 839800 NIL) (-368 836224 837752 837780 "FIELD" 837820 T FIELD (NIL) -9 NIL 837900 NIL) (-367 834844 835229 835740 "FIELD-" 835745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832694 833479 833826 "FGROUP" 834530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831784 831948 832168 "FGLMICPK" 832526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827616 831709 831766 "FFX" 831771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827217 827278 827413 "FFSLPE" 827549 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823207 823989 824785 "FFPOLY" 826453 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822711 822747 822956 "FFPOLY2" 823165 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818557 822630 822693 "FFP" 822698 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813955 818468 818532 "FF" 818537 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809081 813298 813488 "FFNBX" 813809 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804009 808216 808474 "FFNBP" 808935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798642 803293 803504 "FFNB" 803842 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797474 797672 797987 "FFINTBAS" 798439 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793543 795763 795791 "FFIELDC" 796411 T FFIELDC (NIL) -9 NIL 796787 NIL) (-353 792205 792576 793073 "FFIELDC-" 793078 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791774 791820 791944 "FFHOM" 792147 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789469 789956 790473 "FFF" 791289 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785087 789211 789312 "FFCGX" 789412 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780709 784819 784926 "FFCGP" 785030 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775892 780436 780544 "FFCG" 780645 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757288 766369 766455 "FFCAT" 771620 NIL FFCAT (NIL T T T) -9 NIL 773071 NIL) (-346 752485 753533 754847 "FFCAT-" 756077 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751896 751939 752174 "FFCAT2" 752436 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741219 744868 746088 "FEXPR" 750748 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740219 740654 740695 "FEVALAB" 740779 NIL FEVALAB (NIL T) -9 NIL 741040 NIL) (-342 739378 739588 739926 "FEVALAB-" 739931 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737944 738761 738964 "FDIV" 739277 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734964 735705 735820 "FDIVCAT" 737388 NIL FDIVCAT (NIL T T T T) -9 NIL 737825 NIL) (-339 734726 734753 734923 "FDIVCAT-" 734928 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733946 734033 734310 "FDIV2" 734633 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732920 733241 733443 "FCTRDATA" 733764 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731606 731865 732154 "FCPAK1" 732651 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730705 731106 731247 "FCOMP" 731497 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714410 717855 721393 "FC" 727187 T FC (NIL) -8 NIL NIL NIL) (-333 706773 710801 710841 "FAXF" 712643 NIL FAXF (NIL T) -9 NIL 713335 NIL) (-332 704050 704707 705532 "FAXF-" 705997 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699102 703426 703602 "FARRAY" 703907 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693996 696063 696116 "FAMR" 697139 NIL FAMR (NIL T T) -9 NIL 697599 NIL) (-329 692886 693188 693623 "FAMR-" 693628 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692055 692808 692861 "FAMONOID" 692866 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689841 690551 690604 "FAMONC" 691545 NIL FAMONC (NIL T T) -9 NIL 691931 NIL) (-326 688505 689595 689732 "FAGROUP" 689737 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686300 686619 687022 "FACUTIL" 688186 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685399 685584 685806 "FACTFUNC" 686110 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677821 684702 684901 "EXPUPXS" 685255 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675304 675844 676430 "EXPRTUBE" 677255 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671575 672167 672897 "EXPRODE" 674643 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657060 670224 670653 "EXPR" 671179 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651614 652201 653007 "EXPR2UPS" 656358 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651246 651303 651412 "EXPR2" 651551 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642634 650397 650688 "EXPEXPAN" 651082 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642434 642591 642620 "EXIT" 642625 T EXIT (NIL) -8 NIL NIL NIL) (-315 641914 642158 642249 "EXITAST" 642363 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641541 641603 641716 "EVALCYC" 641846 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641082 641200 641241 "EVALAB" 641411 NIL EVALAB (NIL T) -9 NIL 641515 NIL) (-312 640563 640685 640906 "EVALAB-" 640911 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637931 639233 639261 "EUCDOM" 639816 T EUCDOM (NIL) -9 NIL 640166 NIL) (-310 636336 636778 637368 "EUCDOM-" 637373 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623875 626634 629384 "ESTOOLS" 633606 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623507 623564 623673 "ESTOOLS2" 623812 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623258 623300 623380 "ESTOOLS1" 623459 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617295 618903 618931 "ES" 621699 T ES (NIL) -9 NIL 623109 NIL) (-305 612242 613529 615346 "ES-" 615510 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608616 609377 610157 "ESCONT" 611482 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608361 608393 608475 "ESCONT1" 608578 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608036 608086 608186 "ES2" 608305 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607666 607724 607833 "ES1" 607972 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606882 607011 607187 "ERROR" 607510 T ERROR (NIL) -7 NIL NIL NIL) (-299 600274 606741 606832 "EQTBL" 606837 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592777 595588 597037 "EQ" 598858 NIL -2199 (NIL T) -8 NIL NIL NIL) (-297 592409 592466 592575 "EQ2" 592714 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587700 588747 589840 "EP" 591348 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586300 586591 586897 "ENV" 587414 T ENV (NIL) -8 NIL NIL NIL) (-294 585394 585948 585976 "ENTIRER" 585981 T ENTIRER (NIL) -9 NIL 586027 NIL) (-293 581861 583349 583719 "EMR" 585193 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581005 581190 581244 "ELTAGG" 581624 NIL ELTAGG (NIL T T) -9 NIL 581835 NIL) (-291 580724 580786 580927 "ELTAGG-" 580932 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580513 580542 580596 "ELTAB" 580680 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579639 579785 579984 "ELFUTS" 580364 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579381 579437 579465 "ELEMFUN" 579570 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579251 579272 579340 "ELEMFUN-" 579345 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574095 577351 577392 "ELAGG" 578332 NIL ELAGG (NIL T) -9 NIL 578795 NIL) (-285 572380 572814 573477 "ELAGG-" 573482 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571692 571829 571985 "ELABOR" 572244 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570353 570632 570926 "ELABEXPR" 571418 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563217 565020 565847 "EFUPXS" 569629 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556667 558468 559278 "EFULS" 562493 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554152 554510 554982 "EFSTRUC" 556299 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543943 545509 547057 "EF" 552667 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543017 543428 543577 "EAB" 543814 T EAB (NIL) -8 NIL NIL NIL) (-277 542199 542976 543004 "E04UCFA" 543009 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541381 542158 542186 "E04NAFA" 542191 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540563 541340 541368 "E04MBFA" 541373 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539745 540522 540550 "E04JAFA" 540555 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538929 539704 539732 "E04GCFA" 539737 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538113 538888 538916 "E04FDFA" 538921 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537295 538072 538100 "E04DGFA" 538105 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531468 532820 534184 "E04AGNT" 535951 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530148 530654 530694 "DVARCAT" 531169 NIL DVARCAT (NIL T) -9 NIL 531368 NIL) (-268 529352 529564 529878 "DVARCAT-" 529883 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522489 529151 529280 "DSMP" 529285 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517270 518434 519502 "DROPT" 521441 T DROPT (NIL) -8 NIL NIL NIL) (-265 516935 516994 517092 "DROPT1" 517205 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512050 513176 514313 "DROPT0" 515818 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510395 510720 511106 "DRAWPT" 511684 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504982 505905 506984 "DRAW" 509369 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504615 504668 504786 "DRAWHACK" 504923 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503346 503615 503906 "DRAWCX" 504344 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502861 502930 503081 "DRAWCURV" 503272 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493329 495291 497406 "DRAWCFUN" 500766 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490093 492022 492063 "DQAGG" 492692 NIL DQAGG (NIL T) -9 NIL 492966 NIL) (-256 478217 484686 484769 "DPOLCAT" 486621 NIL DPOLCAT (NIL T T T T) -9 NIL 487166 NIL) (-255 473054 474402 476360 "DPOLCAT-" 476365 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466176 472915 473013 "DPMO" 473018 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459201 465956 466123 "DPMM" 466128 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458679 458893 458991 "DOMTMPLT" 459123 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458112 458481 458561 "DOMCTOR" 458619 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457324 457592 457743 "DOMAIN" 457981 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451312 456959 457111 "DMP" 457225 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450912 450968 451112 "DLP" 451250 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444734 450239 450429 "DLIST" 450754 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441531 443587 443628 "DLAGG" 444178 NIL DLAGG (NIL T) -9 NIL 444408 NIL) (-245 440207 440871 440899 "DIVRING" 440991 T DIVRING (NIL) -9 NIL 441074 NIL) (-244 439444 439634 439934 "DIVRING-" 439939 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437546 437903 438309 "DISPLAY" 439058 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431434 437460 437523 "DIRPROD" 437528 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430282 430485 430750 "DIRPROD2" 431227 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419057 425063 425116 "DIRPCAT" 425526 NIL DIRPCAT (NIL NIL T) -9 NIL 426366 NIL) (-239 416383 417025 417906 "DIRPCAT-" 418243 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415670 415830 416016 "DIOSP" 416217 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412325 414582 414623 "DIOPS" 415057 NIL DIOPS (NIL T) -9 NIL 415286 NIL) (-236 411874 411988 412179 "DIOPS-" 412184 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410697 411325 411353 "DIFRING" 411540 T DIFRING (NIL) -9 NIL 411650 NIL) (-234 410343 410420 410572 "DIFRING-" 410577 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408079 409351 409392 "DIFEXT" 409755 NIL DIFEXT (NIL T) -9 NIL 410049 NIL) (-232 406364 406792 407458 "DIFEXT-" 407463 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403639 405896 405937 "DIAGG" 405942 NIL DIAGG (NIL T) -9 NIL 405962 NIL) (-230 403023 403180 403432 "DIAGG-" 403437 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398440 401982 402259 "DHMATRIX" 402792 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394052 394961 395971 "DFSFUN" 397450 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389131 392983 393295 "DFLOAT" 393760 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387394 387675 388064 "DFINTTLS" 388839 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384423 385415 385815 "DERHAM" 387060 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382224 384198 384287 "DEQUEUE" 384367 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381478 381611 381794 "DEGRED" 382086 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377908 378653 379499 "DEFINTRF" 380706 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375463 375932 376524 "DEFINTEF" 377427 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374813 375083 375198 "DEFAST" 375368 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368815 374406 374556 "DECIMAL" 374683 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366327 366785 367291 "DDFACT" 368359 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365923 365966 366117 "DBLRESP" 366278 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363795 364156 364516 "DBASE" 365690 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363037 363275 363421 "DATAARY" 363694 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362143 362996 363024 "D03FAFA" 363029 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361250 362102 362130 "D03EEFA" 362135 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359200 359666 360155 "D03AGNT" 360781 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358489 359159 359187 "D02EJFA" 359192 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357778 358448 358476 "D02CJFA" 358481 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357067 357737 357765 "D02BHFA" 357770 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356356 357026 357054 "D02BBFA" 357059 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349553 351142 352748 "D02AGNT" 354770 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347321 347844 348390 "D01WGTS" 349027 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346388 347280 347308 "D01TRNS" 347313 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345456 346347 346375 "D01GBFA" 346380 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344524 345415 345443 "D01FCFA" 345448 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343592 344483 344511 "D01ASFA" 344516 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342660 343551 343579 "D01AQFA" 343584 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341728 342619 342647 "D01APFA" 342652 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340796 341687 341715 "D01ANFA" 341720 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339864 340755 340783 "D01AMFA" 340788 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338932 339823 339851 "D01ALFA" 339856 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338000 338891 338919 "D01AKFA" 338924 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337068 337959 337987 "D01AJFA" 337992 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330363 331916 333477 "D01AGNT" 335527 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329700 329828 329980 "CYCLOTOM" 330231 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326434 327148 327875 "CYCLES" 328993 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325746 325880 326051 "CVMP" 326295 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323587 323845 324214 "CTRIGMNP" 325474 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323023 323381 323454 "CTOR" 323534 T CTOR (NIL) -8 NIL NIL NIL) (-188 322532 322754 322855 "CTORKIND" 322942 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321823 322139 322167 "CTORCAT" 322349 T CTORCAT (NIL) -9 NIL 322462 NIL) (-186 321421 321532 321691 "CTORCAT-" 321696 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320883 321095 321203 "CTORCALL" 321345 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320257 320356 320509 "CSTTOOLS" 320780 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316056 316713 317471 "CRFP" 319569 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315531 315777 315869 "CRCEAST" 315984 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314578 314763 314991 "CRAPACK" 315335 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313962 314063 314267 "CPMATCH" 314454 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313687 313715 313821 "CPIMA" 313928 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310035 310707 311426 "COORDSYS" 313022 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309447 309568 309710 "CONTOUR" 309913 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305338 307450 307942 "CONTFRAC" 308987 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305218 305239 305267 "CONDUIT" 305304 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304306 304860 304888 "COMRING" 304893 T COMRING (NIL) -9 NIL 304945 NIL) (-173 303360 303664 303848 "COMPPROP" 304142 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303021 303056 303184 "COMPLPAT" 303319 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293312 302830 302939 "COMPLEX" 302944 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292948 293005 293112 "COMPLEX2" 293249 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292287 292408 292568 "COMPILER" 292808 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292005 292040 292138 "COMPFACT" 292246 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276085 286079 286119 "COMPCAT" 287123 NIL COMPCAT (NIL T) -9 NIL 288471 NIL) (-166 265597 268524 272151 "COMPCAT-" 272507 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265326 265354 265457 "COMMUPC" 265563 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265120 265154 265213 "COMMONOP" 265287 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264676 264871 264958 "COMM" 265053 T COMM (NIL) -8 NIL NIL NIL) (-162 264252 264480 264555 "COMMAAST" 264621 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263501 263695 263723 "COMBOPC" 264061 T COMBOPC (NIL) -9 NIL 264236 NIL) (-160 262397 262607 262849 "COMBINAT" 263291 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258854 259428 260055 "COMBF" 261819 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257612 257970 258205 "COLOR" 258639 T COLOR (NIL) -8 NIL NIL NIL) (-157 257088 257333 257425 "COLONAST" 257540 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256728 256775 256900 "CMPLXRT" 257035 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256176 256428 256527 "CLLCTAST" 256649 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251678 252706 253786 "CLIP" 255116 T CLIP (NIL) -7 NIL NIL NIL) (-153 250019 250779 251019 "CLIF" 251505 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246194 248165 248206 "CLAGG" 249135 NIL CLAGG (NIL T) -9 NIL 249671 NIL) (-151 244616 245073 245656 "CLAGG-" 245661 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244160 244245 244385 "CINTSLPE" 244525 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241661 242132 242680 "CHVAR" 243688 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240835 241389 241417 "CHARZ" 241422 T CHARZ (NIL) -9 NIL 241437 NIL) (-147 240589 240629 240707 "CHARPOL" 240789 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239647 240234 240262 "CHARNZ" 240309 T CHARNZ (NIL) -9 NIL 240365 NIL) (-145 237553 238301 238654 "CHAR" 239314 T CHAR (NIL) -8 NIL NIL NIL) (-144 237279 237340 237368 "CFCAT" 237479 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236520 236631 236814 "CDEN" 237163 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232485 235673 235953 "CCLASS" 236260 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231736 231893 232070 "CATEGORY" 232328 T -10 (NIL) -8 NIL NIL NIL) (-140 231309 231655 231703 "CATCTOR" 231708 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230760 231012 231110 "CATAST" 231231 T CATAST (NIL) -8 NIL NIL NIL) (-138 230236 230481 230573 "CASEAST" 230688 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225246 226265 227018 "CARTEN" 229539 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224354 224502 224723 "CARTEN2" 225093 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222670 223504 223761 "CARD" 224117 T CARD (NIL) -8 NIL NIL NIL) (-134 222246 222474 222549 "CAPSLAST" 222615 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221750 221958 221986 "CACHSET" 222118 T CACHSET (NIL) -9 NIL 222196 NIL) (-132 221220 221542 221570 "CABMON" 221620 T CABMON (NIL) -9 NIL 221676 NIL) (-131 220693 220924 221034 "BYTEORD" 221130 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219675 220227 220369 "BYTE" 220532 T BYTE (NIL) -8 NIL NIL 220654) (-129 215025 219180 219352 "BYTEBUF" 219523 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212534 214717 214824 "BTREE" 214951 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209983 212182 212304 "BTOURN" 212444 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207353 209453 209494 "BTCAT" 209562 NIL BTCAT (NIL T) -9 NIL 209639 NIL) (-125 207020 207100 207249 "BTCAT-" 207254 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202430 206309 206337 "BTAGG" 206451 T BTAGG (NIL) -9 NIL 206561 NIL) (-123 201920 202045 202251 "BTAGG-" 202256 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198915 201198 201413 "BSTREE" 201737 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198053 198179 198363 "BRILL" 198771 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194705 196779 196820 "BRAGG" 197469 NIL BRAGG (NIL T) -9 NIL 197727 NIL) (-119 193234 193640 194195 "BRAGG-" 194200 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186461 192578 192763 "BPADICRT" 193081 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184776 186398 186443 "BPADIC" 186448 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184474 184504 184618 "BOUNDZRO" 184740 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179702 180900 181812 "BOP" 183582 T BOP (NIL) -8 NIL NIL NIL) (-114 177483 177887 178362 "BOP1" 179260 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177184 177245 177273 "BOOLE" 177384 T BOOLE (NIL) -9 NIL 177466 NIL) (-112 176009 176758 176907 "BOOLEAN" 177055 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175288 175692 175746 "BMODULE" 175751 NIL BMODULE (NIL T T) -9 NIL 175816 NIL) (-110 171089 175086 175159 "BITS" 175235 T BITS (NIL) -8 NIL NIL NIL) (-109 170510 170629 170769 "BINDING" 170969 T BINDING (NIL) -8 NIL NIL NIL) (-108 164515 170105 170254 "BINARY" 170381 T BINARY (NIL) -8 NIL NIL NIL) (-107 162295 163770 163811 "BGAGG" 164071 NIL BGAGG (NIL T) -9 NIL 164208 NIL) (-106 162126 162158 162249 "BGAGG-" 162254 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161197 161510 161715 "BFUNCT" 161941 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159887 160065 160353 "BEZOUT" 161021 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156356 158739 159069 "BBTREE" 159590 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156090 156143 156171 "BASTYPE" 156290 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155942 155971 156044 "BASTYPE-" 156049 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155376 155452 155604 "BALFACT" 155853 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154232 154791 154977 "AUTOMOR" 155221 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153958 153963 153989 "ATTREG" 153994 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152210 152655 153007 "ATTRBUT" 153624 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151818 152038 152104 "ATTRAST" 152162 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151354 151467 151493 "ATRIG" 151694 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151163 151204 151291 "ATRIG-" 151296 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150808 150994 151020 "ASTCAT" 151025 T ASTCAT (NIL) -9 NIL 151055 NIL) (-92 150535 150594 150713 "ASTCAT-" 150718 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148684 150311 150399 "ASTACK" 150478 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147189 147486 147851 "ASSOCEQ" 148366 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146221 146848 146972 "ASP9" 147096 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145984 146169 146208 "ASP8" 146213 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144852 145589 145731 "ASP80" 145873 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143750 144487 144619 "ASP7" 144751 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142704 143427 143545 "ASP78" 143663 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141673 142384 142501 "ASP77" 142618 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140585 141311 141442 "ASP74" 141573 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139485 140220 140352 "ASP73" 140484 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138589 139311 139411 "ASP6" 139416 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137536 138266 138384 "ASP55" 138502 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136485 137210 137329 "ASP50" 137448 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135573 136186 136296 "ASP4" 136406 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134661 135274 135384 "ASP49" 135494 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133445 134200 134368 "ASP42" 134550 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132222 132978 133148 "ASP41" 133332 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131172 131899 132017 "ASP35" 132135 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130937 131120 131159 "ASP34" 131164 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130674 130741 130817 "ASP33" 130892 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129568 130309 130441 "ASP31" 130573 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129333 129516 129555 "ASP30" 129560 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129068 129137 129213 "ASP29" 129288 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128833 129016 129055 "ASP28" 129060 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128598 128781 128820 "ASP27" 128825 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127682 128296 128407 "ASP24" 128518 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126759 127484 127596 "ASP20" 127601 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125847 126460 126570 "ASP1" 126680 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124790 125521 125640 "ASP19" 125759 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124527 124594 124670 "ASP12" 124745 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123379 124126 124270 "ASP10" 124414 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121230 123223 123314 "ARRAY2" 123319 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116995 120878 120992 "ARRAY1" 121147 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116027 116200 116421 "ARRAY12" 116818 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110339 112257 112332 "ARR2CAT" 114962 NIL ARR2CAT (NIL T T T) -9 NIL 115720 NIL) (-56 107773 108517 109471 "ARR2CAT-" 109476 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107090 107400 107525 "ARITY" 107666 T ARITY (NIL) -8 NIL NIL NIL) (-54 105866 106018 106317 "APPRULE" 106926 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105517 105565 105684 "APPLYORE" 105812 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104871 105110 105230 "ANY" 105415 T ANY (NIL) -8 NIL NIL NIL) (-51 104149 104272 104429 "ANY1" 104745 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101679 102586 102913 "ANTISYM" 103873 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101171 101386 101482 "ANON" 101601 T ANON (NIL) -8 NIL NIL NIL) (-48 95420 99710 100164 "AN" 100735 T AN (NIL) -8 NIL NIL NIL) (-47 91318 92706 92757 "AMR" 93505 NIL AMR (NIL T T) -9 NIL 94105 NIL) (-46 90430 90651 91014 "AMR-" 91019 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74869 90347 90408 "ALIST" 90413 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71674 74463 74632 "ALGSC" 74787 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68230 68784 69391 "ALGPKG" 71114 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67507 67608 67792 "ALGMFACT" 68116 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64121 64715 "ALGMANIP" 67091 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3229124 3229129 3229134 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3229109 3229114 3229119 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3229094 3229099 3229104 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3229079 3229084 3229089 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1306 3228222 3228954 3229031 "ZMOD" 3229036 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1305 3227332 3227496 3227705 "ZLINDEP" 3228054 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1304 3216632 3218400 3220372 "ZDSOLVE" 3225462 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1303 3215878 3216019 3216208 "YSTREAM" 3216478 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1302 3215306 3215552 3215665 "YDIAGRAM" 3215787 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1301 3213080 3214607 3214811 "XRPOLY" 3215149 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3209633 3210951 3211526 "XPR" 3212552 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1299 3207354 3208964 3209168 "XPOLY" 3209464 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1298 3205007 3206375 3206430 "XPOLYC" 3206718 NIL XPOLYC (NIL T T) -9 NIL 3206831 NIL) (-1297 3201383 3203524 3203912 "XPBWPOLY" 3204665 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1296 3197078 3199373 3199415 "XF" 3200036 NIL XF (NIL T) -9 NIL 3200436 NIL) (-1295 3196699 3196787 3196956 "XF-" 3196961 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1294 3191895 3193184 3193239 "XFALG" 3195411 NIL XFALG (NIL T T) -9 NIL 3196200 NIL) (-1293 3191028 3191132 3191337 "XEXPPKG" 3191787 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1292 3189137 3190878 3190974 "XDPOLY" 3190979 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1291 3187944 3188544 3188587 "XALG" 3188592 NIL XALG (NIL T) -9 NIL 3188703 NIL) (-1290 3181386 3185921 3186415 "WUTSET" 3187536 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1289 3179642 3180438 3180761 "WP" 3181197 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1288 3179244 3179464 3179534 "WHILEAST" 3179594 T WHILEAST (NIL) -8 NIL NIL NIL) (-1287 3178716 3178961 3179055 "WHEREAST" 3179172 T WHEREAST (NIL) -8 NIL NIL NIL) (-1286 3177602 3177800 3178095 "WFFINTBS" 3178513 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1285 3175506 3175933 3176395 "WEIER" 3177174 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1284 3174552 3175002 3175044 "VSPACE" 3175180 NIL VSPACE (NIL T) -9 NIL 3175254 NIL) (-1283 3174390 3174417 3174508 "VSPACE-" 3174513 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1282 3174199 3174241 3174309 "VOID" 3174344 T VOID (NIL) -8 NIL NIL NIL) (-1281 3172335 3172694 3173100 "VIEW" 3173815 T VIEW (NIL) -7 NIL NIL NIL) (-1280 3168759 3169398 3170135 "VIEWDEF" 3171620 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1279 3158063 3160307 3162480 "VIEW3D" 3166608 T VIEW3D (NIL) -8 NIL NIL NIL) (-1278 3150314 3151974 3153553 "VIEW2D" 3156506 T VIEW2D (NIL) -8 NIL NIL NIL) (-1277 3145667 3150084 3150176 "VECTOR" 3150257 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1276 3144244 3144503 3144821 "VECTOR2" 3145397 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1275 3137718 3142025 3142068 "VECTCAT" 3143063 NIL VECTCAT (NIL T) -9 NIL 3143650 NIL) (-1274 3136732 3136986 3137376 "VECTCAT-" 3137381 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1273 3136186 3136383 3136503 "VARIABLE" 3136647 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1272 3136119 3136124 3136154 "UTYPE" 3136159 T UTYPE (NIL) -9 NIL NIL NIL) (-1271 3134949 3135103 3135365 "UTSODETL" 3135945 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1270 3132389 3132849 3133373 "UTSODE" 3134490 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1269 3124227 3130015 3130504 "UTS" 3131958 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3115101 3120468 3120511 "UTSCAT" 3121623 NIL UTSCAT (NIL T) -9 NIL 3122381 NIL) (-1267 3112449 3113171 3114160 "UTSCAT-" 3114165 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1266 3112076 3112119 3112252 "UTS2" 3112400 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1265 3106302 3108914 3108957 "URAGG" 3111027 NIL URAGG (NIL T) -9 NIL 3111750 NIL) (-1264 3103241 3104104 3105227 "URAGG-" 3105232 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1263 3098950 3101876 3102341 "UPXSSING" 3102905 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1262 3091016 3098197 3098470 "UPXS" 3098735 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1261 3084089 3090920 3090992 "UPXSCONS" 3090997 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3073834 3080627 3080689 "UPXSCCA" 3081263 NIL UPXSCCA (NIL T T) -9 NIL 3081496 NIL) (-1259 3073472 3073557 3073731 "UPXSCCA-" 3073736 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1258 3063069 3069635 3069678 "UPXSCAT" 3070326 NIL UPXSCAT (NIL T) -9 NIL 3070935 NIL) (-1257 3062499 3062578 3062757 "UPXS2" 3062984 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3061153 3061406 3061757 "UPSQFREE" 3062242 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1255 3054574 3057631 3057686 "UPSCAT" 3058847 NIL UPSCAT (NIL T T) -9 NIL 3059621 NIL) (-1254 3053778 3053985 3054312 "UPSCAT-" 3054317 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1253 3039433 3047201 3047244 "UPOLYC" 3049345 NIL UPOLYC (NIL T) -9 NIL 3050566 NIL) (-1252 3030761 3033187 3036334 "UPOLYC-" 3036339 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1251 3030388 3030431 3030564 "UPOLYC2" 3030712 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3022199 3030071 3030200 "UP" 3030307 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1249 3021538 3021645 3021809 "UPMP" 3022088 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1248 3021091 3021172 3021311 "UPDIVP" 3021451 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1247 3019659 3019908 3020224 "UPDECOMP" 3020840 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1246 3018890 3019002 3019188 "UPCDEN" 3019543 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1245 3018409 3018478 3018627 "UP2" 3018815 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1244 3016876 3017613 3017890 "UNISEG" 3018167 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1243 3016091 3016218 3016423 "UNISEG2" 3016719 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1242 3015151 3015331 3015557 "UNIFACT" 3015907 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1241 2999083 3014328 3014579 "ULS" 3014958 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1240 2987081 2998987 2999059 "ULSCONS" 2999064 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1239 2969098 2981083 2981145 "ULSCCAT" 2981783 NIL ULSCCAT (NIL T T) -9 NIL 2982072 NIL) (-1238 2968148 2968393 2968781 "ULSCCAT-" 2968786 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1237 2957522 2964002 2964045 "ULSCAT" 2964908 NIL ULSCAT (NIL T) -9 NIL 2965639 NIL) (-1236 2956952 2957031 2957210 "ULS2" 2957437 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1235 2956079 2956589 2956696 "UINT8" 2956807 T UINT8 (NIL) -8 NIL NIL 2956892) (-1234 2955205 2955715 2955822 "UINT64" 2955933 T UINT64 (NIL) -8 NIL NIL 2956018) (-1233 2954331 2954841 2954948 "UINT32" 2955059 T UINT32 (NIL) -8 NIL NIL 2955144) (-1232 2953457 2953967 2954074 "UINT16" 2954185 T UINT16 (NIL) -8 NIL NIL 2954270) (-1231 2951760 2952717 2952747 "UFD" 2952959 T UFD (NIL) -9 NIL 2953073 NIL) (-1230 2951554 2951600 2951695 "UFD-" 2951700 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1229 2950636 2950819 2951035 "UDVO" 2951360 T UDVO (NIL) -7 NIL NIL NIL) (-1228 2948452 2948861 2949332 "UDPO" 2950200 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1227 2948385 2948390 2948420 "TYPE" 2948425 T TYPE (NIL) -9 NIL NIL NIL) (-1226 2948145 2948340 2948371 "TYPEAST" 2948376 T TYPEAST (NIL) -8 NIL NIL NIL) (-1225 2947116 2947318 2947558 "TWOFACT" 2947939 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1224 2946139 2946525 2946760 "TUPLE" 2946916 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1223 2943830 2944349 2944888 "TUBETOOL" 2945622 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1222 2942679 2942884 2943125 "TUBE" 2943623 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1221 2937408 2941651 2941934 "TS" 2942431 NIL TS (NIL T) -8 NIL NIL NIL) (-1220 2926048 2930167 2930264 "TSETCAT" 2935533 NIL TSETCAT (NIL T T T T) -9 NIL 2937064 NIL) (-1219 2920780 2922380 2924271 "TSETCAT-" 2924276 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1218 2915419 2916266 2917195 "TRMANIP" 2919916 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1217 2914860 2914923 2915086 "TRIMAT" 2915351 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1216 2912726 2912963 2913320 "TRIGMNIP" 2914609 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1215 2912246 2912359 2912389 "TRIGCAT" 2912602 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1214 2911915 2911994 2912135 "TRIGCAT-" 2912140 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1213 2908760 2910773 2911054 "TREE" 2911669 NIL TREE (NIL T) -8 NIL NIL NIL) (-1212 2908034 2908562 2908592 "TRANFUN" 2908627 T TRANFUN (NIL) -9 NIL 2908693 NIL) (-1211 2907313 2907504 2907784 "TRANFUN-" 2907789 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1210 2907117 2907149 2907210 "TOPSP" 2907274 T TOPSP (NIL) -7 NIL NIL NIL) (-1209 2906465 2906580 2906734 "TOOLSIGN" 2906998 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1208 2905099 2905642 2905881 "TEXTFILE" 2906248 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1207 2903011 2903552 2903981 "TEX" 2904692 T TEX (NIL) -8 NIL NIL NIL) (-1206 2902792 2902823 2902895 "TEX1" 2902974 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1205 2902440 2902503 2902593 "TEMUTL" 2902724 T TEMUTL (NIL) -7 NIL NIL NIL) (-1204 2900594 2900874 2901199 "TBCMPPK" 2902163 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1203 2892371 2898754 2898810 "TBAGG" 2899210 NIL TBAGG (NIL T T) -9 NIL 2899421 NIL) (-1202 2887441 2888929 2890683 "TBAGG-" 2890688 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1201 2886825 2886932 2887077 "TANEXP" 2887330 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1200 2886336 2886600 2886690 "TALGOP" 2886770 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1199 2879726 2886193 2886286 "TABLE" 2886291 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1198 2879138 2879237 2879375 "TABLEAU" 2879623 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1197 2873746 2874966 2876214 "TABLBUMP" 2877924 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1196 2872968 2873115 2873296 "SYSTEM" 2873587 T SYSTEM (NIL) -8 NIL NIL NIL) (-1195 2869427 2870126 2870909 "SYSSOLP" 2872219 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1194 2869225 2869382 2869413 "SYSPTR" 2869418 T SYSPTR (NIL) -8 NIL NIL NIL) (-1193 2868269 2868774 2868893 "SYSNNI" 2869079 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869164) (-1192 2867576 2868035 2868114 "SYSINT" 2868174 NIL SYSINT (NIL NIL) -8 NIL NIL 2868219) (-1191 2863908 2864854 2865564 "SYNTAX" 2866888 T SYNTAX (NIL) -8 NIL NIL NIL) (-1190 2861066 2861668 2862300 "SYMTAB" 2863298 T SYMTAB (NIL) -8 NIL NIL NIL) (-1189 2856315 2857217 2858200 "SYMS" 2860105 T SYMS (NIL) -8 NIL NIL NIL) (-1188 2853550 2855773 2856003 "SYMPOLY" 2856120 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1187 2853067 2853142 2853265 "SYMFUNC" 2853462 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1186 2849087 2850379 2851192 "SYMBOL" 2852276 T SYMBOL (NIL) -8 NIL NIL NIL) (-1185 2842626 2844315 2846035 "SWITCH" 2847389 T SWITCH (NIL) -8 NIL NIL NIL) (-1184 2835860 2841447 2841750 "SUTS" 2842381 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2827926 2835107 2835380 "SUPXS" 2835645 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2819685 2827544 2827670 "SUP" 2827835 NIL SUP (NIL T) -8 NIL NIL NIL) (-1181 2818844 2818971 2819188 "SUPFRACF" 2819553 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1180 2818465 2818524 2818637 "SUP2" 2818779 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1179 2816913 2817187 2817543 "SUMRF" 2818164 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1178 2816248 2816314 2816506 "SUMFS" 2816834 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1177 2800215 2815425 2815676 "SULS" 2816055 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1176 2799817 2800037 2800107 "SUCHTAST" 2800167 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1175 2799112 2799342 2799482 "SUCH" 2799725 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1174 2792979 2794018 2794977 "SUBSPACE" 2798200 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1173 2792409 2792499 2792663 "SUBRESP" 2792867 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1172 2785777 2787074 2788385 "STTF" 2791145 NIL STTF (NIL T) -7 NIL NIL NIL) (-1171 2779950 2781070 2782217 "STTFNC" 2784677 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1170 2771263 2773132 2774926 "STTAYLOR" 2778191 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1169 2764393 2771127 2771210 "STRTBL" 2771215 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1168 2759757 2764348 2764379 "STRING" 2764384 T STRING (NIL) -8 NIL NIL NIL) (-1167 2754618 2759130 2759160 "STRICAT" 2759219 T STRICAT (NIL) -9 NIL 2759281 NIL) (-1166 2747371 2752237 2752848 "STREAM" 2754042 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1165 2746881 2746958 2747102 "STREAM3" 2747288 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1164 2745863 2746046 2746281 "STREAM2" 2746694 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1163 2745551 2745603 2745696 "STREAM1" 2745805 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1162 2744567 2744748 2744979 "STINPROD" 2745367 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1161 2744119 2744329 2744359 "STEP" 2744439 T STEP (NIL) -9 NIL 2744517 NIL) (-1160 2743306 2743608 2743756 "STEPAST" 2743993 T STEPAST (NIL) -8 NIL NIL NIL) (-1159 2736738 2743205 2743282 "STBL" 2743287 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1158 2731864 2735959 2736002 "STAGG" 2736155 NIL STAGG (NIL T) -9 NIL 2736244 NIL) (-1157 2729566 2730168 2731040 "STAGG-" 2731045 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1156 2727713 2729336 2729428 "STACK" 2729509 NIL STACK (NIL T) -8 NIL NIL NIL) (-1155 2720408 2725854 2726310 "SREGSET" 2727343 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1154 2712833 2714202 2715715 "SRDCMPK" 2719014 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1153 2705750 2710273 2710303 "SRAGG" 2711606 T SRAGG (NIL) -9 NIL 2712214 NIL) (-1152 2704767 2705022 2705401 "SRAGG-" 2705406 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1151 2699227 2703714 2704135 "SQMATRIX" 2704393 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1150 2692912 2695945 2696672 "SPLTREE" 2698572 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1149 2688875 2689568 2690214 "SPLNODE" 2692338 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1148 2687922 2688155 2688185 "SPFCAT" 2688629 T SPFCAT (NIL) -9 NIL NIL NIL) (-1147 2686659 2686869 2687133 "SPECOUT" 2687680 T SPECOUT (NIL) -7 NIL NIL NIL) (-1146 2677769 2679641 2679671 "SPADXPT" 2684347 T SPADXPT (NIL) -9 NIL 2686511 NIL) (-1145 2677530 2677570 2677639 "SPADPRSR" 2677722 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1144 2675579 2677485 2677516 "SPADAST" 2677521 T SPADAST (NIL) -8 NIL NIL NIL) (-1143 2667524 2669297 2669340 "SPACEC" 2673713 NIL SPACEC (NIL T) -9 NIL 2675529 NIL) (-1142 2665654 2667456 2667505 "SPACE3" 2667510 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1141 2664406 2664577 2664868 "SORTPAK" 2665459 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1140 2662498 2662801 2663213 "SOLVETRA" 2664070 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1139 2661548 2661770 2662031 "SOLVESER" 2662271 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1138 2656852 2657740 2658735 "SOLVERAD" 2660600 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1137 2652667 2653276 2654005 "SOLVEFOR" 2656219 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1136 2646937 2652016 2652113 "SNTSCAT" 2652118 NIL SNTSCAT (NIL T T T T) -9 NIL 2652188 NIL) (-1135 2641043 2645260 2645651 "SMTS" 2646627 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1134 2635728 2640931 2641008 "SMP" 2641013 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1133 2633887 2634188 2634586 "SMITH" 2635425 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1132 2626600 2630796 2630899 "SMATCAT" 2632250 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632800 NIL) (-1131 2623540 2624363 2625541 "SMATCAT-" 2625546 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1130 2621206 2622776 2622819 "SKAGG" 2623080 NIL SKAGG (NIL T) -9 NIL 2623215 NIL) (-1129 2617532 2620679 2620863 "SINT" 2621015 T SINT (NIL) -8 NIL NIL 2621177) (-1128 2617304 2617342 2617408 "SIMPAN" 2617488 T SIMPAN (NIL) -7 NIL NIL NIL) (-1127 2616583 2616839 2616979 "SIG" 2617186 T SIG (NIL) -8 NIL NIL NIL) (-1126 2615421 2615642 2615917 "SIGNRF" 2616342 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1125 2614254 2614405 2614689 "SIGNEF" 2615250 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1124 2613560 2613837 2613961 "SIGAST" 2614152 T SIGAST (NIL) -8 NIL NIL NIL) (-1123 2611250 2611704 2612210 "SHP" 2613101 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1122 2605102 2611151 2611227 "SHDP" 2611232 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1121 2604675 2604867 2604897 "SGROUP" 2604990 T SGROUP (NIL) -9 NIL 2605052 NIL) (-1120 2604533 2604559 2604632 "SGROUP-" 2604637 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1119 2601324 2602022 2602745 "SGCF" 2603832 T SGCF (NIL) -7 NIL NIL NIL) (-1118 2595692 2600771 2600868 "SFRTCAT" 2600873 NIL SFRTCAT (NIL T T T T) -9 NIL 2600912 NIL) (-1117 2589113 2590131 2591267 "SFRGCD" 2594675 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1116 2582239 2583312 2584498 "SFQCMPK" 2588046 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1115 2581859 2581948 2582059 "SFORT" 2582180 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1114 2580977 2581699 2581820 "SEXOF" 2581825 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1113 2580084 2580858 2580926 "SEX" 2580931 T SEX (NIL) -8 NIL NIL NIL) (-1112 2575597 2576312 2576407 "SEXCAT" 2579344 NIL SEXCAT (NIL T T T T T) -9 NIL 2579922 NIL) (-1111 2572750 2575531 2575579 "SET" 2575584 NIL SET (NIL T) -8 NIL NIL NIL) (-1110 2570974 2571463 2571768 "SETMN" 2572491 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1109 2570470 2570622 2570652 "SETCAT" 2570828 T SETCAT (NIL) -9 NIL 2570938 NIL) (-1108 2570162 2570240 2570370 "SETCAT-" 2570375 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1107 2566523 2568623 2568666 "SETAGG" 2569536 NIL SETAGG (NIL T) -9 NIL 2569876 NIL) (-1106 2565981 2566097 2566334 "SETAGG-" 2566339 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1105 2565424 2565677 2565778 "SEQAST" 2565902 T SEQAST (NIL) -8 NIL NIL NIL) (-1104 2564623 2564917 2564978 "SEGXCAT" 2565264 NIL SEGXCAT (NIL T T) -9 NIL 2565384 NIL) (-1103 2563629 2564289 2564471 "SEG" 2564476 NIL SEG (NIL T) -8 NIL NIL NIL) (-1102 2562608 2562822 2562865 "SEGCAT" 2563387 NIL SEGCAT (NIL T) -9 NIL 2563608 NIL) (-1101 2561540 2561971 2562179 "SEGBIND" 2562435 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1100 2561161 2561220 2561333 "SEGBIND2" 2561475 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1099 2560734 2560962 2561039 "SEGAST" 2561106 T SEGAST (NIL) -8 NIL NIL NIL) (-1098 2559953 2560079 2560283 "SEG2" 2560578 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1097 2559363 2559888 2559935 "SDVAR" 2559940 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1096 2551890 2559133 2559263 "SDPOL" 2559268 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1095 2550483 2550749 2551068 "SCPKG" 2551605 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1094 2549647 2549819 2550011 "SCOPE" 2550313 T SCOPE (NIL) -8 NIL NIL NIL) (-1093 2548867 2549001 2549180 "SCACHE" 2549502 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1092 2548513 2548699 2548729 "SASTCAT" 2548734 T SASTCAT (NIL) -9 NIL 2548747 NIL) (-1091 2548000 2548348 2548424 "SAOS" 2548459 T SAOS (NIL) -8 NIL NIL NIL) (-1090 2547565 2547600 2547773 "SAERFFC" 2547959 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1089 2541504 2547462 2547542 "SAE" 2547547 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1088 2541097 2541132 2541291 "SAEFACT" 2541463 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1087 2539418 2539732 2540133 "RURPK" 2540763 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1086 2538055 2538361 2538666 "RULESET" 2539252 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1085 2535278 2535808 2536266 "RULE" 2537736 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1084 2534890 2535072 2535155 "RULECOLD" 2535230 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1083 2534680 2534708 2534779 "RTVALUE" 2534841 T RTVALUE (NIL) -8 NIL NIL NIL) (-1082 2534151 2534397 2534491 "RSTRCAST" 2534608 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1081 2528999 2529794 2530714 "RSETGCD" 2533350 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1080 2518229 2523308 2523405 "RSETCAT" 2527524 NIL RSETCAT (NIL T T T T) -9 NIL 2528621 NIL) (-1079 2516156 2516695 2517519 "RSETCAT-" 2517524 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1078 2508542 2509918 2511438 "RSDCMPK" 2514755 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1077 2506521 2506988 2507062 "RRCC" 2508148 NIL RRCC (NIL T T) -9 NIL 2508492 NIL) (-1076 2505872 2506046 2506325 "RRCC-" 2506330 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1075 2505315 2505568 2505669 "RPTAST" 2505793 T RPTAST (NIL) -8 NIL NIL NIL) (-1074 2479161 2488520 2488587 "RPOLCAT" 2499253 NIL RPOLCAT (NIL T T T) -9 NIL 2502413 NIL) (-1073 2470659 2472999 2476121 "RPOLCAT-" 2476126 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1072 2461590 2468870 2469352 "ROUTINE" 2470199 T ROUTINE (NIL) -8 NIL NIL NIL) (-1071 2458388 2461216 2461356 "ROMAN" 2461472 T ROMAN (NIL) -8 NIL NIL NIL) (-1070 2456632 2457248 2457508 "ROIRC" 2458193 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1069 2452864 2455148 2455178 "RNS" 2455482 T RNS (NIL) -9 NIL 2455756 NIL) (-1068 2451373 2451756 2452290 "RNS-" 2452365 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1067 2450776 2451184 2451214 "RNG" 2451219 T RNG (NIL) -9 NIL 2451240 NIL) (-1066 2449779 2450141 2450343 "RNGBIND" 2450627 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1065 2449178 2449566 2449609 "RMODULE" 2449614 NIL RMODULE (NIL T) -9 NIL 2449641 NIL) (-1064 2448014 2448108 2448444 "RMCAT2" 2449079 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1063 2444864 2447360 2447657 "RMATRIX" 2447776 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1062 2437691 2439951 2440066 "RMATCAT" 2443425 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444407 NIL) (-1061 2437066 2437213 2437520 "RMATCAT-" 2437525 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1060 2436467 2436688 2436731 "RLINSET" 2436925 NIL RLINSET (NIL T) -9 NIL 2437016 NIL) (-1059 2436034 2436109 2436237 "RINTERP" 2436386 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1058 2435092 2435646 2435676 "RING" 2435732 T RING (NIL) -9 NIL 2435824 NIL) (-1057 2434884 2434928 2435025 "RING-" 2435030 NIL RING- (NIL T) -8 NIL NIL NIL) (-1056 2433725 2433962 2434220 "RIDIST" 2434648 T RIDIST (NIL) -7 NIL NIL NIL) (-1055 2425014 2433193 2433399 "RGCHAIN" 2433573 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1054 2424364 2424770 2424811 "RGBCSPC" 2424869 NIL RGBCSPC (NIL T) -9 NIL 2424921 NIL) (-1053 2423522 2423903 2423944 "RGBCMDL" 2424176 NIL RGBCMDL (NIL T) -9 NIL 2424290 NIL) (-1052 2420516 2421130 2421800 "RF" 2422886 NIL RF (NIL T) -7 NIL NIL NIL) (-1051 2420162 2420225 2420328 "RFFACTOR" 2420447 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1050 2419887 2419922 2420019 "RFFACT" 2420121 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1049 2418004 2418368 2418750 "RFDIST" 2419527 T RFDIST (NIL) -7 NIL NIL NIL) (-1048 2417457 2417549 2417712 "RETSOL" 2417906 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1047 2417093 2417173 2417216 "RETRACT" 2417349 NIL RETRACT (NIL T) -9 NIL 2417436 NIL) (-1046 2416942 2416967 2417054 "RETRACT-" 2417059 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1045 2416544 2416764 2416834 "RETAST" 2416894 T RETAST (NIL) -8 NIL NIL NIL) (-1044 2409282 2416197 2416324 "RESULT" 2416439 T RESULT (NIL) -8 NIL NIL NIL) (-1043 2407873 2408551 2408750 "RESRING" 2409185 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1042 2407509 2407558 2407656 "RESLATC" 2407810 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1041 2407214 2407249 2407356 "REPSQ" 2407468 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1040 2404636 2405216 2405818 "REP" 2406634 T REP (NIL) -7 NIL NIL NIL) (-1039 2404333 2404368 2404479 "REPDB" 2404595 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1038 2398233 2399622 2400845 "REP2" 2403145 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1037 2394610 2395291 2396099 "REP1" 2397460 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1036 2387306 2392751 2393207 "REGSET" 2394240 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1035 2386071 2386454 2386704 "REF" 2387091 NIL REF (NIL T) -8 NIL NIL NIL) (-1034 2385448 2385551 2385718 "REDORDER" 2385955 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1033 2381416 2384661 2384888 "RECLOS" 2385276 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1032 2380468 2380649 2380864 "REALSOLV" 2381223 T REALSOLV (NIL) -7 NIL NIL NIL) (-1031 2380314 2380355 2380385 "REAL" 2380390 T REAL (NIL) -9 NIL 2380425 NIL) (-1030 2376797 2377599 2378483 "REAL0Q" 2379479 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1029 2372398 2373386 2374447 "REAL0" 2375778 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1028 2371869 2372115 2372209 "RDUCEAST" 2372326 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1027 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(-861 1995929 1998213 1998334 "OREUP" 1998339 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-860 1993332 1995620 1995747 "ORESUP" 1995871 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-859 1990860 1991360 1991921 "OREPCTO" 1992821 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-858 1984546 1986747 1986788 "OREPCAT" 1989136 NIL OREPCAT (NIL T) -9 NIL 1990240 NIL) (-857 1981693 1982475 1983533 "OREPCAT-" 1983538 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-856 1980844 1981142 1981170 "ORDSET" 1981479 T ORDSET (NIL) -9 NIL 1981643 NIL) (-855 1980275 1980423 1980647 "ORDSET-" 1980652 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-854 1978840 1979631 1979659 "ORDRING" 1979861 T ORDRING (NIL) -9 NIL 1979986 NIL) (-853 1978485 1978579 1978723 "ORDRING-" 1978728 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-852 1977865 1978328 1978356 "ORDMON" 1978361 T ORDMON (NIL) -9 NIL 1978382 NIL) (-851 1977027 1977174 1977369 "ORDFUNS" 1977714 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-850 1976365 1976784 1976812 "ORDFIN" 1976877 T ORDFIN (NIL) -9 NIL 1976951 NIL) (-849 1972924 1974951 1975360 "ORDCOMP" 1975989 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-848 1972190 1972317 1972503 "ORDCOMP2" 1972784 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-847 1968771 1969681 1970495 "OPTPROB" 1971396 T OPTPROB (NIL) -8 NIL NIL NIL) (-846 1965573 1966212 1966916 "OPTPACK" 1968087 T OPTPACK (NIL) -7 NIL NIL NIL) (-845 1963260 1964026 1964054 "OPTCAT" 1964873 T OPTCAT (NIL) -9 NIL 1965523 NIL) (-844 1962644 1962937 1963042 "OPSIG" 1963175 T OPSIG (NIL) -8 NIL NIL NIL) (-843 1962412 1962451 1962517 "OPQUERY" 1962598 T OPQUERY (NIL) -7 NIL NIL NIL) (-842 1959543 1960723 1961227 "OP" 1961941 NIL OP (NIL T) -8 NIL NIL NIL) (-841 1958917 1959143 1959184 "OPERCAT" 1959396 NIL OPERCAT (NIL T) -9 NIL 1959493 NIL) (-840 1958672 1958728 1958845 "OPERCAT-" 1958850 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-839 1955485 1957469 1957838 "ONECOMP" 1958336 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-838 1954790 1954905 1955079 "ONECOMP2" 1955357 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954209 1954315 1954445 "OMSERVER" 1954680 T OMSERVER (NIL) -7 NIL NIL NIL) (-836 1951071 1953649 1953689 "OMSAGG" 1953750 NIL OMSAGG (NIL T) -9 NIL 1953814 NIL) (-835 1949694 1949957 1950239 "OMPKG" 1950809 T OMPKG (NIL) -7 NIL NIL NIL) (-834 1949124 1949227 1949255 "OM" 1949554 T OM (NIL) -9 NIL NIL NIL) (-833 1947671 1948673 1948842 "OMLO" 1949005 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-832 1946631 1946778 1946998 "OMEXPR" 1947497 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-831 1945922 1946177 1946313 "OMERR" 1946515 T OMERR (NIL) -8 NIL NIL NIL) (-830 1945073 1945343 1945503 "OMERRK" 1945782 T OMERRK (NIL) -8 NIL NIL NIL) (-829 1944524 1944750 1944858 "OMENC" 1944985 T OMENC (NIL) -8 NIL NIL NIL) (-828 1938419 1939604 1940775 "OMDEV" 1943373 T OMDEV (NIL) -8 NIL NIL NIL) (-827 1937488 1937659 1937853 "OMCONN" 1938245 T OMCONN (NIL) -8 NIL NIL NIL) (-826 1936009 1936985 1937013 "OINTDOM" 1937018 T OINTDOM (NIL) -9 NIL 1937039 NIL) (-825 1933347 1934697 1935034 "OFMONOID" 1935704 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-824 1932758 1933284 1933329 "ODVAR" 1933334 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-823 1930181 1932503 1932658 "ODR" 1932663 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-822 1922762 1929957 1930083 "ODPOL" 1930088 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-821 1916584 1922634 1922739 "ODP" 1922744 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-820 1915350 1915565 1915840 "ODETOOLS" 1916358 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-819 1912317 1912975 1913691 "ODESYS" 1914683 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-818 1907199 1908107 1909132 "ODERTRIC" 1911392 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-817 1906625 1906707 1906901 "ODERED" 1907111 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-816 1903513 1904061 1904738 "ODERAT" 1906048 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-815 1900472 1900937 1901534 "ODEPRRIC" 1903042 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-814 1898415 1899011 1899497 "ODEPROB" 1900006 T ODEPROB (NIL) -8 NIL NIL NIL) (-813 1894935 1895420 1896067 "ODEPRIM" 1897894 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-812 1894184 1894286 1894546 "ODEPAL" 1894827 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-811 1890346 1891137 1892001 "ODEPACK" 1893340 T ODEPACK (NIL) -7 NIL NIL NIL) (-810 1889407 1889514 1889736 "ODEINT" 1890235 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-809 1883508 1884933 1886380 "ODEIFTBL" 1887980 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-808 1878906 1879692 1880644 "ODEEF" 1882667 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-807 1878255 1878344 1878567 "ODECONST" 1878811 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-806 1876380 1877041 1877069 "ODECAT" 1877674 T ODECAT (NIL) -9 NIL 1878205 NIL) (-805 1873235 1876085 1876207 "OCT" 1876290 NIL OCT (NIL T) -8 NIL NIL NIL) (-804 1872873 1872916 1873043 "OCTCT2" 1873186 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-803 1867522 1869957 1869997 "OC" 1871094 NIL OC (NIL T) -9 NIL 1871952 NIL) (-802 1864749 1865497 1866487 "OC-" 1866581 NIL OC- (NIL T T) -8 NIL NIL NIL) (-801 1864101 1864569 1864597 "OCAMON" 1864602 T OCAMON (NIL) -9 NIL 1864623 NIL) (-800 1863632 1863973 1864001 "OASGP" 1864006 T OASGP (NIL) -9 NIL 1864026 NIL) (-799 1862893 1863382 1863410 "OAMONS" 1863450 T OAMONS (NIL) -9 NIL 1863493 NIL) (-798 1862307 1862740 1862768 "OAMON" 1862773 T OAMON (NIL) -9 NIL 1862793 NIL) (-797 1861565 1862083 1862111 "OAGROUP" 1862116 T OAGROUP (NIL) -9 NIL 1862136 NIL) (-796 1861255 1861305 1861393 "NUMTUBE" 1861509 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-795 1854828 1856346 1857882 "NUMQUAD" 1859739 T NUMQUAD (NIL) -7 NIL NIL NIL) (-794 1850584 1851572 1852597 "NUMODE" 1853823 T NUMODE (NIL) -7 NIL NIL NIL) (-793 1847939 1848819 1848847 "NUMINT" 1849770 T NUMINT (NIL) -9 NIL 1850534 NIL) (-792 1846887 1847084 1847302 "NUMFMT" 1847741 T NUMFMT (NIL) -7 NIL NIL NIL) (-791 1833246 1836191 1838723 "NUMERIC" 1844394 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-790 1827616 1832695 1832790 "NTSCAT" 1832795 NIL NTSCAT (NIL T T T T) -9 NIL 1832834 NIL) (-789 1826810 1826975 1827168 "NTPOLFN" 1827455 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-788 1814887 1823635 1824447 "NSUP" 1826031 NIL NSUP (NIL T) -8 NIL NIL NIL) (-787 1814519 1814576 1814685 "NSUP2" 1814824 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-786 1804745 1814293 1814426 "NSMP" 1814431 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-785 1803177 1803478 1803835 "NREP" 1804433 NIL NREP (NIL T) -7 NIL NIL NIL) (-784 1801768 1802020 1802378 "NPCOEF" 1802920 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-783 1800834 1800949 1801165 "NORMRETR" 1801649 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-782 1798875 1799165 1799574 "NORMPK" 1800542 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-781 1798560 1798588 1798712 "NORMMA" 1798841 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-780 1798360 1798517 1798546 "NONE" 1798551 T NONE (NIL) -8 NIL NIL NIL) (-779 1798149 1798178 1798247 "NONE1" 1798324 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-778 1797646 1797708 1797887 "NODE1" 1798081 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-777 1795931 1796782 1797037 "NNI" 1797384 T NNI (NIL) -8 NIL NIL 1797619) (-776 1794351 1794664 1795028 "NLINSOL" 1795599 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-775 1790592 1791587 1792486 "NIPROB" 1793472 T NIPROB (NIL) -8 NIL NIL NIL) (-774 1789349 1789583 1789885 "NFINTBAS" 1790354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-773 1788523 1788999 1789040 "NETCLT" 1789212 NIL NETCLT (NIL T) -9 NIL 1789294 NIL) (-772 1787231 1787462 1787743 "NCODIV" 1788291 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-771 1786993 1787030 1787105 "NCNTFRAC" 1787188 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-770 1785173 1785537 1785957 "NCEP" 1786618 NIL NCEP (NIL T) -7 NIL NIL NIL) (-769 1784024 1784797 1784825 "NASRING" 1784935 T NASRING (NIL) -9 NIL 1785015 NIL) (-768 1783819 1783863 1783957 "NASRING-" 1783962 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-767 1782926 1783451 1783479 "NARNG" 1783596 T NARNG (NIL) -9 NIL 1783687 NIL) (-766 1782618 1782685 1782819 "NARNG-" 1782824 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-765 1781497 1781704 1781939 "NAGSP" 1782403 T NAGSP (NIL) -7 NIL NIL NIL) (-764 1772769 1774453 1776126 "NAGS" 1779844 T NAGS (NIL) -7 NIL NIL NIL) (-763 1771317 1771625 1771956 "NAGF07" 1772458 T NAGF07 (NIL) -7 NIL NIL NIL) (-762 1765855 1767146 1768453 "NAGF04" 1770030 T NAGF04 (NIL) -7 NIL NIL NIL) (-761 1758823 1760437 1762070 "NAGF02" 1764242 T NAGF02 (NIL) -7 NIL NIL NIL) (-760 1754047 1755147 1756264 "NAGF01" 1757726 T NAGF01 (NIL) -7 NIL NIL NIL) (-759 1747675 1749241 1750826 "NAGE04" 1752482 T NAGE04 (NIL) -7 NIL NIL NIL) (-758 1738844 1740965 1743095 "NAGE02" 1745565 T NAGE02 (NIL) -7 NIL NIL NIL) (-757 1734797 1735744 1736708 "NAGE01" 1737900 T NAGE01 (NIL) -7 NIL NIL NIL) (-756 1732592 1733126 1733684 "NAGD03" 1734259 T NAGD03 (NIL) -7 NIL NIL NIL) (-755 1724342 1726270 1728224 "NAGD02" 1730658 T NAGD02 (NIL) -7 NIL NIL NIL) (-754 1718153 1719578 1721018 "NAGD01" 1722922 T NAGD01 (NIL) -7 NIL NIL NIL) (-753 1714362 1715184 1716021 "NAGC06" 1717336 T NAGC06 (NIL) -7 NIL NIL NIL) (-752 1712827 1713159 1713515 "NAGC05" 1714026 T NAGC05 (NIL) -7 NIL NIL NIL) (-751 1712203 1712322 1712466 "NAGC02" 1712703 T NAGC02 (NIL) -7 NIL NIL NIL) (-750 1711162 1711745 1711785 "NAALG" 1711864 NIL NAALG (NIL T) -9 NIL 1711925 NIL) (-749 1710997 1711026 1711116 "NAALG-" 1711121 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-748 1704947 1706055 1707242 "MULTSQFR" 1709893 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-747 1704266 1704341 1704525 "MULTFACT" 1704859 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-746 1696990 1700903 1700956 "MTSCAT" 1702026 NIL MTSCAT (NIL T T) -9 NIL 1702541 NIL) (-745 1696702 1696756 1696848 "MTHING" 1696930 NIL MTHING (NIL T) -7 NIL NIL NIL) (-744 1696494 1696527 1696587 "MSYSCMD" 1696662 T MSYSCMD (NIL) -7 NIL NIL NIL) (-743 1692576 1695249 1695569 "MSET" 1696207 NIL MSET (NIL T) -8 NIL NIL NIL) (-742 1689645 1692137 1692178 "MSETAGG" 1692183 NIL MSETAGG (NIL T) -9 NIL 1692217 NIL) (-741 1685487 1687024 1687769 "MRING" 1688945 NIL MRING (NIL T T) -8 NIL NIL NIL) (-740 1685053 1685120 1685251 "MRF2" 1685414 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-739 1684671 1684706 1684850 "MRATFAC" 1685012 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-738 1682283 1682578 1683009 "MPRFF" 1684376 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-737 1676580 1682137 1682234 "MPOLY" 1682239 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-736 1676070 1676105 1676313 "MPCPF" 1676539 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-735 1675584 1675627 1675811 "MPC3" 1676021 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-734 1674779 1674860 1675081 "MPC2" 1675499 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1673080 1673417 1673807 "MONOTOOL" 1674439 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-732 1672305 1672622 1672650 "MONOID" 1672869 T MONOID (NIL) -9 NIL 1673016 NIL) (-731 1671851 1671970 1672151 "MONOID-" 1672156 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-730 1662326 1668277 1668336 "MONOGEN" 1669010 NIL MONOGEN (NIL T T) -9 NIL 1669466 NIL) (-729 1659544 1660279 1661279 "MONOGEN-" 1661398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-728 1658377 1658823 1658851 "MONADWU" 1659243 T MONADWU (NIL) -9 NIL 1659481 NIL) (-727 1657749 1657908 1658156 "MONADWU-" 1658161 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-726 1657108 1657352 1657380 "MONAD" 1657587 T MONAD (NIL) -9 NIL 1657699 NIL) (-725 1656793 1656871 1657003 "MONAD-" 1657008 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-724 1655082 1655706 1655985 "MOEBIUS" 1656546 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-723 1654360 1654764 1654804 "MODULE" 1654809 NIL MODULE (NIL T) -9 NIL 1654848 NIL) (-722 1653928 1654024 1654214 "MODULE-" 1654219 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-721 1651608 1652292 1652619 "MODRING" 1653752 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1648552 1649713 1650234 "MODOP" 1651137 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-719 1647140 1647619 1647896 "MODMONOM" 1648415 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-718 1637184 1645431 1645845 "MODMON" 1646777 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-717 1634340 1636028 1636304 "MODFIELD" 1637059 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-716 1633317 1633621 1633811 "MMLFORM" 1634170 T MMLFORM (NIL) -8 NIL NIL NIL) (-715 1632843 1632886 1633065 "MMAP" 1633268 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-714 1630922 1631689 1631730 "MLO" 1632153 NIL MLO (NIL T) -9 NIL 1632395 NIL) (-713 1628288 1628804 1629406 "MLIFT" 1630403 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-712 1627679 1627763 1627917 "MKUCFUNC" 1628199 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-711 1627278 1627348 1627471 "MKRECORD" 1627602 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-710 1626325 1626487 1626715 "MKFUNC" 1627089 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-709 1625713 1625817 1625973 "MKFLCFN" 1626208 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-708 1624990 1625092 1625277 "MKBCFUNC" 1625606 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-707 1621697 1624544 1624680 "MINT" 1624874 T MINT (NIL) -8 NIL NIL NIL) (-706 1620509 1620752 1621029 "MHROWRED" 1621452 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-705 1615889 1619044 1619449 "MFLOAT" 1620124 T MFLOAT (NIL) -8 NIL NIL NIL) (-704 1615246 1615322 1615493 "MFINFACT" 1615801 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-703 1611561 1612409 1613293 "MESH" 1614382 T MESH (NIL) -7 NIL NIL NIL) (-702 1609951 1610263 1610616 "MDDFACT" 1611248 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-701 1606746 1609110 1609151 "MDAGG" 1609406 NIL MDAGG (NIL T) -9 NIL 1609549 NIL) (-700 1596486 1606039 1606246 "MCMPLX" 1606559 T MCMPLX (NIL) -8 NIL NIL NIL) (-699 1595623 1595769 1595970 "MCDEN" 1596335 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-698 1593513 1593783 1594163 "MCALCFN" 1595353 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-697 1592438 1592678 1592911 "MAYBE" 1593319 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-696 1590050 1590573 1591135 "MATSTOR" 1591909 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-695 1586007 1589422 1589670 "MATRIX" 1589835 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-694 1581773 1582480 1583216 "MATLIN" 1585364 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-693 1571879 1575065 1575142 "MATCAT" 1580022 NIL MATCAT (NIL T T T) -9 NIL 1581439 NIL) (-692 1568235 1569256 1570612 "MATCAT-" 1570617 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-691 1566829 1566982 1567315 "MATCAT2" 1568070 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-690 1564941 1565265 1565649 "MAPPKG3" 1566504 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-689 1563922 1564095 1564317 "MAPPKG2" 1564765 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-688 1562421 1562705 1563032 "MAPPKG1" 1563628 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-687 1561500 1561827 1562004 "MAPPAST" 1562264 T MAPPAST (NIL) -8 NIL NIL NIL) (-686 1561111 1561169 1561292 "MAPHACK3" 1561436 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-685 1560703 1560764 1560878 "MAPHACK2" 1561043 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-684 1560141 1560244 1560386 "MAPHACK1" 1560594 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-683 1558220 1558841 1559145 "MAGMA" 1559869 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-682 1557699 1557944 1558035 "MACROAST" 1558149 T MACROAST (NIL) -8 NIL NIL NIL) (-681 1554117 1555938 1556399 "M3D" 1557271 NIL M3D (NIL T) -8 NIL NIL NIL) (-680 1548223 1552486 1552527 "LZSTAGG" 1553309 NIL LZSTAGG (NIL T) -9 NIL 1553604 NIL) (-679 1544181 1545354 1546811 "LZSTAGG-" 1546816 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-678 1541268 1542072 1542559 "LWORD" 1543726 NIL LWORD (NIL T) -8 NIL NIL NIL) (-677 1540844 1541072 1541147 "LSTAST" 1541213 T LSTAST (NIL) -8 NIL NIL NIL) (-676 1534010 1540615 1540749 "LSQM" 1540754 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-675 1533234 1533373 1533601 "LSPP" 1533865 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-674 1531046 1531347 1531803 "LSMP" 1532923 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-673 1527825 1528499 1529229 "LSMP1" 1530348 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-672 1521702 1526992 1527033 "LSAGG" 1527095 NIL LSAGG (NIL T) -9 NIL 1527173 NIL) (-671 1518397 1519321 1520534 "LSAGG-" 1520539 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-670 1515996 1517541 1517790 "LPOLY" 1518192 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-669 1515578 1515663 1515786 "LPEFRAC" 1515905 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-668 1513899 1514672 1514925 "LO" 1515410 NIL LO (NIL T T T) -8 NIL NIL NIL) (-667 1513551 1513663 1513691 "LOGIC" 1513802 T LOGIC (NIL) -9 NIL 1513883 NIL) (-666 1513413 1513436 1513507 "LOGIC-" 1513512 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-665 1512606 1512746 1512939 "LODOOPS" 1513269 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-664 1510029 1512522 1512588 "LODO" 1512593 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-663 1508567 1508802 1509155 "LODOF" 1509776 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-662 1504785 1507216 1507257 "LODOCAT" 1507695 NIL LODOCAT (NIL T) -9 NIL 1507906 NIL) (-661 1504518 1504576 1504703 "LODOCAT-" 1504708 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-660 1501838 1504359 1504477 "LODO2" 1504482 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-659 1499273 1501775 1501820 "LODO1" 1501825 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-658 1498154 1498319 1498624 "LODEEF" 1499096 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-657 1493393 1496284 1496325 "LNAGG" 1497272 NIL LNAGG (NIL T) -9 NIL 1497716 NIL) (-656 1492540 1492754 1493096 "LNAGG-" 1493101 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-655 1488676 1489465 1490104 "LMOPS" 1491955 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-654 1488079 1488467 1488508 "LMODULE" 1488513 NIL LMODULE (NIL T) -9 NIL 1488539 NIL) (-653 1485277 1487724 1487847 "LMDICT" 1487989 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-652 1484683 1484904 1484945 "LLINSET" 1485136 NIL LLINSET (NIL T) -9 NIL 1485227 NIL) (-651 1484382 1484591 1484651 "LITERAL" 1484656 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-650 1477545 1483316 1483620 "LIST" 1484111 NIL LIST (NIL T) -8 NIL NIL NIL) (-649 1477070 1477144 1477283 "LIST3" 1477465 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-648 1476077 1476255 1476483 "LIST2" 1476888 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-647 1474211 1474523 1474922 "LIST2MAP" 1475724 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-646 1473807 1474044 1474085 "LINSET" 1474090 NIL LINSET (NIL T) -9 NIL 1474124 NIL) (-645 1472468 1473138 1473179 "LINEXP" 1473434 NIL LINEXP (NIL T) -9 NIL 1473583 NIL) (-644 1471115 1471375 1471672 "LINDEP" 1472220 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-643 1467882 1468601 1469378 "LIMITRF" 1470370 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-642 1466185 1466481 1466890 "LIMITPS" 1467577 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-641 1460613 1465696 1465924 "LIE" 1466006 NIL LIE (NIL T T) -8 NIL NIL NIL) (-640 1459561 1460030 1460070 "LIECAT" 1460210 NIL LIECAT (NIL T) -9 NIL 1460361 NIL) (-639 1459402 1459429 1459517 "LIECAT-" 1459522 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-638 1451898 1458851 1459016 "LIB" 1459257 T LIB (NIL) -8 NIL NIL NIL) (-637 1447533 1448416 1449351 "LGROBP" 1451015 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-636 1445531 1445805 1446155 "LF" 1447254 NIL LF (NIL T T) -7 NIL NIL NIL) (-635 1444371 1445063 1445091 "LFCAT" 1445298 T LFCAT (NIL) -9 NIL 1445437 NIL) (-634 1441273 1441903 1442591 "LEXTRIPK" 1443735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-633 1438017 1438843 1439346 "LEXP" 1440853 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-632 1437493 1437738 1437830 "LETAST" 1437945 T LETAST (NIL) -8 NIL NIL NIL) (-631 1435891 1436204 1436605 "LEADCDET" 1437175 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-630 1435081 1435155 1435384 "LAZM3PK" 1435812 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-629 1429998 1433158 1433696 "LAUPOL" 1434593 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-628 1429577 1429621 1429782 "LAPLACE" 1429948 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-627 1427516 1428678 1428929 "LA" 1429410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-626 1426510 1427094 1427135 "LALG" 1427197 NIL LALG (NIL T) -9 NIL 1427256 NIL) (-625 1426224 1426283 1426419 "LALG-" 1426424 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-624 1426059 1426083 1426124 "KVTFROM" 1426186 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-623 1424982 1425426 1425611 "KTVLOGIC" 1425894 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-622 1424817 1424841 1424882 "KRCFROM" 1424944 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-621 1423721 1423908 1424207 "KOVACIC" 1424617 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-620 1423556 1423580 1423621 "KONVERT" 1423683 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-619 1423391 1423415 1423456 "KOERCE" 1423518 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-618 1421221 1421984 1422361 "KERNEL" 1423047 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-617 1420717 1420798 1420930 "KERNEL2" 1421135 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-616 1414487 1419256 1419310 "KDAGG" 1419687 NIL KDAGG (NIL T T) -9 NIL 1419893 NIL) (-615 1414016 1414140 1414345 "KDAGG-" 1414350 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1407164 1413677 1413832 "KAFILE" 1413894 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-613 1401592 1406675 1406903 "JORDAN" 1406985 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-612 1400971 1401241 1401362 "JOINAST" 1401491 T JOINAST (NIL) -8 NIL NIL NIL) (-611 1400817 1400876 1400931 "JAVACODE" 1400936 T JAVACODE (NIL) -8 NIL NIL NIL) (-610 1397069 1399022 1399076 "IXAGG" 1400005 NIL IXAGG (NIL T T) -9 NIL 1400464 NIL) (-609 1395988 1396294 1396713 "IXAGG-" 1396718 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1391518 1395910 1395969 "IVECTOR" 1395974 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-607 1390284 1390521 1390787 "ITUPLE" 1391285 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-606 1388786 1388963 1389258 "ITRIGMNP" 1390106 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-605 1387531 1387735 1388018 "ITFUN3" 1388562 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-604 1387163 1387220 1387329 "ITFUN2" 1387468 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-603 1386322 1386643 1386817 "ITFORM" 1387009 T ITFORM (NIL) -8 NIL NIL NIL) (-602 1384283 1385342 1385620 "ITAYLOR" 1386077 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-601 1373228 1378420 1379583 "ISUPS" 1383153 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-600 1372332 1372472 1372708 "ISUMP" 1373075 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-599 1367707 1372277 1372318 "ISTRING" 1372323 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-598 1367183 1367428 1367520 "ISAST" 1367635 T ISAST (NIL) -8 NIL NIL NIL) (-597 1366392 1366474 1366690 "IRURPK" 1367097 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-596 1365328 1365529 1365769 "IRSN" 1366172 T IRSN (NIL) -7 NIL NIL NIL) (-595 1363399 1363754 1364183 "IRRF2F" 1364966 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-594 1363146 1363184 1363260 "IRREDFFX" 1363355 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-593 1361761 1362020 1362319 "IROOT" 1362879 NIL IROOT (NIL T) -7 NIL NIL NIL) (-592 1358365 1359445 1360137 "IR" 1361101 NIL IR (NIL T) -8 NIL NIL NIL) (-591 1357570 1357858 1358009 "IRFORM" 1358234 T IRFORM (NIL) -8 NIL NIL NIL) (-590 1355183 1355678 1356244 "IR2" 1357048 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-589 1354283 1354396 1354610 "IR2F" 1355066 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-588 1354074 1354108 1354168 "IPRNTPK" 1354243 T IPRNTPK (NIL) -7 NIL NIL NIL) (-587 1350655 1353963 1354032 "IPF" 1354037 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-586 1348982 1350580 1350637 "IPADIC" 1350642 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-585 1348294 1348542 1348672 "IP4ADDR" 1348872 T IP4ADDR (NIL) -8 NIL NIL NIL) (-584 1347668 1347923 1348055 "IOMODE" 1348182 T IOMODE (NIL) -8 NIL NIL NIL) (-583 1346741 1347265 1347392 "IOBFILE" 1347561 T IOBFILE (NIL) -8 NIL NIL NIL) (-582 1346229 1346645 1346673 "IOBCON" 1346678 T IOBCON (NIL) -9 NIL 1346699 NIL) (-581 1345740 1345798 1345981 "INVLAPLA" 1346165 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-580 1335388 1337742 1340128 "INTTR" 1343404 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-579 1331723 1332465 1333330 "INTTOOLS" 1334573 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-578 1331309 1331400 1331517 "INTSLPE" 1331626 T INTSLPE (NIL) -7 NIL NIL NIL) (-577 1329262 1331232 1331291 "INTRVL" 1331296 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-576 1326864 1327376 1327951 "INTRF" 1328747 NIL INTRF (NIL T) -7 NIL NIL NIL) (-575 1326275 1326372 1326514 "INTRET" 1326762 NIL INTRET (NIL T) -7 NIL NIL NIL) (-574 1324272 1324661 1325131 "INTRAT" 1325883 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-573 1321535 1322118 1322737 "INTPM" 1323757 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-572 1318280 1318879 1319617 "INTPAF" 1320921 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-571 1313459 1314421 1315472 "INTPACK" 1317249 T INTPACK (NIL) -7 NIL NIL NIL) (-570 1310407 1313256 1313365 "INT" 1313370 T INT (NIL) -8 NIL NIL NIL) (-569 1309659 1309811 1310019 "INTHERTR" 1310249 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-568 1309098 1309178 1309366 "INTHERAL" 1309573 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-567 1306944 1307387 1307844 "INTHEORY" 1308661 T INTHEORY (NIL) -7 NIL NIL NIL) (-566 1298350 1299971 1301743 "INTG0" 1305296 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-565 1278923 1283713 1288523 "INTFTBL" 1293560 T INTFTBL (NIL) -8 NIL NIL NIL) (-564 1278172 1278310 1278483 "INTFACT" 1278782 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-563 1275599 1276045 1276602 "INTEF" 1277726 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-562 1273966 1274705 1274733 "INTDOM" 1275034 T INTDOM (NIL) -9 NIL 1275241 NIL) (-561 1273335 1273509 1273751 "INTDOM-" 1273756 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-560 1269723 1271651 1271705 "INTCAT" 1272504 NIL INTCAT (NIL T) -9 NIL 1272825 NIL) (-559 1269195 1269298 1269426 "INTBIT" 1269615 T INTBIT (NIL) -7 NIL NIL NIL) (-558 1267894 1268048 1268355 "INTALG" 1269040 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-557 1267377 1267467 1267624 "INTAF" 1267798 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-556 1260720 1267187 1267327 "INTABL" 1267332 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-555 1260061 1260527 1260592 "INT8" 1260626 T INT8 (NIL) -8 NIL NIL 1260671) (-554 1259401 1259867 1259932 "INT64" 1259966 T INT64 (NIL) -8 NIL NIL 1260011) (-553 1258741 1259207 1259272 "INT32" 1259306 T INT32 (NIL) -8 NIL NIL 1259351) (-552 1258081 1258547 1258612 "INT16" 1258646 T INT16 (NIL) -8 NIL NIL 1258691) (-551 1252991 1255704 1255732 "INS" 1256666 T INS (NIL) -9 NIL 1257331 NIL) (-550 1250231 1251002 1251976 "INS-" 1252049 NIL INS- (NIL T) -8 NIL NIL NIL) (-549 1249006 1249233 1249531 "INPSIGN" 1249984 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-548 1248124 1248241 1248438 "INPRODPF" 1248886 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-547 1247018 1247135 1247372 "INPRODFF" 1248004 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-546 1246018 1246170 1246430 "INNMFACT" 1246854 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-545 1245215 1245312 1245500 "INMODGCD" 1245917 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-544 1243723 1243968 1244292 "INFSP" 1244960 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-543 1242907 1243024 1243207 "INFPROD0" 1243603 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-542 1239762 1240972 1241487 "INFORM" 1242400 T INFORM (NIL) -8 NIL NIL NIL) (-541 1239372 1239432 1239530 "INFORM1" 1239697 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-540 1238895 1238984 1239098 "INFINITY" 1239278 T INFINITY (NIL) -7 NIL NIL NIL) (-539 1238071 1238615 1238716 "INETCLTS" 1238814 T INETCLTS (NIL) -8 NIL NIL NIL) (-538 1236687 1236937 1237258 "INEP" 1237819 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-537 1235936 1236584 1236649 "INDE" 1236654 NIL INDE (NIL T) -8 NIL NIL NIL) (-536 1235500 1235568 1235685 "INCRMAPS" 1235863 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-535 1234318 1234769 1234975 "INBFILE" 1235314 T INBFILE (NIL) -8 NIL NIL NIL) (-534 1229617 1230554 1231498 "INBFF" 1233406 NIL INBFF (NIL T) -7 NIL NIL NIL) (-533 1228525 1228794 1228822 "INBCON" 1229335 T INBCON (NIL) -9 NIL 1229601 NIL) (-532 1227777 1228000 1228276 "INBCON-" 1228281 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-531 1227256 1227501 1227592 "INAST" 1227706 T INAST (NIL) -8 NIL NIL NIL) (-530 1226683 1226935 1227041 "IMPTAST" 1227170 T IMPTAST (NIL) -8 NIL NIL NIL) (-529 1223129 1226527 1226631 "IMATRIX" 1226636 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-528 1221837 1221960 1222276 "IMATQF" 1222985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-527 1220057 1220284 1220621 "IMATLIN" 1221593 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-526 1214635 1219981 1220039 "ILIST" 1220044 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-525 1212540 1214495 1214608 "IIARRAY2" 1214613 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-524 1207938 1212451 1212515 "IFF" 1212520 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-523 1207285 1207555 1207671 "IFAST" 1207842 T IFAST (NIL) -8 NIL NIL NIL) (-522 1202280 1206577 1206765 "IFARRAY" 1207142 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-521 1201460 1202184 1202257 "IFAMON" 1202262 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-520 1201044 1201109 1201163 "IEVALAB" 1201370 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-519 1200719 1200787 1200947 "IEVALAB-" 1200952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-518 1200350 1200633 1200696 "IDPO" 1200701 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-517 1199600 1200239 1200314 "IDPOAMS" 1200319 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-516 1198907 1199489 1199564 "IDPOAM" 1199569 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-515 1197966 1198242 1198295 "IDPC" 1198708 NIL IDPC (NIL T T) -9 NIL 1198857 NIL) (-514 1197435 1197858 1197931 "IDPAM" 1197936 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-513 1196811 1197327 1197400 "IDPAG" 1197405 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-512 1196456 1196647 1196722 "IDENT" 1196756 T IDENT (NIL) -8 NIL NIL NIL) (-511 1192711 1193559 1194454 "IDECOMP" 1195613 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-510 1185549 1186634 1187681 "IDEAL" 1191747 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-509 1184709 1184821 1185021 "ICDEN" 1185433 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-508 1183780 1184189 1184336 "ICARD" 1184582 T ICARD (NIL) -8 NIL NIL NIL) (-507 1181840 1182153 1182558 "IBPTOOLS" 1183457 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-506 1177447 1181460 1181573 "IBITS" 1181759 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-505 1174170 1174746 1175441 "IBATOOL" 1176864 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-504 1171949 1172411 1172944 "IBACHIN" 1173705 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-503 1169778 1171795 1171898 "IARRAY2" 1171903 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-502 1165884 1169704 1169761 "IARRAY1" 1169766 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-501 1159993 1164296 1164777 "IAN" 1165423 T IAN (NIL) -8 NIL NIL NIL) (-500 1159504 1159561 1159734 "IALGFACT" 1159930 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-499 1159032 1159145 1159173 "HYPCAT" 1159380 T HYPCAT (NIL) -9 NIL NIL NIL) (-498 1158570 1158687 1158873 "HYPCAT-" 1158878 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-497 1158165 1158365 1158448 "HOSTNAME" 1158507 T HOSTNAME (NIL) -8 NIL NIL NIL) (-496 1158010 1158047 1158088 "HOMOTOP" 1158093 NIL HOMOTOP (NIL T) -9 NIL 1158126 NIL) (-495 1154642 1156020 1156061 "HOAGG" 1157042 NIL HOAGG (NIL T) -9 NIL 1157721 NIL) (-494 1153236 1153635 1154161 "HOAGG-" 1154166 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-493 1147238 1152829 1152979 "HEXADEC" 1153106 T HEXADEC (NIL) -8 NIL NIL NIL) (-492 1145986 1146208 1146471 "HEUGCD" 1147015 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-491 1145062 1145823 1145953 "HELLFDIV" 1145958 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-490 1143241 1144839 1144927 "HEAP" 1145006 NIL HEAP (NIL T) -8 NIL NIL NIL) (-489 1142504 1142793 1142927 "HEADAST" 1143127 T HEADAST (NIL) -8 NIL NIL NIL) (-488 1136370 1142419 1142481 "HDP" 1142486 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-487 1130358 1136005 1136157 "HDMP" 1136271 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-486 1129682 1129822 1129986 "HB" 1130214 T HB (NIL) -7 NIL NIL NIL) (-485 1123068 1129528 1129632 "HASHTBL" 1129637 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-484 1122544 1122789 1122881 "HASAST" 1122996 T HASAST (NIL) -8 NIL NIL NIL) (-483 1120322 1122166 1122348 "HACKPI" 1122382 T HACKPI (NIL) -8 NIL NIL NIL) (-482 1115990 1120175 1120288 "GTSET" 1120293 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-481 1109405 1115868 1115966 "GSTBL" 1115971 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-480 1101683 1108436 1108701 "GSERIES" 1109196 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-479 1100824 1101241 1101269 "GROUP" 1101472 T GROUP (NIL) -9 NIL 1101606 NIL) (-478 1100190 1100349 1100600 "GROUP-" 1100605 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-477 1098557 1098878 1099265 "GROEBSOL" 1099867 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-476 1097471 1097759 1097810 "GRMOD" 1098339 NIL GRMOD (NIL T T) -9 NIL 1098507 NIL) (-475 1097239 1097275 1097403 "GRMOD-" 1097408 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-474 1092529 1093593 1094593 "GRIMAGE" 1096259 T GRIMAGE (NIL) -8 NIL NIL NIL) (-473 1090995 1091256 1091580 "GRDEF" 1092225 T GRDEF (NIL) -7 NIL NIL NIL) (-472 1090439 1090555 1090696 "GRAY" 1090874 T GRAY (NIL) -7 NIL NIL NIL) (-471 1089626 1090032 1090083 "GRALG" 1090236 NIL GRALG (NIL T T) -9 NIL 1090329 NIL) (-470 1089287 1089360 1089523 "GRALG-" 1089528 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-469 1086064 1088872 1089050 "GPOLSET" 1089194 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-468 1085418 1085475 1085733 "GOSPER" 1086001 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-467 1081150 1081856 1082382 "GMODPOL" 1085117 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-466 1080155 1080339 1080577 "GHENSEL" 1080962 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-465 1074311 1075154 1076174 "GENUPS" 1079239 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-464 1074008 1074059 1074148 "GENUFACT" 1074254 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-463 1073420 1073497 1073662 "GENPGCD" 1073926 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-462 1072894 1072929 1073142 "GENMFACT" 1073379 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-461 1071460 1071717 1072024 "GENEEZ" 1072637 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-460 1065608 1071071 1071233 "GDMP" 1071383 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-459 1054951 1059379 1060485 "GCNAALG" 1064591 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-458 1053278 1054140 1054168 "GCDDOM" 1054423 T GCDDOM (NIL) -9 NIL 1054580 NIL) (-457 1052748 1052875 1053090 "GCDDOM-" 1053095 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-456 1051420 1051605 1051909 "GB" 1052527 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-455 1040036 1042366 1044758 "GBINTERN" 1049111 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-454 1037873 1038165 1038586 "GBF" 1039711 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-453 1036654 1036819 1037086 "GBEUCLID" 1037689 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-452 1036003 1036128 1036277 "GAUSSFAC" 1036525 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-451 1034370 1034672 1034986 "GALUTIL" 1035722 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-450 1032678 1032952 1033276 "GALPOLYU" 1034097 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-449 1030043 1030333 1030740 "GALFACTU" 1032375 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-448 1021849 1023348 1024956 "GALFACT" 1028475 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-447 1019237 1019895 1019923 "FVFUN" 1021079 T FVFUN (NIL) -9 NIL 1021799 NIL) (-446 1018503 1018685 1018713 "FVC" 1019004 T FVC (NIL) -9 NIL 1019187 NIL) (-445 1018146 1018328 1018396 "FUNDESC" 1018455 T FUNDESC (NIL) -8 NIL NIL NIL) (-444 1017761 1017943 1018024 "FUNCTION" 1018098 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-443 1015505 1016083 1016549 "FT" 1017315 T FT (NIL) -8 NIL NIL NIL) (-442 1014296 1014806 1015009 "FTEM" 1015322 T FTEM (NIL) -8 NIL NIL NIL) (-441 1012587 1012876 1013273 "FSUPFACT" 1013987 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-440 1010984 1011273 1011605 "FST" 1012275 T FST (NIL) -8 NIL NIL NIL) (-439 1010183 1010289 1010477 "FSRED" 1010866 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-438 1008882 1009138 1009485 "FSPRMELT" 1009898 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-437 1006188 1006626 1007112 "FSPECF" 1008445 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-436 987826 996157 996198 "FS" 1000082 NIL FS (NIL T) -9 NIL 1002371 NIL) (-435 976469 979462 983519 "FS-" 983819 NIL FS- (NIL T T) -8 NIL NIL NIL) (-434 975997 976051 976221 "FSINT" 976410 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-433 974289 974990 975293 "FSERIES" 975776 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-432 973331 973447 973671 "FSCINT" 974169 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-431 969539 972275 972316 "FSAGG" 972686 NIL FSAGG (NIL T) -9 NIL 972945 NIL) (-430 967301 967902 968698 "FSAGG-" 968793 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-429 966343 966486 966713 "FSAGG2" 967154 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-428 964025 964305 964852 "FS2UPS" 966061 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-427 963659 963702 963831 "FS2" 963976 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-426 962537 962708 963010 "FS2EXPXP" 963484 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-425 961963 962078 962230 "FRUTIL" 962417 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-424 953376 957458 958816 "FR" 960637 NIL FR (NIL T) -8 NIL NIL NIL) (-423 948345 951019 951059 "FRNAALG" 952455 NIL FRNAALG (NIL T) -9 NIL 953062 NIL) (-422 944018 945094 946369 "FRNAALG-" 947119 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-421 943656 943699 943826 "FRNAAF2" 943969 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-420 942031 942505 942801 "FRMOD" 943468 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-419 939774 940406 940724 "FRIDEAL" 941822 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-418 938965 939052 939343 "FRIDEAL2" 939681 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-417 938098 938512 938553 "FRETRCT" 938558 NIL FRETRCT (NIL T) -9 NIL 938734 NIL) (-416 937210 937441 937792 "FRETRCT-" 937797 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-415 934298 935508 935567 "FRAMALG" 936449 NIL FRAMALG (NIL T T) -9 NIL 936741 NIL) (-414 932432 932887 933517 "FRAMALG-" 933740 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-413 926351 931905 932182 "FRAC" 932187 NIL FRAC (NIL T) -8 NIL NIL NIL) (-412 925987 926044 926151 "FRAC2" 926288 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-411 925623 925680 925787 "FR2" 925924 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-410 920136 923029 923057 "FPS" 924176 T FPS (NIL) -9 NIL 924733 NIL) (-409 919585 919694 919858 "FPS-" 920004 NIL FPS- (NIL T) -8 NIL NIL NIL) (-408 916887 918556 918584 "FPC" 918809 T FPC (NIL) -9 NIL 918951 NIL) (-407 916680 916720 916817 "FPC-" 916822 NIL FPC- (NIL T) -8 NIL NIL NIL) (-406 915470 916168 916209 "FPATMAB" 916214 NIL FPATMAB (NIL T) -9 NIL 916366 NIL) (-405 913143 913646 914072 "FPARFRAC" 915107 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-404 908537 909035 909717 "FORTRAN" 912575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-403 906253 906753 907292 "FORT" 908018 T FORT (NIL) -7 NIL NIL NIL) (-402 903929 904491 904519 "FORTFN" 905579 T FORTFN (NIL) -9 NIL 906203 NIL) (-401 903693 903743 903771 "FORTCAT" 903830 T FORTCAT (NIL) -9 NIL 903892 NIL) (-400 901799 902309 902699 "FORMULA" 903323 T FORMULA (NIL) -8 NIL NIL NIL) (-399 901587 901617 901686 "FORMULA1" 901763 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-398 901110 901162 901335 "FORDER" 901529 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-397 900206 900370 900563 "FOP" 900937 T FOP (NIL) -7 NIL NIL NIL) (-396 898787 899486 899660 "FNLA" 900088 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-395 897516 897931 897959 "FNCAT" 898419 T FNCAT (NIL) -9 NIL 898679 NIL) (-394 897055 897475 897503 "FNAME" 897508 T FNAME (NIL) -8 NIL NIL NIL) (-393 895618 896581 896609 "FMTC" 896614 T FMTC (NIL) -9 NIL 896650 NIL) (-392 894364 895554 895600 "FMONOID" 895605 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-391 891192 892360 892401 "FMONCAT" 893618 NIL FMONCAT (NIL T) -9 NIL 894223 NIL) (-390 890384 890934 891083 "FM" 891088 NIL FM (NIL T T) -8 NIL NIL NIL) (-389 887808 888454 888482 "FMFUN" 889626 T FMFUN (NIL) -9 NIL 890334 NIL) (-388 887077 887258 887286 "FMC" 887576 T FMC (NIL) -9 NIL 887758 NIL) (-387 884156 885016 885070 "FMCAT" 886265 NIL FMCAT (NIL T T) -9 NIL 886760 NIL) (-386 883022 883922 884022 "FM1" 884101 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-385 880796 881212 881706 "FLOATRP" 882573 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-384 874374 878525 879146 "FLOAT" 880195 T FLOAT (NIL) -8 NIL NIL NIL) (-383 871812 872312 872890 "FLOATCP" 873841 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-382 870552 871390 871431 "FLINEXP" 871436 NIL FLINEXP (NIL T) -9 NIL 871529 NIL) (-381 869706 869941 870269 "FLINEXP-" 870274 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-380 868782 868926 869150 "FLASORT" 869558 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-379 865898 866766 866818 "FLALG" 868045 NIL FLALG (NIL T T) -9 NIL 868512 NIL) (-378 859634 863384 863425 "FLAGG" 864687 NIL FLAGG (NIL T) -9 NIL 865339 NIL) (-377 858360 858699 859189 "FLAGG-" 859194 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-376 857402 857545 857772 "FLAGG2" 858213 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-375 854253 855261 855320 "FINRALG" 856448 NIL FINRALG (NIL T T) -9 NIL 856956 NIL) (-374 853413 853642 853981 "FINRALG-" 853986 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-373 852793 853032 853060 "FINITE" 853256 T FINITE (NIL) -9 NIL 853363 NIL) (-372 845150 847337 847377 "FINAALG" 851044 NIL FINAALG (NIL T) -9 NIL 852497 NIL) (-371 840482 841532 842676 "FINAALG-" 844055 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-370 839850 840237 840340 "FILE" 840412 NIL FILE (NIL T) -8 NIL NIL NIL) (-369 838508 838846 838900 "FILECAT" 839584 NIL FILECAT (NIL T T) -9 NIL 839800 NIL) (-368 836224 837752 837780 "FIELD" 837820 T FIELD (NIL) -9 NIL 837900 NIL) (-367 834844 835229 835740 "FIELD-" 835745 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-366 832694 833479 833826 "FGROUP" 834530 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-365 831784 831948 832168 "FGLMICPK" 832526 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-364 827616 831709 831766 "FFX" 831771 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-363 827217 827278 827413 "FFSLPE" 827549 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-362 823207 823989 824785 "FFPOLY" 826453 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-361 822711 822747 822956 "FFPOLY2" 823165 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-360 818557 822630 822693 "FFP" 822698 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-359 813955 818468 818532 "FF" 818537 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-358 809081 813298 813488 "FFNBX" 813809 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-357 804009 808216 808474 "FFNBP" 808935 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-356 798642 803293 803504 "FFNB" 803842 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-355 797474 797672 797987 "FFINTBAS" 798439 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-354 793543 795763 795791 "FFIELDC" 796411 T FFIELDC (NIL) -9 NIL 796787 NIL) (-353 792205 792576 793073 "FFIELDC-" 793078 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-352 791774 791820 791944 "FFHOM" 792147 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-351 789469 789956 790473 "FFF" 791289 NIL FFF (NIL T) -7 NIL NIL NIL) (-350 785087 789211 789312 "FFCGX" 789412 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-349 780709 784819 784926 "FFCGP" 785030 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-348 775892 780436 780544 "FFCG" 780645 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-347 757288 766369 766455 "FFCAT" 771620 NIL FFCAT (NIL T T T) -9 NIL 773071 NIL) (-346 752485 753533 754847 "FFCAT-" 756077 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-345 751896 751939 752174 "FFCAT2" 752436 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 741219 744868 746088 "FEXPR" 750748 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-343 740219 740654 740695 "FEVALAB" 740779 NIL FEVALAB (NIL T) -9 NIL 741040 NIL) (-342 739378 739588 739926 "FEVALAB-" 739931 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-341 737944 738761 738964 "FDIV" 739277 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-340 734964 735705 735820 "FDIVCAT" 737388 NIL FDIVCAT (NIL T T T T) -9 NIL 737825 NIL) (-339 734726 734753 734923 "FDIVCAT-" 734928 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-338 733946 734033 734310 "FDIV2" 734633 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-337 732920 733241 733443 "FCTRDATA" 733764 T FCTRDATA (NIL) -8 NIL NIL NIL) (-336 731606 731865 732154 "FCPAK1" 732651 T FCPAK1 (NIL) -7 NIL NIL NIL) (-335 730705 731106 731247 "FCOMP" 731497 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-334 714410 717855 721393 "FC" 727187 T FC (NIL) -8 NIL NIL NIL) (-333 706773 710801 710841 "FAXF" 712643 NIL FAXF (NIL T) -9 NIL 713335 NIL) (-332 704050 704707 705532 "FAXF-" 705997 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-331 699102 703426 703602 "FARRAY" 703907 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-330 693996 696063 696116 "FAMR" 697139 NIL FAMR (NIL T T) -9 NIL 697599 NIL) (-329 692886 693188 693623 "FAMR-" 693628 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-328 692055 692808 692861 "FAMONOID" 692866 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-327 689841 690551 690604 "FAMONC" 691545 NIL FAMONC (NIL T T) -9 NIL 691931 NIL) (-326 688505 689595 689732 "FAGROUP" 689737 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-325 686300 686619 687022 "FACUTIL" 688186 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-324 685399 685584 685806 "FACTFUNC" 686110 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-323 677821 684702 684901 "EXPUPXS" 685255 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-322 675304 675844 676430 "EXPRTUBE" 677255 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-321 671575 672167 672897 "EXPRODE" 674643 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-320 657060 670224 670653 "EXPR" 671179 NIL EXPR (NIL T) -8 NIL NIL NIL) (-319 651614 652201 653007 "EXPR2UPS" 656358 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-318 651246 651303 651412 "EXPR2" 651551 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-317 642634 650397 650688 "EXPEXPAN" 651082 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-316 642434 642591 642620 "EXIT" 642625 T EXIT (NIL) -8 NIL NIL NIL) (-315 641914 642158 642249 "EXITAST" 642363 T EXITAST (NIL) -8 NIL NIL NIL) (-314 641541 641603 641716 "EVALCYC" 641846 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-313 641082 641200 641241 "EVALAB" 641411 NIL EVALAB (NIL T) -9 NIL 641515 NIL) (-312 640563 640685 640906 "EVALAB-" 640911 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-311 637931 639233 639261 "EUCDOM" 639816 T EUCDOM (NIL) -9 NIL 640166 NIL) (-310 636336 636778 637368 "EUCDOM-" 637373 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-309 623875 626634 629384 "ESTOOLS" 633606 T ESTOOLS (NIL) -7 NIL NIL NIL) (-308 623507 623564 623673 "ESTOOLS2" 623812 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-307 623258 623300 623380 "ESTOOLS1" 623459 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-306 617295 618903 618931 "ES" 621699 T ES (NIL) -9 NIL 623109 NIL) (-305 612242 613529 615346 "ES-" 615510 NIL ES- (NIL T) -8 NIL NIL NIL) (-304 608616 609377 610157 "ESCONT" 611482 T ESCONT (NIL) -7 NIL NIL NIL) (-303 608361 608393 608475 "ESCONT1" 608578 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-302 608036 608086 608186 "ES2" 608305 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-301 607666 607724 607833 "ES1" 607972 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-300 606882 607011 607187 "ERROR" 607510 T ERROR (NIL) -7 NIL NIL NIL) (-299 600274 606741 606832 "EQTBL" 606837 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-298 592777 595588 597037 "EQ" 598858 NIL -2200 (NIL T) -8 NIL NIL NIL) (-297 592409 592466 592575 "EQ2" 592714 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-296 587700 588747 589840 "EP" 591348 NIL EP (NIL T) -7 NIL NIL NIL) (-295 586300 586591 586897 "ENV" 587414 T ENV (NIL) -8 NIL NIL NIL) (-294 585394 585948 585976 "ENTIRER" 585981 T ENTIRER (NIL) -9 NIL 586027 NIL) (-293 581861 583349 583719 "EMR" 585193 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-292 581005 581190 581244 "ELTAGG" 581624 NIL ELTAGG (NIL T T) -9 NIL 581835 NIL) (-291 580724 580786 580927 "ELTAGG-" 580932 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-290 580513 580542 580596 "ELTAB" 580680 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-289 579639 579785 579984 "ELFUTS" 580364 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-288 579381 579437 579465 "ELEMFUN" 579570 T ELEMFUN (NIL) -9 NIL NIL NIL) (-287 579251 579272 579340 "ELEMFUN-" 579345 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-286 574095 577351 577392 "ELAGG" 578332 NIL ELAGG (NIL T) -9 NIL 578795 NIL) (-285 572380 572814 573477 "ELAGG-" 573482 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-284 571692 571829 571985 "ELABOR" 572244 T ELABOR (NIL) -8 NIL NIL NIL) (-283 570353 570632 570926 "ELABEXPR" 571418 T ELABEXPR (NIL) -8 NIL NIL NIL) (-282 563217 565020 565847 "EFUPXS" 569629 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-281 556667 558468 559278 "EFULS" 562493 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-280 554152 554510 554982 "EFSTRUC" 556299 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-279 543943 545509 547057 "EF" 552667 NIL EF (NIL T T) -7 NIL NIL NIL) (-278 543017 543428 543577 "EAB" 543814 T EAB (NIL) -8 NIL NIL NIL) (-277 542199 542976 543004 "E04UCFA" 543009 T E04UCFA (NIL) -8 NIL NIL NIL) (-276 541381 542158 542186 "E04NAFA" 542191 T E04NAFA (NIL) -8 NIL NIL NIL) (-275 540563 541340 541368 "E04MBFA" 541373 T E04MBFA (NIL) -8 NIL NIL NIL) (-274 539745 540522 540550 "E04JAFA" 540555 T E04JAFA (NIL) -8 NIL NIL NIL) (-273 538929 539704 539732 "E04GCFA" 539737 T E04GCFA (NIL) -8 NIL NIL NIL) (-272 538113 538888 538916 "E04FDFA" 538921 T E04FDFA (NIL) -8 NIL NIL NIL) (-271 537295 538072 538100 "E04DGFA" 538105 T E04DGFA (NIL) -8 NIL NIL NIL) (-270 531468 532820 534184 "E04AGNT" 535951 T E04AGNT (NIL) -7 NIL NIL NIL) (-269 530148 530654 530694 "DVARCAT" 531169 NIL DVARCAT (NIL T) -9 NIL 531368 NIL) (-268 529352 529564 529878 "DVARCAT-" 529883 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-267 522489 529151 529280 "DSMP" 529285 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-266 517270 518434 519502 "DROPT" 521441 T DROPT (NIL) -8 NIL NIL NIL) (-265 516935 516994 517092 "DROPT1" 517205 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-264 512050 513176 514313 "DROPT0" 515818 T DROPT0 (NIL) -7 NIL NIL NIL) (-263 510395 510720 511106 "DRAWPT" 511684 T DRAWPT (NIL) -7 NIL NIL NIL) (-262 504982 505905 506984 "DRAW" 509369 NIL DRAW (NIL T) -7 NIL NIL NIL) (-261 504615 504668 504786 "DRAWHACK" 504923 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-260 503346 503615 503906 "DRAWCX" 504344 T DRAWCX (NIL) -7 NIL NIL NIL) (-259 502861 502930 503081 "DRAWCURV" 503272 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-258 493329 495291 497406 "DRAWCFUN" 500766 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-257 490093 492022 492063 "DQAGG" 492692 NIL DQAGG (NIL T) -9 NIL 492966 NIL) (-256 478217 484686 484769 "DPOLCAT" 486621 NIL DPOLCAT (NIL T T T T) -9 NIL 487166 NIL) (-255 473054 474402 476360 "DPOLCAT-" 476365 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-254 466176 472915 473013 "DPMO" 473018 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-253 459201 465956 466123 "DPMM" 466128 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-252 458679 458893 458991 "DOMTMPLT" 459123 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-251 458112 458481 458561 "DOMCTOR" 458619 T DOMCTOR (NIL) -8 NIL NIL NIL) (-250 457324 457592 457743 "DOMAIN" 457981 T DOMAIN (NIL) -8 NIL NIL NIL) (-249 451312 456959 457111 "DMP" 457225 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-248 450912 450968 451112 "DLP" 451250 NIL DLP (NIL T) -7 NIL NIL NIL) (-247 444734 450239 450429 "DLIST" 450754 NIL DLIST (NIL T) -8 NIL NIL NIL) (-246 441531 443587 443628 "DLAGG" 444178 NIL DLAGG (NIL T) -9 NIL 444408 NIL) (-245 440207 440871 440899 "DIVRING" 440991 T DIVRING (NIL) -9 NIL 441074 NIL) (-244 439444 439634 439934 "DIVRING-" 439939 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-243 437546 437903 438309 "DISPLAY" 439058 T DISPLAY (NIL) -7 NIL NIL NIL) (-242 431434 437460 437523 "DIRPROD" 437528 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-241 430282 430485 430750 "DIRPROD2" 431227 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-240 419057 425063 425116 "DIRPCAT" 425526 NIL DIRPCAT (NIL NIL T) -9 NIL 426366 NIL) (-239 416383 417025 417906 "DIRPCAT-" 418243 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-238 415670 415830 416016 "DIOSP" 416217 T DIOSP (NIL) -7 NIL NIL NIL) (-237 412325 414582 414623 "DIOPS" 415057 NIL DIOPS (NIL T) -9 NIL 415286 NIL) (-236 411874 411988 412179 "DIOPS-" 412184 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-235 410697 411325 411353 "DIFRING" 411540 T DIFRING (NIL) -9 NIL 411650 NIL) (-234 410343 410420 410572 "DIFRING-" 410577 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-233 408079 409351 409392 "DIFEXT" 409755 NIL DIFEXT (NIL T) -9 NIL 410049 NIL) (-232 406364 406792 407458 "DIFEXT-" 407463 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 403639 405896 405937 "DIAGG" 405942 NIL DIAGG (NIL T) -9 NIL 405962 NIL) (-230 403023 403180 403432 "DIAGG-" 403437 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 398440 401982 402259 "DHMATRIX" 402792 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 394052 394961 395971 "DFSFUN" 397450 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 389131 392983 393295 "DFLOAT" 393760 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 387394 387675 388064 "DFINTTLS" 388839 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 384423 385415 385815 "DERHAM" 387060 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 382224 384198 384287 "DEQUEUE" 384367 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 381478 381611 381794 "DEGRED" 382086 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 377908 378653 379499 "DEFINTRF" 380706 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 375463 375932 376524 "DEFINTEF" 377427 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 374813 375083 375198 "DEFAST" 375368 T DEFAST (NIL) -8 NIL NIL NIL) (-219 368815 374406 374556 "DECIMAL" 374683 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 366327 366785 367291 "DDFACT" 368359 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 365923 365966 366117 "DBLRESP" 366278 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 363795 364156 364516 "DBASE" 365690 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 363037 363275 363421 "DATAARY" 363694 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 362143 362996 363024 "D03FAFA" 363029 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 361250 362102 362130 "D03EEFA" 362135 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 359200 359666 360155 "D03AGNT" 360781 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 358489 359159 359187 "D02EJFA" 359192 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 357778 358448 358476 "D02CJFA" 358481 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 357067 357737 357765 "D02BHFA" 357770 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 356356 357026 357054 "D02BBFA" 357059 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 349553 351142 352748 "D02AGNT" 354770 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 347321 347844 348390 "D01WGTS" 349027 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 346388 347280 347308 "D01TRNS" 347313 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 345456 346347 346375 "D01GBFA" 346380 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 344524 345415 345443 "D01FCFA" 345448 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 343592 344483 344511 "D01ASFA" 344516 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 342660 343551 343579 "D01AQFA" 343584 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 341728 342619 342647 "D01APFA" 342652 T D01APFA (NIL) -8 NIL NIL NIL) (-199 340796 341687 341715 "D01ANFA" 341720 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 339864 340755 340783 "D01AMFA" 340788 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 338932 339823 339851 "D01ALFA" 339856 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 338000 338891 338919 "D01AKFA" 338924 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 337068 337959 337987 "D01AJFA" 337992 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 330363 331916 333477 "D01AGNT" 335527 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 329700 329828 329980 "CYCLOTOM" 330231 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 326434 327148 327875 "CYCLES" 328993 T CYCLES (NIL) -7 NIL NIL NIL) (-191 325746 325880 326051 "CVMP" 326295 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 323587 323845 324214 "CTRIGMNP" 325474 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 323023 323381 323454 "CTOR" 323534 T CTOR (NIL) -8 NIL NIL NIL) (-188 322532 322754 322855 "CTORKIND" 322942 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 321823 322139 322167 "CTORCAT" 322349 T CTORCAT (NIL) -9 NIL 322462 NIL) (-186 321421 321532 321691 "CTORCAT-" 321696 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 320883 321095 321203 "CTORCALL" 321345 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 320257 320356 320509 "CSTTOOLS" 320780 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 316056 316713 317471 "CRFP" 319569 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 315531 315777 315869 "CRCEAST" 315984 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 314578 314763 314991 "CRAPACK" 315335 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 313962 314063 314267 "CPMATCH" 314454 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 313687 313715 313821 "CPIMA" 313928 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 310035 310707 311426 "COORDSYS" 313022 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 309447 309568 309710 "CONTOUR" 309913 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 305338 307450 307942 "CONTFRAC" 308987 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 305218 305239 305267 "CONDUIT" 305304 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 304306 304860 304888 "COMRING" 304893 T COMRING (NIL) -9 NIL 304945 NIL) (-173 303360 303664 303848 "COMPPROP" 304142 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 303021 303056 303184 "COMPLPAT" 303319 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 293312 302830 302939 "COMPLEX" 302944 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 292948 293005 293112 "COMPLEX2" 293249 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 292287 292408 292568 "COMPILER" 292808 T COMPILER (NIL) -8 NIL NIL NIL) (-168 292005 292040 292138 "COMPFACT" 292246 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276085 286079 286119 "COMPCAT" 287123 NIL COMPCAT (NIL T) -9 NIL 288471 NIL) (-166 265597 268524 272151 "COMPCAT-" 272507 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265326 265354 265457 "COMMUPC" 265563 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265120 265154 265213 "COMMONOP" 265287 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 264676 264871 264958 "COMM" 265053 T COMM (NIL) -8 NIL NIL NIL) (-162 264252 264480 264555 "COMMAAST" 264621 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 263501 263695 263723 "COMBOPC" 264061 T COMBOPC (NIL) -9 NIL 264236 NIL) (-160 262397 262607 262849 "COMBINAT" 263291 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 258854 259428 260055 "COMBF" 261819 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 257612 257970 258205 "COLOR" 258639 T COLOR (NIL) -8 NIL NIL NIL) (-157 257088 257333 257425 "COLONAST" 257540 T COLONAST (NIL) -8 NIL NIL NIL) (-156 256728 256775 256900 "CMPLXRT" 257035 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256176 256428 256527 "CLLCTAST" 256649 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 251678 252706 253786 "CLIP" 255116 T CLIP (NIL) -7 NIL NIL NIL) (-153 250019 250779 251019 "CLIF" 251505 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246194 248165 248206 "CLAGG" 249135 NIL CLAGG (NIL T) -9 NIL 249671 NIL) (-151 244616 245073 245656 "CLAGG-" 245661 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244160 244245 244385 "CINTSLPE" 244525 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 241661 242132 242680 "CHVAR" 243688 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 240835 241389 241417 "CHARZ" 241422 T CHARZ (NIL) -9 NIL 241437 NIL) (-147 240589 240629 240707 "CHARPOL" 240789 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 239647 240234 240262 "CHARNZ" 240309 T CHARNZ (NIL) -9 NIL 240365 NIL) (-145 237553 238301 238654 "CHAR" 239314 T CHAR (NIL) -8 NIL NIL NIL) (-144 237279 237340 237368 "CFCAT" 237479 T CFCAT (NIL) -9 NIL NIL NIL) (-143 236520 236631 236814 "CDEN" 237163 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 232485 235673 235953 "CCLASS" 236260 T CCLASS (NIL) -8 NIL NIL NIL) (-141 231736 231893 232070 "CATEGORY" 232328 T -10 (NIL) -8 NIL NIL NIL) (-140 231309 231655 231703 "CATCTOR" 231708 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 230760 231012 231110 "CATAST" 231231 T CATAST (NIL) -8 NIL NIL NIL) (-138 230236 230481 230573 "CASEAST" 230688 T CASEAST (NIL) -8 NIL NIL NIL) (-137 225246 226265 227018 "CARTEN" 229539 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 224354 224502 224723 "CARTEN2" 225093 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 222670 223504 223761 "CARD" 224117 T CARD (NIL) -8 NIL NIL NIL) (-134 222246 222474 222549 "CAPSLAST" 222615 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 221750 221958 221986 "CACHSET" 222118 T CACHSET (NIL) -9 NIL 222196 NIL) (-132 221220 221542 221570 "CABMON" 221620 T CABMON (NIL) -9 NIL 221676 NIL) (-131 220693 220924 221034 "BYTEORD" 221130 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 219675 220227 220369 "BYTE" 220532 T BYTE (NIL) -8 NIL NIL 220654) (-129 215025 219180 219352 "BYTEBUF" 219523 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 212534 214717 214824 "BTREE" 214951 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 209983 212182 212304 "BTOURN" 212444 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 207353 209453 209494 "BTCAT" 209562 NIL BTCAT (NIL T) -9 NIL 209639 NIL) (-125 207020 207100 207249 "BTCAT-" 207254 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 202430 206309 206337 "BTAGG" 206451 T BTAGG (NIL) -9 NIL 206561 NIL) (-123 201920 202045 202251 "BTAGG-" 202256 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 198915 201198 201413 "BSTREE" 201737 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198053 198179 198363 "BRILL" 198771 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 194705 196779 196820 "BRAGG" 197469 NIL BRAGG (NIL T) -9 NIL 197727 NIL) (-119 193234 193640 194195 "BRAGG-" 194200 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 186461 192578 192763 "BPADICRT" 193081 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 184776 186398 186443 "BPADIC" 186448 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 184474 184504 184618 "BOUNDZRO" 184740 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 179702 180900 181812 "BOP" 183582 T BOP (NIL) -8 NIL NIL NIL) (-114 177483 177887 178362 "BOP1" 179260 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177184 177245 177273 "BOOLE" 177384 T BOOLE (NIL) -9 NIL 177466 NIL) (-112 176009 176758 176907 "BOOLEAN" 177055 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175288 175692 175746 "BMODULE" 175751 NIL BMODULE (NIL T T) -9 NIL 175816 NIL) (-110 171089 175086 175159 "BITS" 175235 T BITS (NIL) -8 NIL NIL NIL) (-109 170510 170629 170769 "BINDING" 170969 T BINDING (NIL) -8 NIL NIL NIL) (-108 164515 170105 170254 "BINARY" 170381 T BINARY (NIL) -8 NIL NIL NIL) (-107 162295 163770 163811 "BGAGG" 164071 NIL BGAGG (NIL T) -9 NIL 164208 NIL) (-106 162126 162158 162249 "BGAGG-" 162254 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161197 161510 161715 "BFUNCT" 161941 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159887 160065 160353 "BEZOUT" 161021 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156356 158739 159069 "BBTREE" 159590 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156090 156143 156171 "BASTYPE" 156290 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155942 155971 156044 "BASTYPE-" 156049 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155376 155452 155604 "BALFACT" 155853 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154232 154791 154977 "AUTOMOR" 155221 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153958 153963 153989 "ATTREG" 153994 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152210 152655 153007 "ATTRBUT" 153624 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151818 152038 152104 "ATTRAST" 152162 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151354 151467 151493 "ATRIG" 151694 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151163 151204 151291 "ATRIG-" 151296 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150808 150994 151020 "ASTCAT" 151025 T ASTCAT (NIL) -9 NIL 151055 NIL) (-92 150535 150594 150713 "ASTCAT-" 150718 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148684 150311 150399 "ASTACK" 150478 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147189 147486 147851 "ASSOCEQ" 148366 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146221 146848 146972 "ASP9" 147096 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145984 146169 146208 "ASP8" 146213 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144852 145589 145731 "ASP80" 145873 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143750 144487 144619 "ASP7" 144751 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142704 143427 143545 "ASP78" 143663 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141673 142384 142501 "ASP77" 142618 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140585 141311 141442 "ASP74" 141573 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139485 140220 140352 "ASP73" 140484 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138589 139311 139411 "ASP6" 139416 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137536 138266 138384 "ASP55" 138502 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136485 137210 137329 "ASP50" 137448 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135573 136186 136296 "ASP4" 136406 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134661 135274 135384 "ASP49" 135494 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133445 134200 134368 "ASP42" 134550 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132222 132978 133148 "ASP41" 133332 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131172 131899 132017 "ASP35" 132135 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130937 131120 131159 "ASP34" 131164 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130674 130741 130817 "ASP33" 130892 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129568 130309 130441 "ASP31" 130573 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129333 129516 129555 "ASP30" 129560 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129068 129137 129213 "ASP29" 129288 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128833 129016 129055 "ASP28" 129060 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128598 128781 128820 "ASP27" 128825 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127682 128296 128407 "ASP24" 128518 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126759 127484 127596 "ASP20" 127601 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125847 126460 126570 "ASP1" 126680 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124790 125521 125640 "ASP19" 125759 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124527 124594 124670 "ASP12" 124745 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123379 124126 124270 "ASP10" 124414 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121230 123223 123314 "ARRAY2" 123319 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116995 120878 120992 "ARRAY1" 121147 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116027 116200 116421 "ARRAY12" 116818 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110339 112257 112332 "ARR2CAT" 114962 NIL ARR2CAT (NIL T T T) -9 NIL 115720 NIL) (-56 107773 108517 109471 "ARR2CAT-" 109476 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107090 107400 107525 "ARITY" 107666 T ARITY (NIL) -8 NIL NIL NIL) (-54 105866 106018 106317 "APPRULE" 106926 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105517 105565 105684 "APPLYORE" 105812 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104871 105110 105230 "ANY" 105415 T ANY (NIL) -8 NIL NIL NIL) (-51 104149 104272 104429 "ANY1" 104745 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101679 102586 102913 "ANTISYM" 103873 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101171 101386 101482 "ANON" 101601 T ANON (NIL) -8 NIL NIL NIL) (-48 95420 99710 100164 "AN" 100735 T AN (NIL) -8 NIL NIL NIL) (-47 91318 92706 92757 "AMR" 93505 NIL AMR (NIL T T) -9 NIL 94105 NIL) (-46 90430 90651 91014 "AMR-" 91019 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74869 90347 90408 "ALIST" 90413 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71674 74463 74632 "ALGSC" 74787 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68230 68784 69391 "ALGPKG" 71114 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67507 67608 67792 "ALGMFACT" 68116 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64121 64715 "ALGMANIP" 67091 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index a9808ba4..5a65fd42 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,55 +1,87 @@ -(733597 . 3480886513) -(((*1 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-695 *1)) (-4 *1 (-354)) (-5 *2 (-1277 *1)))) +(733710 . 3480912611) +(((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-158))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-1250 *5 *4)) (-4 *4 (-826)) (-14 *5 (-1186)) + (-5 *2 (-570)) (-5 *1 (-1123 *4 *5))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *4 (-1186)) (-4 *5 (-620 (-899 (-570)))) + (-4 *5 (-893 (-570))) + (-4 *5 (-13 (-1047 (-570)) (-458) (-645 (-570)))) + (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) + (-5 *1 (-573 *5 *3)) (-4 *3 (-635)) + (-4 *3 (-13 (-27) (-1212) (-436 *5)))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-368)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-510 *4 *5 *6 *3)) (-4 *3 (-956 *4 *5 *6))))) +(((*1 *2 *1) + (-12 (-5 *2 (-176 (-413 (-570)))) (-5 *1 (-118 *3)) (-14 *3 (-570)))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *3 (-1166 *2)) (-4 *2 (-311)) (-5 *1 (-176 *2)))) + ((*1 *1 *2) (-12 (-5 *2 (-413 *3)) (-4 *3 (-311)) (-5 *1 (-176 *3)))) ((*1 *2 *3) - (|partial| -12 (-5 *3 (-695 *1)) (-4 *1 (-146)) (-4 *1 (-916)) - (-5 *2 (-1277 *1))))) -(((*1 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-373)) (-4 *2 (-1109))))) -(((*1 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-373)) (-4 *2 (-368))))) -(((*1 *2 *3) - (-12 (-4 *4 (-368)) (-4 *4 (-562)) (-4 *5 (-1253 *4)) - (-5 *2 (-2 (|:| -4288 (-629 *4 *5)) (|:| -1338 (-413 *5)))) - (-5 *1 (-629 *4 *5)) (-5 *3 (-413 *5)))) + (-12 (-5 *2 (-176 (-570))) (-5 *1 (-771 *3)) (-4 *3 (-410)))) ((*1 *2 *1) - (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) - (-14 *3 (-928)) (-4 *4 (-1058)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-458)) (-4 *3 (-1058)) - (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) - (-4 *1 (-1253 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-562)) (-4 *2 (-13 (-436 (-171 *4)) (-1011) (-1212))) - (-5 *1 (-606 *4 *3 *2)) (-4 *3 (-13 (-436 *4) (-1011) (-1212)))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-368)) (-4 *7 (-1253 *5)) (-4 *4 (-730 *5 *7)) - (-5 *2 (-2 (|:| -2415 (-695 *6)) (|:| |vec| (-1277 *5)))) - (-5 *1 (-817 *5 *6 *7 *4 *3)) (-4 *6 (-662 *5)) (-4 *3 (-662 *4))))) -(((*1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705)))) - ((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-705))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-695 *7)) (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *6 *5)) - (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *1 (-931 *4 *5 *6 *7))))) -(((*1 *1 *1 *1) (-4 *1 (-667)))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-570)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1227)) - (-4 *3 (-378 *4)) (-4 *5 (-378 *4))))) -(((*1 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280)))) - ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1280))))) + (-12 (-5 *2 (-176 (-413 (-570)))) (-5 *1 (-877 *3)) (-14 *3 (-570)))) + ((*1 *2 *1) + (-12 (-14 *3 (-570)) (-5 *2 (-176 (-413 (-570)))) + (-5 *1 (-878 *3 *4)) (-4 *4 (-875 *3))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-985 *4 *5 *6 *3)) (-4 *4 (-1058)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-4 *4 (-562)) + (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4)))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-458)) (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2407 *4))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-650 *3)) (-4 *3 (-1080 *5 *6 *7 *8)) (-4 *5 (-458)) + (-4 *6 (-799)) (-4 *7 (-856)) (-4 *8 (-1074 *5 *6 *7)) + (-5 *2 (-112)) (-5 *1 (-997 *5 *6 *7 *8 *3)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-650 *3)) (-4 *3 (-1080 *5 *6 *7 *8)) (-4 *5 (-458)) + (-4 *6 (-799)) (-4 *7 (-856)) (-4 *8 (-1074 *5 *6 *7)) + (-5 *2 (-112)) (-5 *1 (-1116 *5 *6 *7 *8 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3570 *4))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) + (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-562)) + (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-986 *4 *5 *6 *7))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 (-650 (-950 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-650 (-950 *3))) (-4 *3 (-1058)) (-4 *1 (-1143 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-650 (-650 *3))) (-4 *1 (-1143 *3)) (-4 *3 (-1058)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-650 (-950 *3))) (-4 *1 (-1143 *3)) (-4 *3 (-1058))))) +(((*1 *1 *1 *1) (-4 *1 (-667)))) (((*1 *2 *3) - (-12 (-5 *3 (-650 *5)) (-4 *5 (-436 *4)) (-4 *4 (-562)) - (-5 *2 (-868)) (-5 *1 (-32 *4 *5))))) + (-12 (-5 *3 (-1103 (-849 (-227)))) (-5 *2 (-227)) (-5 *1 (-194)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1103 (-849 (-227)))) (-5 *2 (-227)) (-5 *1 (-304)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1103 (-849 (-227)))) (-5 *2 (-227)) (-5 *1 (-309))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-1282)) (-5 *1 (-1278)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-1282)) (-5 *1 (-1279))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562))))) +(((*1 *2 *2) (-12 (-5 *1 (-968 *2)) (-4 *2 (-551))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1047 (-570))) (-4 *1 (-306)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-551)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-1001 *2)) (-4 *4 (-1253 *3)) (-4 *2 (-311)) @@ -66,8 +98,11 @@ (-5 *1 (-668 *3 *4 *2)) (-4 *3 (-723 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) (((*1 *2 *3) (-12 (-5 *3 (-650 (-52))) (-5 *2 (-1282)) (-5 *1 (-869))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4450)) (-4 *1 (-246 *2)) (-4 *2 (-1227))))) +(((*1 *2 *1) + (-12 (-4 *1 (-378 *3)) (-4 *3 (-1227)) (-4 *3 (-856)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-378 *4)) (-4 *4 (-1227)) + (-5 *2 (-112))))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -76,10 +111,17 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-1094))))) -(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) - (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-171 (-227)))) - (-5 *2 (-1044)) (-5 *1 (-760))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3) + (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) + (-5 *2 (-1044)) (-5 *1 (-756))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 (-2 (|:| |val| (-650 *6)) (|:| -3687 *7)))) + (-4 *6 (-1074 *3 *4 *5)) (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-997 *3 *4 *5 *6 *7)))) + ((*1 *2 *2) + (-12 (-5 *2 (-650 (-2 (|:| |val| (-650 *6)) (|:| -3687 *7)))) + (-4 *6 (-1074 *3 *4 *5)) (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) + (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-1116 *3 *4 *5 *6 *7))))) (((*1 *1 *1 *1) (-4 *1 (-667)))) (((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-31)))) ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) ((*1 *1) (-4 *1 (-551))) @@ -90,40 +132,21 @@ (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) (((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-1182 (-959 *4))) (-5 *1 (-422 *3 *4)) - (-4 *3 (-423 *4)))) - ((*1 *2) - (-12 (-4 *1 (-423 *3)) (-4 *3 (-174)) (-4 *3 (-368)) - (-5 *2 (-1182 (-959 *3))))) - ((*1 *2) - (-12 (-5 *2 (-1182 (-413 (-959 *3)))) (-5 *1 (-459 *3 *4 *5 *6)) - (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) - (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1058)) (-14 *3 (-650 (-1186))))) - ((*1 *1 *1) - (-12 (-5 *1 (-225 *2 *3)) (-4 *2 (-13 (-1058) (-856))) - (-14 *3 (-650 (-1186)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-311)) - (-5 *2 (-413 (-424 (-959 *4)))) (-5 *1 (-1051 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-570)) (-5 *2 (-650 (-2 (|:| -3801 *3) (|:| -2130 *4)))) - (-5 *1 (-702 *3)) (-4 *3 (-1253 *4))))) -(((*1 *2 *3 *2) - (|partial| -12 (-5 *2 (-1277 *4)) (-5 *3 (-695 *4)) (-4 *4 (-368)) - (-5 *1 (-673 *4)))) - ((*1 *2 *3 *2) - (|partial| -12 (-4 *4 (-368)) - (-4 *5 (-13 (-378 *4) (-10 -7 (-6 -4450)))) - (-4 *2 (-13 (-378 *4) (-10 -7 (-6 -4450)))) - (-5 *1 (-674 *4 *5 *2 *3)) (-4 *3 (-693 *4 *5 *2)))) - ((*1 *2 *3 *2 *4 *5) - (|partial| -12 (-5 *4 (-650 *2)) (-5 *5 (-1 *2 *2)) (-4 *2 (-368)) - (-5 *1 (-820 *2 *3)) (-4 *3 (-662 *2)))) - ((*1 *2 *3) - (-12 (-4 *2 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) - (-5 *1 (-1137 *3 *2)) (-4 *3 (-1253 *2))))) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) + (-4 *3 (-372 *4)))) + ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *2) + (-12 (-5 *2 (-950 *3)) (-4 *3 (-13 (-368) (-1212) (-1011))) + (-5 *1 (-178 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-697 (-1144))) (-5 *1 (-1160))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1186)) + (-4 *5 (-13 (-458) (-148) (-1047 (-570)) (-645 (-570)))) + (-5 *2 (-2 (|:| -4341 *3) (|:| |coeff| *3))) (-5 *1 (-563 *5 *3)) + (-4 *3 (-13 (-27) (-1212) (-436 *5)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1111 *3)) (-5 *1 (-912 *3)) (-4 *3 (-373)) + (-4 *3 (-1109))))) (((*1 *2 *1) (-12 (-5 *2 (-1134 (-570) (-618 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-311)) (-4 *4 (-1001 *3)) (-4 *5 (-1253 *4)) @@ -140,8 +163,7 @@ (-12 (-4 *3 (-174)) (-4 *2 (-723 *3)) (-5 *1 (-668 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-732) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1001 *2)) (-4 *2 (-562))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *1) (-12 (-4 *1 (-533)) (-5 *2 (-697 (-1235)))))) (((*1 *1 *1) (-12 (-4 *1 (-120 *2)) (-4 *2 (-1227)))) ((*1 *1 *1) (-12 (-5 *1 (-678 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) @@ -150,92 +172,82 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-854) (-368))) (-5 *1 (-1070 *2 *3)) (-4 *3 (-1253 *2))))) -(((*1 *2 *3) - (-12 (-4 *3 (-13 (-311) (-10 -8 (-15 -1652 ((-424 $) $))))) - (-4 *4 (-1253 *3)) - (-5 *2 - (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) - (|:| |basisInv| (-695 *3)))) - (-5 *1 (-355 *3 *4 *5)) (-4 *5 (-415 *3 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-570)) (-4 *4 (-1253 *3)) - (-5 *2 - (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) - (|:| |basisInv| (-695 *3)))) - (-5 *1 (-774 *4 *5)) (-4 *5 (-415 *3 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-354)) (-4 *3 (-1253 *4)) (-4 *5 (-1253 *3)) - (-5 *2 - (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) - (|:| |basisInv| (-695 *3)))) - (-5 *1 (-994 *4 *3 *5 *6)) (-4 *6 (-730 *3 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-354)) (-4 *3 (-1253 *4)) (-4 *5 (-1253 *3)) - (-5 *2 - (-2 (|:| -1972 (-695 *3)) (|:| |basisDen| *3) - (|:| |basisInv| (-695 *3)))) - (-5 *1 (-1286 *4 *3 *5 *6)) (-4 *6 (-415 *3 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-854)) (-5 *2 (-570)))) - ((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-912 *3)) (-4 *3 (-1109)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) - (-4 *3 (-1253 *4)) (-5 *2 (-570)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-562) (-1047 *2) (-645 *2) (-458))) - (-5 *2 (-570)) (-5 *1 (-1125 *4 *3)) - (-4 *3 (-13 (-27) (-1212) (-436 *4))))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-849 *3)) - (-4 *3 (-13 (-27) (-1212) (-436 *6))) - (-4 *6 (-13 (-562) (-1047 *2) (-645 *2) (-458))) (-5 *2 (-570)) - (-5 *1 (-1125 *6 *3)))) - ((*1 *2 *3 *4 *3 *5) - (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-1168)) - (-4 *6 (-13 (-562) (-1047 *2) (-645 *2) (-458))) (-5 *2 (-570)) - (-5 *1 (-1125 *6 *3)) (-4 *3 (-13 (-27) (-1212) (-436 *6))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-618 (-48)))) (-5 *1 (-48)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-618 (-48))) (-5 *1 (-48)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1182 (-48))) (-5 *3 (-650 (-618 (-48)))) (-5 *1 (-48)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1182 (-48))) (-5 *3 (-618 (-48))) (-5 *1 (-48)))) + ((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)))) ((*1 *2 *3) - (|partial| -12 (-5 *3 (-413 (-959 *4))) (-4 *4 (-458)) (-5 *2 (-570)) - (-5 *1 (-1126 *4)))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1186)) (-5 *5 (-849 (-413 (-959 *6)))) - (-5 *3 (-413 (-959 *6))) (-4 *6 (-458)) (-5 *2 (-570)) - (-5 *1 (-1126 *6)))) - ((*1 *2 *3 *4 *3 *5) - (|partial| -12 (-5 *3 (-413 (-959 *6))) (-5 *4 (-1186)) - (-5 *5 (-1168)) (-4 *6 (-458)) (-5 *2 (-570)) (-5 *1 (-1126 *6)))) + (-12 (-4 *2 (-13 (-368) (-854))) (-5 *1 (-183 *2 *3)) + (-4 *3 (-1253 (-171 *2))))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-928)) (-4 *1 (-333 *3)) (-4 *3 (-368)) (-4 *3 (-373)))) + ((*1 *2 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-368)))) + ((*1 *2 *1) + (-12 (-4 *1 (-375 *2 *3)) (-4 *3 (-1253 *2)) (-4 *2 (-174)))) + ((*1 *2 *1) + (-12 (-4 *4 (-1253 *2)) (-4 *2 (-1001 *3)) (-5 *1 (-419 *3 *2 *4 *5)) + (-4 *3 (-311)) (-4 *5 (-13 (-415 *2 *4) (-1047 *2))))) + ((*1 *2 *1) + (-12 (-4 *4 (-1253 *2)) (-4 *2 (-1001 *3)) + (-5 *1 (-420 *3 *2 *4 *5 *6)) (-4 *3 (-311)) (-4 *5 (-415 *2 *4)) + (-14 *6 (-1277 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-928)) (-4 *5 (-1058)) + (-4 *2 (-13 (-410) (-1047 *5) (-368) (-1212) (-288))) + (-5 *1 (-449 *5 *3 *2)) (-4 *3 (-1253 *5)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-618 (-501)))) (-5 *1 (-501)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-618 (-501))) (-5 *1 (-501)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1182 (-501))) (-5 *3 (-650 (-618 (-501)))) + (-5 *1 (-501)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1182 (-501))) (-5 *3 (-618 (-501))) (-5 *1 (-501)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-1277 *4)) (-5 *3 (-928)) (-4 *4 (-354)) + (-5 *1 (-534 *4)))) ((*1 *2 *3) - (|partial| -12 (-5 *2 (-570)) (-5 *1 (-1209 *3)) (-4 *3 (-1058))))) + (-12 (-4 *4 (-458)) (-4 *5 (-730 *4 *2)) (-4 *2 (-1253 *4)) + (-5 *1 (-781 *4 *2 *5 *3)) (-4 *3 (-1253 *5)))) + ((*1 *2 *1) (-12 (-4 *1 (-803 *2)) (-4 *2 (-174)))) + ((*1 *2 *1) (-12 (-4 *1 (-1006 *2)) (-4 *2 (-174)))) + ((*1 *1 *1) (-4 *1 (-1069)))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-2 (|:| -3930 *3) (|:| |coef1| (-788 *3)))) + (-5 *1 (-788 *3)) (-4 *3 (-562)) (-4 *3 (-1058))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-1207))))) (((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 - (-2 (|:| -1981 (-777)) (|:| |curves| (-777)) + (-2 (|:| -3917 (-777)) (|:| |curves| (-777)) (|:| |polygons| (-777)) (|:| |constructs| (-777))))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1220 *3 *4 *5 *6)) (-4 *3 (-562)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-4 *5 (-373)) - (-5 *2 (-777))))) -(((*1 *1 *1 *1) (-4 *1 (-479))) ((*1 *1 *1 *1) (-4 *1 (-767)))) -(((*1 *2 *3 *3 *4 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-753))))) -(((*1 *2 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-650 *3)) - (-5 *1 (-986 *4 *5 *6 *3)) (-4 *3 (-1074 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-650 *3)) (-4 *3 (-1074 *4 *5 *6)) (-4 *4 (-562)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *1 (-986 *4 *5 *6 *3)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-562)) - (-4 *4 (-799)) (-4 *5 (-856)) (-5 *1 (-986 *3 *4 *5 *6)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-1 (-650 *7) (-650 *7))) (-5 *2 (-650 *7)) - (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-562)) (-4 *5 (-799)) - (-4 *6 (-856)) (-5 *1 (-986 *4 *5 *6 *7))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-115) (-115))) (-5 *1 (-115))))) +(((*1 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) + (-5 *1 (-1137 *3 *2)) (-4 *3 (-1253 *2))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) +(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) +(((*1 *1 *1 *1) (-5 *1 (-868)))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-650 (-320 (-227)))) (-5 *3 (-227)) (-5 *2 (-112)) + (-5 *1 (-212))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-650 (-959 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-854) (-311) (-148) (-1031))) + (-5 *2 (-650 (-1055 *5 *6))) (-5 *1 (-1304 *5 *6 *7)) + (-14 *6 (-650 (-1186))) (-14 *7 (-650 (-1186))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-959 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-854) (-311) (-148) (-1031))) + (-5 *2 (-650 (-1055 *5 *6))) (-5 *1 (-1304 *5 *6 *7)) + (-14 *6 (-650 (-1186))) (-14 *7 (-650 (-1186))))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-959 *4))) + (-4 *4 (-13 (-854) (-311) (-148) (-1031))) + (-5 *2 (-650 (-1055 *4 *5))) (-5 *1 (-1304 *4 *5 *6)) + (-14 *5 (-650 (-1186))) (-14 *6 (-650 (-1186)))))) (((*1 *1 *2) (-12 (-5 *2 (-650 (-570))) (-5 *1 (-50 *3 *4)) (-4 *3 (-1058)) (-14 *4 (-650 (-1186))))) @@ -268,31 +280,19 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-1297 *3 *4)) (-4 *4 (-723 (-413 (-570)))) (-4 *3 (-856)) (-4 *4 (-174))))) -(((*1 *1 *1) (-5 *1 (-1072)))) -(((*1 *2 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) (((*1 *1 *1) (-5 *1 (-542)))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-562)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-562))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) -(((*1 *2 *3 *4 *5 *6 *5 *3 *7) - (-12 (-5 *4 (-570)) - (-5 *6 - (-2 (|:| |try| (-384)) (|:| |did| (-384)) (|:| -2158 (-384)))) - (-5 *7 (-1 (-1282) (-1277 *5) (-1277 *5) (-384))) - (-5 *3 (-1277 (-384))) (-5 *5 (-384)) (-5 *2 (-1282)) - (-5 *1 (-794)))) - ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) - (-12 (-5 *4 (-570)) - (-5 *6 - (-2 (|:| |try| (-384)) (|:| |did| (-384)) (|:| -2158 (-384)))) - (-5 *7 (-1 (-1282) (-1277 *5) (-1277 *5) (-384))) - (-5 *3 (-1277 (-384))) (-5 *5 (-384)) (-5 *2 (-1282)) - (-5 *1 (-794))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *3 (-777)) (-4 *4 (-354)) (-5 *1 (-218 *4 *2)) + (-4 *2 (-1253 *4)))) + ((*1 *2 *2 *3 *2 *3) + (-12 (-5 *3 (-570)) (-5 *1 (-702 *2)) (-4 *2 (-1253 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1212)))) + ((*1 *2 *1) (-12 (-5 *1 (-335 *2)) (-4 *2 (-856)))) + ((*1 *2 *1) (-12 (-5 *2 (-650 *3)) (-5 *1 (-618 *3)) (-4 *3 (-1109))))) +(((*1 *2) (-12 (-5 *2 (-384)) (-5 *1 (-1049))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) @@ -368,26 +368,26 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(-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1058)) + (-5 *2 (-2 (|:| -3959 *3) (|:| -3971 *3))) (-5 *1 (-859 *5 *3)) + (-4 *3 (-858 *5))))) +(((*1 *2 *3) (-12 (-5 *2 (-413 (-570))) (-5 *1 (-567)) (-5 *3 (-570)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1182 (-413 (-570)))) (-5 *1 (-949)) (-5 *3 (-570))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1432,25 +1309,32 @@ ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) -(((*1 *1 *1 *1) (-5 *1 (-868)))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1129)) (-5 *2 (-1282)) (-5 *1 (-837))))) -(((*1 *1 *1) - (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-803 *2)) (-4 *2 (-174)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-1008 *3)) (-4 *3 (-174)) (-5 *1 (-805 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-368) (-1047 (-413 *2)))) (-5 *2 (-570)) - (-5 *1 (-116 *4 *3)) (-4 *3 (-1253 *4))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 (-650 *2) *2 *2 *2)) (-4 *2 (-1109)) - (-5 *1 (-103 *2)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1109)) (-5 *1 (-103 *2))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *4)) (-4 *4 (-368)) (-4 *2 (-1253 *4)) - (-5 *1 (-929 *4 *2))))) + (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) + (-5 *1 (-986 *4 *5 *6 *3)) (-4 *3 (-1074 *4 *5 *6))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-650 + (-2 + (|:| -2107 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1277 (-320 (-227)))) + (|:| |yinit| (-650 (-227))) (|:| |intvals| (-650 (-227))) + (|:| |g| (-320 (-227))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -2340 + (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) + (|:| |expense| (-384)) (|:| |accuracy| (-384)) + (|:| |intermediateResults| (-384))))))) + (-5 *1 (-809))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-758))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-122 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1467,28 +1351,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *2) (-12 (-5 *2 (-928)) (|has| *1 (-6 -4440)) (-4 *1 (-410)))) +(((*1 *2 *2) (-12 (-5 *2 (-928)) (|has| *1 (-6 -4443)) (-4 *1 (-410)))) ((*1 *2) (-12 (-4 *1 (-410)) (-5 *2 (-928)))) ((*1 *2 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705)))) ((*1 *2) (-12 (-5 *2 (-928)) (-5 *1 (-705))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-227)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-413 (-570))) (-5 *1 (-384))))) -(((*1 *2 *1) (-12 (-5 *2 (-777)) (-5 *1 (-145))))) +(((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1277 *1)) (-4 *1 (-372 *2)) (-4 *2 (-174)))) + ((*1 *2) (-12 (-4 *2 (-174)) (-5 *1 (-422 *3 *2)) (-4 *3 (-423 *2)))) + ((*1 *2) (-12 (-4 *1 (-423 *2)) (-4 *2 (-174))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 (-570)) (-5 *1 (-206))))) (((*1 *2 *3) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)) (-5 *3 (-1168)))) ((*1 *2 *2) (-12 (-5 *2 (-650 (-1168))) (-5 *1 (-243)))) ((*1 *1 *2) (-12 (-5 *2 (-158)) (-5 *1 (-880))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1 (-112) *7 (-650 *7))) (-4 *1 (-1220 *4 *5 *6 *7)) - (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *2 *2) + (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1212)))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-868))) (-5 *1 (-115)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-868) (-650 (-868)))) (-5 *1 (-115)))) ((*1 *2 *1) @@ -1497,32 +1382,26 @@ (-12 (-5 *2 (-1282)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -1941 ((-1168) $ (-1186))) (-15 -4147 (*2 $)) - (-15 -2176 (*2 $))))))) + (-10 -8 (-15 -1942 ((-1168) $ (-1186))) (-15 -4150 (*2 $)) + (-15 -2353 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-400)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-508)))) ((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-716)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1207)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-570)) (-5 *2 (-1282)) (-5 *1 (-1207))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-928))) (-5 *2 (-911 (-570))) (-5 *1 (-924))))) -(((*1 *2 *3 *4 *5 *5 *5 *6 *4 *4 *4 *5 *4 *5 *7) - (-12 (-5 *3 (-1168)) (-5 *5 (-695 (-227))) (-5 *6 (-227)) - (-5 *7 (-695 (-570))) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-758))))) +(((*1 *2) + (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) + (-4 *4 (-1109))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-4 *3 (-174)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *1 (-694 *3 *4 *5 *2)) + (-4 *2 (-693 *3 *4 *5))))) (((*1 *1) (-5 *1 (-334)))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-618 *1)) (-4 *1 (-306))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-158)) (-5 *2 (-1282)) (-5 *1 (-1279))))) -(((*1 *2 *1) - (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-1109)) - (-5 *2 (-650 (-2 (|:| |k| *4) (|:| |c| *3)))))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-2 (|:| |k| (-900 *3)) (|:| |c| *4)))) - (-5 *1 (-633 *3 *4 *5)) (-4 *3 (-856)) - (-4 *4 (-13 (-174) (-723 (-413 (-570))))) (-14 *5 (-928)))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-678 *3))) (-5 *1 (-900 *3)) (-4 *3 (-856))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1109)) (-5 *1 (-224 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-257 *3)))) + ((*1 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-177))) (-5 *1 (-1094))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1539,6 +1418,10 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-171 *5)) (-4 *5 (-13 (-436 *4) (-1011) (-1212))) + (-4 *4 (-562)) (-4 *2 (-13 (-436 (-171 *4)) (-1011) (-1212))) + (-5 *1 (-606 *4 *5 *2))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *6)) (-4 *5 (-1109)) (-4 *6 (-1227)) (-5 *2 (-1 *6 *5)) (-5 *1 (-647 *5 *6)))) @@ -1558,38 +1441,38 @@ (-12 (-5 *3 (-650 *5)) (-5 *4 (-650 *2)) (-5 *6 (-1 *2 *5)) (-4 *5 (-1109)) (-4 *2 (-1227)) (-5 *1 (-647 *5 *2)))) ((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1153)) (-5 *3 (-145)) (-5 *2 (-777))))) -(((*1 *2) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-5 *2 (-695 (-413 *4)))))) -(((*1 *2 *2) (-12 (-5 *2 (-384)) (-5 *1 (-97))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-311)) (-4 *6 (-378 *5)) (-4 *4 (-378 *5)) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1972 (-650 *4)))) - (-5 *1 (-1133 *5 *6 *4 *3)) (-4 *3 (-693 *5 *6 *4))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266))))) +(((*1 *2 *3) + (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-368) (-1212) (-1011)))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) + ((*1 *2 *1) + (-12 (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-112)) + (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5)))) + ((*1 *2 *1) (-12 (-4 *1 (-728)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-732)) (-5 *2 (-112))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-985 *3 *4 *2 *5)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *2 (-856)) (-4 *5 (-1074 *3 *4 *2))))) +(((*1 *2 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-854)) (-5 *1 (-307 *3))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-512)) (-5 *1 (-283)))) + ((*1 *2 *1) + (-12 (-5 *2 (-3 (-570) (-227) (-512) (-1168) (-1191))) + (-5 *1 (-1191))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-391 *2)) (-4 *2 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-980)) (-5 *1 (-912 *3)) (-4 *3 (-1109))))) +(((*1 *2 *1) (-12 (-5 *2 (-650 (-1186))) (-5 *1 (-1190))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1253 *5)) (-4 *5 (-368)) - (-5 *2 - (-2 (|:| |ir| (-592 (-413 *6))) (|:| |specpart| (-413 *6)) - (|:| |polypart| *6))) - (-5 *1 (-580 *5 *6)) (-5 *3 (-413 *6))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1253 *5)) - (-4 *5 (-13 (-27) (-436 *4))) (-4 *4 (-13 (-562) (-1047 (-570)))) - (-4 *7 (-1253 (-413 *6))) (-5 *1 (-558 *4 *5 *6 *7 *2)) - (-4 *2 (-347 *5 *6 *7))))) + (-12 (-5 *3 (-650 (-1 (-112) *8))) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) + (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1160))))) (((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) - (-4 *5 (-378 *3)) (-5 *2 (-570)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) - (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-618 *5))) (-4 *4 (-1109)) (-5 *2 (-618 *5)) - (-5 *1 (-579 *4 *5)) (-4 *5 (-436 *4))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-928)) (-5 *4 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278))))) + (-12 (-5 *2 (-650 *4)) (-5 *1 (-1150 *3 *4)) + (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34)))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -1606,40 +1489,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-650 (-650 (-650 *5)))) (-5 *3 (-1 (-112) *5 *5)) - (-5 *4 (-650 *5)) (-4 *5 (-856)) (-5 *1 (-1197 *5))))) -(((*1 *2 *1) - (-12 (-5 *2 (-650 *4)) (-5 *1 (-1150 *3 *4)) - (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-695 *6)) (-5 *5 (-1 (-424 (-1182 *6)) (-1182 *6))) - (-4 *6 (-368)) - (-5 *2 - (-650 - (-2 (|:| |outval| *7) (|:| |outmult| (-570)) - (|:| |outvect| (-650 (-695 *7)))))) - (-5 *1 (-538 *6 *7 *4)) (-4 *7 (-368)) (-4 *4 (-13 (-368) (-854)))))) -(((*1 *2 *1) - (-12 (-5 *2 (-413 (-959 *3))) (-5 *1 (-459 *3 *4 *5 *6)) - (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) - (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -1942 *3))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *1) (-5 *1 (-443)))) +(((*1 *1) (-5 *1 (-1279)))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-777)) (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-173)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1278)))) ((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-1279))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *3) - (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) (-5 *4 (-227)) - (-5 *2 (-1044)) (-5 *1 (-758))))) -(((*1 *1 *2 *2 *3 *1) - (-12 (-5 *2 (-512)) (-5 *3 (-1113)) (-5 *1 (-295))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-368)) (-5 *1 (-772 *2 *3)) (-4 *2 (-714 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-2 (|:| -3804 *4) (|:| -3079 (-570))))) + (-4 *4 (-1253 (-570))) (-5 *2 (-743 (-777))) (-5 *1 (-448 *4)))) + ((*1 *2 *3) + (-12 (-5 *3 (-424 *5)) (-4 *5 (-1253 *4)) (-4 *4 (-1058)) + (-5 *2 (-743 (-777))) (-5 *1 (-450 *4 *5))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-650 (-1186))) (-4 *4 (-1109)) + (-4 *5 (-13 (-1058) (-893 *4) (-620 (-899 *4)))) + (-5 *1 (-54 *4 *5 *2)) + (-4 *2 (-13 (-436 *5) (-893 *4) (-620 (-899 *4))))))) +(((*1 *2 *3 *4 *3 *5) + (-12 (-5 *3 (-1168)) (-5 *4 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*2)) (-4 *2 (-174)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-320 *4)) @@ -3084,8 +3164,6 @@ (-5 *1 (-1216 *3 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *3)))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-512))) (-5 *1 (-49)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-882))) (-5 *1 (-489))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-570)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-378 *2)) (-4 *5 (-378 *2)) (-4 *2 (-1227)))) @@ -3097,15 +3175,26 @@ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-570)) (-4 *1 (-1062 *4 *5 *2 *6 *7)) (-4 *6 (-240 *5 *2)) (-4 *7 (-240 *4 *2)) (-4 *2 (-1058))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *1 *1 *1) (-5 *1 (-163))) - ((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-163))))) -(((*1 *2 *1) (-12 (-4 *1 (-1019 *3)) (-4 *3 (-1227)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1213 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3) 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(-14 *3 (-650 (-1186))) (-4 *4 (-393)))) @@ -3115,23 +3204,28 @@ ((*1 *1 *2) (-12 (-5 *2 (-413 (-570))) (-4 *1 (-1021)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1021)) (-5 *2 (-928)))) ((*1 *1 *1) (-4 *1 (-1021)))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-1109)) - (-5 *2 (-2 (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1))) - (-4 *1 (-391 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1112 *3 *4 *5 *6 *7)) (-4 *3 (-1109)) (-4 *4 (-1109)) - (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *7 (-1109)) (-5 *2 (-112))))) +(((*1 *1 *1) (-4 *1 (-635))) + ((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-413 (-959 *5))) (-5 *4 (-1186)) + (-4 *5 (-13 (-311) (-148))) (-5 *2 (-650 (-320 *5))) + (-5 *1 (-1138 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-413 (-959 *5)))) (-5 *4 (-650 (-1186))) + (-4 *5 (-13 (-311) (-148))) (-5 *2 (-650 (-650 (-320 *5)))) + (-5 *1 (-1138 *5))))) (((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-1227)) (-4 *1 (-152 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-650 (-2 (|:| -3357 (-777)) (|:| -2288 *4) (|:| |num| *4)))) + (-5 *2 (-650 (-2 (|:| -3994 (-777)) (|:| -2289 *4) (|:| |num| *4)))) (-4 *4 (-1253 *3)) (-4 *3 (-13 (-368) (-148))) (-5 *1 (-405 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2716 "void"))) (-5 *3 (-650 (-959 (-570)))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2713 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-440)) (|:| -2716 "void"))) (-5 *3 (-650 (-1186))) (-5 *4 (-112)) (-5 *1 (-443)))) ((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1227)))) @@ -3151,24 +3245,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-719 *2 *3 *4)) (-4 *2 (-856)) (-4 *3 (-1109)) (-14 *4 - (-1 (-112) (-2 (|:| -2268 *2) (|:| -3357 *3)) - (-2 (|:| -2268 *2) (|:| -3357 *3)))))) + (-1 (-112) (-2 (|:| -2267 *2) (|:| -3994 *3)) + (-2 (|:| -2267 *2) (|:| -3994 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-512)) (-5 *3 (-1127)) (-5 *1 (-844)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-879 *2 *3)) (-4 *2 (-1227)) (-4 *3 (-1227)))) ((*1 *1 *2) - (-12 (-5 *2 (-650 (-2 (|:| -2106 (-1186)) (|:| -2340 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -2107 (-1186)) (|:| -2340 *4)))) (-4 *4 (-1109)) (-5 *1 (-896 *3 *4)) (-4 *3 (-1109)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-650 *5)) (-4 *5 (-13 (-1109) (-34))) (-5 *2 (-650 (-1149 *3 *5))) (-5 *1 (-1149 *3 *5)) (-4 *3 (-13 (-1109) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-650 (-2 (|:| |val| *4) (|:| -3684 *5)))) + (-12 (-5 *3 (-650 (-2 (|:| |val| *4) (|:| -3687 *5)))) (-4 *4 (-13 (-1109) (-34))) (-4 *5 (-13 (-1109) (-34))) (-5 *2 (-650 (-1149 *4 *5))) (-5 *1 (-1149 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3684 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3687 *4))) (-4 *3 (-13 (-1109) (-34))) (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1149 *3 *4)))) ((*1 *1 *2 *3) @@ -3191,9 +3285,18 @@ (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1175 *2 *3)) (-4 *2 (-1109)) (-4 *3 (-1109))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1) (-12 (-5 *1 (-921 *2)) (-4 *2 (-311))))) -(((*1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-765))))) +(((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 (-1058))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-413 (-570))) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-562)) (-4 *8 (-956 *7 *5 *6)) + (-5 *2 (-2 (|:| -3994 (-777)) (|:| -1453 *9) (|:| |radicand| *9))) + (-5 *1 (-960 *5 *6 *7 *8 *9)) (-5 *4 (-777)) + (-4 *9 + (-13 (-368) + (-10 -8 (-15 -3802 ($ *8)) (-15 -4402 (*8 $)) (-15 -4416 (*8 $)))))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-171 (-227))) (-5 *5 (-570)) (-5 *6 (-1168)) + (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-764))))) (((*1 *2 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) @@ -3202,28 +3305,17 @@ ((*1 *1 *1) (-5 *1 (-868))) ((*1 *2 *3) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-1170 *3)) (-4 *3 (-1058))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -3684 *4)))) - (-5 *1 (-1117 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) -(((*1 *2 *3 *2 *4 *5) - (-12 (-5 *2 (-650 *3)) (-5 *5 (-928)) (-4 *3 (-1253 *4)) - (-4 *4 (-311)) (-5 *1 (-466 *4 *3))))) -(((*1 *1 *2) (-12 (-5 *2 (-777)) (-5 *1 (-278))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| |polnum| (-788 *3)) (|:| |polden| *3) (|:| -1521 (-777)))) - (-5 *1 (-788 *3)) (-4 *3 (-1058)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -1521 (-777)))) - (-4 *1 (-1074 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) +(((*1 *1 *1) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) (((*1 *2 *3 *4 *4 *5) (-12 (-5 *4 (-618 *3)) (-5 *5 (-1 (-1182 *3) (-1182 *3))) (-4 *3 (-13 (-27) (-436 *6))) (-4 *6 (-562)) (-5 *2 (-592 *3)) (-5 *1 (-557 *6 *3))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856)) (-4 *2 (-562))))) +(((*1 *2 *1) (-12 (-4 *1 (-533)) (-5 *2 (-697 (-1233)))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-650 (-48))) (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1253 (-48))))) @@ -3272,8 +3364,8 @@ (-12 (-4 *4 (-13 (-856) - (-10 -8 (-15 -1425 ((-1186) $)) - (-15 -2798 ((-3 $ "failed") (-1186)))))) + (-10 -8 (-15 -1426 ((-1186) $)) + (-15 -2800 ((-3 $ "failed") (-1186)))))) (-4 *5 (-799)) (-4 *7 (-562)) (-5 *2 (-424 *3)) (-5 *1 (-462 *4 *5 *6 *7 *3)) (-4 *6 (-562)) (-4 *3 (-956 *7 *5 *4)))) @@ -3322,13 +3414,13 @@ (-12 (-4 *4 (-799)) (-4 *5 (-13 (-856) - (-10 -8 (-15 -1425 ((-1186) $)) - (-15 -2798 ((-3 $ "failed") (-1186)))))) + (-10 -8 (-15 -1426 ((-1186) $)) + (-15 -2800 ((-3 $ "failed") (-1186)))))) (-4 *6 (-311)) (-5 *2 (-424 *3)) (-5 *1 (-736 *4 *5 *6 *3)) (-4 *3 (-956 (-959 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-799)) - (-4 *5 (-13 (-856) (-10 -8 (-15 -1425 ((-1186) $))))) (-4 *6 (-562)) + (-4 *5 (-13 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(-14 *4 (-3 (|:| |fst| (-440)) (|:| -2716 "void"))) (-14 *5 (-650 (-1186))) (-14 *6 (-1190)))) ((*1 *1 *2) (-12 (-5 *2 (-335 *4)) (-4 *4 (-13 (-856) (-21))) @@ -3585,14 +3675,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-440)) (-5 *1 (-443)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3261 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3265 (-650 (-334))))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 (-5 *2 (-1277 (-705))) (-4 *1 (-446)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3261 (-650 (-334))))) + (-5 *2 (-2 (|:| |localSymbols| (-1190)) (|:| -3265 (-650 (-334))))) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-334)) (-4 *1 (-447)))) ((*1 *1 *2) (-12 (-5 *2 (-650 (-334))) (-4 *1 (-447)))) @@ -3661,7 +3751,7 @@ (-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 (-650 (-2 (|:| -1452 *3) (|:| -3384 *4)))) + (-12 (-5 *2 (-650 (-2 (|:| -1453 *3) (|:| -3387 *4)))) (-4 *3 (-1058)) (-4 *4 (-732)) (-5 *1 (-741 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-769)))) ((*1 *1 *2) @@ -3670,25 +3760,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -2521 (-650 (-1103 (-849 (-227))))) + (|:| -1600 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-320 (-227))) - (|:| -2521 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) + (|:| -1600 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-775)))) ((*1 *2 *3) (-12 (-5 *2 (-780)) (-5 *1 (-779 *3)) (-4 *3 (-1227)))) @@ -3706,23 +3796,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2438 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -2439 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2438 (-650 (-227))))))) + (|:| -2439 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2438 (-650 (-227))))) + (-2 (|:| |lfn| (-650 (-320 (-227)))) (|:| -2439 (-650 (-227))))) (-5 *1 (-847)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-320 (-227))) (|:| -2438 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -2439 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (-5 *1 (-847)))) @@ -3823,137 +3913,83 @@ ((*1 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(-413 (-1182 *1))))) @@ -3977,12 +4013,12 @@ (-5 *1 (-957 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-368) - (-10 -8 (-15 -3799 ($ *7)) (-15 -4399 (*7 $)) (-15 -4413 (*7 $))))))) + (-10 -8 (-15 -3802 ($ *7)) (-15 -4402 (*7 $)) (-15 -4416 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1182 *3)) (-4 *3 (-13 (-368) - (-10 -8 (-15 -3799 ($ *7)) (-15 -4399 (*7 $)) (-15 -4413 (*7 $))))) + (-10 -8 (-15 -3802 ($ *7)) (-15 -4402 (*7 $)) (-15 -4416 (*7 $))))) (-4 *7 (-956 *6 *5 *4)) (-4 *5 (-799)) (-4 *4 (-856)) (-4 *6 (-1058)) (-5 *1 (-957 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) @@ -3990,73 +4026,58 @@ (-5 *2 (-413 (-1182 (-413 (-959 *5))))) (-5 *1 (-1052 *5)) (-5 *3 (-413 (-959 *5)))))) (((*1 *2 *3) - (-12 (-5 *2 (-424 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1253 (-48))))) - ((*1 *2 *3 *1) - (-12 (-5 *2 (-2 (|:| |less| (-122 *3)) (|:| |greater| (-122 *3)))) - (-5 *1 (-122 *3)) (-4 *3 (-856)))) - ((*1 *2 *2) - (-12 (-5 *2 (-592 *4)) (-4 *4 (-13 (-29 *3) (-1212))) - (-4 *3 (-13 (-458) (-1047 (-570)) (-645 (-570)))) - (-5 *1 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+ (-4 *4 (-13 (-1109) (-34))) (-4 *5 (-13 (-1109) (-34))) + (-5 *1 (-1150 *4 *5)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-650 (-1149 *3 *4))) (-4 *3 (-13 (-1109) (-34))) + (-4 *4 (-13 (-1109) (-34))) (-5 *1 (-1150 *3 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-458)) (-4 *4 (-799)) (-4 *5 (-856)) + (-4 *6 (-1074 *3 *4 *5)) (-5 *1 (-630 *3 *4 *5 *6 *7 *2)) + (-4 *7 (-1080 *3 *4 *5 *6)) (-4 *2 (-1118 *3 *4 *5 *6))))) +(((*1 *2 *3 *4 *4 *3 *3 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-757))))) (((*1 *1 *1) (-12 (-5 *1 (-683 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-825 *2)) (-4 *2 (-856)))) ((*1 *1 *1) (-12 (-5 *1 (-900 *2)) (-4 *2 (-856)))) @@ -5070,62 +5214,34 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-777)) (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *1 *1) (-12 (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1058)) (-5 *2 (-650 *1)) (-4 *1 (-1143 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-695 *2)) (-4 *2 (-174)) (-5 *1 (-147 *2)))) - ((*1 *2 *3) - 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(-755))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-650 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-777)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-799)) (-4 *6 (-956 *3 *4 *5)) (-4 *3 (-458)) (-4 *5 (-856)) + (-5 *1 (-455 *3 *4 *5 *6))))) +(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-442))))) (((*1 *1 *1) (-12 (-5 *1 (-506 *2)) (-14 *2 (-570)))) ((*1 *1 *1) (-5 *1 (-1129)))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *2)) (-5 *1 (-181 *2)) (-4 *2 (-311)))) - ((*1 *2 *3 *2) - (-12 (-5 *3 (-650 (-650 *4))) (-5 *2 (-650 *4)) (-4 *4 (-311)) - (-5 *1 (-181 *4)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 *8)) - (-5 *4 - (-650 - (-2 (|:| -1972 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7))))) - (-5 *5 (-777)) (-4 *8 (-1253 *7)) (-4 *7 (-1253 *6)) (-4 *6 (-354)) - (-5 *2 - (-2 (|:| -1972 (-695 *7)) (|:| |basisDen| *7) - (|:| |basisInv| (-695 *7)))) - (-5 *1 (-504 *6 *7 *8)))) - ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-567))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-799)) (-4 *4 (-856)) (-4 *6 (-311)) (-5 *2 (-424 *3)) + (-5 *1 (-748 *5 *4 *6 *3)) (-4 *3 (-956 *6 *5 *4))))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1 *4 *4)) (-5 *3 (-777)) (-4 *1 (-233 *4)) (-4 *4 (-1058)))) @@ -5181,14 +5297,25 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-1273 *4)) (-14 *4 (-1186)) (-5 *1 (-1269 *3 *4 *5)) (-4 *3 (-1058)) (-14 *5 *3)))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-777)) (-5 *1 (-789 *2)) (-4 *2 (-38 (-413 (-570)))) - (-4 *2 (-174))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058))))) -(((*1 *2 *3) - (-12 (-4 *4 (-354)) (-4 *5 (-333 *4)) (-4 *6 (-1253 *5)) - (-5 *2 (-650 *3)) (-5 *1 (-783 *4 *5 *6 *3 *7)) (-4 *3 (-1253 *6)) - (-14 *7 (-928))))) +(((*1 *2 *2) + (-12 (-5 *2 (-650 *6)) (-4 *6 (-1074 *3 *4 *5)) (-4 *3 (-148)) + (-4 *3 (-311)) (-4 *3 (-562)) (-4 *4 (-799)) (-4 *5 (-856)) + (-5 *1 (-986 *3 *4 *5 *6))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-458)) (-4 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*1 (-437 *3 *2)) (-4 *2 (-436 *3))))) + (-12 (-4 *1 (-902)) + (-5 *3 + (-2 (|:| |pde| (-650 (-320 (-227)))) + (|:| |constraints| + (-650 + (-2 (|:| |start| (-227)) (|:| |finish| (-227)) + (|:| |grid| (-777)) (|:| |boundaryType| (-570)) + (|:| |dStart| (-695 (-227))) (|:| |dFinish| (-695 (-227)))))) + (|:| |f| (-650 (-650 (-320 (-227))))) (|:| |st| (-1168)) + (|:| |tol| (-227)))) + (-5 *2 (-1044))))) +(((*1 *2 *3 *4 *4 *3) + (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-758))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473))))) (((*1 *2 *3 *3) (-12 (-5 *2 (-1 (-384))) (-5 *1 (-1049)) (-5 *3 (-384))))) -(((*1 *2) - (-12 (-4 *2 (-13 (-436 *3) (-1011))) (-5 *1 (-279 *3 *2)) - (-4 *3 (-562))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1227)) (-5 *2 (-650 *1)) (-4 *1 (-1019 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-1174 *3 *4))) (-5 *1 (-1174 *3 *4)) - (-14 *3 (-928)) (-4 *4 (-1058))))) +(((*1 *1 *1 *1) (-4 *1 (-144))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-159 *3 *2)) (-4 *2 (-436 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-551))))) (((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-62 *3)) (-14 *3 (-1186)))) ((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-69 *3)) (-14 *3 (-1186)))) ((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-72 *3)) (-14 *3 (-1186)))) @@ -6198,20 +6116,12 @@ ((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-1147)))) ((*1 *2 *3) (-12 (-5 *3 (-650 (-868))) (-5 *2 (-1282)) (-5 *1 (-1147))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-910 *3)) (-4 *3 (-1109)) (-5 *2 (-1111 *3)))) - ((*1 *2 *1 *3) - (-12 (-4 *4 (-1109)) (-5 *2 (-1111 (-650 *4))) (-5 *1 (-911 *4)) - (-5 *3 (-650 *4)))) - ((*1 *2 *1 *3) - (-12 (-4 *4 (-1109)) (-5 *2 (-1111 (-1111 *4))) (-5 *1 (-911 *4)) - (-5 *3 (-1111 *4)))) - ((*1 *2 *1 *3) - (-12 (-5 *2 (-1111 *3)) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-562)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-978 *4 *3)) (-4 *3 (-1253 *4))))) +(((*1 *1 *2 *2 *2 *2) (-12 (-4 *1 (-1006 *2)) (-4 *2 (-174))))) +(((*1 *2 *3) (-12 (-5 *3 (-1186)) (-5 *2 (-1282)) (-5 *1 (-1189))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) + (-5 *5 (-3 (|:| |fn| (-394)) (|:| |fp| (-64 -1709)))) + (-5 *2 (-1044)) (-5 *1 (-754))))) (((*1 *1 *1) (-12 (-4 *1 (-378 *2)) (-4 *2 (-1227)) (-4 *2 (-856)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-378 *3)) (-4 *3 (-1227)))) @@ -6220,31 +6130,45 @@ ((*1 *2 *1 *3) (-12 (-4 *4 (-1058)) (-4 *5 (-799)) (-4 *3 (-856)) (-4 *6 (-1074 *4 *5 *3)) - (-5 *2 (-2 (|:| |under| *1) (|:| -3665 *1) (|:| |upper| *1))) + (-5 *2 (-2 (|:| |under| *1) (|:| -1920 *1) (|:| |upper| *1))) (-4 *1 (-985 *4 *5 *3 *6))))) (((*1 *1 *2) (-12 (-5 *2 (-1129)) (-5 *1 (-334))))) -(((*1 *2 *1 *3) - (|partial| -12 (-5 *3 (-899 *4)) (-4 *4 (-1109)) (-5 *2 (-112)) - (-5 *1 (-896 *4 *5)) (-4 *5 (-1109)))) - ((*1 *2 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- (-5 *1 (-510 *4 *5 *6 *7)) (-4 *7 (-956 *4 *5 *6))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 *2 (-562))))) -(((*1 *2 *2) - (|partial| -12 (-5 *2 (-1182 *3)) (-4 *3 (-354)) (-5 *1 (-362 *3))))) + (-2 + (|:| |rgl| + (-650 + (-2 (|:| |eqzro| (-650 *11)) (|:| |neqzro| (-650 *11)) + (|:| |wcond| (-650 (-959 *8))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1277 (-413 (-959 *8)))) + (|:| -3827 (-650 (-1277 (-413 (-959 *8)))))))))) + (|:| |rgsz| (-570)))) + (-5 *1 (-931 *8 *9 *10 *11)) (-5 *7 (-570))))) +(((*1 *2) + (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) + (-4 *5 (-1253 (-413 *4))) (-5 *2 (-112))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) + ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266)))) + ((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-473))))) +(((*1 *2 *3 *2) + (-12 + (-5 *2 + (-650 + (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-777)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *3 (-799)) (-4 *6 (-956 *4 *3 *5)) (-4 *4 (-458)) (-4 *5 (-856)) + (-5 *1 (-455 *4 *3 *5 *6))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1278)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1278)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-650 (-266))) (-5 *1 (-1279)))) @@ -6258,25 +6182,24 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-825 *4)) (-4 *4 (-856)) (-4 *1 (-1294 *4 *3)) (-4 *3 (-1058))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-443))))) -(((*1 *2 *1 *1) - (-12 (-4 *3 (-562)) (-4 *3 (-1058)) - (-5 *2 (-2 (|:| -2573 *1) (|:| -3691 *1))) (-4 *1 (-858 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-562)) (-4 *5 (-1058)) - (-5 *2 (-2 (|:| -2573 *3) (|:| -3691 *3))) (-5 *1 (-859 *5 *3)) - (-4 *3 (-858 *5))))) -(((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-448 *3)) (-4 *3 (-1253 (-570)))))) -(((*1 *2) (-12 (-5 *2 (-1282)) (-5 *1 (-397))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-266))))) -(((*1 *2 *3 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(-767)))) (((*1 *2 *1 *3 *4) (-12 (-5 *3 (-950 (-227))) (-5 *4 (-880)) (-5 *2 (-1282)) (-5 *1 (-474)))) @@ -6294,30 +6217,22 @@ ((*1 *2 *3 *3 *3 *3) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223)) (-5 *3 (-227))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-956 *4 *5 *6)) (-5 *2 (-650 (-650 *7))) - (-5 *1 (-454 *4 *5 *6 *7)) (-5 *3 (-650 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-13 (-311) (-148))) (-4 *6 (-799)) - (-4 *7 (-856)) (-4 *8 (-956 *5 *6 *7)) (-5 *2 (-650 (-650 *8))) - (-5 *1 (-454 *5 *6 *7 *8)) (-5 *3 (-650 *8))))) -(((*1 *2 *3) - (-12 (-5 *3 (-650 (-320 (-227)))) (-5 *2 (-112)) (-5 *1 (-270)))) - ((*1 *2 *3) (-12 (-5 *3 (-320 (-227))) (-5 *2 (-112)) (-5 *1 (-270)))) - ((*1 *2 *3) - (-12 (-4 *4 (-562)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-986 *4 *5 *6 *3)) (-4 *3 (-1074 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-695 (-320 (-227)))) - (-5 *2 - (-2 (|:| |stiffnessFactor| (-384)) (|:| |stabilityFactor| (-384)))) - (-5 *1 (-207))))) -(((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *4 (-227)) + (-12 (-4 *1 (-354)) (-5 *3 (-570)) (-5 *2 (-1199 (-928) (-777)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 (-1 (-112) *8))) (-4 *8 (-1074 *5 *6 *7)) + (-4 *5 (-562)) (-4 *6 (-799)) (-4 *7 (-856)) + (-5 *2 (-2 (|:| |goodPols| (-650 *8)) (|:| |badPols| (-650 *8)))) + (-5 *1 (-986 *5 *6 *7 *8)) (-5 *4 (-650 *8))))) +(((*1 *2 *2) + (-12 (-4 *3 (-1058)) (-4 *4 (-1253 *3)) (-5 *1 (-165 *3 *4 *2)) + (-4 *2 (-1253 *4)))) + ((*1 *1 *1) (-12 (-5 *1 (-298 *2)) (-4 *2 (-1227))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-368)) (-4 *5 (-562)) (-5 *2 - (-2 (|:| |brans| (-650 (-650 (-950 *4)))) - (|:| |xValues| (-1103 *4)) (|:| |yValues| (-1103 *4)))) - (-5 *1 (-154)) (-5 *3 (-650 (-650 (-950 *4))))))) + (-2 (|:| |minor| (-650 (-928))) (|:| -4308 *3) + (|:| |minors| (-650 (-650 (-928)))) (|:| |ops| (-650 *3)))) + (-5 *1 (-90 *5 *3)) (-5 *4 (-928)) (-4 *3 (-662 *5))))) (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-777)) (-4 *1 (-746 *4 *5)) (-4 *4 (-1058)) (-4 *5 (-856)) (-5 *2 (-959 *4)))) @@ -6330,9 +6245,8 @@ ((*1 *2 *1 *3) (-12 (-5 *3 (-777)) (-4 *1 (-1268 *4)) (-4 *4 (-1058)) (-5 *2 (-959 *4))))) -(((*1 *2) - (-12 (-5 *2 (-2 (|:| -2762 (-650 *3)) (|:| -1458 (-650 *3)))) - (-5 *1 (-1228 *3)) (-4 *3 (-1109))))) +(((*1 *2) (-12 (-5 *2 (-650 (-928))) (-5 *1 (-1280)))) + ((*1 *2 *2) (-12 (-5 *2 (-650 (-928))) (-5 *1 (-1280))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-1109)) (-5 *1 (-686 *5 *6 *2))))) @@ -6341,130 +6255,96 @@ ((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-266)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1279))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-458)) (-4 *6 (-799)) (-4 *7 (-856)) - (-4 *3 (-1074 *5 *6 *7)) - (-5 *2 (-650 (-2 (|:| |val| (-112)) (|:| -3684 *4)))) - (-5 *1 (-1117 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3))))) -(((*1 *2 *1) (-12 (-4 *1 (-680 *3)) (-4 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(-13 (-311) (-148))) (-4 *6 (-13 (-856) (-620 (-1186)))) - (-4 *7 (-799)) - (-5 *2 - (-650 - (-2 (|:| |det| *8) (|:| |rows| (-650 (-570))) - (|:| |cols| (-650 (-570)))))) - (-5 *1 (-931 *5 *6 *7 *8))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) (-12 (-5 *2 (-959 (-384))) (-5 *1 (-344 *3 *4 *5)) @@ -7137,11 +7006,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-320 (-227))) - (|:| -2521 (-650 (-1103 (-849 (-227))))) + (|:| -1600 (-650 (-1103 (-849 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-775)))) ((*1 *2 *1) @@ -7157,13 +7026,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-320 (-227))) (|:| -2438 (-650 (-227))) + (-2 (|:| |fn| (-320 (-227))) (|:| -2439 (-650 (-227))) (|:| |lb| (-650 (-849 (-227)))) (|:| |cf| (-650 (-320 (-227)))) (|:| |ub| (-650 (-849 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-650 (-320 (-227)))) - (|:| -2438 (-650 (-227))))))) + (|:| -2439 (-650 (-227))))))) (-5 *1 (-847)))) ((*1 *2 *1) (-12 @@ -7182,26 +7051,26 @@ (-4 *4 (-799)) (-4 *5 (-856)) (-4 *1 (-985 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1047 *2)) (-4 *2 (-1227)))) ((*1 *1 *2) - (-2892 + (-2895 (-12 (-5 *2 (-959 *3)) - (-12 (-1795 (-4 *3 (-38 (-413 (-570))))) - (-1795 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) + (-12 (-1796 (-4 *3 (-38 (-413 (-570))))) + (-1796 (-4 *3 (-38 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1795 (-4 *3 (-551))) (-1795 (-4 *3 (-38 (-413 (-570))))) + (-12 (-1796 (-4 *3 (-551))) (-1796 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 *3)) - (-12 (-1795 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) + (-12 (-1796 (-4 *3 (-1001 (-570)))) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *1 (-1074 *3 *4 *5)) (-4 *4 (-799)) (-4 *5 (-856))))) ((*1 *1 *2) - (-2892 + (-2895 (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) - (-12 (-1795 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) + (-12 (-1796 (-4 *3 (-38 (-413 (-570))))) (-4 *3 (-38 (-570))) (-4 *5 (-620 (-1186)))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))) (-12 (-5 *2 (-959 (-570))) (-4 *1 (-1074 *3 *4 *5)) @@ -7211,49 +7080,26 @@ (-12 (-5 *2 (-959 (-413 (-570)))) (-4 *1 (-1074 *3 *4 *5)) (-4 *3 (-38 (-413 (-570)))) (-4 *5 (-620 (-1186))) (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856))))) -(((*1 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) - (-4 *2 (-13 (-436 *3) (-1011)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-4 *4 (-1058)) - (-5 *2 (-2 (|:| -2573 *1) (|:| -3691 *1))) (-4 *1 (-1253 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-650 *6)) (-5 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(-585))))) +(((*1 *2 *1 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1213 *3)) (-4 *3 (-1109))))) +(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) + (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) + (-5 *6 (-3 (|:| |fn| (-394)) (|:| |fp| (-70 APROD)))) (-5 *4 (-227)) + (-5 *2 (-1044)) (-5 *1 (-762))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-560 *2)) (-4 *2 (-13 (-410) (-1212)))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-928)) (-4 *1 (-333 *3)) (-4 *3 (-368)) (-4 *3 (-373)))) ((*1 *2 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-368)))) @@ -7265,134 +7111,164 @@ ((*1 *2 *1) (-12 (-4 *1 (-1132 *3 *2 *4 *5)) (-4 *4 (-240 *3 *2)) (-4 *5 (-240 *3 *2)) (-4 *2 (-1058))))) -(((*1 *2 *1) (-12 (-4 *1 (-773 *3)) (-4 *3 (-1109)) (-5 *2 (-112))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-413 (-959 (-171 (-570))))) (-5 *2 (-650 (-171 *4))) - (-5 *1 (-383 *4)) (-4 *4 (-13 (-368) (-854))))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-650 (-413 (-959 (-171 (-570)))))) - (-5 *4 (-650 (-1186))) (-5 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(-5 *4 (-1277 *5))))) +(((*1 *2 *3) (-12 (-5 *3 (-777)) (-5 *2 (-1282)) (-5 *1 (-384))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-171 (-227))) (-5 *5 (-570)) (-5 *6 (-1168)) + (-5 *3 (-227)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) +(((*1 *2 *2 *2) + (-12 + (-5 *2 + (-2 (|:| -3827 (-695 *3)) (|:| |basisDen| *3) + (|:| |basisInv| (-695 *3)))) + (-4 *3 (-13 (-311) (-10 -8 (-15 -3871 ((-424 $) $))))) + (-4 *4 (-1253 *3)) (-5 *1 (-505 *3 *4 *5)) (-4 *5 (-415 *3 *4))))) (((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) + (-12 (-4 *4 (-174)) (-5 *2 (-650 (-1277 *4))) (-5 *1 (-371 *3 *4)) (-4 *3 (-372 *4)))) - ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-650 *5) *6)) - (-4 *5 (-13 (-368) (-148) (-1047 (-413 (-570))))) (-4 *6 (-1253 *5)) - (-5 *2 (-650 (-2 (|:| -3725 *5) (|:| -4305 *3)))) - (-5 *1 (-815 *5 *6 *3 *7)) (-4 *3 (-662 *6)) - (-4 *7 (-662 (-413 *6)))))) + ((*1 *2) + (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-4 *3 (-562)) + (-5 *2 (-650 (-1277 *3)))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1166 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1600 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet 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*2 (-570))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1109)) (-4 *5 (-1109)) + (-4 *6 (-1109)) (-5 *2 (-1 *6 *5)) (-5 *1 (-690 *4 *5 *6))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *2) (-12 (-5 *2 (-1103 (-849 (-227)))) (-5 *1 (-309))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9170,60 +8930,51 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1 *1) - (|partial| -12 (-5 *1 (-153 *2 *3 *4)) (-14 *2 (-928)) (-4 *3 (-368)) - (-14 *4 (-1002 *2 *3)))) - ((*1 *1 *1) - (|partial| -12 (-4 *2 (-174)) (-5 *1 (-293 *2 *3 *4 *5 *6 *7)) - (-4 *3 (-1253 *2)) (-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) - (|partial| -12 (-4 *1 (-372 *2)) (-4 *2 (-174)) (-4 *2 (-562)))) - ((*1 *1 *1) - (|partial| -12 (-5 *1 (-721 *2 *3 *4 *5 *6)) (-4 *2 (-174)) - (-4 *3 (-23)) (-14 *4 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*3 *4)) (-4 *3 (-1058)) + (-4 *4 (-732))))) +(((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-497))))) (((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1182 *4)) (-5 *1 (-362 *4)) - (-4 *4 (-354))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-512)) (-5 *2 (-112)) (-5 *1 (-115))))) + (-12 (-5 *3 (-650 (-570))) (-5 *2 (-911 (-570))) (-5 *1 (-924)))) + ((*1 *2) (-12 (-5 *2 (-911 (-570))) (-5 *1 (-924))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1277 *1)) (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) + (-4 *4 (-1253 *3)) (-4 *5 (-1253 (-413 *4)))))) +(((*1 *2 *2) (-12 (-5 *2 (-384)) (-5 *1 (-97))))) (((*1 *2 *3 *2 *3) (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1189)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1189)))) @@ -9276,19 +9024,19 @@ (-12 (-5 *2 (-443)) (-5 *3 (-1186)) (-5 *1 (-1190)))) ((*1 *2 *3 *2 *1) (-12 (-5 *2 (-443)) (-5 *3 (-650 (-1186))) (-5 *1 (-1190))))) -(((*1 *1 *1 *1) (-4 *1 (-144))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-562)) (-5 *1 (-159 *3 *2)) (-4 *2 (-436 *3)))) - ((*1 *2 *2 *2) (-12 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*1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -9305,34 +9053,51 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *4 *3 *5 *5 *3 *5 *4) - (-12 (-5 *4 (-695 (-227))) (-5 *5 (-695 (-570))) (-5 *3 (-570)) - (-5 *2 (-1044)) (-5 *1 (-762))))) -(((*1 *1 *1) (-12 (-5 *1 (-176 *2)) (-4 *2 (-311)))) - ((*1 *2 *3) - (-12 (-5 *3 (-928)) (-5 *2 (-1188 (-413 (-570)))) (-5 *1 (-192)))) - ((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227)))) - ((*1 *1 *1) (-4 *1 (-875 *2))) - ((*1 *1 *1) - (-12 (-4 *1 (-982 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-798)) - (-4 *4 (-856))))) -(((*1 *2 *3) - (-12 (-5 *3 (-695 (-413 (-959 *4)))) (-4 *4 (-458)) - (-5 *2 (-650 (-3 (-413 (-959 *4)) (-1175 (-1186) (-959 *4))))) - (-5 *1 (-296 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-959 (-227))) (-5 *2 (-320 (-384))) (-5 *1 (-309))))) -(((*1 *2 *1) (|partial| -12 (-5 *2 (-1113)) (-5 *1 (-283))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-570)) (-5 *1 (-424 *2)) (-4 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+ (-4 *3 (-423 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-867)))) + ((*1 *1 *2) (-12 (-5 *2 (-394)) (-5 *1 (-867))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -9441,59 +9167,29 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-368)) (-5 *1 (-772 *2 *3)) (-4 *2 (-714 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) -(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-933))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1186)) - (-4 *4 (-13 (-311) (-1047 (-570)) (-645 (-570)) (-148))) - (-5 *2 (-1 *5 *5)) (-5 *1 (-810 *4 *5)) - (-4 *5 (-13 (-29 *4) (-1212) (-966)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-320 *4)) (-4 *4 (-13 (-834) (-1058))) (-5 *2 (-1168)) - (-5 *1 (-832 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-320 *5)) (-5 *4 (-112)) (-4 *5 (-13 (-834) (-1058))) - (-5 *2 (-1168)) (-5 *1 (-832 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-828)) (-5 *4 (-320 *5)) (-4 *5 (-13 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(-695 (-227))) (-5 *2 (-1044)) + (-5 *1 (-753))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *2 (-413 (-959 *4))) (-5 *1 (-931 *4 *5 *6 *3)) - (-4 *3 (-956 *4 *6 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-695 *7)) (-4 *7 (-956 *4 *6 *5)) - (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *2 (-695 (-413 (-959 *4)))) - (-5 *1 (-931 *4 *5 *6 *7)))) - ((*1 *2 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *6 *5)) - (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) (-5 *2 (-650 (-413 (-959 *4)))) - (-5 *1 (-931 *4 *5 *6 *7))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-570)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-424 *2)) (-4 *2 (-562))))) -(((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-371 *3 *4)) - (-4 *3 (-372 *4)))) - ((*1 *2) (-12 (-4 *1 (-372 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) + (|partial| -12 (-4 *4 (-1231)) (-4 *5 (-1253 *4)) + (-5 *2 (-2 (|:| |radicand| (-413 *5)) (|:| |deg| (-777)))) + (-5 *1 (-149 *4 *5 *3)) (-4 *3 (-1253 (-413 *5)))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1253 *5)) + (-4 *5 (-13 (-27) (-436 *4))) (-4 *4 (-13 (-562) (-1047 (-570)))) + (-4 *7 (-1253 (-413 *6))) (-5 *1 (-558 *4 *5 *6 *7 *2)) + (-4 *2 (-347 *5 *6 *7))))) +(((*1 *2 *1) + (-12 (-5 *2 (-650 (-912 *3))) (-5 *1 (-911 *3)) (-4 *3 (-1109))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-391 *2)) (-4 *2 (-1109))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1277 *4)) (-5 *3 (-570)) (-4 *4 (-354)) + (-5 *1 (-534 *4))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) ((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) @@ -9514,45 +9210,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *3 *3 *3 *4 *5 *3 *6 *6 *3) - (-12 (-5 *3 (-570)) (-5 *5 (-112)) (-5 *6 (-695 (-227))) - (-5 *4 (-227)) (-5 *2 (-1044)) (-5 *1 (-761))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1168)) (-5 *4 (-570)) (-5 *5 (-695 (-171 (-227)))) - (-5 *2 (-1044)) (-5 *1 (-760))))) -(((*1 *2 *3) - (-12 (-4 *4 (-799)) (-4 *5 (-856)) (-4 *6 (-311)) (-5 *2 (-424 *3)) - (-5 *1 (-748 *4 *5 *6 *3)) (-4 *3 (-956 *6 *4 *5))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-650 (-950 *4))) (-4 *1 (-1143 *4)) (-4 *4 (-1058)) - (-5 *2 (-777))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-726)) (-5 *2 (-928)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-728)) (-5 *2 (-777))))) (((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (-5 *2 (-2 (|:| -3897 (-115)) (|:| |w| (-227)))) (-5 *1 (-206))))) + (-12 (-5 *3 (-1182 (-570))) (-5 *2 (-570)) (-5 *1 (-949))))) +(((*1 *2 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1227))))) +(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-1153)) (-5 *2 (-1244 (-570)))))) +(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-523))))) (((*1 *2 *1) - (-12 (-4 *1 (-1080 *3 *4 *5 *6)) (-4 *3 (-458)) (-4 *4 (-799)) - (-4 *5 (-856)) (-4 *6 (-1074 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) - (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1277 *1)) (-4 *1 (-375 *4 *5)) (-4 *4 (-174)) - (-4 *5 (-1253 *4)) (-5 *2 (-695 *4)))) + (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1227)) (-4 *4 (-378 *3)) + (-4 *5 (-378 *3)) (-5 *2 (-570)))) ((*1 *2 *1) - (-12 (-4 *1 (-415 *3 *4)) (-4 *3 (-174)) (-4 *4 (-1253 *3)) - (-5 *2 (-695 *3))))) + (-12 (-4 *1 (-1062 *3 *4 *5 *6 *7)) (-4 *5 (-1058)) + (-4 *6 (-240 *4 *5)) (-4 *7 (-240 *3 *5)) (-5 *2 (-570))))) (((*1 *2 *3) - (-12 (-4 *4 (-1227)) (-5 *2 (-777)) (-5 *1 (-184 *4 *3)) - (-4 *3 (-680 *4))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1072))))) + (-12 (-5 *2 (-1 (-227) (-227))) (-5 *1 (-322)) (-5 *3 (-227))))) +(((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011)))))) +(((*1 *1 *2) (-12 (-5 *2 (-650 (-868))) (-5 *1 (-868)))) + ((*1 *1 *1) (-5 *1 (-868)))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1709 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -9574,59 +9255,37 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-650 (-879 (-928) (-928)))) (-5 *1 (-980))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-1080 *4 *5 *6 *3)) (-4 *4 (-458)) (-4 *5 (-799)) + (-4 *6 (-856)) (-4 *3 (-1074 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-570)) (-4 *1 (-1102 *3)) (-4 *3 (-1227))))) (((*1 *2 *1) (-12 (-5 *2 (-650 (-1144))) (-5 *1 (-155)))) ((*1 *2 *1) (-12 (-5 *2 (-650 (-1144))) (-5 *1 (-1075))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1174 *2 *3)) (-14 *2 (-928)) (-4 *3 (-1058))))) +(((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1182 *7)) + (-4 *5 (-1058)) (-4 *7 (-1058)) (-4 *2 (-1253 *5)) + (-5 *1 (-507 *5 *2 *6 *7)) (-4 *6 (-1253 *2))))) +(((*1 *2 *2) (-12 (-5 *2 (-570)) (-5 *1 (-260))))) +(((*1 *2) + (-12 (-4 *3 (-562)) (-5 *2 (-650 (-695 *3))) (-5 *1 (-43 *3 *4)) + (-4 *4 (-423 *3))))) (((*1 *2 *3) - (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-193)) (-5 *3 (-570)))) - ((*1 *2 *3 *2) (-12 (-5 *3 (-777)) (-5 *1 (-789 *2)) (-4 *2 (-174)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) -(((*1 *1 *2) (-12 (-5 *2 (-650 *3)) (-4 *3 (-856)) (-5 *1 (-490 *3))))) + (-12 (-5 *3 (-650 (-618 *5))) (-4 *4 (-1109)) (-5 *2 (-618 *5)) + (-5 *1 (-579 *4 *5)) (-4 *5 (-436 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-828))))) (((*1 *2 *3) - (|partial| -12 (-4 *5 (-1047 (-48))) - (-4 *4 (-13 (-562) (-1047 (-570)))) (-4 *5 (-436 *4)) - (-5 *2 (-424 (-1182 (-48)))) (-5 *1 (-441 *4 *5 *3)) - (-4 *3 (-1253 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-173))))) -(((*1 *2 *2) - (-12 (-4 *2 (-13 (-368) (-854))) (-5 *1 (-183 *2 *3)) - (-4 *3 (-1253 (-171 *2)))))) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-167 *3)) (-4 *3 (-174)) (-4 *3 (-551)) - (-5 *2 (-413 (-570))))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-424 *3)) (-4 *3 (-551)) - (-4 *3 (-562)))) - ((*1 *2 *1) (|partial| -12 (-4 *1 (-551)) (-5 *2 (-413 (-570))))) - ((*1 *2 *1) - (|partial| -12 (-4 *1 (-803 *3)) (-4 *3 (-174)) (-4 *3 (-551)) - (-5 *2 (-413 (-570))))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-839 *3)) (-4 *3 (-551)) - (-4 *3 (-1109)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-849 *3)) (-4 *3 (-551)) - (-4 *3 (-1109)))) - ((*1 *2 *1) - (|partial| -12 (-4 *1 (-1006 *3)) (-4 *3 (-174)) (-4 *3 (-551)) - (-5 *2 (-413 (-570))))) + (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-689 *4 *3)) (-4 *4 (-1109)) + (-4 *3 (-1109))))) +(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-1147)))) ((*1 *2 *3) - (|partial| -12 (-5 *2 (-413 (-570))) (-5 *1 (-1017 *3)) - (-4 *3 (-1047 *2))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227))) (-5 *1 (-709 *3)) - (-4 *3 (-620 (-542))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-1186)) (-5 *2 (-1 (-227) (-227) (-227))) - (-5 *1 (-709 *3)) (-4 *3 (-620 (-542)))))) -(((*1 *2 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-928)) (-5 *1 (-792))))) + (-12 (-5 *3 (-650 (-868))) (-5 *2 (-1282)) (-5 *1 (-1147))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1709 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *1 *1) (-4 *1 (-95))) @@ -9648,13 +9307,19 @@ ((*1 *2 *2) (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3))))) -(((*1 *1) - (-12 (-4 *1 (-410)) (-1795 (|has| *1 (-6 -4440))) - (-1795 (|has| *1 (-6 -4432))))) - ((*1 *2 *1) (-12 (-4 *1 (-431 *2)) (-4 *2 (-1109)) (-4 *2 (-856)))) - ((*1 *1) (-4 *1 (-850))) ((*1 *1 *1 *1) (-4 *1 (-856))) - ((*1 *2 *1) (-12 (-4 *1 (-977 *2)) (-4 *2 (-856))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-934))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1058)) (-4 *4 (-799)) (-4 *5 (-856)) (-5 *2 (-650 *1)) + (-4 *1 (-1074 *3 *4 *5))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1074 *3 *4 *2)) (-4 *3 (-1058)) (-4 *4 (-799)) + (-4 *2 (-856)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-788 *2)) (-4 *2 (-1058)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) + (-4 *4 (-856))))) (((*1 *2 *1) (-12 (-4 *1 (-269 *2)) (-4 *2 (-856)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-1186)) (-5 *1 (-870 *3)) (-14 *3 (-650 *2)))) @@ -9667,42 +9332,26 @@ (-12 (-4 *1 (-1255 *3 *4)) (-4 *3 (-1058)) (-4 *4 (-798)) (-5 *2 (-1186)))) ((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1273 *3)) (-14 *3 *2)))) -(((*1 *1 *2) - (-12 (-5 *2 (-928)) (-4 *1 (-240 *3 *4)) (-4 *4 (-1058)) - (-4 *4 (-1227)))) - ((*1 *1 *2) - (-12 (-14 *3 (-650 (-1186))) (-4 *4 (-174)) - (-4 *5 (-240 (-2569 *3) (-777))) - (-14 *6 - (-1 (-112) (-2 (|:| -2268 *2) (|:| -3357 *5)) - (-2 (|:| -2268 *2) (|:| -3357 *5)))) - (-5 *1 (-467 *3 *4 *2 *5 *6 *7)) (-4 *2 (-856)) - (-4 *7 (-956 *4 *5 (-870 *3))))) - ((*1 *2 *2) (-12 (-5 *2 (-950 (-227))) (-5 *1 (-1223))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1109)) (-4 *6 (-1109)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-690 *4 *5 *6)) (-4 *5 (-1109))))) -(((*1 *2 *1) (-12 (-5 *2 (-215 4 (-130))) (-5 *1 (-585))))) +(((*1 *2 *2) + (-12 (-4 *3 (-458)) (-5 *1 (-1218 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1212)))))) (((*1 *1 *1) - (-12 (-4 *1 (-1074 *2 *3 *4)) (-4 *2 (-1058)) (-4 *3 (-799)) - (-4 *4 (-856)) (-4 *2 (-562))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-650 (-959 *6))) (-5 *4 (-650 (-1186))) (-4 *6 (-458)) - (-5 *2 (-650 (-650 *7))) (-5 *1 (-544 *6 *7 *5)) (-4 *7 (-368)) - (-4 *5 (-13 (-368) (-854)))))) -(((*1 *2 *3 *3) - (-12 (-4 *3 (-1231)) (-4 *5 (-1253 *3)) (-4 *6 (-1253 (-413 *5))) - (-5 *2 (-112)) (-5 *1 (-346 *4 *3 *5 *6)) (-4 *4 (-347 *3 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *1 (-347 *3 *4 *5)) (-4 *3 (-1231)) (-4 *4 (-1253 *3)) - (-4 *5 (-1253 (-413 *4))) (-5 *2 (-112))))) + (-12 (-5 *1 (-601 *2)) (-4 *2 (-38 (-413 (-570)))) (-4 *2 (-1058))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *3 (-570)) (-4 *4 (-174)) (-4 *5 (-378 *4)) + (-4 *6 (-378 *4)) (-5 *1 (-694 *4 *5 *6 *2)) + (-4 *2 (-693 *4 *5 *6))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1277 *4)) (-5 *3 (-1129)) (-4 *4 (-354)) + (-5 *1 (-534 *4))))) (((*1 *2 *2 *3) - (-12 (-4 *4 (-1109)) (-4 *2 (-907 *4)) (-5 *1 (-698 *4 *2 *5 *3)) - (-4 *5 (-378 *2)) (-4 *3 (-13 (-378 *4) (-10 -7 (-6 -4449))))))) + (|partial| -12 (-5 *2 (-413 (-959 *4))) (-5 *3 (-1186)) + (-4 *4 (-13 (-562) (-1047 (-570)) (-148))) (-5 *1 (-576 *4))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1709 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *2 *2) @@ -9717,7 +9366,7 @@ ((*1 *1 *1) (-4 *1 (-288))) ((*1 *2 *3) (-12 (-5 *3 (-424 *4)) (-4 *4 (-562)) - (-5 *2 (-650 (-2 (|:| -1452 (-777)) (|:| |logand| *4)))) + (-5 *2 (-650 (-2 (|:| -1453 (-777)) (|:| |logand| *4)))) (-5 *1 (-324 *4)))) ((*1 *1 *1) (-12 (-5 *1 (-344 *2 *3 *4)) (-14 *2 (-650 (-1186))) @@ -9754,66 +9403,40 @@ (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) (((*1 *2 *3) - (-12 (-5 *2 (-1166 (-570))) (-5 *1 (-1170 *4)) (-4 *4 (-1058)) - (-5 *3 (-570))))) + (-12 (-5 *2 (-1182 (-570))) (-5 *1 (-949)) (-5 *3 (-570))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1279))))) (((*1 *2 *1) - (-12 (-5 *2 (-650 (-2 (|:| |k| (-1186)) (|:| |c| (-1299 *3))))) - (-5 *1 (-1299 *3)) (-4 *3 (-1058)))) - ((*1 *2 *1) - (-12 (-5 *2 (-650 (-2 (|:| |k| *3) (|:| |c| (-1301 *3 *4))))) - (-5 *1 (-1301 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058))))) -(((*1 *1) (-5 *1 (-158))) - ((*1 *2 *1) (-12 (-4 *1 (-1053 *2)) (-4 *2 (-23))))) + (-12 (-4 *1 (-560 *3)) (-4 *3 (-13 (-410) (-1212))) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-854)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1077 *4 *3)) (-4 *4 (-13 (-854) (-368))) + (-4 *3 (-1253 *4)) (-5 *2 (-112))))) (((*1 *1 *1 *1) (-4 *1 (-551)))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-1277 - (-2 (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)) (|:| -1981 (-570)) - (|:| -4130 (-570)) (|:| |spline| (-570)) (|:| -1643 (-570)) - (|:| |axesColor| (-880)) (|:| -3222 (-570)) - (|:| |unitsColor| (-880)) (|:| |showing| (-570))))) - (-5 *1 (-1278))))) +(((*1 *2) + (-12 (-4 *3 (-562)) (-5 *2 (-650 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-423 *3))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-928)) (-5 *4 (-1168)) (-5 *2 (-1282)) (-5 *1 (-1278))))) (((*1 *2 *3 *2) (-12 (-5 *3 (-928)) (-5 *1 (-1039 *2)) - (-4 *2 (-13 (-1109) (-10 -8 (-15 -3101 ($ $ $)))))))) -(((*1 *2 *3 *4 *5 *6 *7 *7 *8) - (-12 - (-5 *3 - (-2 (|:| |det| *12) (|:| |rows| (-650 (-570))) - (|:| |cols| (-650 (-570))))) - (-5 *4 (-695 *12)) (-5 *5 (-650 (-413 (-959 *9)))) - (-5 *6 (-650 (-650 *12))) (-5 *7 (-777)) (-5 *8 (-570)) - (-4 *9 (-13 (-311) (-148))) (-4 *12 (-956 *9 *11 *10)) - (-4 *10 (-13 (-856) (-620 (-1186)))) (-4 *11 (-799)) - (-5 *2 - (-2 (|:| |eqzro| (-650 *12)) (|:| |neqzro| (-650 *12)) - (|:| |wcond| (-650 (-959 *9))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1277 (-413 (-959 *9)))) - (|:| -1972 (-650 (-1277 (-413 (-959 *9))))))))) - (-5 *1 (-931 *9 *10 *11 *12))))) + (-4 *2 (-13 (-1109) (-10 -8 (-15 -3104 ($ $ $)))))))) (((*1 *2 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-1282)) - (-5 *1 (-455 *4 *5 *6 *3)) (-4 *3 (-956 *4 *5 *6))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1109)) - (-5 *2 (-2 (|:| -1452 (-570)) (|:| |var| (-618 *1)))) - (-4 *1 (-436 *3))))) + (-12 (-5 *3 (-249 *4 *5)) (-14 *4 (-650 (-1186))) (-4 *5 (-1058)) + (-5 *2 (-959 *5)) (-5 *1 (-951 *4 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) +(((*1 *2 *1) (-12 (-4 *1 (-257 *2)) (-4 *2 (-1227))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-320 (-570))) (|:| -1708 (-320 (-384))) + (-3 (|:| I (-320 (-570))) (|:| -1709 (-320 (-384))) (|:| CF (-320 (-171 (-384)))) (|:| |switch| (-1185)))) (-5 *1 (-1185))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-777)) (-4 *5 (-1058)) (-4 *2 (-1253 *5)) - (-5 *1 (-1271 *5 *2 *6 *3)) (-4 *6 (-662 *2)) (-4 *3 (-1268 *5))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-368)) (-5 *1 (-772 *2 *3)) (-4 *2 (-714 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-858 *2)) (-4 *2 (-1058)) (-4 *2 (-368))))) + (-12 (-5 *3 (-650 (-413 (-959 *5)))) (-5 *4 (-650 (-1186))) + (-4 *5 (-562)) (-5 *2 (-650 (-650 (-959 *5)))) (-5 *1 (-1195 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9830,45 +9453,39 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-618 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *4))) + (-4 *4 (-13 (-562) (-1047 (-570)) (-645 (-570)))) + (-5 *1 (-280 *4 *2))))) (((*1 *2 *3) - (-12 (-5 *3 (-1166 (-227))) (-5 *2 (-650 (-1168))) (-5 *1 (-194)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1166 (-227))) (-5 *2 (-650 (-1168))) (-5 *1 (-304)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1166 (-227))) (-5 *2 (-650 (-1168))) (-5 *1 (-309))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -2415 (-695 (-413 (-959 *4)))) - (|:| |vec| (-650 (-413 (-959 *4)))) (|:| -4006 (-777)) - (|:| |rows| (-650 (-570))) (|:| |cols| (-650 (-570))))) - (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) - (-4 *6 (-799)) - (-5 *2 - (-2 (|:| |partsol| (-1277 (-413 (-959 *4)))) - (|:| -1972 (-650 (-1277 (-413 (-959 *4))))))) - (-5 *1 (-931 *4 *5 *6 *7)) (-4 *7 (-956 *4 *6 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166 *3)) (-5 *1 (-176 *3)) (-4 *3 (-311))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-866)) (-5 *3 (-129)) (-5 *2 (-777))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) - (-5 *2 (-650 *4)) (-5 *1 (-1137 *3 *4)) (-4 *3 (-1253 *4)))) - ((*1 *2 *3 *3 *3) - (-12 (-4 *3 (-13 (-368) (-10 -8 (-15 ** ($ $ (-413 (-570))))))) - (-5 *2 (-650 *3)) (-5 *1 (-1137 *4 *3)) (-4 *4 (-1253 *3))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) - (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (-5 *2 (-384)) (-5 *1 (-207))))) -(((*1 *2 *3) - (-12 (-4 *4 (-27)) - (-4 *4 (-13 (-368) (-148) (-1047 (-570)) (-1047 (-413 (-570))))) - (-4 *5 (-1253 *4)) (-5 *2 (-650 (-659 (-413 *5)))) - (-5 *1 (-663 *4 *5)) (-5 *3 (-659 (-413 *5)))))) + (-12 (-4 *4 (-311)) (-4 *5 (-378 *4)) (-4 *6 (-378 *4)) + (-5 *2 (-2 (|:| |Hermite| *3) (|:| |eqMat| *3))) + (-5 *1 (-1133 *4 *5 *6 *3)) (-4 *3 (-693 *4 *5 *6))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-458) (-1047 (-570)))) (-4 *3 (-562)) + (-5 *1 (-41 *3 *2)) (-4 *2 (-436 *3)) + (-4 *2 + (-13 (-368) (-306) + (-10 -8 (-15 -4402 ((-1134 *3 (-618 $)) $)) + (-15 -4416 ((-1134 *3 (-618 $)) $)) + (-15 -3802 ($ (-1134 *3 (-618 $)))))))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-650 (-650 (-650 *5)))) (-5 *3 (-1 (-112) *5 *5)) + (-5 *4 (-650 *5)) (-4 *5 (-856)) (-5 *1 (-1197 *5))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) + (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) + (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7))))) +(((*1 *2 *1 *2) + (-12 (-4 *1 (-369 *3 *2)) (-4 *3 (-1109)) (-4 *2 (-1109))))) +(((*1 *2 *3 *1) + (|partial| -12 (-5 *3 (-1 (-112) *2)) (-4 *1 (-152 *2)) + (-4 *2 (-1227))))) +(((*1 *1 *1) (-4 *1 (-875 *2)))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9885,58 +9502,49 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *4 *4 *4 *3 *4 *3) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *2 (-1044)) - (-5 *1 (-757))))) +(((*1 *2 *1) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-654 *3)) (-4 *3 (-1058)) + (-5 *1 (-720 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1058)) (-5 *1 (-842 *3))))) +(((*1 *2 *3) (-12 (-5 *3 (-384)) (-5 *2 (-227)) (-5 *1 (-1280)))) + ((*1 *2) (-12 (-5 *2 (-227)) (-5 *1 (-1280))))) +(((*1 *1 *1 *1) (-5 *1 (-163))) + ((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-163))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-695 *6)) (-5 *5 (-1 (-424 (-1182 *6)) (-1182 *6))) + (-4 *6 (-368)) + (-5 *2 + (-650 + (-2 (|:| |outval| *7) (|:| |outmult| (-570)) + (|:| |outvect| (-650 (-695 *7)))))) + (-5 *1 (-538 *6 *7 *4)) (-4 *7 (-368)) (-4 *4 (-13 (-368) (-854)))))) +(((*1 *2 *3 *1) (-12 (-5 *3 (-1186)) (-5 *2 (-1190)) (-5 *1 (-1189))))) (((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-570))) (-5 *1 (-1056))))) -(((*1 *2 *2) (-12 (-5 *2 (-1168)) (-5 *1 (-868))))) -(((*1 *2 *1) (-12 (-4 *1 (-1102 *2)) (-4 *2 (-1227))))) -(((*1 *2) - (-12 (-4 *3 (-562)) (-5 *2 (-650 (-695 *3))) (-5 *1 (-43 *3 *4)) - (-4 *4 (-423 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279))))) + (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-368) (-1212) (-1011)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-695 *2)) (-4 *4 (-1253 *2)) + (-4 *2 (-13 (-311) (-10 -8 (-15 -3871 ((-424 $) $))))) + (-5 *1 (-505 *2 *4 *5)) (-4 *5 (-415 *2 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1132 *3 *2 *4 *5)) (-4 *4 (-240 *3 *2)) + (-4 *5 (-240 *3 *2)) (-4 *2 (-1058))))) +(((*1 *2 *1) (-12 (-4 *1 (-1019 *3)) (-4 *3 (-1227)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1213 *3)) (-4 *3 (-1109))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-997 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-458)) (-4 *5 (-799)) (-4 *6 (-856)) - (-4 *7 (-1074 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1116 *4 *5 *6 *7 *3)) (-4 *3 (-1080 *4 *5 *6 *7))))) + (-12 (-5 *3 (-1277 *5)) (-4 *5 (-798)) (-5 *2 (-112)) + (-5 *1 (-851 *4 *5)) (-14 *4 (-777))))) (((*1 *2 *3 *3 *2) - (-12 (-5 *2 (-1044)) (-5 *3 (-1186)) (-5 *1 (-194))))) -(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 (-777))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3 *4)) (-14 *3 (-928)) - (-4 *4 (-1058))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1047 (-570))) (-4 *3 (-562)) (-5 *1 (-32 *3 *2)) - (-4 *2 (-436 *3)))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-1182 *4)) (-5 *1 (-166 *3 *4)) - (-4 *3 (-167 *4)))) - ((*1 *1 *1) (-12 (-4 *1 (-1058)) (-4 *1 (-306)))) - ((*1 *2) (-12 (-4 *1 (-333 *3)) (-4 *3 (-368)) (-5 *2 (-1182 *3)))) - ((*1 *2) (-12 (-4 *1 (-730 *3 *2)) 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*2 (-650 (-445))) (-5 *1 (-871))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -9956,78 +9564,74 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) - (-12 (-5 *3 (-570)) (-5 *5 (-695 (-227))) - (-5 *6 (-3 (|:| |fn| (-394)) (|:| |fp| (-70 APROD)))) (-5 *4 (-227)) - (-5 *2 (-1044)) (-5 *1 (-762))))) +(((*1 *1 *1) (-4 *1 (-635))) + ((*1 *2 *2) + (-12 (-4 *3 (-562)) (-5 *1 (-636 *3 *2)) + (-4 *2 (-13 (-436 *3) (-1011) (-1212)))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1166 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2521 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *2 (-1044)) (-5 *1 (-309))))) + (-12 (-4 *4 (-13 (-562) (-1047 (-570)))) (-5 *2 (-413 (-570))) + (-5 *1 (-439 *4 *3)) (-4 *3 (-436 *4)))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-618 *3)) (-4 *3 (-436 *5)) + (-4 *5 (-13 (-562) (-1047 (-570)))) (-5 *2 (-1182 (-413 (-570)))) + (-5 *1 (-439 *5 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-1132 *3 *4 *2 *5)) (-4 *4 (-1058)) (-4 *5 (-240 *3 *4)) - (-4 *2 (-240 *3 *4))))) + (-12 (-5 *2 (-413 (-959 *3))) (-5 *1 (-459 *3 *4 *5 *6)) + (-4 *3 (-562)) (-4 *3 (-174)) (-14 *4 (-928)) + (-14 *5 (-650 (-1186))) (-14 *6 (-1277 (-695 *3)))))) (((*1 *2 *2) - 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(-368)) (-4 *6 (-13 (-368) (-854)))))) +(((*1 *2 *3) + (-12 (-5 *3 (-959 *4)) (-4 *4 (-13 (-311) (-148))) + (-4 *2 (-956 *4 *6 *5)) (-5 *1 (-931 *4 *5 *6 *2)) + (-4 *5 (-13 (-856) (-620 (-1186)))) (-4 *6 (-799))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-1168)) (-5 *4 (-1129)) (-5 *2 (-112)) (-5 *1 (-827))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-650 (-777))) (-5 *3 (-112)) (-5 *1 (-1174 *4 *5)) + (-14 *4 (-928)) (-4 *5 (-1058))))) +(((*1 *2 *1 *1 *3 *4) + (-12 (-5 *3 (-1 (-112) *5 *5)) (-5 *4 (-1 (-112) *6 *6)) + (-4 *5 (-13 (-1109) (-34))) (-4 *6 (-13 (-1109) (-34))) + (-5 *2 (-112)) (-5 *1 (-1149 *5 *6))))) +(((*1 *2 *3) (-12 (-5 *3 (-868)) (-5 *2 (-1282)) (-5 *1 (-1147)))) + ((*1 *2 *3) + (-12 (-5 *3 (-650 (-868))) (-5 *2 (-1282)) (-5 *1 (-1147))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -10048,57 +9652,26 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) (-5 *1 (-1172 *3)))) ((*1 *1 *1) (-4 *1 (-1215)))) -(((*1 *2 *3 *1) - (-12 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(-368) (-148) (-1047 (-570)) (-1047 (-413 (-570)))))))) +(((*1 *2 *1) (-12 (-4 *1 (-1296 *3)) (-4 *3 (-368)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-551)))) -(((*1 *2 *3 *2) - (-12 - (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) - (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) - (-5 *3 (-650 (-266))) (-5 *1 (-264)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) - (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) - (-5 *1 (-266)))) - ((*1 *2 *1 *3 *3 *3) - (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279)))) - ((*1 *2 *1 *3 *3 *4 *4 *4) - (-12 (-5 *3 (-570)) (-5 *4 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279)))) - ((*1 *2 *1 *3) - (-12 - (-5 *3 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) - (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) - (-5 *2 (-1282)) (-5 *1 (-1279)))) - ((*1 *2 *1) - (-12 - (-5 *2 - (-2 (|:| |theta| (-227)) (|:| |phi| (-227)) (|:| -2548 (-227)) - (|:| |scaleX| (-227)) (|:| |scaleY| (-227)) (|:| |scaleZ| (-227)) - (|:| |deltaX| (-227)) (|:| |deltaY| (-227)))) - (-5 *1 (-1279)))) - ((*1 *2 *1 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-384)) (-5 *2 (-1282)) (-5 *1 (-1279))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-777)) (-5 *3 (-950 *5)) (-4 *5 (-1058)) + (-5 *1 (-1174 *4 *5)) (-14 *4 (-928)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-650 (-777))) (-5 *3 (-777)) (-5 *1 (-1174 *4 *5)) + (-14 *4 (-928)) (-4 *5 (-1058)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-650 (-777))) (-5 *3 (-950 *5)) (-4 *5 (-1058)) + (-5 *1 (-1174 *4 *5)) (-14 *4 (-928))))) (((*1 *2 *2) (-12 (-4 *3 (-562)) (-5 *1 (-279 *3 *2)) (-4 *2 (-13 (-436 *3) (-1011))))) @@ -10119,141 +9692,34 @@ (-12 (-5 *2 (-1166 *3)) (-4 *3 (-38 (-413 (-570)))) 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(-378 *2)))) @@ -13756,14 +13587,14 @@ (-12 (-5 *3 (-1186)) (-5 *2 (-247 (-1168))) (-5 *1 (-216 *4)) (-4 *4 (-13 (-856) - (-10 -8 (-15 -1941 ((-1168) $ *3)) (-15 -4147 ((-1282) $)) - (-15 -2176 ((-1282) $))))))) + (-10 -8 (-15 -1942 ((-1168) $ *3)) (-15 -4150 ((-1282) $)) + (-15 -2353 ((-1282) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-998)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-856) - (-10 -8 (-15 -1941 ((-1168) $ (-1186))) (-15 -4147 ((-1282) $)) - (-15 -2176 ((-1282) $))))))) + (-10 -8 (-15 -1942 ((-1168) $ (-1186))) (-15 -4150 ((-1282) $)) + (-15 -2353 ((-1282) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-777)) (-5 *1 (-247 *4)) (-4 *4 (-856)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-247 *3)) (-4 *3 (-856)))) @@ -13850,67 +13681,97 @@ (-12 (-5 *2 "rest") (-4 *1 (-1265 *3)) (-4 *3 (-1227)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) -(((*1 *2 *3) - (-12 (-4 *4 (-311)) (-4 *5 (-378 *4)) (-4 *6 (-378 *4)) - (-5 *2 - (-2 (|:| |Smith| *3) (|:| 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*3))) + (-5 *1 (-782 *5 *6 *7 *3 *4)) (-4 *4 (-1080 *5 *6 *7 *3)))) + ((*1 *2 *2 *1) + (|partial| -12 (-4 *1 (-1077 *3 *2)) (-4 *3 (-13 (-854) (-368))) + (-4 *2 (-1253 *3)))) + ((*1 *2 *2) + (|partial| -12 (-5 *2 (-1166 *3)) (-4 *3 (-1058)) (-5 *1 (-1170 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-798)) (-4 *2 (-1058)))) ((*1 *2 *1) (-12 (-4 *2 (-1058)) (-5 *1 (-50 *2 *3)) (-14 *3 (-650 (-1186))))) @@ -13920,10 +13781,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-387 *2 *3)) (-4 *3 (-1109)) (-4 *2 (-1058)))) ((*1 *2 *1) - (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2569 *3) (-777))) + (-12 (-14 *3 (-650 (-1186))) (-4 *5 (-240 (-2570 *3) (-777))) (-14 *6 - (-1 (-112) (-2 (|:| -2268 *4) (|:| -3357 *5)) - (-2 (|:| -2268 *4) (|:| -3357 *5)))) + (-1 (-112) (-2 (|:| -2267 *4) (|:| -3994 *5)) + (-2 (|:| -2267 *4) (|:| -3994 *5)))) (-4 *2 (-174)) (-5 *1 (-467 *3 *2 *4 *5 *6 *7)) (-4 *4 (-856)) (-4 *7 (-956 *2 *5 (-870 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-515 *2 *3)) (-4 *3 (-856)) (-4 *2 (-1109)))) 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(|:| -2267 (-1129)))))) + (-5 *1 (-351 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-653 *3)) (-4 *3 (-1109))))) (((*1 *2 *3 *2) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1227)) (-5 *1 (-380 *4 *2)) - (-4 *2 (-13 (-378 *4) (-10 -7 (-6 -4450))))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-570)) (-5 *4 (-695 (-227))) (-5 *5 (-112)) - (-5 *6 (-227)) (-5 *7 (-3 (|:| |fn| (-394)) (|:| |fp| (-68 APROD)))) - (-5 *8 (-3 (|:| |fn| (-394)) (|:| |fp| (-73 MSOLVE)))) - (-5 *2 (-1044)) (-5 *1 (-762))))) + (-12 (-5 *2 (-112)) (-5 *3 (-650 (-266))) (-5 *1 (-264))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) (((*1 *2 *3) - (-12 (-5 *2 (-1 (-950 *3) (-950 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-368) (-1212) (-1011)))))) -(((*1 *2) - (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) - (-4 *4 (-1109))))) + (-12 + (-5 *3 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| "There are singularities at both end points") + (|:| |notEvaluated| "End point continuity not yet evaluated"))) + (-5 *1 (-194))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4453)) (-4 *1 (-1265 *2)) (-4 *2 (-1227))))) (((*1 *2 *3) (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) (-5 *2 (-52)) @@ -14329,14 +14215,16 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-413 (-570))) (-4 *4 (-1058)) (-4 *1 (-1260 *4 *3)) (-4 *3 (-1237 *4))))) +(((*1 *2) (-12 (-5 *2 (-880)) (-5 *1 (-1280)))) + ((*1 *2 *2) (-12 (-5 *2 (-880)) (-5 *1 (-1280))))) (((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -3106)) (-5 *2 (-112)) (-5 *1 (-623)))) + (-12 (-5 *3 (|[\|\|]| -3109)) (-5 *2 (-112)) (-5 *1 (-623)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -1664)) (-5 *2 (-112)) (-5 *1 (-623)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -1954)) (-5 *2 (-112)) (-5 *1 (-623)))) + (-12 (-5 *3 (|[\|\|]| -1953)) (-5 *2 (-112)) (-5 *1 (-623)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (|[\|\|]| -1623)) (-5 *2 (-112)) (-5 *1 (-697 *4)) + (-12 (-5 *3 (|[\|\|]| -1624)) (-5 *2 (-112)) (-5 *1 (-697 *4)) (-4 *4 (-619 (-868))))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| *4)) (-4 *4 (-619 (-868))) (-5 *2 (-112)) @@ -14419,48 +14307,108 @@ (-12 (-5 *3 (|[\|\|]| (-227))) (-5 *2 (-112)) (-5 *1 (-1191)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| (-570))) (-5 *2 (-112)) (-5 *1 (-1191))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-997 *4 *5 *6 *7 *8)) (-4 *8 (-1080 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-650 *7)) (-4 *7 (-1074 *4 *5 *6)) (-4 *4 (-458)) - (-4 *5 (-799)) (-4 *6 (-856)) (-5 *2 (-112)) - (-5 *1 (-1116 *4 *5 *6 *7 *8)) (-4 *8 (-1080 *4 *5 *6 *7))))) -(((*1 *2 *3) 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+(((*1 *2 *2) + (-12 (-4 *3 (-13 (-562) (-1047 (-570)))) (-5 *1 (-190 *3 *2)) + (-4 *2 (-13 (-27) (-1212) (-436 (-171 *3)))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1186)) (-4 *4 (-13 (-562) (-1047 (-570)))) + (-5 *1 (-190 *4 *2)) (-4 *2 (-13 (-27) (-1212) (-436 (-171 *4)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-458) (-1047 (-570)) (-645 (-570)))) + (-5 *1 (-1216 *3 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *3))))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1186)) + (-4 *4 (-13 (-458) (-1047 (-570)) (-645 (-570)))) + (-5 *1 (-1216 *4 *2)) (-4 *2 (-13 (-27) (-1212) (-436 *4)))))) +(((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-777)) (-4 *5 (-562)) + (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) + (-5 *1 (-978 *5 *3)) (-4 *3 (-1253 *5))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1301 *4 *2)) (-4 *1 (-379 *4 *2)) (-4 *4 (-856)) (-4 *2 (-174)))) @@ -16238,48 +16241,39 @@ (-4 *2 (-1058)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1058)) (-5 *1 (-1300 *2 *3)) (-4 *3 (-852))))) -(((*1 *2 *1) (-12 (-4 *1 (-1143 *3)) (-4 *3 (-1058)) (-5 *2 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*1 (-789 *2)) (-4 *2 (-38 (-413 (-570)))) + (-4 *2 (-174))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) + (|:| -1600 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) (-5 *2 - (-2 (|:| -2308 *4) (|:| -3670 *4) (|:| |totalpts| (-570)) - (|:| |success| (-112)))) - (-5 *1 (-795)) (-5 *5 (-570))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-112)) (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4))))) - ((*1 *2 *3 *4) - (-12 (-4 *4 (-13 (-368) (-854))) (-5 *2 (-424 *3)) - (-5 *1 (-183 *4 *3)) (-4 *3 (-1253 (-171 *4)))))) + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))) + (-5 *1 (-194))))) (((*1 *2 *3) - (-12 (-5 *3 (-777)) (-5 *2 (-695 (-959 *4))) (-5 *1 (-1037 *4)) - (-4 *4 (-1058))))) + (-12 (-4 *4 (-354)) (-5 *2 (-424 (-1182 (-1182 *4)))) + (-5 *1 (-1225 *4)) (-5 *3 (-1182 (-1182 *4)))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-928)) (-4 *6 (-562)) (-5 *2 (-650 (-320 *6))) (-5 *1 (-223 *5 *6)) (-5 *3 (-320 *6)) (-4 *5 (-1058)))) @@ -16665,102 +16707,57 @@ ((*1 *2 *1) (-12 (-5 *2 (-1292 *3 *4)) (-5 *1 (-1301 *3 *4)) (-4 *3 (-856)) (-4 *4 (-1058))))) -(((*1 *2 *3) (-12 (-5 *3 (-950 *2)) (-5 *1 (-991 *2)) (-4 *2 (-1058))))) -(((*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1287))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-992 *2)) (-4 *2 (-1212))))) -(((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) (-5 *1 (-32 *4 *5)) - (-4 *5 (-436 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) - (-5 *1 (-159 *4 *5)) (-4 *5 (-436 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-115)) (-4 *4 (-562)) (-5 *2 (-112)) - (-5 *1 (-279 *4 *5)) (-4 *5 (-13 (-436 *4) (-1011))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-570)) (-5 *2 (-1044)) (-5 *1 (-764))))) 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(-112)) - (-5 *1 (-636 *4 *5)) (-4 *5 (-13 (-436 *4) (-1011) (-1212)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1282)) (-5 *1 (-828))))) -(((*1 *1 *2) (-12 (-5 *2 (-570)) (-5 *1 (-868))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1227)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-856)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-856)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-570)) (-4 *1 (-286 *3)) (-4 *3 (-1227)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-570)) (-4 *1 (-286 *2)) (-4 *2 (-1227)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -2106 - (-2 (|:| |var| (-1186)) (|:| |fn| (-320 (-227))) - (|:| -2521 (-1103 (-849 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -2340 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1166 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2521 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))))) - (-5 *1 (-565)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-777)) (-4 *1 (-701 *2)) (-4 *2 (-1109)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -2106 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1277 (-320 (-227)))) (|:| |yinit| (-650 (-227))) - (|:| |intvals| (-650 (-227))) (|:| |g| (-320 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (|:| -2340 - (-2 (|:| |stiffness| (-384)) (|:| |stability| (-384)) - (|:| |expense| (-384)) (|:| |accuracy| (-384)) - (|:| |intermediateResults| (-384)))))) - (-5 *1 (-809)))) - ((*1 *2 *3 *4) - (-12 (-5 *2 (-1282)) (-5 *1 (-1204 *3 *4)) (-4 *3 (-1109)) - (-4 *4 (-1109))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-413 (-1182 (-320 *3)))) (-4 *3 (-562)) - (-5 *1 (-1139 *3))))) -(((*1 *2 *2) (|partial| -12 (-5 *1 (-593 *2)) (-4 *2 (-551))))) -(((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |mval| (-695 *3)) (|:| |invmval| (-695 *3)) - (|:| |genIdeal| (-510 *3 *4 *5 *6)))) - (-4 *3 (-368)) (-4 *4 (-799)) (-4 *5 (-856)) - (-5 *1 (-510 *3 *4 *5 *6)) (-4 *6 (-956 *3 *4 *5))))) + (-12 (-5 *3 (-650 *7)) (-4 *7 (-956 *4 *6 *5)) + (-4 *4 (-13 (-311) (-148))) (-4 *5 (-13 (-856) (-620 (-1186)))) + (-4 *6 (-799)) (-5 *2 (-650 (-413 (-959 *4)))) + (-5 *1 (-931 *4 *5 *6 *7))))) +(((*1 *2 *2) (|partial| -12 (-5 *2 (-320 (-227))) (-5 *1 (-270))))) +(((*1 *2 *3) + (-12 (-5 *3 (-650 (-928))) (-5 *2 (-1188 (-413 (-570)))) + (-5 *1 (-192))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 (-227) (-227))) (-5 *4 (-1103 (-384))) (-5 *5 (-650 (-266))) (-5 *2 (-1278)) (-5 *1 (-258)))) @@ -16858,9 +16855,12 @@ ((*1 *2 *3 *3 *3 *4) (-12 (-5 *3 (-650 (-227))) (-5 *4 (-650 (-266))) (-5 *2 (-1279)) (-5 *1 (-263))))) -(((*1 *2 *1) - (-12 (-5 *2 (-697 (-879 (-973 *3) (-973 *3)))) (-5 *1 (-973 *3)) - (-4 *3 (-1109))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-1166 (-650 (-928)))) (-5 *1 (-890)))) + ((*1 *2 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-1166 (-650 (-928)))) (-5 *1 (-890)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-777)) (-5 *2 (-1166 (-650 (-928)))) (-5 *1 (-890))))) (((*1 *1 *1 *1) (-5 *1 (-130))) ((*1 *1 *1 *1) (-12 (-5 *1 (-1193 *2)) (-14 *2 (-928)))) ((*1 *1 *1 *1) (-5 *1 (-1232))) ((*1 *1 *1 *1) (-5 *1 (-1233))) @@ -16868,101 +16868,101 @@ (((*1 *2 *1 *1) (-12 (-4 *1 (-1275 *3)) (-4 *3 (-1227)) (-4 *3 (-1058)) (-5 *2 (-695 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-650 (-52))) (-5 *1 (-899 *3)) (-4 *3 (-1109))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1186)) (-5 *2 (-1 (-1182 (-959 *4)) (-959 *4))) - (-5 *1 (-1285 *4)) (-4 *4 (-368))))) -(((*1 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