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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/modmonom.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra modmonom.spad}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{domain MODMONOM ModuleMonomial}
+<<domain MODMONOM ModuleMonomial>>=
+)abbrev domain MODMONOM ModuleMonomial
+++ Description:
+++ This package \undocumented
+ModuleMonomial(IS: OrderedSet,
+ E: SetCategory,
+ ff:(MM, MM) -> Boolean): T == C where
+
+ MM ==> Record(index:IS, exponent:E)
+
+ T == OrderedSet with
+ exponent: $ -> E
+ ++ exponent(x) \undocumented
+ index: $ -> IS
+ ++ index(x) \undocumented
+ coerce: MM -> $
+ ++ coerce(x) \undocumented
+ coerce: $ -> MM
+ ++ coerce(x) \undocumented
+ construct: (IS, E) -> $
+ ++ construct(i,e) \undocumented
+ C == MM add
+ Rep:= MM
+ x:$ < y:$ == ff(x::Rep, y::Rep)
+ exponent(x:$):E == x.exponent
+ index(x:$): IS == x.index
+ coerce(x:$):MM == x::Rep::MM
+ coerce(x:MM):$ == x::Rep::$
+ construct(i:IS, e:E):$ == [i, e]$MM::Rep::$
+
+@
+\section{domain GMODPOL GeneralModulePolynomial}
+<<domain GMODPOL GeneralModulePolynomial>>=
+)abbrev domain GMODPOL GeneralModulePolynomial
+++ Description:
+++ This package \undocumented
+GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where
+ vl: List(Symbol)
+ R: CommutativeRing
+ IS: OrderedSet
+ NNI ==> NonNegativeInteger
+ E: DirectProductCategory(#vl, NNI)
+ MM ==> Record(index:IS, exponent:E)
+ ff: (MM, MM) -> Boolean
+ OV ==> OrderedVariableList(vl)
+ P: PolynomialCategory(R, E, OV)
+ ModMonom ==> ModuleMonomial(IS, E, ff)
+
+
+ public == Join(Module(P), Module(R)) with
+ leadingCoefficient: $ -> R
+ ++ leadingCoefficient(x) \undocumented
+ leadingMonomial: $ -> ModMonom
+ ++ leadingMonomial(x) \undocumented
+ leadingExponent: $ -> E
+ ++ leadingExponent(x) \undocumented
+ leadingIndex: $ -> IS
+ ++ leadingIndex(x) \undocumented
+ reductum: $ -> $
+ ++ reductum(x) \undocumented
+ monomial: (R, ModMonom) -> $
+ ++ monomial(r,x) \undocumented
+ unitVector: IS -> $
+ ++ unitVector(x) \undocumented
+ build: (R, IS, E) -> $
+ ++ build(r,i,e) \undocumented
+ multMonom: (R, E, $) -> $
+ ++ multMonom(r,e,x) \undocumented
+ "*": (P,$) -> $
+ ++ p*x \undocumented
+
+
+ private == FreeModule(R, ModMonom) add
+ Rep:= FreeModule(R, ModMonom)
+ leadingMonomial(p:$):ModMonom == leadingSupport(p)$Rep
+ leadingExponent(p:$):E == exponent(leadingMonomial p)
+ leadingIndex(p:$):IS == index(leadingMonomial p)
+ unitVector(i:IS):$ == monomial(1,[i, 0$E]$ModMonom)
+
+
+ -----------------------------------------------------------------------------
+
+ build(c:R, i:IS, e:E):$ == monomial(c, construct(i, e))
+
+ -----------------------------------------------------------------------------
+
+ ---- WARNING: assumes c ^= 0
+
+ multMonom(c:R, e:E, mp:$):$ ==
+ zero? mp => mp
+ monomial(c * leadingCoefficient mp, [leadingIndex mp,
+ e + leadingExponent mp]) + multMonom(c, e, reductum mp)
+
+ -----------------------------------------------------------------------------
+
+
+ ((p:P) * (mp:$)):$ ==
+ zero? p => 0
+ multMonom(leadingCoefficient p, degree p, mp) +
+ reductum(p) * mp
+
+@
+\section{License}
+<<license>>=
+--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
+--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 MODMONOM ModuleMonomial>>
+<<domain GMODPOL GeneralModulePolynomial>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}