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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/pgrobner.spad.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/algebra/pgrobner.spad.pamphlet')
-rw-r--r-- | src/algebra/pgrobner.spad.pamphlet | 121 |
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diff --git a/src/algebra/pgrobner.spad.pamphlet b/src/algebra/pgrobner.spad.pamphlet new file mode 100644 index 00000000..c90a46df --- /dev/null +++ b/src/algebra/pgrobner.spad.pamphlet @@ -0,0 +1,121 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra pgrobner.spad} +\author{Patrizia Gianni} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{package PGROEB PolyGroebner} +<<package PGROEB PolyGroebner>>= +)abbrev package PGROEB PolyGroebner +++ Author: P. Gianni +++ Date Created: Summer 1988 +++ Date Last Updated: +++ Basic Functions: +++ Related Constructors: GroebnerPackage +++ Also See: +++ AMS Classifications: +++ Keywords: groebner basis, polynomial ideals +++ References: +++ Description: +++ Groebner functions for P F +++ This package is an interface package to the groebner basis +++ package which allows you to compute groebner bases for polynomials +++ in either lexicographic ordering or total degree ordering refined +++ by reverse lex. The input is the ordinary polynomial type which +++ is internally converted to a type with the required ordering. +++ The resulting grobner basis is converted back to ordinary polynomials. +++ The ordering among the variables is controlled by an explicit list +++ of variables which is passed as a second argument. The coefficient +++ domain is allowed to be any gcd domain, but the groebner basis is +++ computed as if the polynomials were over a field. + +PolyGroebner(F) : C == T + + where + F : GcdDomain + NNI ==> NonNegativeInteger + P ==> Polynomial F + L ==> List + E ==> Symbol + + C == with + lexGroebner : (L P,L E) -> L P + ++ lexGroebner(lp,lv) computes Groebner basis + ++ for the list of polynomials lp in lexicographic order. + ++ The variables are ordered by their position in the list lv. + + totalGroebner : (L P, L E) -> L P + ++ totalGroebner(lp,lv) computes Groebner basis + ++ for the list of polynomials 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 lv. + + T == add + lexGroebner(lp: L P,lv:L E) : L P == + PP:= PolToPol(lv,F) + DPoly := DistributedMultivariatePolynomial(lv,F) + DP:=DirectProduct(#lv,NNI) + OV:=OrderedVariableList lv + b:L DPoly:=[pToDmp(pol)$PP for pol in lp] + gb:L DPoly :=groebner(b)$GroebnerPackage(F,DP,OV,DPoly) + [dmpToP(pp)$PP for pp in gb] + + totalGroebner(lp: L P,lv:L E) : L P == + PP:= PolToPol(lv,F) + HDPoly := HomogeneousDistributedMultivariatePolynomial(lv,F) + HDP:=HomogeneousDirectProduct(#lv,NNI) + OV:=OrderedVariableList lv + b:L HDPoly:=[pToHdmp(pol)$PP for pol in lp] + gb:=groebner(b)$GroebnerPackage(F,HDP,OV,HDPoly) + [hdmpToP(pp)$PP for pp in gb] + +@ +\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>> + +<<package PGROEB PolyGroebner>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |