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\documentclass{article}
\usepackage{open-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}
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