/usr/lib/open-axiom/src/algebra/pgrobner.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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)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]
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