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dyn_modules
gfanlib
witness.h
Go to the documentation of this file.
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#ifndef WITNESS_H
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#define WITNESS_H
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#include "
polys/monomials/monomials.h
"
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#include "
polys/simpleideals.h
"
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/**
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* Computes a division discarding remainder of f with respect to G.
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* Given f a polynomial and G={g1,...,gk} a set of polynomials in r,
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* returns a matrix Q=(q1,...,qk) over r such that
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* f = q1*g1+...+qk*gk+s
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* is a determinate division with remainder s.
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*/
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matrix
divisionDiscardingRemainder
(
const
poly
f
,
const
ideal
G
,
const
ring r);
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/**
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* Computes a division discarding remainder of F with respect to G.
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* Given F={f1,...,fl} and G={g1,...,gk} two sets of polynomials in r,
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* returns a matrix Q=(qij) i=1,..,k j=1,...,l over r such that
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* fj = q1j*g1+...+qkj*gk+sj
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* is a determinate division with remainder sj for all j=1,...,l.
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*/
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matrix
divisionDiscardingRemainder
(
const
ideal F,
const
ideal
G
,
const
ring r);
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/**
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* Let w be the uppermost weight vector in the matrix defining the ordering on r.
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* Let I be a Groebner basis of an ideal in r, inI its initial form with respect w.
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* Given an w-homogeneous element m of inI, computes a witness g of m in I,
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* i.e. g in I such that in_w(g)=m.
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*/
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poly
witness
(
const
poly
m
,
const
ideal I,
const
ideal inI,
const
ring r);
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/**
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* Computes witnesses in J for inI
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* Given inI={h1,...,hl} and J={g1,...,gk} two sets of polynomials in r,
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* returns a set I={f1,...,fl} of <g1,...,gk> such that
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* in_w(fj)=hj for all j=1,...,l,
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* where w denotes the uppoermost weight vector in the matrix defining the ordering on r.
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* Assumes that hj is an element of <in_w(g1),...,in_w(gk)>
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*/
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ideal
witness
(
const
ideal inI,
const
ideal J,
const
ring r);
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#endif
m
int m
Definition:
cfEzgcd.cc:128
f
FILE * f
Definition:
checklibs.c:9
ip_smatrix
Definition:
matpol.h:15
G
STATIC_VAR TreeM * G
Definition:
janet.cc:31
monomials.h
simpleideals.h
divisionDiscardingRemainder
matrix divisionDiscardingRemainder(const poly f, const ideal G, const ring r)
Computes a division discarding remainder of f with respect to G.
Definition:
witness.cc:9
witness
poly witness(const poly m, const ideal I, const ideal inI, const ring r)
Let w be the uppermost weight vector in the matrix defining the ordering on r.
Definition:
witness.cc:34
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