groebner_alg.h
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/*
* groebner_alg.h
* PolyBoRi
*
* Created by Michael Brickenstein on 20.04.06.
* Copyright 2006 The PolyBoRi Team. See LICENSE file.
*
*/
#ifndef PBORI_GB_ALG_H
#define PBORI_GB_ALG_H
#include "PairStatusSet.h"
#include "PairManager.h"
#include "MonomialHasher.h"
#include "ReductionStrategy.h"
#include "GroebnerStrategy.h"
#include "LessWeightedLengthInStrat.h"
#include "LargerDegreeComparer.h"
#include "LessWeightedLengthInStratModified.h"
#include "LessEcartThenLessWeightedLengthInStrat.h"
#include "LessUsedTailVariablesThenLessWeightedLengthInStrat.h"
#include "LessCombinedManySizesInStrat.h"
#include <polybori.h>
#include "groebner_defs.h"
#include "pairs.h"
#include <boost/dynamic_bitset.hpp>
#include <vector>
#include <string>
#include <algorithm>
#include <utility>
#include <iostream>
#include "cache_manager.h"
#include "polynomial_properties.h"
BEGIN_NAMESPACE_PBORIGB
#define LL_RED_FOR_GROEBNER 1
Polynomial map_every_x_to_x_plus_one(Polynomial p);
MonomialSet mod_var_set(const MonomialSet& as, const MonomialSet& vs);
void groebner(GroebnerStrategy& strat);
Polynomial reduce_by_binom(const Polynomial& p, const Polynomial& binom);
Polynomial reduce_by_monom(const Polynomial& p, const Monomial& m);
Polynomial reduce_complete(const Polynomial& p, const Polynomial& reductor);
Polynomial mult_fast_sim(const std::vector<Polynomial>& vec,
const BoolePolyRing& ring);
std::vector<Polynomial> full_implication_gb(const Polynomial & p,CacheManager& cache,GroebnerStrategy& strat);
Polynomial reduce_complete(const Polynomial &p, const PolyEntry& reductor, wlen_type &len);
MonomialSet recursively_insert(MonomialSet::navigator p, idx_type idx, MonomialSet mset);
inline Polynomial
cancel_monomial_in_tail(const Polynomial& p, const Monomial & m){
Monomial lm=p.lead();
Polynomial res=reduce_by_monom(p,m);
if ((!res.isZero()) && (res.lead()==lm)){
return res;
} else {
return res+lm;
}
/*Polynomial tail=p-lm;
Monomial used_var=tail.usedVariables();
if (used_var.reducibleBy(m)){
tail=Polynomial(BooleSet(tail).diff(m.multiples(used_var)));
}
return tail+lm;*/
}
inline Polynomial
reduce_by_binom(const Polynomial& p, const Polynomial& binom){
PBORI_ASSERT(binom.length()==2);
Monomial bin_lead=binom.lead();
Monomial bin_last=*(++(binom.orderedBegin()));
MonomialSet dividing_terms=((MonomialSet)p).multiplesOf(bin_lead);
Monomial b_p_gcd=bin_last.GCD(bin_lead);
Monomial divide_by=bin_lead/b_p_gcd;
Monomial multiply_by=bin_last/b_p_gcd;
Polynomial rewritten=((Polynomial) dividing_terms)/divide_by;
return p-dividing_terms+rewritten*multiply_by;
}
inline Polynomial
reduce_by_binom_in_tail (const Polynomial& p, const Polynomial& binom){
PBORI_ASSERT(binom.length()==2);
Monomial lm=p.lead();
return lm+reduce_by_binom(p-lm,binom);
}
END_NAMESPACE_PBORIGB
#endif