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#include "division.h"
#include "printer.h"
#include "timer.h"
static Timer divisionTimer("Division",1);
static Timer divisionTimer1("Division1",1);
static Timer divisionTimer2("Division2",1);
static Timer divisionTimer3("Division3",1);
static Timer divisionTimer4("Division4",1);
Polynomial division1(Polynomial p, PolynomialSet const &l, TermOrder const &termOrder, PolynomialSet *q);
typedef map<Monomial,Polynomial,TermMapCompare> ReductionCache;
Polynomial division(Polynomial p, PolynomialSet const &l, TermOrder const &termOrder, PolynomialSet *q)
{
return division1(p,l,termOrder,q);
}
Polynomial smartDivision(Polynomial p, PolynomialSet l, TermOrder const &termOrder)
{
Polynomial r(p.getRing());
for(TermMap::const_iterator i=p.terms.begin();i!=p.terms.end();i++)
{
r+=division(Term(i->second,Monomial(p.getRing(),i->first.exponent)),l,termOrder);
}
return r;
}
Polynomial division1(Polynomial p, PolynomialSet const &l, TermOrder const &termOrder, PolynomialSet *q)
{
PolynomialRing theRing=p.getRing();
TimerScope ts(&divisionTimer);
if(q)
{
*q=PolynomialSet(theRing);
for(PolynomialSet::const_iterator i=l.begin();i!=l.end();i++)
q->push_back(Polynomial(p.getRing()));
}
Polynomial r(p.getRing());
while(!p.isZero())
{
// AsciiPrinter(Stderr).printPolynomial(p);
// fprintf(Stderr,"Number Of terms: %i\n",p.terms.size());
p.mark(termOrder);
Term initial=p.getMarked();
PolynomialSet::const_iterator i;
PolynomialSet::iterator j;
if(q)j=q->begin();
{
TimerScope ts(&divisionTimer2);
for(i=l.begin();i!=l.end();i++)
{
if(i->getMarked().m.exponent.divides(initial.m.exponent))break;
if(q)j++;
}
}
{
TimerScope ts(&divisionTimer3);
if(i!=l.end())
{
Term s(-initial.c*i->getMarked().c.inverse(),Monomial(p.getRing(),initial.m.exponent-i->getMarked().m.exponent));
p.madd(s,*i);
if(q)*j+=Polynomial(s);
}
else
{
TimerScope ts(&divisionTimer4);
p-=initial;
r+=initial;
}
}
}
return r;
}
Polynomial divisionLift(Polynomial p, PolynomialSet l, PolynomialSet lLift, TermOrder const &termOrder)
{
Polynomial lift(p.getRing());
Polynomial r(p.getRing());
Monomial marked=p.getMarked().m;
for(PolynomialSet::iterator i=l.begin();i!=l.end();i++)
i->scaleMarkedCoefficientToOne();
while(!p.isZero())
{
p.mark(termOrder);
/* fprintf(Stderr,"Polynomial:\n");
AsciiPrinter(Stderr).printPolynomial(p);
fprintf(Stderr,"\n");
fprintf(Stderr,"Remainder:\n");
AsciiPrinter(Stderr).printPolynomial(r);
fprintf(Stderr,"\n");
*/
Term initial=p.getMarked();
PolynomialSet::const_iterator i;
PolynomialSet::const_iterator iLift=lLift.begin();
for(i=l.begin();i!=l.end();i++)
{
if(i->getMarked().m.exponent.divides(initial.m.exponent))break;
iLift++;
}
if(i!=l.end())
{
Term s(initial.c,Monomial(p.getRing(),initial.m.exponent-i->getMarked().m.exponent));
p-=((*i)*s);
lift+=(*iLift)*s;
}
else
{
p-=initial;
r+=initial;
}
}
lift.mark(marked);
return lift;
}
bool isIdealContainedInIdeal(PolynomialSet const &generators, PolynomialSet const &groebnerBasis)
{
for(PolynomialSet::const_iterator i=generators.begin();i!=generators.end();i++)
{
// if(!division(*i,groebnerBasis,LexicographicTermOrder()).isZero())return false;
if(!division(*i,groebnerBasis,StandardGradedLexicographicTermOrder()).isZero())return false;
// fprintf(Stderr,".\n");
}
return true;
}
bool areIdealsEqual(PolynomialSet const &groebnerBasis1, PolynomialSet const &groebnerBasis2)
{
return isIdealContainedInIdeal(groebnerBasis1,groebnerBasis2)
&& isIdealContainedInIdeal(groebnerBasis2,groebnerBasis1);
}
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