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#include "restrictedautoreduction.h"
#include "wallideal.h"
#include "tropical2.h"
#include "division.h"
#include <iostream>
void autoReduceRestricted(PolynomialSet *g, PolynomialSet const &initialIdeal)
{
/* AsciiPrinter P(Stderr);
P.printPolynomialSet(*g);
P.printPolynomialSet(initialIdeal);
*/
assert(g->size()==initialIdeal.size());
PolyhedralCone V=homogeneitySpace(initialIdeal);
PolyhedralCone C=groebnerCone(*g,false);//no algebraic test - we hope that polyhedral methods are better
PolyhedralCone C2=intersection(C,V);
IntegerVector omega=C2.getRelativeInteriorPoint();
while(1)
{
PolyhedralCone C=intersection(groebnerCone(*g,false),V);
C.findFacets();
IntegerVectorList normals=C.getHalfSpaces();
bool allAreTrueFacets=true;
for(IntegerVectorList::const_iterator i=normals.begin();i!=normals.end();i++)
{
IntegerVectorList equations=C.getEquations();
equations.push_back(*i);
PolyhedralCone C2(C.getHalfSpaces(),equations,C.ambientDimension());
IntegerVector omega2=C2.getRelativeInteriorPoint();
// C2.print(&P);
bool isTrueFacet=false;
for(PolynomialSet::iterator j=g->begin();j!=g->end();j++)
{
Polynomial p=initialForm(*j,omega2)-initialForm(*j,omega);
if(!p.isZero())
{
/* cerr << "poly1:";
P.printPolynomial(*j);
cerr << endl << "in_omega";
P.printPolynomial(initialForm(*j,omega));
cerr << endl << "in_omega2";
P.printPolynomial(initialForm(*j,omega2));
*/
Polynomial q=divisionLift(p,initialIdeal,*g,LexicographicTermOrder(),true);
*j-=q;
/*cerr << endl << "q";
P.printPolynomial(q);
cerr << endl << "r";
P.printPolynomial(division(p,initialIdeal,LexicographicTermOrder()));
cerr << endl << "poly2:";
P.printPolynomial(*j);
cerr << endl;
*/
if(!division(p,initialIdeal,LexicographicTermOrder()).isZero())isTrueFacet=true;
}
}
if(!isTrueFacet)allAreTrueFacets=false;
}
if(allAreTrueFacets)break;
}
}
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