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#include "vektor.h"
#include "printer.h"
#include "parser.h"
#include "gfanapplication.h"
#include "minkowskisum.h"
#include "newtonpolytope.h"
#include "buchberger.h"
#include "wallideal.h"
#include "lp.h"
class IsGroebnerBasisApplication : public GFanApplication
{
FieldOption theFieldOption;
SimpleOption optionUGBTest;
public:
bool includeInDefaultInstallation() // Not included since it requires Christophe's Minkowski sum program
{
return false;
}
const char *helpText()
{
return "Checks if an unmarked polynomial set is a Groebner basis with respect to some termorder.\n";
}
IsGroebnerBasisApplication():
optionUGBTest("--ugb","Universal Groebner Basis test. Check if something is a Groebner basis with respect to any termorder.")
{
registerOptions();
}
char *name()
{
return "_isgroebnerbasis";
}
int main()
{
lpSetSolver("cddgmp");
FileParser P(Stdin);
PolynomialSet g=P.parsePolynomialSetWithRing();
PolynomialRing theRing=g.getRing();
IntegerVectorListList polytopes;
for(PolynomialSet::const_iterator i=g.begin();i!=g.end();i++)
{
polytopes.push_back(newtonPolytope(*i));
}
IntegerVectorListList sums;
IntegerVectorList polytope=minkowski(polytopes,&sums);
fprintf(Stderr,"Number of extreme vertices in Minkowski sum: %i\n",polytope.size());
bool isGroebnerBasis=false;
int counter=0;
for(IntegerVectorListList::const_iterator i=sums.begin();i!=sums.end();i++)
{
fprintf(Stderr,"Checking vertex %i\n",counter++);
IntegerVectorList::const_iterator j=i->begin();
for(PolynomialSet::iterator k=g.begin();k!=g.end();k++)
{
k->mark(Monomial(theRing,*j));
j++;
}
IntegerVectorList normals=wallInequalities(g);
if(hasInteriorPoint(normals,true))
{
if(isMarkedGroebnerBasis(g))
{
AsciiPrinter(Stderr).printPolynomialSet(g);
isGroebnerBasis=true;
if(!optionUGBTest.getValue())break;
}
else
{
fprintf(Stderr,"Marking is not a Groebner basis\n");
if(optionUGBTest.getValue())
{
AsciiPrinter(Stderr).printPolynomialSet(g);
assert(0);
}
}
}
else
fprintf(Stderr,"Cone has no positive interior point\n");
}
fprintf(Stdout,isGroebnerBasis?"true\n":"false\n");
return 0;
}
};
static IsGroebnerBasisApplication theApplication;
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