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#include "vektor.h"
#include "printer.h"
#include "parser.h"
#include "gfanapplication.h"
#include "buchberger.h"
#include "wallideal.h"
#include "dimension.h"
#include "saturation.h"
#include "determinantpoly.h"
#include "tropical2.h"
#include "log.h"
class IsSmoothApplication : public GFanApplication
{
SimpleOption optionInitialForms;
public:
bool includeInDefaultInstallation()
{
return false;
}
const char *helpText()
{
return "Checks if the input ideal defines a smooth variety in $(C^*)^n$.\n";
}
IsSmoothApplication():
optionInitialForms("--initialideals","Check the condition for the initial ideals of the ideals with respect to a given list of weight vectors. THE INPUT IDEAL MUST BE HOMOGENEOUS.")
{
registerOptions();
}
const char *name()
{
return "_issmooth";
}
bool processSingle(PolynomialSet g)const
{
g=g.multiDeHomogenization();
PolynomialRing theRing=g.getRing();
PolynomialSet G=nonHomogeneousSaturation(g);
log1 debug<<G;
PolynomialSet G2=G;
IntegerVector v=IntegerVector::allOnes(G2.getRing().getNumberOfVariables());
buchberger(&G2,WeightReverseLexicographicTermOrder(v));
log1 debug<<G2;
int d=krullDimension(G2);
PolynomialSet A=jacobiMinors(G,theRing.getNumberOfVariables()-d);
for(PolynomialSet::const_iterator i=G.begin();i!=G.end();i++)
A.push_back(*i);
A.removeZeros();
A.removeDuplicates();
// debug<<A;
A=nonHomogeneousSaturation(A);
// debug<<A;
return (A.isUnitIdeal());
}
int main()
{
FileParser P(Stdin);
PolynomialSet g=P.parsePolynomialSetWithRing();
PolynomialRing theRing=g.getRing();
if(optionInitialForms.getValue())
{
IntegerVectorList l=P.parseIntegerVectorList();
bool isSchoen=true;
for(IntegerVectorList::const_iterator i=l.begin();i!=l.end();i++)
{
bool smooth=processSingle(initialIdeal(g,*i));
if(!smooth)isSchoen=false;
log1 debug<<smooth<<"\n";
}
pout<<int(isSchoen)<<"\n";
}
else
pout<<int(processSingle(g))<<"\n";
return 0;
}
};
static IsSmoothApplication theApplication;
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