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#include "dimension.h"
#include "buchberger.h"
PolynomialSet radicalOfMonomialIdeal(PolynomialSet const &monomialGenerators)
{
PolynomialRing theRing=monomialGenerators.getRing();
PolynomialSet temp=monomialGenerators;
temp.markAndScale(LexicographicTermOrder()); //just to make sure that some term is marked
PolynomialSet ret(theRing);
for(PolynomialSet::const_iterator i=temp.begin();i!=temp.end();i++)
{
IntegerVector e=i->getMarked().m.exponent;
e=e.supportVector();
ret.push_back(Polynomial(Term(i->getMarked().c,Monomial(theRing,e))));
}
return ret;
}
static bool increase(IntegerVector &v, int &numberOfOnes)
{
int i=0;
while(i<v.size() && v[i]==1)
{
v[i]=0;
numberOfOnes--;
i++;
}
if(i==v.size())return false;
v[i]=1;
numberOfOnes++;
return true;
}
int krullDimensionOfMonomialIdeal(PolynomialSet const &monomialGenerators)
{
PolynomialSet temp=radicalOfMonomialIdeal(monomialGenerators);
minimize(&temp);
IntegerVectorList vectors;
for(PolynomialSet::const_iterator i=temp.begin();i!=temp.end();i++)
vectors.push_back(i->getMarked().m.exponent);
assert(!vectors.empty());
int n=vectors.begin()->size();
IntegerVector subset(n);
int numberOfOnes=0;
int dimension=0;
do
{
// AsciiPrinter(Stderr).printVector(subset);
if(numberOfOnes>dimension)
{
bool ok=true;
for(IntegerVectorList::const_iterator i=vectors.begin();i!=vectors.end();i++)
if(i->divides(subset))
{
ok=false;
break;
}
if(ok)
dimension=numberOfOnes;
}
}
while(increase(subset,numberOfOnes));
return dimension;
}
int krullDimension(PolynomialSet const &groebnerBasis)
{
return krullDimensionOfMonomialIdeal(groebnerBasis.markedTermIdeal());
}
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