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#include "subspace.h"
#include "division.h"
#include "buchberger.h"
#include "field_rationals.h"
static Polynomial vectorToPolynomial(PolynomialRing const &r, IntegerVector const &v)
{
/*static Field* field;
if(!field)field=Field::find("GmpRationals"); // this is a bit stupid. We should add a field_rationals header file instead
assert(field);
*/
Polynomial ret(r);
for(int i=0;i<v.size();i++)
if(v[i])
{
ret+=Term(r.getField().zHomomorphism(v[i]),Monomial(r,IntegerVector::standardVector(v.size(),i)));
}
return ret;
}
static IntegerVector polynomialToVector(Polynomial const &f)
{
/* static Field* field;
if(!field)field=Field::find("GmpRationals"); // this is a bit stupid. We should add a field_rationals header file instead
assert(field);
*/
int n=f.getNumberOfVariables();
// fprintf(Stderr,"%i\n",n);
vector<FieldElement> r(n);
for(int i=0;i<n;i++)
r[i]=f.getRing().getField().zHomomorphism(0);
for(TermMap::const_iterator i=f.terms.begin();i!=f.terms.end();i++)
{
for(int j=0;j<n;j++)
if(i->first.exponent==IntegerVector::standardVector(n,j))
{
r[j]=i->second;
}
}
return primitiveVector(r);
}
Subspace::Subspace(IntegerVectorList const &generators, int ambientDimension):
basis2(integerMatrixToFieldMatrix(rowsToIntegerMatrix(generators,ambientDimension),Q))
// , basis(PolynomialRing(Q,ambientDimension))
{
// n=ambientDimension;
n=basis2.getWidth();
/* {
PolynomialRing theRing=basis.getRing();
if(n==-1)
{
assert(!generators.empty());
n=generators.begin()->size();
}
for(IntegerVectorList::const_iterator i=generators.begin();i!=generators.end();i++)
{
assert(i->size()==n);
basis.push_back(vectorToPolynomial(theRing,*i));
}
buchberger(&basis,LexicographicTermOrder());
}*/
basis2.reduce();
basis2.REformToRREform();
basis2.scaleFirstNonZeroEntryToOne();
basis2.removeZeroRows();
integerRep=getRepresentation();
integerRep.sort();
}
bool Subspace::contains(IntegerVector const &v)const
{
if(v.size()!=n)
{
fprintf(Stderr,"v.size()=%i, n=%i",v.size(),n);
}
assert(v.size()==n);
// bool oldRet=division(vectorToPolynomial(PolynomialRing(Q,v.size()),v),basis,LexicographicTermOrder()).isZero();
bool ret=basis2.canonicalize(integerVectorToFieldVector(v,Q)).isZero();
// assert(oldRet==ret);
return ret;
}
int Subspace::dimension()
{
// assert(basis2.reduceAndComputeRank()==basis.size());
return basis2.reduceAndComputeRank();
// return basis.size();
}
int Subspace::ambientDimension()const
{
return n;
}
Subspace sum(Subspace const &a, Subspace const &b)
{
/*Subspace ret=a;
ret.basis.insert(ret.basis.end(),b.basis.begin(),b.basis.end());
buchberger(&ret.basis,LexicographicTermOrder());
return ret;
*/
Subspace ret=a;
ret.basis2=combineOnTop(a.basis2,b.basis2);
ret.basis2.reduce();
ret.basis2.REformToRREform();
ret.basis2.scaleFirstNonZeroEntryToOne();
ret.basis2.removeZeroRows();
ret.integerRep=ret.getRepresentation();
ret.integerRep.sort();
return ret;
}
IntegerVectorList Subspace::getRepresentation()const
{
/*IntegerVectorList ret;
for(PolynomialSet::const_iterator i=basis.begin();i!=basis.end();i++)
{
ret.push_back(polynomialToVector(*i));
}
*/
IntegerVectorList ret2;
for(int i=0;i<basis2.getHeight();i++)
{
if(!basis2[i].isZero())
{
/* int sign=0;*/
IntegerVector temp=basis2[i].primitive();
/* for(int j=0;j<n;j++)if(temp[j]!=0){sign=temp[j];break;}
if(sign>0)*/
ret2.push_back(temp);
/* else
ret2.push_back(-temp);
*/ }
}
/* AsciiPrinter(Stderr).printVectorList(ret);
AsciiPrinter(Stderr).printVectorList(ret2);
fprintf(Stderr,"------------------\n");
*/
return ret2;
}
IntegerVector Subspace::canonicalizeVector(IntegerVector const &v)const
{
/* Polynomial f=vectorToPolynomial(PolynomialRing(Q,v.size()),v);
f=division(f,basis,LexicographicTermOrder());
IntegerVector ret=polynomialToVector(f);
*/
IntegerVector ret2=basis2.canonicalize(integerVectorToFieldVector(v,Q)).primitive();
// assert((ret-ret2).isZero());
return ret2;
}
bool Subspace::operator<(Subspace const &b)const
{
return integerRep<b.integerRep;
}
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