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#include "multiplicity.h"
#include "lll.h"
#include "polyhedralcone.h"
#include "wallideal.h"
#include "saturation.h"
#include "linalg.h"
#include "log.h"
IntegerVector writeInTermsOf(IntegerVector const &v, IntegerMatrix const &b)
{//write the row vector v as a integer linear combination of the basis elements of the basis b. Asserts if v is not in the lattice generated by b
/* AsciiPrinter Q(Stderr);
fprintf(Stderr,"Dimensions %ix%i\n",b.getHeight(),b.getWidth());
Q.printVector(v);
Q.printVectorList(b.getRows());
*/
int m=b.getHeight();//dimension of lattice
assert(v.size()==b.getWidth());
IntegerVectorList equations=b.getRows();
equations.push_back(v);
IntegerVectorList inequalities;
inequalities.push_back(-IntegerVector::standardVector(m+1,m));
PolyhedralCone p(inequalities,rowsToIntegerMatrix(equations).transposed().getRows(),m+1);
IntegerVector w=p.getRelativeInteriorPoint();
//Q.printVector(w);
assert(w[m]==-1);
IntegerVector ret=w.subvector(0,m);
{
IntegerMatrix ret2(1,m);
ret2[0]=ret;
//fprintf(Stderr,"%i\n",(ret2*b)[0].size());
assert(((ret2*b)[0]-v).isZero());
}
/* Q.printVector(ret);
fprintf(Stderr,"Returning!!1\n");*/
return ret;
}
Polynomial notLaurent(Polynomial p)
{
if(!p.isZero())
{
IntegerVector v=p.terms.begin()->first.exponent;
for(TermMap::const_iterator i=p.terms.begin();i!=p.terms.end();i++)
v=min(v,i->first.exponent);
p*=Monomial(p.getRing(),-v);
}
return p;
}
Polynomial multiplicativeChangeInv(Polynomial const &p, IntegerMatrix const &lattice, PolynomialRing const &r2)
{
PolynomialRing theRing=p.getRing();
Polynomial ret(r2);
if(!p.isZero())
{
IntegerVector rel=p.terms.begin()->first.exponent;
for(TermMap::const_iterator i=p.terms.begin();i!=p.terms.end();i++)
ret+=Term(i->second,Monomial(r2,writeInTermsOf(i->first.exponent-rel,lattice)));
}
return ret;
}
/*
//Old implementation
PolynomialSet multiplicativeChangeInv(PolynomialSet const &g, IntegerMatrix const &lattice, PolynomialRing const &r2)
{
PolynomialRing theRing=g.getRing();
PolynomialSet ret(r2);
for(PolynomialSet::const_iterator i=g.begin();i!=g.end();i++)
ret.push_back(multiplicativeChangeInv(*i,lattice,r2));
return ret;
}
*/
PolynomialSet multiplicativeChangeInv(PolynomialSet const &g, IntegerMatrix const &lattice, PolynomialRing const &r2)
{
PolynomialRing theRing=g.getRing();
PolynomialSet ret(r2);
FieldMatrix bigMatrix=combineLeftRight(integerMatrixToFieldMatrix(lattice,Q),FieldMatrix::identity(Q,lattice.getHeight()));
bigMatrix.reduce();
FieldMatrix reducedLatticeBasis=bigMatrix.submatrix(0,0,lattice.getHeight(),lattice.getWidth());
FieldMatrix inverseMatrix=bigMatrix.submatrix(0,lattice.getWidth(),lattice.getHeight(),lattice.getWidth()+lattice.getHeight());
for(PolynomialSet::const_iterator i=g.begin();i!=g.end();i++)
{
Polynomial q(r2);
Polynomial const &p=*i;
if(!p.isZero())
{
IntegerVector rel=p.terms.begin()->first.exponent;
for(TermMap::const_iterator i=p.terms.begin();i!=p.terms.end();i++)
{
IntegerVector diff=i->first.exponent-rel;
FieldVector diff2=integerVectorToFieldVector(diff,Q);
FieldVector temp(Q,0);
reducedLatticeBasis.normalForm(diff2,&temp);
FieldVector temp2=temp*inverseMatrix;
q+=Term(i->second,Monomial(r2,fieldVectorToIntegerVector(temp2)));
}
}
ret.push_back(q);
}
return ret;
}
PolynomialSet notLaurent(PolynomialSet const &s)
{
PolynomialRing theRing=s.getRing();
PolynomialSet ret(theRing);
for(PolynomialSet::const_iterator i=s.begin();i!=s.end();i++)
ret.push_back(notLaurent(*i));
return ret;
}
PolynomialSet idealWithSameMultiplicity(PolynomialSet const &g)
{
PolynomialRing r1=g.getRing();
PolyhedralCone H=homogeneitySpace(g).dualCone();
H.findFacets();
IntegerVectorList a=H.getEquations();
//log3 IntegerMatrix latticeBasis=rowsToIntegerMatrix(a);
IntegerMatrix temp(H.ambientDimension(),0);
if(a.size()!=0)temp=rowsToIntegerMatrix(a).transposed();
IntegerMatrix latticeBasis=latticeKernelOfTransposed(temp);
mlll(latticeBasis);
// log3 AsciiPrinter(Stderr).printVectorList(latticeBasis.getRows());
PolynomialRing r2(r1.getField(),latticeBasis.getHeight());
return notLaurent(multiplicativeChangeInv(g,latticeBasis,r2));
}
int multiplicity(PolynomialSet const &g)
{
PolynomialSet g2=idealWithSameMultiplicity(g);
log3 AsciiPrinter(Stderr).printPolynomialSet(g2);
PolynomialSet g3=nonHomogeneousSaturation(g2);
log3 AsciiPrinter(Stderr).printPolynomialSet(g3);
return numberOfStandardMonomials(g3);
}
bool isStandard(IntegerVector const &v, PolynomialSet const &markedGroebnerBasis)
{
for(PolynomialSet::const_iterator i=markedGroebnerBasis.begin();i!=markedGroebnerBasis.end();i++)
if(i->getMarked().m.exponent.divides(v))return false;
return true;
}
int numberOfStandardMonomials(PolynomialSet const &markedGroebnerBasis)
{
int ret=0;
int n=markedGroebnerBasis.numberOfVariablesInRing();
IntegerVector v(n);
int i=0;
while(1)
{
// AsciiPrinter(Stderr).printVector(v);
if(isStandard(v,markedGroebnerBasis))
{
//AsciiPrinter(Stderr).printVector(v);
//fprintf(Stderr,"\n");
ret++;
i=n-1;
}
else
{
v[i]=0;
i--;
}
if(i==-1)break;
v[i]++;
}
return ret;
}
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