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#include "saturation.h"
#include "matrix.h"
#include "multiplicity.h"
#include "buchberger.h"
#include "division.h"
#include "tropical.h"
#include "printer.h"
/*
#include "substitution.h"
PolynomialSet colonIdeal(PolynomialSet const &ideal, polynomial f)
{
int n=ideal.numberOfVariablesInRing();
IntegerMatrix mat(n+1,n);
for(int i=0;i<n;i++)mat[i][i]=1;
PolynomialSet ret=multiplicativeChange(mat,ideal);
f=multiplicativeChange(mat,f);
f*=Monomial(IntegerVector::standardVector(n+1,n));
ret.push_back();
}
*/
FieldElement getFieldElement(PolynomialSet const &s)
{
FieldElement a;
for(PolynomialSet::const_iterator i=s.begin();i!=s.end();i++)
for(TermMap::const_iterator j=i->terms.begin();j!=i->terms.end();j++)
return j->second;
assert(0);
return a;
}
/*
* This procedure does not work
*/
static PolynomialSet singleSaturation(PolynomialSet const &s)//TO DO: call idealIntersection to do the intersection
{
assert(0);
PolynomialRing theRing=s.getRing();
int n=s.numberOfVariablesInRing();
FieldElement one=getFieldElement(s).one();
// add a variable
// PolynomialSet s2=s;s2.changeNumberOfVariables(n+1);
IntegerVector temp(theRing.getNumberOfVariables());
PolynomialSet s2=s.homogenization(theRing.withVariablesAppended("T"),&temp);
/* IntegerMatrix mat(n+1,n);
for(int i=0;i<n;i++)mat[i][i]=1;
PolynomialSet s2=multiplicativeChangeInv(s,mat);*/
// multiply by (1-t)
Monomial m(s2.getRing(),IntegerVector::standardVector(n+1,n));
PolynomialSet s3(s2.getRing());
for(PolynomialSet::const_iterator i=s2.begin();i!=s2.end();i++)
{
s3.push_back(*i-((*i)*m));
}
for(int i=0;i<n;i++)
s3.push_back(Polynomial(Term(one,Monomial(s3.getRing(),IntegerVector::standardVector(n+1,n)+IntegerVector::standardVector(n+1,i)))));
// WeightReverseLexicographicTermOrder T(IntegerVector::standardVector(n+1,n));
LexicographicTermOrder T(n);
buchberger(&s3,T);
PolynomialSet s4=s3.polynomialRingIntersection(theRing);
s4.saturate();
return s4;
}
/*
*
*/
PolynomialSet nonHomogeneousSaturation(PolynomialSet const &s)
{
PolynomialSet s2=s.homogenization(s.getRing().withVariablesAppended("T"));
PolynomialSet s3=saturatedIdeal(s2);
PolynomialSet s4=s3.deHomogenizationInSameRing();
return s4.polynomialRingIntersection(s.getRing());
/* PolynomialRing theRing=s.getRing();
StandardGradedLexicographicTermOrder T;
PolynomialSet s1=s;
PolynomialSet s2(theRing);
buchberger(&s1,T);
s1.sort_();
do
{
s2=s1;
s1=singleSaturation(s2);
buchberger(&s1,T);
s1.sort_();
}
while(!s1.isEqualTo(s2));
return s1;
*/
}
PolynomialSet idealIntersection(PolynomialSet const &a, PolynomialSet const &b)
{
PolynomialRing theRing=a.getRing();
int n=a.numberOfVariablesInRing();
assert(n==b.numberOfVariablesInRing());
FieldElement one=getFieldElement(a).one();
// add a variable
PolynomialRing theRing2=theRing.withVariablesAppended("T");
IntegerVector temp(theRing.getNumberOfVariables());
PolynomialSet A=a.homogenization(theRing2,&temp);
PolynomialSet B=b.homogenization(theRing2,&temp);
// PolynomialSet A=a;A.changeNumberOfVariables(n+1);
// PolynomialSet B=b;B.changeNumberOfVariables(n+1);
// multiply by (1-t)
Monomial m(theRing2,IntegerVector::standardVector(n+1,n));
PolynomialSet C(theRing2);
for(PolynomialSet::const_iterator i=B.begin();i!=B.end();i++)
C.push_back(*i-((*i)*m));
for(PolynomialSet::const_iterator i=A.begin();i!=A.end();i++)
C.push_back(((*i)*m));
LexicographicTermOrder T(n);
buchberger(&C,T);
return C.polynomialRingIntersection(theRing);
}
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