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#include "tropicalmap.h"
#include <iostream>
using namespace std;
#include "log.h"
static IntegerVectorList vectorImages(PolynomialSet const &polynomialMap, IntegerVectorList const &l)
{
int d=polynomialMap.size();
IntegerVectorList ret;
for(IntegerVectorList::const_iterator i=l.begin();i!=l.end();i++)
{
IntegerVector v(d);
int j=0;
for(PolynomialSet::const_iterator J=polynomialMap.begin();J!=polynomialMap.end();J++,j++)
v[j]=J->degree(*i);
ret.push_back(v);
}
return ret;
}
PolyhedralCone imageOfConeUnderTropicalMap(PolynomialSet const &polynomialMap, PolyhedralCone const &cone)
{
int d=polynomialMap.size();
IntegerVectorList linealitySpace=cone.linealitySpace().dualCone().getEquations();
IntegerVectorList rays=cone.extremeRays();
PolyhedralCone C=PolyhedralCone::givenByRays(vectorImages(polynomialMap,rays),vectorImages(polynomialMap,linealitySpace),d);
C.canonicalize();
return C;
}
PolyhedralFan imageOfTropicalMap(PolynomialSet const &polynomialMap, PolyhedralFan domain)
{
for(PolynomialSet::const_iterator i=polynomialMap.begin();i!=polynomialMap.end();i++)
{
domain=refinement(domain,PolyhedralFan::normalFanOfNewtonPolytope(*i));
}
return imageOfTropicalMapGivenLinearityCones(polynomialMap,domain);
}
PolyhedralFan imageOfTropicalMapGivenLinearityCones(PolynomialSet const &polynomialMap, PolyhedralFan linearityCones)
{
int d=polynomialMap.size();
PolyhedralFan ret(d);
/*
We first put the images of the cones of the domain into the
imageCones set. This automatically removes duplicates.
*/
set<PolyhedralCone> imageCones;
for(PolyhedralFan::coneIterator i=linearityCones.conesBegin();i!=linearityCones.conesEnd();i++)
imageCones.insert(imageOfConeUnderTropicalMap(polynomialMap,*i));
log0 cerr << "Number of image cones "<<imageCones.size()<<endl;
/*
We then remove any cone which is contained in another.
*/
for(set<PolyhedralCone>::iterator i=imageCones.begin();i!=imageCones.end();)
{
bool isContainedInOther=false;
IntegerVectorList linealitySpace=i->linealitySpace().dualCone().getEquations();
IntegerVectorList rays=i->extremeRays();
for(set<PolyhedralCone>::iterator j=imageCones.begin();j!=imageCones.end();j++)
{
if(j!=i)
if(j->contains(rays) && j->contains(linealitySpace))
{
isContainedInOther=true;break;
}
}
if(isContainedInOther)
{
set<PolyhedralCone>::iterator k=i;
i++;
imageCones.erase(k);
}
else
i++;
}
log0 cerr << "Number of image cones "<<imageCones.size()<<endl;
int I=0;
for(set<PolyhedralCone>::const_iterator i=imageCones.begin();i!=imageCones.end();i++,I++)
{
// if(I<31)continue;
// if(I==32)break;
// AsciiPrinter P(Stderr);
// P<<C;
ret.merge(*i);
//ret.insert(*i);
cerr<<"After merge"<< ret.size()<<endl;
ret.removeNonMaximal();
cerr<<"After simplification"<< ret.size()<<endl;
}
return ret;
}
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