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#include "mixedvolume.h"
#include "tropical_weildivisor.h"
#include "multiplicity.h"
int64 mixedVolume(PolynomialSet const &g_)
{
PolynomialSet g=idealWithSameMultiplicity(g_);
g.simplestPolynomialsFirst();
int n=g.getRing().getNumberOfVariables();
assert(g.size()<=n);
PolyhedralFan f=PolyhedralFan::fullSpace(n);
for(PolynomialSet::const_iterator i=g.begin();i!=g.end();i++)
{
PolyhedralFan f2=PolyhedralFan::normalFanOfNewtonPolytope(*i);
if(f.size()==0)return 0;
f=weilDivisor(f,f2);
}
if(f.size()==0)return 0;
assert(f.size()==1);
return f.conesBegin()->getMultiplicity();
}
#include "halfopencone.h"
bool mixedVolumePositive(PolynomialSet const &g)
{
return nonEmptyStableIntersection(g);
}
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