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#include "parser.h"
#include "printer.h"
#include "polynomial.h"
#include "wallideal.h"
#include "lp.h"
#include "polyhedralcone.h"
#include "gfanapplication.h"
#include "polyhedralfan.h"
#include "halfopencone.h"
class GroebnerConeApplication : public GFanApplication
{
SimpleOption optionRestrict;
SimpleOption optionPair;
SimpleOption optionAsFan;
public:
const char *helpText()
{
return "This program computes a Groebner cone. Three different cases are handled. The input may be a marked reduced Groebner basis in which case its Groebner cone is computed. The input may be just a marked minimal basis in which case the cone computed is not a Groebner cone in the usual sense but smaller. (These cones are described in [Fukuda, Jensen, Lauritzen, Thomas]). The third possible case is that the Groebner cone is possibly lower dimensional and given by a pair of Groebner bases as it is useful to do for tropical varieties, see option --pair. The facets of the cone can be read off in section FACETS and the equations in section IMPLIED_EQUATIONS.\n";
}
GroebnerConeApplication():
optionRestrict("--restrict","Add an inequality for each coordinate, so that the the cone is restricted to the non-negative orthant."),
optionPair("--pair","The Groebner cone is given by a pair of compatible Groebner bases. The first basis is for the initial ideal and the second for the ideal itself. See the tropical section of the manual."),
optionAsFan("--asfan","Writes the cone as a polyhedral fan with all its faces instead. In this way the extreme rays of the cone are also computed.")
{
registerOptions();
}
char *name()
{
return "_groebnercone";
}
int main()
{
PolynomialSet m=FileParser(Stdin).parsePolynomialSetWithRing();
PolynomialSet g(m.getRing());
if(optionPair.getValue())
{
g=FileParser(Stdin).parsePolynomialSet(m.getRing());
}
else
{
g=m;
m=g.markedTermIdeal();
}
int n=g.getRing().getNumberOfVariables();
IntegerVectorList equalities=wallInequalities(m);
IntegerVectorList normals=algebraicTest(wallInequalities(g),g);
if(optionRestrict.getValue())
{
for(int i=0;i<n;i++)
normals.push_back(IntegerVector::standardVector(n,i));
}
// AsciiPrinter(Stderr).printVectorList(normals);
PolyhedralCone c(normals,equalities,n);
c.canonicalize();
if(!optionAsFan.getValue())
AsciiPrinter(Stdout).printPolyhedralCone(c);
else
{
AsciiPrinter P(Stdout);
IntegerVectorList empty;
HalfOpenCone C(n,c.getEquations(),c.getHalfSpaces(),empty,true);
// PolyhedralFan F=faceComplexOfCone(C);
PolyhedralFan F(n);F.insert(C.closure());
F.printWithIndices(&P,false,0);
}
return 0;
}
};
static GroebnerConeApplication theApplication;
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