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#include "parser.h"
#include "printer.h"
#include "polynomial.h"
#include "division.h"
#include "buchberger.h"
#include "wallideal.h"
#include "lp.h"
#include "reversesearch.h"
#include "termorder.h"
#include "ep_standard.h"
#include "ep_xfig.h"
#include "gfanapplication.h"
#include "polyhedralcone.h"
#include "polyhedralfan.h"
#include "tropical.h"
#include "tropical2.h"
#include "halfopencone.h"
#include "multiplicity.h"
#include "tropicalbasis.h"
#include "log.h"
class TropicalLiftingApplication : public GFanApplication
{
SimpleOption optionNoMultiplicity;
// FieldOption theFieldOption;
IntegerOption optionNumberOfNegativeVariables;
SimpleOption optionOnlyOutputChoices;
public:
const char *helpText()
{
return "This program is part of the Puiseux lifting algorithm implemented in Gfan and Singular. The Singular part of the implementation can be found in:\n\n"
"Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig:\n tropical.lib. A SINGULAR 3.0 library for computations in tropical geometry, 2007 \n\n"
"See also\n\nhttp://www.mathematik.uni-kl.de/~keilen/de/tropical.html\n\n"
"and the paper\n\n Jensen, Markwig, Markwig: \"An algorithm for lifting points in a tropical variety\".\n\n"
"Example:\n\n"
"Run Singular from the directory where tropical.lib is located.\n"
"Give the following sequence of commands to Singular:\n\n"
"LIB \"tropical.lib\";\n"
"ring R=0,(t,x,y,z),dp;\n"
"ideal i=-y2t4+x2,yt3+xz+y;\n"
"intvec w=1,-2,0,2;\n"
"list L=tropicallifting(i,w,3);\n"
"displaytropicallifting(L,\"subst\");\n"
"This produces a Puiseux series solution to i with valuation (2,0,-2)\n";
}
TropicalLiftingApplication():
optionNoMultiplicity("--noMult","Disable the multiplicity computation."),
optionNumberOfNegativeVariables("-n","Number of variables that should have negative weight."),
optionOnlyOutputChoices("-c","Only output a list of vectors being the possible choices.")
{
registerOptions();
}
const char *name()
{
return "_tropicallifting";
}
int main()
{
FileParser P(Stdin);
PolynomialSet theInput=P.parsePolynomialSetWithRing();
PolynomialRing theRing=theInput.getRing();
int n=theInput.numberOfVariablesInRing();
int homog=-1;
{
log1 debug.printString("Computing homogeneity space\n");
PolynomialSet idealGroebnerBasis=theInput;
IntegerVector grading=IntegerVector::allOnes(theInput.numberOfVariablesInRing());
WeightReverseLexicographicTermOrder t(grading);
buchberger(&idealGroebnerBasis,t);
PolyhedralCone hspace=homogeneitySpace(idealGroebnerBasis);
IntegerVectorList hv=hspace.dualCone().getEquations();
homog=hv.size();
log1 debug.printString("..done homogeneity space.\n");
}
PolynomialSet theOutput=tropicalBasisOfCurve(n,theInput,0,homog);
/* if(optionHomogenize.getValue())
{
theOutput=theOutput.deHomogenization();
}
*/
if(!optionOnlyOutputChoices.getValue())
AsciiPrinter(Stdout).printPolynomialSet(theOutput);
// PolyhedralFan F=tropicalHyperSurfaceIntersectionClosed(n, theOutput);
PolyhedralFan F=tropicalPrincipalIntersection(n, theOutput,homog); // dimension of lineality space could be computed to speed up computations
// fprintf(Stderr,"---------------------------\n");
//AsciiPrinter(Stdout).printPolyhedralFan(F);
// fprintf(Stderr,"---------------------------\n");
if(!optionOnlyOutputChoices.getValue())
fprintf(Stdout,"\nA list of relative interior points:\n");
IntegerVectorList rays=F.getRelativeInteriorPoints();
if(!optionOnlyOutputChoices.getValue())
AsciiPrinter(Stdout).printVectorList(rays);
if(!optionOnlyOutputChoices.getValue())
if(!optionNoMultiplicity.getValue())
{
fprintf(Stdout,"Multiplicities:\n");
for(IntegerVectorList::const_iterator i=rays.begin();i!=rays.end();i++)
{
if(!(i->isZero()))
{
AsciiPrinter(Stdout).printVector(*i);
fprintf(Stdout," :");
AsciiPrinter(Stdout).printInteger(multiplicity(initialIdeal(theInput,*i)));
fprintf(Stdout,"\n");
}
}
}
int t=optionNumberOfNegativeVariables.getValue();
assert(t<=n);
IntegerVectorList equations,inequalities;
for(int i=0;i<t;i++)
inequalities.push_back(-IntegerVector::standardVector(n,i));
for(int i=t;i<n;i++)
equations.push_back(IntegerVector::standardVector(n,i));
PolyhedralCone C(inequalities,equations,n);
if(!optionOnlyOutputChoices.getValue())
fprintf(Stdout,"Possible choices:\n");
for(PolyhedralConeList::const_iterator i=F.conesBegin();i!=F.conesEnd();i++)
// for(IntegerVectorList::const_iterator i=rays.begin();i!=rays.end();i++)
{
PolyhedralCone C2=intersection(C,*i);
IntegerVector v=C2.getRelativeInteriorPoint();
// AsciiPrinter(Stdout).printVector(v);
bool isNeg=true;
for(int j=0;j<t;j++)
{
if(v[j]>=0)isNeg=false;
}
if(isNeg)
{
AsciiPrinter(Stdout).printVector(v);fprintf(Stdout,"\n");
}
}
return 0;
}
};
static TropicalLiftingApplication theApplication;
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