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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 "tropicalbasis.h"
#include "log.h"
class TropicalBasisApplication : public GFanApplication
{
SimpleOption optionHomogenize;
public:
const char *helpText()
{
return "This program computes a tropical basis for an ideal defining a tropical curve. Defining a tropical curve means that the Krull dimension of R/I is at most 1 + the dimension of the homogeneity space of I where R is the polynomial ring. The input is a generating set for the ideal. If the input is not homogeneous option -h must be used.\n";
}
TropicalBasisApplication():
optionHomogenize("-h","Homogenise the input before computing a tropical basis and dehomogenise the output. This is needed if the input generators are not already homogeneous.")
{
registerOptions();
}
const char *name()
{
return "_tropicalbasis";
}
int main()
{
FileParser P(Stdin);
/* StringParser P1("{1+76*a2*b*c+6*a2*c4+72*a*b3*c3,"
"46*b3*c+68*b3*a2*c+42*a3*c4+47*b6*a2}");
StringParser P2("{1-79ab^4-27b^3c^2+32a^4b^2c,"
"-36c-35b^3c^3+11a^4b^2c^2+90a^3b^6}");
*/
PolynomialSet theInput=P.parsePolynomialSetWithRing();
PolynomialRing originalRing=theInput.getRing();
if(optionHomogenize.getValue())
{
log1 fprintf(Stderr,"Homogenizing...\n");
IntegerVector grading=IntegerVector::allOnes(theInput.numberOfVariablesInRing());
/* { // It is not necessary to compute the true homogenization
WeightReverseLexicographicTermOrder t(grading);
buchberger(&theInput,t);
}*/
PolynomialSet h=theInput.homogenization(theInput.getRing().withVariablesAppended("H"));
wallInequalities(h);
log1 fprintf(Stderr,"The homogenized ideal:\n");
log1 AsciiPrinter(Stderr).printPolynomialSet(h);
theInput=h;
}
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.embeddedInto(originalRing);
}
AsciiPrinter(Stdout).printPolynomialRing(theOutput.getRing());
AsciiPrinter(Stdout).printNewLine();
AsciiPrinter(Stdout).printPolynomialSet(theOutput);
return 0;
}
};
static TropicalBasisApplication theApplication;
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