tropicalCurves.h File Reference

#include "gfanlib/gfanlib_zcone.h"
#include "gfanlib/gfanlib_zfan.h"
#include "polys/monomials/p_polys.h"
#include "tropicalStrategy.h"
#include "tropicalVarietyOfPolynomials.h"

Go to the source code of this file.

Functions
ZConesSortedByDimension	tropicalStar (const ideal I, const ring r, const gfan::ZVector &u, const tropicalStrategy *currentStrategy)
gfan::ZMatrix	raysOfTropicalStar (ideal I, const ring r, const gfan::ZVector &u, const tropicalStrategy *currentStrategy)

Function Documentation

raysOfTropicalStar()

gfan::ZMatrix raysOfTropicalStar	(	ideal	I,
		const ring	r,
		const gfan::ZVector &	u,
		const tropicalStrategy *	currentStrategy )

Definition at line 243 of file tropicalCurves.cc.

{
  ZConesSortedByDimension C = tropicalStar(I,r,u,currentStrategy);
  // gfan::ZFan* zf = toFanStar(C);
  // std::cout << zf->toString();
  // delete zf;
  gfan::ZMatrix raysOfC(0,u.size());
  if (!currentStrategy->restrictToLowerHalfSpace())
  {
    for (ZConesSortedByDimension::iterator zc=C.begin(); zc!=C.end(); zc++)
    {
      assume(zc->dimensionOfLinealitySpace()+1 >= zc->dimension());
      if (zc->dimensionOfLinealitySpace()+1 >= zc->dimension())
        raysOfC.appendRow(zc->getRelativeInteriorPoint());
      else
      {
        gfan::ZVector interiorPoint = zc->getRelativeInteriorPoint();
        if (!currentStrategy->homogeneitySpaceContains(interiorPoint))
        {
          raysOfC.appendRow(interiorPoint);
          raysOfC.appendRow(currentStrategy->negateWeight(interiorPoint));
        }
        else
        {
          gfan::ZMatrix zm = zc->generatorsOfLinealitySpace();
          for (int i=0; i<zm.getHeight(); i++)
          {
            gfan::ZVector point = zm[i];
            if (currentStrategy->homogeneitySpaceContains(point))
            {
              raysOfC.appendRow(point);
              raysOfC.appendRow(currentStrategy->negateWeight(point));
              break;
            }
          }
        }
      }
    }
  }
  else
  {
    for (ZConesSortedByDimension::iterator zc=C.begin(); zc!=C.end(); zc++)
    {
      assume(zc->dimensionOfLinealitySpace()+2 >= zc->dimension());
      if (zc->dimensionOfLinealitySpace()+2 == zc->dimension())
        raysOfC.appendRow(zc->getRelativeInteriorPoint());
      else
      {
        gfan::ZVector interiorPoint = zc->getRelativeInteriorPoint();
        if (!currentStrategy->homogeneitySpaceContains(interiorPoint))
        {
          raysOfC.appendRow(interiorPoint);
          raysOfC.appendRow(currentStrategy->negateWeight(interiorPoint));
        }
        else
        {
          gfan::ZMatrix zm = zc->generatorsOfLinealitySpace();
          for (int i=0; i<zm.getHeight(); i++)
          {
            gfan::ZVector point = zm[i];
            if (currentStrategy->homogeneitySpaceContains(point))
            {
              raysOfC.appendRow(point);
              raysOfC.appendRow(currentStrategy->negateWeight(point));
              break;
            }
          }
        }
      }
    }
  }
  return raysOfC;
}

tropicalStar()

ZConesSortedByDimension tropicalStar	(	const ideal	I,
		const ring	r,
		const gfan::ZVector &	u,
		const tropicalStrategy *	currentStrategy )

Definition at line 107 of file tropicalCurves.cc.

{
  int k = IDELEMS(inI);
  int d = currentStrategy->getExpectedDimension();
 
  /* Compute the common refinement over all tropical varieties
   * of the polynomials in the generating set */
  ZConesSortedByDimension C = tropicalVarietySortedByDimension(inI->m[0],r,currentStrategy);
  int PayneOsserman = rVar(r)-1;
  for (int i=0; i<k; i++)
  {
    if(inI->m[i]!=NULL)
    {
      PayneOsserman--;
      C = intersect(C,tropicalVarietySortedByDimension(inI->m[i],r,currentStrategy),si_max(PayneOsserman,d));
    }
  }
 
  /* Cycle through all maximal cones of the refinement.
   * Pick a monomial ordering corresponding to a generic weight vector in it
   * and check if the initial ideal is monomial free, generic meaning
   * that it lies in a maximal Groebner cone in the maximal cone of the refinement.
   * If the initial ideal is not monomial free, compute a witness for the monomial
   * and compute the common refinement with its tropical variety.
   * If all initial ideals are monomial free, then we have our tropical curve */
  // gfan::ZFan* zf = toFanStar(C);
  // std::cout << zf->toString(2+4+8+128) << std::endl;
  // delete zf;
  for (std::set<gfan::ZCone>::iterator zc=C.begin(); zc!=C.end();)
  {
    gfan::ZVector w = zc->getRelativeInteriorPoint();
    gfan::ZMatrix W = zc->generatorsOfSpan();
    // std::cout << zc->extremeRays() << std::endl;
 
    ring s = genericlyWeightedOrdering(r,u,w,W,currentStrategy);
    nMapFunc identity = n_SetMap(r->cf,s->cf);
    ideal inIs = idInit(k);
    for (int j=0; j<k; j++)
      inIs->m[j] = p_PermPoly(inI->m[j],NULL,r,s,identity,NULL,0);
 
    ideal inIsSTD = gfanlib_kStd_wrapper(inIs,s,isHomog);
    id_Delete(&inIs,s);
    ideal ininIs = initial(inIsSTD,s,w,W);
 
    std::pair<poly,int> mons = currentStrategy->checkInitialIdealForMonomial(ininIs,s);
 
    if (mons.first!=NULL)
    {
      poly gs;
      if (mons.second>=0)
        // cheap way out, ininIsSTD already contains a monomial in its generators
        gs = inIsSTD->m[mons.second];
      else
        // compute witness
        gs = witness(mons.first,inIsSTD,ininIs,s);
 
      C = intersect(C,tropicalVarietySortedByDimension(gs,s,currentStrategy),d);
      nMapFunc mMap = n_SetMap(s->cf,r->cf);
      poly gr = p_PermPoly(gs,NULL,s,r,mMap,NULL,0);
      idInsertPoly(inI,gr);
      k++;
 
      if (mons.second<0)
      {
        // if necessary, cleanup mons and gs
        p_Delete(&mons.first,s);
        p_Delete(&gs,s);
      }
      // cleanup rest, reset zc
      id_Delete(&inIsSTD,s);
      id_Delete(&ininIs,s);
      rDelete(s);
      zc = C.begin();
    }
    else
    {
      // cleanup remaining data of first stage
      id_Delete(&inIsSTD,s);
      id_Delete(&ininIs,s);
      rDelete(s);
 
      gfan::ZVector wNeg = currentStrategy->negateWeight(w);
      if (zc->contains(wNeg))
      {
        s = genericlyWeightedOrdering(r,u,wNeg,W,currentStrategy);
        identity = n_SetMap(r->cf,s->cf);
        inIs = idInit(k);
        for (int j=0; j<k; j++)
          inIs->m[j] = p_PermPoly(inI->m[j],NULL,r,s,identity,NULL,0);
 
        inIsSTD = gfanlib_kStd_wrapper(inIs,s,isHomog);
        id_Delete(&inIs,s);
        ininIs = initial(inIsSTD,s,wNeg,W);
 
        mons = currentStrategy->checkInitialIdealForMonomial(ininIs,s);
        if (mons.first!=NULL)
        {
          poly gs;
          if (mons.second>=0)
            // cheap way out, ininIsSTD already contains a monomial in its generators
            gs = inIsSTD->m[mons.second];
          else
            // compute witness
            gs = witness(mons.first,inIsSTD,ininIs,s);
 
          C = intersect(C,tropicalVarietySortedByDimension(gs,s,currentStrategy),d);
          nMapFunc mMap = n_SetMap(s->cf,r->cf);
          poly gr = p_PermPoly(gs,NULL,s,r,mMap,NULL,0);
          idInsertPoly(inI,gr);
          k++;
 
          if (mons.second<0)
          {
            // if necessary, cleanup mons and gs
            p_Delete(&mons.first,s);
            p_Delete(&gs,s);
          }
          // reset zc
          zc = C.begin();
        }
        else
          zc++;
        // cleanup remaining data of second stage
        id_Delete(&inIsSTD,s);
        id_Delete(&ininIs,s);
        rDelete(s);
      }
      else
        zc++;
    }
  }
  return C;
}