startingCone.h File Reference

#include "groebnerCone.h"
#include "tropicalStrategy.h"

Go to the source code of this file.

Functions
groebnerCone	groebnerStartingCone (const tropicalStrategy &currentStrategy)
groebnerCone	tropicalStartingCone (const tropicalStrategy &currentCase)
BOOLEAN	tropicalStartingPoint (leftv res, leftv args)
BOOLEAN	positiveTropicalStartingPoint (leftv res, leftv args)
BOOLEAN	nonNegativeTropicalStartingPoint (leftv res, leftv args)
BOOLEAN	negativeTropicalStartingPoint (leftv res, leftv args)
BOOLEAN	nonPositiveTropicalStartingPoint (leftv res, leftv args)
BOOLEAN	tropicalStartingCone (leftv res, leftv args)

Variables
gfan::ZMatrix	tropicalStartingPoints

Function Documentation

groebnerStartingCone()

groebnerCone groebnerStartingCone

(

const tropicalStrategy &

currentStrategy

)

Definition at line 21 of file startingCone.cc.

{
  groebnerCone sigma(currentStrategy.getStartingIdeal(), currentStrategy.getStartingRing(), currentStrategy);
  return sigma;
}

negativeTropicalStartingPoint()

BOOLEAN negativeTropicalStartingPoint	(	leftv	res,
		leftv	args
	)

Definition at line 191 of file startingCone.cc.

{
  leftv u = args;
  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
  {
    ideal I = (ideal) u->Data();
    if ((I->m[0]!=NULL) && (idElem(I)==1))
    {
      tropicalStrategy currentStrategy(I,currRing);
      poly g = I->m[0];
      std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,&currentStrategy);
      for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++)
      {
        gfan::ZMatrix ray = zc->extremeRays();
        for (int i=0; i<ray.getHeight(); i++)
        {
          gfan::ZVector negatedRay = gfan::Integer(-1)*ray[i].toVector();
          if (negatedRay.isPositive())
          {
            res->rtyp = BIGINTMAT_CMD;
            res->data = (void*) zVectorToBigintmat(ray[i].toVector());
            return FALSE;
          }
        }
      }
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(gfan::ZVector(0));
      return FALSE;
    }
    WerrorS("negativeTropicalStartingPoint: ideal not principal");
    return TRUE;
  }
  WerrorS("negativeTropicalStartingPoint: unexpected parameters");
  return TRUE;
}

nonNegativeTropicalStartingPoint()

BOOLEAN nonNegativeTropicalStartingPoint	(	leftv	res,
		leftv	args
	)

Definition at line 156 of file startingCone.cc.

{
  leftv u = args;
  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
  {
    ideal I = (ideal) u->Data();
    if ((I->m[0]!=NULL) && (idElem(I)==1))
    {
      tropicalStrategy currentStrategy(I,currRing);
      poly g = I->m[0];
      std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,&currentStrategy);
      for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++)
      {
        gfan::ZMatrix ray = zc->extremeRays();
        for (int i=0; i<ray.getHeight(); i++)
        {
          if (ray[i].toVector().isNonNegative())
          {
            res->rtyp = BIGINTMAT_CMD;
            res->data = (void*) zVectorToBigintmat(ray[i].toVector());
            return FALSE;
          }
        }
      }
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(gfan::ZVector(0));
      return FALSE;
    }
    WerrorS("nonNegativeTropicalStartingPoint: ideal not principal");
    return TRUE;
  }
  WerrorS("nonNegativeTropicalStartingPoint: unexpected parameters");
  return TRUE;
}

nonPositiveTropicalStartingPoint()

BOOLEAN nonPositiveTropicalStartingPoint	(	leftv	res,
		leftv	args
	)

Definition at line 227 of file startingCone.cc.

{
  leftv u = args;
  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
  {
    ideal I = (ideal) u->Data();
    if ((I->m[0]!=NULL) && (idElem(I)==1))
    {
      tropicalStrategy currentStrategy(I,currRing);
      poly g = I->m[0];
      std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,&currentStrategy);
      for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++)
      {
        gfan::ZMatrix ray = zc->extremeRays();
        for (int i=0; i<ray.getHeight(); i++)
        {
          gfan::ZVector negatedRay = gfan::Integer(-1)*ray[i].toVector();
          if (negatedRay.isNonNegative())
          {
            res->rtyp = BIGINTMAT_CMD;
            res->data = (void*) zVectorToBigintmat(ray[i]);
            return FALSE;
          }
        }
      }
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(gfan::ZVector(0));
      return FALSE;
    }
    WerrorS("nonPositiveTropicalStartingPoint: ideal not principal");
    return TRUE;
  }
  WerrorS("nonPositiveTropicalStartingPoint: unexpected parameters");
  return TRUE;
}

positiveTropicalStartingPoint()

BOOLEAN positiveTropicalStartingPoint	(	leftv	res,
		leftv	args
	)

Definition at line 121 of file startingCone.cc.

{
  leftv u = args;
  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
  {
    ideal I = (ideal) u->Data();
    if ((I->m[0]!=NULL) && (idElem(I)==1))
    {
      tropicalStrategy currentStrategy(I,currRing);
      poly g = I->m[0];
      std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,&currentStrategy);
      for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++)
      {
        gfan::ZMatrix ray = zc->extremeRays();
        for (int i=0; i<ray.getHeight(); i++)
        {
          if (ray[i].toVector().isPositive())
          {
            res->rtyp = BIGINTMAT_CMD;
            res->data = (void*) zVectorToBigintmat(ray[i].toVector());
            return FALSE;
          }
        }
      }
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(gfan::ZVector(0));
      return FALSE;
    }
    WerrorS("positiveTropicalStartingPoint: ideal not principal");
    return TRUE;
  }
  WerrorS("positiveTropicalStartingPoint: unexpected parameters");
  return TRUE;
}

tropicalStartingCone() [1/2]

groebnerCone tropicalStartingCone

(

const tropicalStrategy &

currentCase

)

Definition at line 374 of file startingCone.cc.

{
  ring r = currentStrategy.getStartingRing();
  ideal I = currentStrategy.getStartingIdeal();
  currentStrategy.reduce(I,r);
  if (currentStrategy.isValuationTrivial())
  {
    // copy the data, so that it be deleted when passed to the loop
    // s <- r
    // inI <- I
    ring s = rCopy(r);
    int k = IDELEMS(I); ideal inI = idInit(k);
    nMapFunc identityMap = n_SetMap(r->cf,s->cf);
    for (int i=0; i<k; i++)
    {
      if(I->m[i]!=NULL)
      {
        inI->m[i] = p_PermPoly(I->m[i],NULL,r,s,identityMap,NULL,0);
      }
    }
 
    // repeatedly computes a point in the tropical variety outside the lineality space,
    // take the initial ideal with respect to it
    // and check whether the dimension of its homogeneity space
    // equals the dimension of the tropical variety
    gfan::ZCone zc = linealitySpaceOfGroebnerFan(inI,s);
    groebnerCone ambientMaximalCone;
    if (zc.dimension()>=currentStrategy.getExpectedDimension())
    {
      // check whether the lineality space is contained in the tropical variety
      // i.e. whether the ideal does not contain a monomial
      poly mon = checkForMonomialViaSuddenSaturation(I,r);
      if (mon)
      {
        groebnerCone emptyCone = groebnerCone();
        p_Delete(&mon,r);
        id_Delete(&inI,s);
        return emptyCone;
      }
      groebnerCone startingCone(inI,inI,s,currentStrategy);
      id_Delete(&inI,s);
      return startingCone;
    }
    while (zc.dimension()<currentStrategy.getExpectedDimension())
    {
      // compute a point in the tropical variety outside the lineality space
      std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(inI,s,currentStrategy);
      gfan::ZVector startingPoint = startingData.first;
      tropicalStartingPoints.appendRow(startingPoint);
      ambientMaximalCone = groebnerCone(startingData.second);
 
      id_Delete(&inI,s); rDelete(s);
      inI = ambientMaximalCone.getPolynomialIdeal();
      s = ambientMaximalCone.getPolynomialRing();
 
      // compute the initial ideal with respect to the weight
      inI = initial(inI,s,startingPoint);
      zc = linealitySpaceOfGroebnerFan(inI,s);
    }
 
    // once the dimension of the homogeneity space equals that of the tropical variety
    // we know that we have an initial ideal with respect to a weight
    // in the relative interior of a maximal cone in the tropical variety
    // from this we can read of the inequalities and equations
 
    ring s0 = createTraversalStartingRing(s,tropicalStartingPoints,currentStrategy);
    nMapFunc identity = n_SetMap(s->cf,s0->cf);
    k = IDELEMS(inI);
    ideal inI0 = idInit(k);
    for (int i=0; i<k; i++)
      inI0->m[i] = p_PermPoly(inI->m[i],NULL,s,s0,identity,NULL,0);
 
    identity = n_SetMap(r->cf,s0->cf);
    k = IDELEMS(I);
    ideal I0 = idInit(k);
    for (int i=0; i<k; i++)
      I0->m[i] = p_PermPoly(I->m[i],NULL,r,s0,identity,NULL,0);
 
 
    // but before doing so, we must lift the generating set of inI
    // to a generating set of I
    // ideal J0 = lift(I,r,inI0,s0); // todo: use computeLift from tropicalStrategy
    ideal J0 = gfanlib_kStd_wrapper(I0,s0);
    assume(areIdealsEqual(J0,s0,I,r));
    id_Delete(&I0,s0);
    groebnerCone startingCone(J0,inI0,s0,currentStrategy);
    id_Delete(&J0,s0);
    id_Delete(&inI0,s0);
    rDelete(s0);
 
    // assume(checkContainmentInTropicalVariety(startingCone));
    return startingCone;
  }
  else
  {
    // copy the data, so that it be deleted when passed to the loop
    // s <- r
    // inJ <- I
    ring s = rCopy(r);
    int k = IDELEMS(I); ideal inJ = idInit(k);
    nMapFunc identityMap = n_SetMap(r->cf,s->cf);
    for (int i=0; i<k; i++)
    {
      if(I->m[i]!=NULL)
      {
        inJ->m[i] = p_PermPoly(I->m[i],NULL,r,s,identityMap,NULL,0);
      }
    }
 
    // and check whether the dimension of its homogeneity space
    // equals the dimension of the tropical variety
    gfan::ZCone zc = linealitySpaceOfGroebnerFan(inJ,s);
    if (zc.dimension()>=currentStrategy.getExpectedDimension())
    { // this shouldn't happen as trivial cases should be caught beforehand
      // this is the case that the tropical variety consists soely out of the lineality space
      poly mon = checkForMonomialViaSuddenSaturation(I,r);
      if (mon)
      {
        groebnerCone emptyCone = groebnerCone();
        p_Delete(&mon,r);
        return emptyCone;
      }
      groebnerCone startingCone(I,inJ,s,currentStrategy);
      id_Delete(&inJ,s);
      rDelete(s);
      return startingCone;
    }
 
    // compute a point in the tropical variety outside the lineality space
    // compute the initial ideal with respect to the weight
    std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(inJ,s,currentStrategy);
    gfan::ZVector startingPoint = startingData.first;
    tropicalStartingPoints.appendRow(startingPoint);
    groebnerCone ambientMaximalCone = groebnerCone(startingData.second);
    id_Delete(&inJ,s); rDelete(s);
    inJ = ambientMaximalCone.getPolynomialIdeal();
    s = ambientMaximalCone.getPolynomialRing();
    inJ = initial(inJ,s,startingPoint);
    ideal inI = initial(I,r,startingPoint);
    zc = linealitySpaceOfGroebnerFan(inJ,s);
 
    // and check whether the dimension of its homogeneity space
    // equals the dimension of the tropical variety
    if (zc.dimension()==currentStrategy.getExpectedDimension())
    { // this case shouldn't happen as trivial cases should be caught beforehand
      // this is the case that the tropical variety has a one-codimensional lineality space
      ideal J = lift(I,r,inJ,s); // todo: use computeLift from tropicalStrategy
      groebnerCone startingCone(J,inJ,s,currentStrategy);
      id_Delete(&inJ,s);
      id_Delete(&J,s);
      return startingCone;
    }
 
    // from this point on, inJ contains the uniformizing parameter,
    // hence it contains a monomial if and only if its residue over the residue field does.
    // so we will switch to the residue field
    ring rShortcut = rCopy0(r);
    nKillChar(rShortcut->cf);
    rShortcut->cf = nCopyCoeff((currentStrategy.getShortcutRing())->cf);
    rComplete(rShortcut);
    rTest(rShortcut);
    k = IDELEMS(inJ);
    ideal inJShortcut = idInit(k);
    nMapFunc takingResidues = n_SetMap(s->cf,rShortcut->cf);
    for (int i=0; i<k; i++)
    {
      if(inJ->m[i]!=NULL)
      {
        inJShortcut->m[i] = p_PermPoly(inJ->m[i],NULL,s,rShortcut,takingResidues,NULL,0);
      }
    }
    idSkipZeroes(inJShortcut);
    id_Delete(&inJ,s);
 
    // we are interested in a maximal cone of the tropical variety of inJShortcut
    // this basically equivalent to the case without valuation (or constant coefficient case)
    // except that our ideal is still only homogeneous in the later variables,
    // hence we set the optional parameter completelyHomogeneous as 'false'
    tropicalStrategy shortcutStrategy(inJShortcut,rShortcut,false);
    groebnerCone startingConeShortcut = tropicalStartingCone(shortcutStrategy);
    id_Delete(&inJShortcut,rShortcut); rDelete(rShortcut);
 
    // now we need to obtain the initial of the residue of inJ
    // with respect to a weight in the tropical cone,
    // and obtain the initial of inJ with respect to the same weight
    ring sShortcut = startingConeShortcut.getPolynomialRing();
    inJShortcut = startingConeShortcut.getPolynomialIdeal();
    gfan::ZCone zd = startingConeShortcut.getPolyhedralCone();
    gfan::ZVector interiorPoint = startingConeShortcut.getInteriorPoint();
    inJShortcut = initial(inJShortcut,sShortcut,interiorPoint);
    inI = initial(inI,r,interiorPoint);
 
    s = rCopy0(sShortcut); // s will be a ring over the valuation ring
    nKillChar(s->cf);      // with the same ordering as sShortcut
    s->cf = nCopyCoeff(r->cf);
    rComplete(s);
    rTest(s);
 
    k = IDELEMS(inJShortcut); // inJ will be overwritten with initial of inJ
    inJ = idInit(k+1);
    inJ->m[0] = p_One(s);    // with respect to that weight
    identityMap = n_SetMap(r->cf,s->cf); // first element will obviously be p
    p_SetCoeff(inJ->m[0],identityMap(currentStrategy.getUniformizingParameter(),r->cf,s->cf),s);
    nMapFunc findingRepresentatives = n_SetMap(sShortcut->cf,s->cf);
    for (int i=0; i<k; i++)              // and then come the rest
    {
      if(inJShortcut->m[i]!=NULL)
      {
        inJ->m[i+1] = p_PermPoly(inJShortcut->m[i],NULL,sShortcut,s,findingRepresentatives,NULL,0);
      }
    }
 
    ring s0 = createTraversalStartingRing(s,tropicalStartingPoints,currentStrategy);
    nMapFunc identity = n_SetMap(s->cf,s0->cf);
    k = IDELEMS(inJ);
    ideal inI0 = idInit(k);
    for (int i=0; i<k; i++)
      inI0->m[i] = p_PermPoly(inJ->m[i],NULL,s,s0,identity,NULL,0);
 
    identity = n_SetMap(r->cf,s0->cf);
    k = IDELEMS(I);
    ideal I0 = idInit(k);
    for (int i=0; i<k; i++)
      I0->m[i] = p_PermPoly(I->m[i],NULL,r,s0,identity,NULL,0);
    ideal J0 = gfanlib_kStd_wrapper(I0,s0);
    groebnerCone startingCone(J0,inI0,s0,currentStrategy);
 
    // ideal J = currentStrategy.computeLift(inJ,s,inI,I,r);
    // currentStrategy.reduce(J,s);
    // groebnerCone startingCone(J,inJ,s,currentStrategy);
    id_Delete(&inJ,s);
    // id_Delete(&J,s);
    rDelete(s);
    id_Delete(&inI,r);
 
    // assume(checkContainmentInTropicalVariety(startingCone));
    return startingCone;
  }
}

tropicalStartingCone() [2/2]

BOOLEAN tropicalStartingCone	(	leftv	res,
		leftv	args
	)

Definition at line 614 of file startingCone.cc.

{
  leftv u = args;
  if ((u != NULL) && (u->Typ() == IDEAL_CMD))
  {
    ideal I = (ideal) u->CopyD();
    leftv v = u->next;
    if ((v != NULL) && (v->Typ() == NUMBER_CMD))
    {
      number p = (number) v->Data();
      leftv w = v->next;
      if (w==NULL)
      {
        tropicalStrategy currentStrategy(I,p,currRing);
        groebnerCone sigma = tropicalStartingCone(currentStrategy);
        gfan::ZCone* startingCone = new gfan::ZCone(sigma.getPolyhedralCone());
        res->rtyp = coneID;
        res->data = (char*) startingCone;
        return FALSE;
      }
    }
    else
    {
      if (v==NULL)
      {
        tropicalStrategy currentStrategy(I,currRing);
        groebnerCone sigma = tropicalStartingCone(currentStrategy);
        res->rtyp = coneID;
        res->data = (char*) new gfan::ZCone(sigma.getPolyhedralCone());
        return FALSE;
      }
    }
  }
  WerrorS("tropicalStartingCone: unexpected parameters");
  return TRUE;
}

tropicalStartingPoint()

BOOLEAN tropicalStartingPoint	(	leftv	res,
		leftv	args
	)

Definition at line 263 of file startingCone.cc.

{
  leftv u = args;
  if ((u!=NULL) && (u->Typ()==IDEAL_CMD))
  {
    ideal I = (ideal) u->Data();
    tropicalStrategy currentStrategy(I,currRing);
    if ((I->m[0]!=NULL) && (idElem(I)==1))
    {
      poly g = I->m[0];
      std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,&currentStrategy);
      if (Tg.empty())
      {
        res->rtyp = BIGINTMAT_CMD;
        res->data = (void*) zVectorToBigintmat(gfan::ZVector(0));
        return FALSE;
      }
      gfan::ZCone C = *(Tg.begin());
      gfan::ZMatrix rays = C.extremeRays();
      if (rays.getHeight()==0)
      {
        gfan::ZMatrix lin = C.generatorsOfLinealitySpace();
        res->rtyp = BIGINTMAT_CMD;
        res->data = (void*) zVectorToBigintmat(lin[0]);
        return FALSE;
      }
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(rays[0]);
      return FALSE;
    }
    gfan::ZCone C0 = currentStrategy.getHomogeneitySpace();
    if (C0.dimension()==currentStrategy.getExpectedDimension())
    {
      gfan::ZMatrix lin = C0.generatorsOfLinealitySpace();
      res->rtyp = BIGINTMAT_CMD;
      res->data = (void*) zVectorToBigintmat(lin[0]);
      return FALSE;
    }
    std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(I,currRing,currentStrategy);
    gfan::ZVector startingPoint = startingData.first;
    res->rtyp = BIGINTMAT_CMD;
    res->data = (void*) zVectorToBigintmat(startingPoint);
    return FALSE;
  }
  WerrorS("tropicalStartingPoint: unexpected parameters");
  return TRUE;
}

Variable Documentation

tropicalStartingPoints

gfan::ZMatrix tropicalStartingPoints

extern

Definition at line 18 of file startingCone.cc.