stairc.h File Reference

#include "polys/monomials/ring.h"
#include "kernel/polys.h"
#include "misc/intvec.h"

Go to the source code of this file.

Functions
void	scComputeHC (ideal s, ideal Q, int k, poly &hEdge, ring tailRing=currRing)
intvec *	scIndIntvec (ideal S, ideal Q=NULL)
int	scDimInt (ideal s, ideal Q=NULL)
	ideal dimension More...
int	scDimIntRing (ideal s, ideal Q=NULL)
	scDimInt for ring-coefficients More...
int	scMultInt (ideal s, ideal Q=NULL)
int	scMult0Int (ideal s, ideal Q=NULL, const ring tailRing=currRing)
void	scPrintDegree (int co, int mu)
void	scDegree (ideal s, intvec *modulweight, ideal Q=NULL)
ideal	scKBase (int deg, ideal s, ideal Q=NULL, intvec *mv=NULL)
int	lp_gkDim (const ideal G)
int	lp_kDim (const ideal G)
intvec *	lp_ufnarovskiGraph (ideal G, ideal &standardWords)

Function Documentation

lp_gkDim()

int lp_gkDim

(

const ideal

G

)

Definition at line 1840 of file hdegree.cc.

{
  id_Test(_G, currRing);
 
  if (rField_is_Ring(currRing)) {
      WerrorS("GK-Dim not implemented for rings");
      return -2;
  }
 
  for (int i=IDELEMS(_G)-1;i>=0; i--)
  {
    if (_G->m[i] != NULL)
    {
      if (pGetComp(_G->m[i]) != 0)
      {
        WerrorS("GK-Dim not implemented for modules");
        return -2;
      }
      if (pGetNCGen(_G->m[i]) != 0)
      {
        WerrorS("GK-Dim not implemented for bi-modules");
        return -2;
      }
    }
  }
 
  ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
  idSkipZeroes(G); // remove zeros
  id_DelLmEquals(G, currRing); // remove duplicates
 
  // check if G is the zero ideal
  if (IDELEMS(G) == 1 && G->m[0] == NULL)
  {
    // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
    int lV = currRing->isLPring;
    int ncGenCount = currRing->LPncGenCount;
    if (lV - ncGenCount == 0)
    {
      idDelete(&G);
      return 0;
    }
    if (lV - ncGenCount == 1)
    {
      idDelete(&G);
      return 1;
    }
    if (lV - ncGenCount >= 2)
    {
      idDelete(&G);
      return -1;
    }
  }
 
  // get the max deg
  long maxDeg = 0;
  for (int i = 0; i < IDELEMS(G); i++)
  {
    maxDeg = si_max(maxDeg, pTotaldegree(G->m[i]));
 
    // also check whether G = <1>
    if (pIsConstantComp(G->m[i]))
    {
      WerrorS("GK-Dim not defined for 0-ring");
      idDelete(&G);
      return -2;
    }
  }
 
  // early termination if G \subset X
  if (maxDeg <= 1)
  {
    int lV = currRing->isLPring;
    int ncGenCount = currRing->LPncGenCount;
    if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
    {
      idDelete(&G);
      return 0;
    }
    if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
    {
      idDelete(&G);
      return 1;
    }
    if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
    {
      idDelete(&G);
      return -1;
    }
  }
 
  ideal standardWords;
  intvec* UG = lp_ufnarovskiGraph(G, standardWords);
  if (UG == NULL)
  {
    idDelete(&G);
    return -2;
  }
  if (errorreported)
  {
    delete UG;
    idDelete(&G);
    return -2;
  }
  int gkDim = graphGrowth(UG);
  delete UG;
  idDelete(&G);
  return gkDim;
}

lp_kDim()

int lp_kDim

(

const ideal

G

)

Definition at line 2090 of file hdegree.cc.

{
  if (rField_is_Ring(currRing)) {
      WerrorS("K-Dim not implemented for rings");
      return -2;
  }
 
  for (int i=IDELEMS(_G)-1;i>=0; i--)
  {
    if (_G->m[i] != NULL)
    {
      if (pGetComp(_G->m[i]) != 0)
      {
        WerrorS("K-Dim not implemented for modules");
        return -2;
      }
      if (pGetNCGen(_G->m[i]) != 0)
      {
        WerrorS("K-Dim not implemented for bi-modules");
        return -2;
      }
    }
  }
 
  ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
  if (TEST_OPT_PROT)
    Print("%d original generators\n", IDELEMS(G));
  idSkipZeroes(G); // remove zeros
  id_DelLmEquals(G, currRing); // remove duplicates
  if (TEST_OPT_PROT)
    Print("%d non-zero unique generators\n", IDELEMS(G));
 
  // check if G is the zero ideal
  if (IDELEMS(G) == 1 && G->m[0] == NULL)
  {
    // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
    int lV = currRing->isLPring;
    int ncGenCount = currRing->LPncGenCount;
    if (lV - ncGenCount == 0)
    {
      idDelete(&G);
      return 1;
    }
    if (lV - ncGenCount == 1)
    {
      idDelete(&G);
      return -1;
    }
    if (lV - ncGenCount >= 2)
    {
      idDelete(&G);
      return -1;
    }
  }
 
  // get the max deg
  long maxDeg = 0;
  for (int i = 0; i < IDELEMS(G); i++)
  {
    maxDeg = si_max(maxDeg, pTotaldegree(G->m[i]));
 
    // also check whether G = <1>
    if (pIsConstantComp(G->m[i]))
    {
      WerrorS("K-Dim not defined for 0-ring"); // TODO is it minus infinity ?
      idDelete(&G);
      return -2;
    }
  }
  if (TEST_OPT_PROT)
    Print("max deg: %ld\n", maxDeg);
 
 
  // for normal words of length minDeg ... maxDeg-1
  // brute-force the normal words
  if (TEST_OPT_PROT)
    PrintS("Computing normal words normally...\n");
  long numberOfNormalWords = lp_countNormalWords(maxDeg - 1, G);
 
  if (TEST_OPT_PROT)
    Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1);
 
  // early termination if G \subset X
  if (maxDeg <= 1)
  {
    int lV = currRing->isLPring;
    int ncGenCount = currRing->LPncGenCount;
    if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
    {
      idDelete(&G);
      return numberOfNormalWords;
    }
    if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
    {
      idDelete(&G);
      return -1;
    }
    if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
    {
      idDelete(&G);
      return -1;
    }
  }
 
  if (TEST_OPT_PROT)
    PrintS("Computing Ufnarovski graph...\n");
 
  ideal standardWords;
  intvec* UG = lp_ufnarovskiGraph(G, standardWords);
  if (UG == NULL)
  {
    idDelete(&G);
    return -2;
  }
  if (errorreported)
  {
    delete UG;
    idDelete(&G);
    return -2;
  }
 
  if (TEST_OPT_PROT)
    Print("Ufnarovski graph is %dx%d.\n", UG->rows(), UG->cols());
 
  if (TEST_OPT_PROT)
    PrintS("Checking whether Ufnarovski graph is acyclic...\n");
 
  if (!isAcyclic(UG))
  {
    // in this case we have infinitely many normal words
    return -1;
  }
 
  std::vector<std::vector<int> > vvUG = iv2vv(UG);
  for (int i = 0; i < vvUG.size(); i++)
  {
    if (vvIsRowZero(vvUG, i) && vvIsColumnZero(vvUG, i)) // i is isolated vertex
    {
      vvDeleteRow(vvUG, i);
      vvDeleteColumn(vvUG, i);
      i--;
    }
  }
  if (TEST_OPT_PROT)
    Print("Simplified Ufnarovski graph to %dx%d.\n", (int)vvUG.size(), (int)vvUG.size());
 
  // for normal words of length >= maxDeg
  // use Ufnarovski graph
  if (TEST_OPT_PROT)
    PrintS("Computing normal words via Ufnarovski graph...\n");
  std::vector<std::vector<int> > UGpower = vvUG;
  long nUGpower = 1;
  while (!vvIsZero(UGpower))
  {
    if (TEST_OPT_PROT)
      PrintS("Start count graph entries.\n");
    for (int i = 0; i < UGpower.size(); i++)
    {
      for (int j = 0; j < UGpower[i].size(); j++)
      {
        numberOfNormalWords += UGpower[i][j];
      }
    }
 
    if (TEST_OPT_PROT)
    {
      PrintS("Done count graph entries.\n");
      Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1 + nUGpower);
    }
 
    if (TEST_OPT_PROT)
      PrintS("Start mat mult.\n");
    UGpower = vvMult(UGpower, vvUG); // TODO: avoid creation of new intvec
    if (TEST_OPT_PROT)
      PrintS("Done mat mult.\n");
    nUGpower++;
  }
 
  delete UG;
  idDelete(&G);
  return numberOfNormalWords;
}

lp_ufnarovskiGraph()

intvec * lp_ufnarovskiGraph	(	ideal	G,
		ideal &	standardWords
	)

Definition at line 1779 of file hdegree.cc.

{
  long l = 0;
  for (int i = 0; i < IDELEMS(G); i++)
    l = si_max(pTotaldegree(G->m[i]), l);
  l--;
  if (l <= 0)
  {
    WerrorS("Ufnarovski graph not implemented for l <= 0");
    return NULL;
  }
  int lV = currRing->isLPring;
 
  standardWords = lp_computeNormalWords(l, G);
 
  int n = IDELEMS(standardWords);
  intvec* UG = new intvec(n, n, 0);
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      poly v = standardWords->m[i];
      poly w = standardWords->m[j];
 
      // check whether v*x1 = x2*w (overlap)
      bool overlap = true;
      for (int k = 1; k <= (l - 1) * lV; k++)
      {
        if (pGetExp(v, k + lV) != pGetExp(w, k)) {
          overlap = false;
          break;
        }
      }
 
      if (overlap)
      {
        // create the overlap
        poly p = pMult(pCopy(v), p_LPVarAt(w, l, currRing));
 
        // check whether the overlap is normal
        bool normal = true;
        for (int k = 0; k < IDELEMS(G); k++)
        {
          if (p_LPDivisibleBy(G->m[k], p, currRing))
          {
            normal = false;
            break;
          }
        }
 
        if (normal)
        {
          IMATELEM(*UG, i + 1, j + 1) = 1;
        }
      }
    }
  }
  return UG;
}

scComputeHC()

void scComputeHC	(	ideal	s,
		ideal	Q,
		int	k,
		poly &	hEdge,
		ring	tailRing = currRing
	)

Definition at line 1079 of file hdegree.cc.

{
  id_TestTail(S, currRing, tailRing);
  if (Q!=NULL) id_TestTail(Q, currRing, tailRing);
 
  int  i;
  int  k = ak;
  #ifdef HAVE_RINGS
  if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1))
  {
    //consider just monic generators (over rings with zero-divisors)
    ideal SS=id_Copy(S,tailRing);
    for(i=0;i<=idElem(S);i++)
    {
      if((SS->m[i]!=NULL)
      && ((p_IsPurePower(SS->m[i],tailRing)==0)
        ||(!n_IsUnit(pGetCoeff(SS->m[i]), tailRing->cf))))
      {
        p_Delete(&SS->m[i],tailRing);
      }
    }
    S=id_Copy(SS,tailRing);
    idSkipZeroes(S);
  }
  #if 0
  printf("\nThis is HC:\n");
  for(int ii=0;ii<=idElem(S);ii++)
  {
    pWrite(S->m[ii]);
  }
  //getchar();
  #endif
  #endif
  if(idElem(S) == 0)
    return;
  hNvar = (currRing->N);
  hexist = hInit(S, Q, &hNexist, tailRing); // tailRing?
  if (k!=0)
    hComp(hexist, hNexist, k, hexist, &hNstc);
  else
    hNstc = hNexist;
  assume(hNexist > 0);
  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
  hvar = (varset)omAlloc((hNvar + 1) * sizeof(int));
  hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int));
  stcmem = hCreate(hNvar - 1);
  for (i = hNvar; i>0; i--)
    hvar[i] = i;
  hStaircase(hexist, &hNstc, hvar, hNvar);
  if ((hNvar > 2) && (hNstc > 10))
    hOrdSupp(hexist, hNstc, hvar, hNvar);
  memset(hpure, 0, (hNvar + 1) * sizeof(int));
  hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure);
  hLexS(hexist, hNstc, hvar, hNvar);
  if (hEdge!=NULL)
    pLmFree(hEdge);
  hEdge = pInit();
  pWork = pInit();
  hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge);
  pSetComp(hEdge,ak);
  hKill(stcmem, hNvar - 1);
  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
  omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int));
  omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int));
  hDelete(hexist, hNexist);
  pLmFree(pWork);
}

scDegree()

void scDegree	(	ideal	s,
		intvec *	modulweight,
		ideal	Q = NULL
	)

Definition at line 895 of file hdegree.cc.

{
  id_Test(S, currRing);
  if( Q!=NULL ) id_Test(Q, currRing);
 
  int co, mu, l;
  intvec *hseries2;
  intvec *hseries1 = hFirstSeries(S, modulweight, Q);
  if (errorreported) return;
  l = hseries1->length()-1;
  if (l > 1)
    hseries2 = hSecondSeries(hseries1);
  else
    hseries2 = hseries1;
  hDegreeSeries(hseries1, hseries2, &co, &mu);
  if ((l == 1) &&(mu == 0))
    scPrintDegree((currRing->N)+1, 0);
  else
    scPrintDegree(co, mu);
  if (l>1)
    delete hseries1;
  delete hseries2;
}

scDimInt()

int scDimInt	(	ideal	s,
		ideal	Q = NULL
	)

ideal dimension

Definition at line 77 of file hdegree.cc.

{
  id_Test(S, currRing);
  if( Q!=NULL ) id_Test(Q, currRing);
 
  int  mc;
  hexist = hInit(S, Q, &hNexist, currRing);
  if (!hNexist)
    return (currRing->N);
  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
  hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
  hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
  mc = hisModule;
  if (!mc)
  {
    hrad = hexist;
    hNrad = hNexist;
  }
  else
    hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
  radmem = hCreate((currRing->N) - 1);
  hCo = (currRing->N) + 1;
  loop
  {
    if (mc)
      hComp(hexist, hNexist, mc, hrad, &hNrad);
    if (hNrad)
    {
      hNvar = (currRing->N);
      hRadical(hrad, &hNrad, hNvar);
      hSupp(hrad, hNrad, hvar, &hNvar);
      if (hNvar)
      {
        memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
        hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
        hLexR(hrad, hNrad, hvar, hNvar);
        hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
      }
    }
    else
    {
      hCo = 0;
      break;
    }
    mc--;
    if (mc <= 0)
      break;
  }
  hKill(radmem, (currRing->N) - 1);
  omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
  omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
  hDelete(hexist, hNexist);
  if (hisModule)
    omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
  return (currRing->N) - hCo;
}

scDimIntRing()

int scDimIntRing	(	ideal	s,
		ideal	Q = NULL
	)

scDimInt for ring-coefficients

Definition at line 135 of file hdegree.cc.

{
#ifdef HAVE_RINGS
  if (rField_is_Ring(currRing))
  {
    int i = idPosConstant(vid);
    if ((i != -1) && (n_IsUnit(pGetCoeff(vid->m[i]),currRing->cf)))
    { /* ideal v contains unit; dim = -1 */
      return(-1);
    }
    ideal vv = id_Head(vid,currRing);
    idSkipZeroes(vv);
    i = idPosConstant(vid);
    int d;
    if(i == -1)
    {
      d = scDimInt(vv, Q);
      if(rField_is_Z(currRing))
        d++;
    }
    else
    {
      if(n_IsUnit(pGetCoeff(vv->m[i]),currRing->cf))
        d = -1;
      else
        d = scDimInt(vv, Q);
    }
    //Anne's Idea for std(4,2x) = 0 bug
    int dcurr = d;
    for(unsigned ii=0;ii<(unsigned)IDELEMS(vv);ii++)
    {
      if(vv->m[ii] != NULL && !n_IsUnit(pGetCoeff(vv->m[ii]),currRing->cf))
      {
        ideal vc = idCopy(vv);
        poly c = pInit();
        pSetCoeff0(c,nCopy(pGetCoeff(vv->m[ii])));
        idInsertPoly(vc,c);
        idSkipZeroes(vc);
        for(unsigned jj = 0;jj<(unsigned)IDELEMS(vc)-1;jj++)
        {
          if((vc->m[jj]!=NULL)
          && (n_DivBy(pGetCoeff(vc->m[jj]),pGetCoeff(c),currRing->cf)))
          {
            pDelete(&vc->m[jj]);
          }
        }
        idSkipZeroes(vc);
        i = idPosConstant(vc);
        if (i != -1) pDelete(&vc->m[i]);
        dcurr = scDimInt(vc, Q);
        // the following assumes the ground rings to be either zero- or one-dimensional
        if((i==-1) && rField_is_Z(currRing))
        {
          // should also be activated for other euclidean domains as groundfield
          dcurr++;
        }
        idDelete(&vc);
      }
      if(dcurr > d)
          d = dcurr;
    }
    idDelete(&vv);
    return d;
  }
#endif
  return scDimInt(vid,Q);
}

scIndIntvec()

intvec * scIndIntvec	(	ideal	S,
		ideal	Q = NULL
	)

Definition at line 285 of file hdegree.cc.

{
  id_Test(S, currRing);
  if( Q!=NULL ) id_Test(Q, currRing);
 
  intvec *Set=new intvec((currRing->N));
  int  mc,i;
  hexist = hInit(S, Q, &hNexist, currRing);
  if (hNexist==0)
  {
    for(i=0; i<(currRing->N); i++)
      (*Set)[i]=1;
    return Set;
  }
  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
  hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
  hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
  hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int));
  mc = hisModule;
  if (mc==0)
  {
    hrad = hexist;
    hNrad = hNexist;
  }
  else
    hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
  radmem = hCreate((currRing->N) - 1);
  hCo = (currRing->N) + 1;
  loop
  {
    if (mc!=0)
      hComp(hexist, hNexist, mc, hrad, &hNrad);
    if (hNrad!=0)
    {
      hNvar = (currRing->N);
      hRadical(hrad, &hNrad, hNvar);
      hSupp(hrad, hNrad, hvar, &hNvar);
      if (hNvar!=0)
      {
        memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
        hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
        hLexR(hrad, hNrad, hvar, hNvar);
        hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
      }
    }
    else
    {
      hCo = 0;
      break;
    }
    mc--;
    if (mc <= 0)
      break;
  }
  for(i=0; i<(currRing->N); i++)
    (*Set)[i] = hInd[i+1];
  hKill(radmem, (currRing->N) - 1);
  omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
  omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int));
  omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
  hDelete(hexist, hNexist);
  if (hisModule)
    omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
  return Set;
}

scKBase()

ideal scKBase	(	int	deg,
		ideal	s,
		ideal	Q = NULL,
		intvec *	mv = NULL
	)

Definition at line 1427 of file hdegree.cc.

{
  if( Q!=NULL) id_Test(Q, currRing);
 
  int  i, di;
  poly p;
 
  if (deg < 0)
  {
    di = scDimInt(s, Q);
    if (di != 0)
    {
      //Werror("KBase not finite");
      return idInit(1,s->rank);
    }
  }
  stcmem = hCreate((currRing->N) - 1);
  hexist = hInit(s, Q, &hNexist, currRing);
  p = last = pInit();
  /*pNext(p) = NULL;*/
  act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int));
  *act = 0;
  if (!hNexist)
  {
    scAll((currRing->N), deg);
    goto ende;
  }
  if (!hisModule)
  {
    if (deg < 0) scInKbase(hexist, hNexist, (currRing->N));
    else scDegKbase(hexist, hNexist, (currRing->N), deg);
  }
  else
  {
    hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
    for (i = 1; i <= hisModule; i++)
    {
      *act = i;
      hComp(hexist, hNexist, i, hstc, &hNstc);
      int deg_ei=deg;
      if (mv!=NULL) deg_ei -= (*mv)[i-1];
      if ((deg < 0) || (deg_ei>=0))
      {
        if (hNstc)
        {
          if (deg < 0) scInKbase(hstc, hNstc, (currRing->N));
          else scDegKbase(hstc, hNstc, (currRing->N), deg_ei);
        }
        else
          scAll((currRing->N), deg_ei);
      }
    }
    omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
  }
ende:
  hDelete(hexist, hNexist);
  omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int));
  hKill(stcmem, (currRing->N) - 1);
  pLmFree(&p);
  if (p == NULL)
    return idInit(1,s->rank);
 
  last = p;
  return scIdKbase(p, s->rank);
}

scMult0Int()

int scMult0Int	(	ideal	s,
		ideal	Q = NULL,
		const ring	tailRing = currRing
	)

Definition at line 993 of file hdegree.cc.

{
  id_TestTail(S, currRing, tailRing);
  if (Q!=NULL) id_TestTail(Q, currRing, tailRing);
 
  hDegree0(S, Q, tailRing);
  return hMu;
}

scMultInt()

int scMultInt	(	ideal	s,
		ideal	Q = NULL
	)

Definition at line 872 of file hdegree.cc.

{
  id_Test(S, currRing);
  if( Q!=NULL ) id_Test(Q, currRing);
 
  hDegree(S, Q);
  return hMu;
}

scPrintDegree()

void scPrintDegree	(	int	co,
		int	mu
	)

Definition at line 881 of file hdegree.cc.

{
  int di = (currRing->N)-co;
  if (currRing->OrdSgn == 1)
  {
    if (di>0)
      Print("// dimension (proj.)  = %d\n// degree (proj.)   = %d\n", di-1, mu);
    else
      Print("// dimension (affine) = 0\n// degree (affine)  = %d\n",       mu);
  }
  else
    Print("// dimension (local)   = %d\n// multiplicity = %d\n", di, mu);
}