simpleideals.cc File Reference

#include <misc/auxiliary.h>
#include <omalloc/omalloc.h>
#include <misc/options.h>
#include <misc/intvec.h>
#include "matpol.h"
#include "monomials/p_polys.h"
#include "weight.h"
#include "sbuckets.h"
#include "clapsing.h"
#include "simpleideals.h"

Go to the source code of this file.

Functions
ideal	idInit (int idsize, int rank)
void	idShow (const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
int	id_PosConstant (ideal id, const ring r)
	index of generator with leading term in ground ring (if any); otherwise -1 More...
ideal	id_MaxIdeal (const ring r)
void	id_Delete (ideal *h, ring r)
void	id_ShallowDelete (ideal *h, ring r)
void	idSkipZeroes (ideal ide)
int	idElem (const ideal F)
	number of non-zero polys in F More...
ideal	id_CopyFirstK (const ideal ide, const int k, const ring r)
void	id_Norm (ideal id, const ring r)
void	id_DelMultiples (ideal id, const ring r)
void	id_DelEquals (ideal id, const ring r)
void	id_DelLmEquals (ideal id, const ring r)
void	id_DelDiv (ideal id, const ring r)
BOOLEAN	id_IsConstant (ideal id, const ring r)
ideal	id_Copy (ideal h1, const ring r)
void	id_DBTest (ideal h1, int level, const char *f, const int l, const ring r, const ring tailRing)
static int	p_Comp_RevLex (poly a, poly b, BOOLEAN nolex, const ring R)
	3 for idSort: compare a and b revlex inclusive module comp. More...
intvec *	id_Sort (const ideal id, const BOOLEAN nolex, const ring r)
	sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE More...
ideal	id_SimpleAdd (ideal h1, ideal h2, const ring R)
BOOLEAN	idInsertPoly (ideal h1, poly h2)
BOOLEAN	id_InsertPolyWithTests (ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk, const ring r)
	insert h2 into h1 depending on the two boolean parameters: More...
ideal	id_Add (ideal h1, ideal h2, const ring r)
ideal	id_Mult (ideal h1, ideal h2, const ring r)
BOOLEAN	idIs0 (ideal h)
long	id_RankFreeModule (ideal s, ring lmRing, ring tailRing)
BOOLEAN	idIsModule (ideal id, ring r)
BOOLEAN	id_HomIdeal (ideal id, ideal Q, const ring r)
void	idInitChoise (int r, int beg, int end, BOOLEAN *endch, int *choise)
void	idGetNextChoise (int r, int end, BOOLEAN *endch, int *choise)
int	idGetNumberOfChoise (int t, int d, int begin, int end, int *choise)
int	binom (int n, int r)
ideal	id_FreeModule (int i, const ring r)
static void	makemonoms (int vars, int actvar, int deg, int monomdeg, const ring r)
ideal	id_MaxIdeal (int deg, const ring r)
static void	id_NextPotence (ideal given, ideal result, int begin, int end, int deg, int restdeg, poly ap, const ring r)
ideal	id_Power (ideal given, int exp, const ring r)
void	id_Compactify (ideal id, const ring r)
ideal	id_Head (ideal h, const ring r)
ideal	id_Homogen (ideal h, int varnum, const ring r)
ideal	id_Vec2Ideal (poly vec, const ring R)
ideal	id_Matrix2Module (matrix mat, const ring R)
matrix	id_Module2Matrix (ideal mod, const ring R)
matrix	id_Module2formatedMatrix (ideal mod, int rows, int cols, const ring R)
ideal	id_Subst (ideal id, int n, poly e, const ring r)
BOOLEAN	id_HomModule (ideal m, ideal Q, intvec **w, const ring R)
ideal	id_Jet (ideal i, int d, const ring R)
ideal	id_JetW (ideal i, int d, intvec *iv, const ring R)
int	id_ReadOutPivot (ideal arg, int *comp, const ring r)
intvec *	id_QHomWeight (ideal id, const ring r)
BOOLEAN	id_IsZeroDim (ideal I, const ring r)
void	id_Normalize (ideal I, const ring r)
	normialize all polys in id More...
int	id_MinDegW (ideal M, intvec *w, const ring r)
ideal	id_Transp (ideal a, const ring rRing)
ideal	id_TensorModuleMult (const int m, const ideal M, const ring rRing)
ideal	id_ChineseRemainder (ideal *xx, number *q, int rl, const ring r)
void	id_Shift (ideal M, int s, const ring r)

Variables
omBin	sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal))
static poly *	idpower
static int	idpowerpoint

Function Documentation

int binom	(	int	n,
		int	r
	)

Definition at line 877 of file simpleideals.cc.

{
  int i,result;

  if (r==0) return 1;
  if (n-r<r) return binom(n,n-r);
  result = n-r+1;
  for (i=2;i<=r;i++)
  {
    result *= n-r+i;
    if (result<0)
    {
      WarnS("overflow in binomials");
      return 0;
    }
    result /= i;
  }
  return result;
}

ideal id_Add	(	ideal	h1,
		ideal	h2,
		const ring	r
	)

Definition at line 656 of file simpleideals.cc.

{
  ideal result = id_SimpleAdd(h1,h2,r);
  id_Compactify(result,r);
  return result;
}

ideal id_ChineseRemainder	(	ideal *	xx,
		number *	q,
		int	rl,
		const ring	r
	)

Definition at line 1709 of file simpleideals.cc.

{
  int cnt=IDELEMS(xx[0])*xx[0]->nrows;
  ideal result=idInit(cnt,xx[0]->rank);
  result->nrows=xx[0]->nrows; // for lifting matrices
  result->ncols=xx[0]->ncols; // for lifting matrices
  int i,j;
  number *x=(number *)omAlloc(rl*sizeof(number));
  poly *p=(poly *)omAlloc(rl*sizeof(poly));
  for(i=cnt-1;i>=0;i--)
  {
    for(j=rl-1;j>=0;j--)
    {
      p[j]=xx[j]->m[i];
    }
    result->m[i]=p_ChineseRemainder(p,x,q,rl,r);
    for(j=rl-1;j>=0;j--)
    {
      xx[j]->m[i]=p[j];
    }
  }
  omFreeSize(p,rl*sizeof(poly));
  omFreeSize(x,rl*sizeof(number));
  for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]),r);
  omFreeSize(xx,rl*sizeof(ideal));
  return result;
}

void id_Compactify	(	ideal	id,
		const ring	r
	)

Definition at line 1052 of file simpleideals.cc.

{
  int i;
  BOOLEAN b=FALSE;

  i = IDELEMS(id)-1;
  while ((! b) && (i>=0))
  {
    b=p_IsUnit(id->m[i],r);
    i--;
  }
  if (b)
  {
    for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r);
    id->m[0]=p_One(r);
  }
  else
  {
    id_DelMultiples(id,r);
  }
  idSkipZeroes(id);
}

ideal id_Copy	(	ideal	h1,
		const ring	r
	)

Definition at line 398 of file simpleideals.cc.

{
  int i;
  ideal h2;

//#ifdef TEST
  if (h1 == NULL)
  {
    h2=idInit(1,1);
  }
  else
//#endif
  {
    h2=idInit(IDELEMS(h1),h1->rank);
    for (i=IDELEMS(h1)-1; i>=0; i--)
      h2->m[i] = p_Copy(h1->m[i],r);
  }
  return h2;
}

ideal id_CopyFirstK	(	const ideal	ide,
		const int	k,
		const ring	r
	)

Definition at line 217 of file simpleideals.cc.

{
  ideal newI = idInit(k, 0);
  for (int i = 0; i < k; i++)
    newI->m[i] = p_Copy(ide->m[i],r);
  return newI;
}

void id_DBTest	(	ideal	h1,
		int	level,
		const char *	f,
		const int	l,
		const ring	r,
		const ring	tailRing
	)

Definition at line 419 of file simpleideals.cc.

{
  int i;

  if (h1 != NULL)
  {
    // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix
    omCheckAddrSize(h1,sizeof(*h1));
    omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly));

    /* to be able to test matrices: */
    for (i=(h1->ncols*h1->nrows)-1; i>=0; i--)
      _pp_Test(h1->m[i], r, tailRing, level);

    int new_rk=id_RankFreeModule(h1, r, tailRing);
    if(new_rk > h1->rank)
    {
      dReportError("wrong rank %d (should be %d) in %s:%d\n",
                   h1->rank, new_rk, f,l);
      omPrintAddrInfo(stderr, h1, " for ideal");
      h1->rank=new_rk;
    }
  }
}

void id_DelDiv	(	ideal	id,
		const ring	r
	)

Definition at line 334 of file simpleideals.cc.

{
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i] != NULL)
    {
      for (j=k; j>i; j--)
      {
        if (id->m[j]!=NULL)
        {
#ifdef HAVE_RINGS
          if (rField_is_Ring(r))
          {
            if (p_DivisibleByRingCase(id->m[i], id->m[j],r))
            {
              p_Delete(&id->m[j],r);
            }
            else if (p_DivisibleByRingCase(id->m[j], id->m[i],r))
            {
              p_Delete(&id->m[i],r);
              break;
            }
          }
          else
          {
#endif
          /* the case of a ground field: */
          if (p_DivisibleBy(id->m[i], id->m[j],r))
          {
            p_Delete(&id->m[j],r);
          }
          else if (p_DivisibleBy(id->m[j], id->m[i],r))
          {
            p_Delete(&id->m[i],r);
            break;
          }
#ifdef HAVE_RINGS
          }
#endif
        }
      }
    }
  }
}

void id_DelEquals	(	ideal	id,
		const ring	r
	)

Definition at line 283 of file simpleideals.cc.

{
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i]!=NULL)
    {
      for (j=k; j>i; j--)
      {
        if ((id->m[j]!=NULL)
        && (p_EqualPolys(id->m[i], id->m[j],r)))
        {
          p_Delete(&id->m[j],r);
        }
      }
    }
  }
}

void id_Delete	(	ideal *	h,
		ring	r
	)

Definition at line 119 of file simpleideals.cc.

{
  int j,elems;
  if (*h == NULL)
    return;
  elems=j=(*h)->nrows*(*h)->ncols;
  if (j>0)
  {
    do
    {
      j--;
      poly pp=((*h)->m[j]);
      if (pp!=NULL) p_Delete(&pp, r);
    }
    while (j>0);
    omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
  }
  omFreeBin((ADDRESS)*h, sip_sideal_bin);
  *h=NULL;
}

void id_DelLmEquals	(	ideal	id,
		const ring	r
	)

Definition at line 306 of file simpleideals.cc.

{
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i] != NULL)
    {
      for (j=k; j>i; j--)
      {
        if ((id->m[j] != NULL)
        && p_LmEqual(id->m[i], id->m[j],r)
#ifdef HAVE_RINGS
        && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf)
#endif
        )
        {
          p_Delete(&id->m[j],r);
        }
      }
    }
  }
}

void id_DelMultiples	(	ideal	id,
		const ring	r
	)

Definition at line 244 of file simpleideals.cc.

{
  int i, j;
  int k = IDELEMS(id)-1;
  for (i=k; i>=0; i--)
  {
    if (id->m[i]!=NULL)
    {
      for (j=k; j>i; j--)
      {
        if (id->m[j]!=NULL)
        {
#ifdef HAVE_RINGS
          if (rField_is_Ring(r))
          {
            /* if id[j] = c*id[i] then delete id[j].
               In the below cases of a ground field, we
               check whether id[i] = c*id[j] and, if so,
               delete id[j] for historical reasons (so
               that previous output does not change) */
            if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r);
          }
          else
          {
            if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r);
          }
#else
          if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r);
#endif
        }
      }
    }
  }
}

ideal id_FreeModule	(	int	i,
		const ring	r
	)

Definition at line 900 of file simpleideals.cc.

{
  int j;
  ideal h;

  h=idInit(i,i);
  for (j=0; j<i; j++)
  {
    h->m[j] = p_One(r);
    p_SetComp(h->m[j],j+1,r);
    p_SetmComp(h->m[j],r);
  }
  return h;
}

ideal id_Head	(	ideal	h,
		const ring	r
	)

Definition at line 1078 of file simpleideals.cc.

{
  ideal m = idInit(IDELEMS(h),h->rank);
  int i;

  for (i=IDELEMS(h)-1;i>=0; i--)
  {
    if (h->m[i]!=NULL) m->m[i]=p_Head(h->m[i],r);
  }
  return m;
}

BOOLEAN id_HomIdeal	(	ideal	id,
		ideal	Q,
		const ring	r
	)

Definition at line 769 of file simpleideals.cc.

{
  int i;
  BOOLEAN     b;
  if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE;
  i = 0;
  b = TRUE;
  while ((i < IDELEMS(id)) && b)
  {
    b = p_IsHomogeneous(id->m[i],r);
    i++;
  }
  if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
  {
    i=0;
    while ((i < IDELEMS(Q)) && b)
    {
      b = p_IsHomogeneous(Q->m[i],r);
      i++;
    }
  }
  return b;
}

BOOLEAN id_HomModule	(	ideal	m,
		ideal	Q,
		intvec **	w,
		const ring	R
	)

Definition at line 1245 of file simpleideals.cc.

{
  if (w!=NULL) *w=NULL;
  if ((Q!=NULL) && (!id_HomIdeal(Q,NULL,R))) return FALSE;
  if (idIs0(m))
  {
    if (w!=NULL) (*w)=new intvec(m->rank);
    return TRUE;
  }

  long cmax=1,order=0,ord,* diff,diffmin=32000;
  int *iscom;
  int i;
  poly p=NULL;
  pFDegProc d;
  if (R->pLexOrder && (R->order[0]==ringorder_lp))
     d=p_Totaldegree;
  else
     d=R->pFDeg;
  int length=IDELEMS(m);
  poly* P=m->m;
  poly* F=(poly*)omAlloc(length*sizeof(poly));
  for (i=length-1;i>=0;i--)
  {
    p=F[i]=P[i];
    cmax=si_max(cmax,(long)p_MaxComp(p,R));
  }
  cmax++;
  diff = (long *)omAlloc0(cmax*sizeof(long));
  if (w!=NULL) *w=new intvec(cmax-1);
  iscom = (int *)omAlloc0(cmax*sizeof(int));
  i=0;
  while (i<=length)
  {
    if (i<length)
    {
      p=F[i];
      while ((p!=NULL) && (iscom[p_GetComp(p,R)]==0)) pIter(p);
    }
    if ((p==NULL) && (i<length))
    {
      i++;
    }
    else
    {
      if (p==NULL) /* && (i==length) */
      {
        i=0;
        while ((i<length) && (F[i]==NULL)) i++;
        if (i>=length) break;
        p = F[i];
      }
      //if (pLexOrder && (currRing->order[0]==ringorder_lp))
      //  order=pTotaldegree(p);
      //else
      //  order = p->order;
      //  order = pFDeg(p,currRing);
      order = d(p,R) +diff[p_GetComp(p,R)];
      //order += diff[pGetComp(p)];
      p = F[i];
//Print("Actual p=F[%d]: ",i);pWrite(p);
      F[i] = NULL;
      i=0;
    }
    while (p!=NULL)
    {
      if (R->pLexOrder && (R->order[0]==ringorder_lp))
        ord=p_Totaldegree(p,R);
      else
      //  ord = p->order;
        ord = R->pFDeg(p,R);
      if (iscom[p_GetComp(p,R)]==0)
      {
        diff[p_GetComp(p,R)] = order-ord;
        iscom[p_GetComp(p,R)] = 1;
/*
*PrintS("new diff: ");
*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
*PrintLn();
*PrintS("new iscom: ");
*for (j=0;j<cmax;j++) Print("%d ",iscom[j]);
*PrintLn();
*Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]);
*/
      }
      else
      {
/*
*PrintS("new diff: ");
*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
*PrintLn();
*Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]);
*/
        if (order != (ord+diff[p_GetComp(p,R)]))
        {
          omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
          omFreeSize((ADDRESS) diff,cmax*sizeof(long));
          omFreeSize((ADDRESS) F,length*sizeof(poly));
          delete *w;*w=NULL;
          return FALSE;
        }
      }
      pIter(p);
    }
  }
  omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
  omFreeSize((ADDRESS) F,length*sizeof(poly));
  for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]);
  for (i=1;i<cmax;i++)
  {
    if (diff[i]<diffmin) diffmin=diff[i];
  }
  if (w!=NULL)
  {
    for (i=1;i<cmax;i++)
    {
      (**w)[i-1]=(int)(diff[i]-diffmin);
    }
  }
  omFreeSize((ADDRESS) diff,cmax*sizeof(long));
  return TRUE;
}

ideal id_Homogen	(	ideal	h,
		int	varnum,
		const ring	r
	)

Definition at line 1090 of file simpleideals.cc.

{
  ideal m = idInit(IDELEMS(h),h->rank);
  int i;

  for (i=IDELEMS(h)-1;i>=0; i--)
  {
    m->m[i]=p_Homogen(h->m[i],varnum,r);
  }
  return m;
}

BOOLEAN id_InsertPolyWithTests	(	ideal	h1,
		const int	validEntries,
		const poly	h2,
		const bool	zeroOk,
		const bool	duplicateOk,
		const ring	r
	)

insert h2 into h1 depending on the two boolean parameters:

• if zeroOk is true, then h2 will also be inserted when it is zero
• if duplicateOk is true, then h2 will also be inserted when it is already present in h1 return TRUE iff h2 was indeed inserted

Definition at line 629 of file simpleideals.cc.

{
  if ((!zeroOk) && (h2 == NULL)) return FALSE;
  if (!duplicateOk)
  {
    bool h2FoundInH1 = false;
    int i = 0;
    while ((i < validEntries) && (!h2FoundInH1))
    {
      h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r);
      i++;
    }
    if (h2FoundInH1) return FALSE;
  }
  if (validEntries == IDELEMS(h1))
  {
    pEnlargeSet(&(h1->m), IDELEMS(h1), 16);
    IDELEMS(h1) += 16;
  }
  h1->m[validEntries] = h2;
  return TRUE;
}

BOOLEAN id_IsConstant	(	ideal	id,
		const ring	r
	)

Definition at line 384 of file simpleideals.cc.

{
  int k;
  for (k = IDELEMS(id)-1; k>=0; k--)
  {
    if (!p_IsConstantPoly(id->m[k],r))
      return FALSE;
  }
  return TRUE;
}

BOOLEAN id_IsZeroDim	(	ideal	I,
		const ring	r
	)

Definition at line 1535 of file simpleideals.cc.

{
  BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN));
  int i,n;
  poly po;
  BOOLEAN res=TRUE;
  for(i=IDELEMS(I)-1;i>=0;i--)
  {
    po=I->m[i];
    if ((po!=NULL) &&((n=p_IsPurePower(po,r))!=0)) UsedAxis[n-1]=TRUE;
  }
  for(i=rVar(r)-1;i>=0;i--)
  {
    if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim.
  }
  omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN));
  return res;
}

ideal id_Jet	(	ideal	i,
		int	d,
		const ring	R
	)

Definition at line 1368 of file simpleideals.cc.

{
  ideal r=idInit((i->nrows)*(i->ncols),i->rank);
  r->nrows = i-> nrows;
  r->ncols = i-> ncols;
  //r->rank = i-> rank;
  int k;
  for(k=(i->nrows)*(i->ncols)-1;k>=0; k--)
  {
    r->m[k]=pp_Jet(i->m[k],d,R);
  }
  return r;
}

ideal id_JetW	(	ideal	i,
		int	d,
		intvec *	iv,
		const ring	R
	)

Definition at line 1382 of file simpleideals.cc.

{
  ideal r=idInit(IDELEMS(i),i->rank);
  if (ecartWeights!=NULL)
  {
    WerrorS("cannot compute weighted jets now");
  }
  else
  {
    short *w=iv2array(iv,R);
    int k;
    for(k=0; k<IDELEMS(i); k++)
    {
      r->m[k]=pp_JetW(i->m[k],d,w,R);
    }
    omFreeSize((ADDRESS)w,(rVar(R)+1)*sizeof(short));
  }
  return r;
}

ideal id_Matrix2Module	(	matrix	mat,
		const ring	R
	)

Definition at line 1114 of file simpleideals.cc.

{
  int mc=MATCOLS(mat);
  int mr=MATROWS(mat);
  ideal result = idInit(si_max(mc,1),si_max(mr,1));
  int i,j,l;
  poly h;
  sBucket_pt bucket = sBucketCreate(R);

  for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */
  {
    for (i=1;i<=mr /*MATROWS(mat)*/;i++)
    {
      h = MATELEM(mat,i,j+1);
      if (h!=NULL)
      {
        l=pLength(h);
        MATELEM(mat,i,j+1)=NULL;
        p_SetCompP(h,i, R);
        sBucket_Merge_p(bucket, h, l);
      }
    }
    sBucketClearMerge(bucket, &(result->m[j]), &l);
  }
  sBucketDestroy(&bucket);

  // obachman: need to clean this up
  id_Delete((ideal*) &mat,R);
  return result;
}

ideal id_MaxIdeal

(

const ring

r

)

Definition at line 101 of file simpleideals.cc.

{
  int l;
  ideal hh=NULL;

  hh=idInit(rVar(r),1);
  for (l=0; l<rVar(r); l++)
  {
    hh->m[l] = p_One(r);
    p_SetExp(hh->m[l],l+1,1,r);
    p_Setm(hh->m[l],r);
  }
  return hh;
}

ideal id_MaxIdeal	(	int	deg,
		const ring	r
	)

Definition at line 970 of file simpleideals.cc.

{
  if (deg < 0)
  {
    WarnS("maxideal: power must be non-negative");
  }
  if (deg < 1)
  {
    ideal I=idInit(1,1);
    I->m[0]=p_One(r);
    return I;
  }
  if (deg == 1)
  {
    return id_MaxIdeal(r);
  }

  int vars = rVar(r);
  int i = binom(vars+deg-1,deg);
  if (i<=0) return idInit(1,1);
  ideal id=idInit(i,1);
  idpower = id->m;
  idpowerpoint = 0;
  makemonoms(vars,1,deg,0,r);
  idpower = NULL;
  idpowerpoint = 0;
  return id;
}

int id_MinDegW	(	ideal	M,
		intvec *	w,
		const ring	r
	)

Definition at line 1564 of file simpleideals.cc.

{
  int d=-1;
  for(int i=0;i<IDELEMS(M);i++)
  {
    if (M->m[i]!=NULL)
    {
      int d0=p_MinDeg(M->m[i],w,r);
      if(-1<d0&&((d0<d)||(d==-1)))
        d=d0;
    }
  }
  return d;
}

matrix id_Module2formatedMatrix	(	ideal	mod,
		int	rows,
		int	cols,
		const ring	R
	)

Definition at line 1194 of file simpleideals.cc.

{
  matrix result = mpNew(rows,cols);
  int i,cp,r=id_RankFreeModule(mod,R),c=IDELEMS(mod);
  poly p,h;

  if (r>rows) r = rows;
  if (c>cols) c = cols;
  for(i=0;i<c;i++)
  {
    p=pReverse(mod->m[i]);
    mod->m[i]=NULL;
    while (p!=NULL)
    {
      h=p;
      pIter(p);
      pNext(h)=NULL;
      cp = p_GetComp(h,R);
      if (cp<=r)
      {
        p_SetComp(h,0,R);
        p_SetmComp(h,R);
        MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R);
      }
      else
        p_Delete(&h,R);
    }
  }
  id_Delete(&mod,R);
  return result;
}

matrix id_Module2Matrix	(	ideal	mod,
		const ring	R
	)

Definition at line 1148 of file simpleideals.cc.

{
  matrix result = mpNew(mod->rank,IDELEMS(mod));
  long i; long cp;
  poly p,h;

  for(i=0;i<IDELEMS(mod);i++)
  {
    p=pReverse(mod->m[i]);
    mod->m[i]=NULL;
    while (p!=NULL)
    {
      h=p;
      pIter(p);
      pNext(h)=NULL;
      cp = si_max((long)1,p_GetComp(h, R));     // if used for ideals too
      //cp = p_GetComp(h,R);
      p_SetComp(h,0,R);
      p_SetmComp(h,R);
#ifdef TEST
      if (cp>mod->rank)
      {
        Print("## inv. rank %ld -> %ld\n",mod->rank,cp);
        int k,l,o=mod->rank;
        mod->rank=cp;
        matrix d=mpNew(mod->rank,IDELEMS(mod));
        for (l=1; l<=o; l++)
        {
          for (k=1; k<=IDELEMS(mod); k++)
          {
            MATELEM(d,l,k)=MATELEM(result,l,k);
            MATELEM(result,l,k)=NULL;
          }
        }
        id_Delete((ideal *)&result,R);
        result=d;
      }
#endif
      MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R);
    }
  }
  // obachman 10/99: added the following line, otherwise memory leack!
  id_Delete(&mod,R);
  return result;
}

ideal id_Mult	(	ideal	h1,
		ideal	h2,
		const ring	r
	)

Definition at line 666 of file simpleideals.cc.

{
  int i,j,k;
  ideal  hh;

  j = IDELEMS(h1);
  while ((j > 0) && (h1->m[j-1] == NULL)) j--;
  i = IDELEMS(h2);
  while ((i > 0) && (h2->m[i-1] == NULL)) i--;
  j = j * i;
  if (j == 0)
    hh = idInit(1,1);
  else
    hh=idInit(j,1);
  if (h1->rank<h2->rank)
    hh->rank = h2->rank;
  else
    hh->rank = h1->rank;
  if (j==0) return hh;
  k = 0;
  for (i=0; i<IDELEMS(h1); i++)
  {
    if (h1->m[i] != NULL)
    {
      for (j=0; j<IDELEMS(h2); j++)
      {
        if (h2->m[j] != NULL)
        {
          hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],r);
          k++;
        }
      }
    }
  }
  {
    id_Compactify(hh,r);
    return hh;
  }
}

static void id_NextPotence ( ideal  given, ideal  result, int  begin, int  end, int  deg, int  restdeg, poly  ap, const ring  r  )

static

Definition at line 999 of file simpleideals.cc.

{
  poly p;
  int i;

  p = p_Power(p_Copy(given->m[begin],r),restdeg,r);
  i = result->nrows;
  result->m[i] = p_Mult_q(p_Copy(ap,r),p,r);
//PrintS(".");
  (result->nrows)++;
  if (result->nrows >= IDELEMS(result))
  {
    pEnlargeSet(&(result->m),IDELEMS(result),16);
    IDELEMS(result) += 16;
  }
  if (begin == end) return;
  for (i=restdeg-1;i>0;i--)
  {
    p = p_Power(p_Copy(given->m[begin],r),i,r);
    p = p_Mult_q(p_Copy(ap,r),p,r);
    id_NextPotence(given, result, begin+1, end, deg, restdeg-i, p,r);
    p_Delete(&p,r);
  }
  id_NextPotence(given, result, begin+1, end, deg, restdeg, ap,r);
}

void id_Norm	(	ideal	id,
		const ring	r
	)

Definition at line 229 of file simpleideals.cc.

{
  for (int i=IDELEMS(id)-1; i>=0; i--)
  {
    if (id->m[i] != NULL)
    {
      p_Norm(id->m[i],r);
    }
  }
}

void id_Normalize	(	ideal	I,
		const ring	r
	)

normialize all polys in id

Definition at line 1554 of file simpleideals.cc.

{
  if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */
  int i;
  for(i=I->nrows*I->ncols-1;i>=0;i--)
  {
    p_Normalize(I->m[i],r);
  }
}

int id_PosConstant	(	ideal	id,
		const ring	r
	)

index of generator with leading term in ground ring (if any); otherwise -1

Definition at line 81 of file simpleideals.cc.

{
  id_Test(id, r);
  const int N = IDELEMS(id) - 1;
  const poly * m = id->m + N;

  for (int k = N; k >= 0; --k, --m)
  {
    const poly p = *m;
    if (p!=NULL)
       if (p_LmIsConstantComp(p, r) == TRUE)
         return k;
  }

  return -1;
}

ideal id_Power	(	ideal	given,
		int	exp,
		const ring	r
	)

Definition at line 1026 of file simpleideals.cc.

{
  ideal result,temp;
  poly p1;
  int i;

  if (idIs0(given)) return idInit(1,1);
  temp = id_Copy(given,r);
  idSkipZeroes(temp);
  i = binom(IDELEMS(temp)+exp-1,exp);
  result = idInit(i,1);
  result->nrows = 0;
//Print("ideal contains %d elements\n",i);
  p1=p_One(r);
  id_NextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1,r);
  p_Delete(&p1,r);
  id_Delete(&temp,r);
  result->nrows = 1;
  id_DelEquals(result,r);
  idSkipZeroes(result);
  return result;
}

intvec* id_QHomWeight	(	ideal	id,
		const ring	r
	)

Definition at line 1488 of file simpleideals.cc.

{
  poly head, tail;
  int k;
  int in=IDELEMS(id)-1, ready=0, all=0,
      coldim=rVar(r), rowmax=2*coldim;
  if (in<0) return NULL;
  intvec *imat=new intvec(rowmax+1,coldim,0);

  do
  {
    head = id->m[in--];
    if (head!=NULL)
    {
      tail = pNext(head);
      while (tail!=NULL)
      {
        all++;
        for (k=1;k<=coldim;k++)
          IMATELEM(*imat,all,k) = p_GetExpDiff(head,tail,k,r);
        if (all==rowmax)
        {
          ivTriangIntern(imat, ready, all);
          if (ready==coldim)
          {
            delete imat;
            return NULL;
          }
        }
        pIter(tail);
      }
    }
  } while (in>=0);
  if (all>ready)
  {
    ivTriangIntern(imat, ready, all);
    if (ready==coldim)
    {
      delete imat;
      return NULL;
    }
  }
  intvec *result = ivSolveKern(imat, ready);
  delete imat;
  return result;
}

long id_RankFreeModule	(	ideal	s,
		ring	lmRing,
		ring	tailRing
	)

Definition at line 728 of file simpleideals.cc.

{
  if (s!=NULL)
  {
    long  j=0;

    if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing))
    {
      poly *p=s->m;
      for (unsigned int l=IDELEMS(s); l != 0; --l, ++p)
      {
        if (*p!=NULL)
        {
          pp_Test(*p, lmRing, tailRing);
          const long k = p_MaxComp(*p, lmRing, tailRing);
          if (k>j) j = k;
        }
      }
    }
    return j;
  }
  return -1;
}

int id_ReadOutPivot	(	ideal	arg,
		int *	comp,
		const ring	r
	)

Definition at line 1406 of file simpleideals.cc.

{
  if (idIs0(arg)) return -1;
  int i=0,j, generator=-1;
  int rk_arg=arg->rank; //idRankFreeModule(arg);
  int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int));
  poly p;

  while ((generator<0) && (i<IDELEMS(arg)))
  {
    memset(componentIsUsed,0,(rk_arg+1)*sizeof(int));
    p = arg->m[i];
    while (p!=NULL)
    {
      j = p_GetComp(p,r);
      if (componentIsUsed[j]==0)
      {
#ifdef HAVE_RINGS
        if (p_LmIsConstantComp(p,r) &&
            (!rField_is_Ring(r) || n_IsUnit(pGetCoeff(p),r->cf)))
        {
#else
        if (p_LmIsConstantComp(p,r))
        {
#endif
          generator = i;
          componentIsUsed[j] = 1;
        }
        else
        {
          componentIsUsed[j] = -1;
        }
      }
      else if (componentIsUsed[j]>0)
      {
        (componentIsUsed[j])++;
      }
      pIter(p);
    }
    i++;
  }
  i = 0;
  *comp = -1;
  for (j=0;j<=rk_arg;j++)
  {
    if (componentIsUsed[j]>0)
    {
      if ((*comp==-1) || (componentIsUsed[j]<i))
      {
        *comp = j;
        i= componentIsUsed[j];
      }
    }
  }
  omFree(componentIsUsed);
  return generator;
}

void id_ShallowDelete	(	ideal *	h,
		ring	r
	)

Definition at line 144 of file simpleideals.cc.

{
  int j,elems;
  if (*h == NULL)
    return;
  elems=j=(*h)->nrows*(*h)->ncols;
  if (j>0)
  {
    do
    {
      p_ShallowDelete(&((*h)->m[--j]), r);
    }
    while (j>0);
    omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
  }
  omFreeBin((ADDRESS)*h, sip_sideal_bin);
  *h=NULL;
}

void id_Shift	(	ideal	M,
		int	s,
		const ring	r
	)

Definition at line 1737 of file simpleideals.cc.

{
  for(int i=IDELEMS(M)-1; i>=0;i--)
  {
    p_Shift(&(M->m[i]),s,r);
  }
  M->rank += s;
}

ideal id_SimpleAdd	(	ideal	h1,
		ideal	h2,
		const ring	R
	)

Definition at line 575 of file simpleideals.cc.

{
  int i,j,r,l;
  ideal result;

  if (h1==NULL) return id_Copy(h2,R);
  if (h2==NULL) return id_Copy(h1,R);
  j = IDELEMS(h1)-1;
  while ((j >= 0) && (h1->m[j] == NULL)) j--;
  i = IDELEMS(h2)-1;
  while ((i >= 0) && (h2->m[i] == NULL)) i--;
  r = si_max(h1->rank,h2->rank);
  if (i+j==(-2))
    return idInit(1,r);
  else
    result=idInit(i+j+2,r);
  for (l=j; l>=0; l--)
  {
    result->m[l] = p_Copy(h1->m[l],R);
  }
  r = i+j+1;
  for (l=i; l>=0; l--, r--)
  {
    result->m[r] = p_Copy(h2->m[l],R);
  }
  return result;
}

intvec* id_Sort	(	const ideal	id,
		const BOOLEAN	nolex,
		const ring	r
	)

sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE

Definition at line 480 of file simpleideals.cc.

{
  intvec * result = new intvec(IDELEMS(id));
  int i, j, actpos=0, newpos;
  int diff, olddiff, lastcomp, newcomp;
  BOOLEAN notFound;

  for (i=0;i<IDELEMS(id);i++)
  {
    if (id->m[i]!=NULL)
    {
      notFound = TRUE;
      newpos = actpos / 2;
      diff = (actpos+1) / 2;
      diff = (diff+1) / 2;
      lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
      if (lastcomp<0)
      {
        newpos -= diff;
      }
      else if (lastcomp>0)
      {
        newpos += diff;
      }
      else
      {
        notFound = FALSE;
      }
      //while ((newpos>=0) && (newpos<actpos) && (notFound))
      while (notFound && (newpos>=0) && (newpos<actpos))
      {
        newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
        olddiff = diff;
        if (diff>1)
        {
          diff = (diff+1) / 2;
          if ((newcomp==1)
          && (actpos-newpos>1)
          && (diff>1)
          && (newpos+diff>=actpos))
          {
            diff = actpos-newpos-1;
          }
          else if ((newcomp==-1)
          && (diff>1)
          && (newpos<diff))
          {
            diff = newpos;
          }
        }
        if (newcomp<0)
        {
          if ((olddiff==1) && (lastcomp>0))
            notFound = FALSE;
          else
            newpos -= diff;
        }
        else if (newcomp>0)
        {
          if ((olddiff==1) && (lastcomp<0))
          {
            notFound = FALSE;
            newpos++;
          }
          else
          {
            newpos += diff;
          }
        }
        else
        {
          notFound = FALSE;
        }
        lastcomp = newcomp;
        if (diff==0) notFound=FALSE; /*hs*/
      }
      if (newpos<0) newpos = 0;
      if (newpos>actpos) newpos = actpos;
      while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0))
        newpos++;
      for (j=actpos;j>newpos;j--)
      {
        (*result)[j] = (*result)[j-1];
      }
      (*result)[newpos] = i;
      actpos++;
    }
  }
  for (j=0;j<actpos;j++) (*result)[j]++;
  return result;
}

ideal id_Subst	(	ideal	id,
		int	n,
		poly	e,
		const ring	r
	)

Definition at line 1230 of file simpleideals.cc.

{
  int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
  ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id));

  res->rank = id->rank;
  for(k--;k>=0;k--)
  {
    res->m[k]=p_Subst(id->m[k],n,e,r);
    id->m[k]=NULL;
  }
  id_Delete(&id,r);
  return res;
}

ideal id_TensorModuleMult	(	const int	m,
		const ideal	M,
		const ring	rRing
	)

Definition at line 1629 of file simpleideals.cc.

{
// #ifdef DEBU
//  WarnS("tensorModuleMult!!!!");

  assume(m > 0);
  assume(M != NULL);

  const int n = rRing->N;

  assume(M->rank <= m * n);

  const int k = IDELEMS(M);

  ideal idTemp =  idInit(k,m); // = {f_1, ..., f_k }

  for( int i = 0; i < k; i++ ) // for every w \in M
  {
    poly pTempSum = NULL;

    poly w = M->m[i];

    while(w != NULL) // for each term of w...
    {
      poly h = p_Head(w, rRing);

      const int  gen = p_GetComp(h, rRing); // 1 ...

      assume(gen > 0);
      assume(gen <= n*m);

      // TODO: write a formula with %, / instead of while!
      /*
      int c = gen;
      int v = 1;
      while(c > m)
      {
        c -= m;
        v++;
      }
      */

      int cc = gen % m;
      if( cc == 0) cc = m;
      int vv = 1 + (gen - cc) / m;

//      assume( cc == c );
//      assume( vv == v );

      //  1<= c <= m
      assume( cc > 0 );
      assume( cc <= m );

      assume( vv > 0 );
      assume( vv <= n );

      assume( (cc + (vv-1)*m) == gen );

      p_IncrExp(h, vv, rRing); // h *= var(j) && //      p_AddExp(h, vv, 1, rRing);
      p_SetComp(h, cc, rRing);

      p_Setm(h, rRing);         // addjust degree after the previous steps!

      pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!!

      pIter(w);
    }

    idTemp->m[i] = pTempSum;
  }

  // simplify idTemp???

  ideal idResult = id_Transp(idTemp, rRing);

  id_Delete(&idTemp, rRing);

  return(idResult);
}

ideal id_Transp	(	ideal	a,
		const ring	rRing
	)

Definition at line 1584 of file simpleideals.cc.

{
  int r = a->rank, c = IDELEMS(a);
  ideal b =  idInit(r,c);

  for (int i=c; i>0; i--)
  {
    poly p=a->m[i-1];
    while(p!=NULL)
    {
      poly h=p_Head(p, rRing);
      int co=p_GetComp(h, rRing)-1;
      p_SetComp(h, i, rRing);
      p_Setm(h, rRing);
      b->m[co] = p_Add_q(b->m[co], h, rRing);
      pIter(p);
    }
  }
  return b;
}

ideal id_Vec2Ideal	(	poly	vec,
		const ring	R
	)

Definition at line 1103 of file simpleideals.cc.

{
   ideal result=idInit(1,1);
   omFree((ADDRESS)result->m);
   result->m=NULL; // remove later
   p_Vec2Polys(vec, &(result->m), &(IDELEMS(result)),R);
   return result;
}

int idElem

(

const ideal

F

)

number of non-zero polys in F

Definition at line 200 of file simpleideals.cc.

{
  int i=0,j=IDELEMS(F)-1;

  while(j>=0)
  {
    if ((F->m)[j]!=NULL) i++;
    j--;
  }
  return i;
}

void idGetNextChoise	(	int	r,
		int	end,
		BOOLEAN *	endch,
		int *	choise
	)

Definition at line 819 of file simpleideals.cc.

{
  int i = r-1,j;
  while ((i >= 0) && (choise[i] == end))
  {
    i--;
    end--;
  }
  if (i == -1)
    *endch = TRUE;
  else
  {
    choise[i]++;
    for (j=i+1; j<r; j++)
    {
      choise[j] = choise[i]+j-i;
    }
    *endch = FALSE;
  }
}

int idGetNumberOfChoise	(	int	t,
		int	d,
		int	begin,
		int	end,
		int *	choise
	)

Definition at line 845 of file simpleideals.cc.

{
  int * localchoise,i,result=0;
  BOOLEAN b=FALSE;

  if (d<=1) return 1;
  localchoise=(int*)omAlloc((d-1)*sizeof(int));
  idInitChoise(d-1,begin,end,&b,localchoise);
  while (!b)
  {
    result++;
    i = 0;
    while ((i<t) && (localchoise[i]==choise[i])) i++;
    if (i>=t)
    {
      i = t+1;
      while ((i<d) && (localchoise[i-1]==choise[i])) i++;
      if (i>=d)
      {
        omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
        return result;
      }
    }
    idGetNextChoise(d-1,end,&b,localchoise);
  }
  omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
  return 0;
}

ideal idInit	(	int	idsize,
		int	rank
	)

Definition at line 40 of file simpleideals.cc.

{
  /*- initialise an ideal -*/
  ideal hh = (ideal )omAllocBin(sip_sideal_bin);
  hh->nrows = 1;
  hh->rank = rank;
  IDELEMS(hh) = idsize;
  if (idsize>0)
  {
    hh->m = (poly *)omAlloc0(idsize*sizeof(poly));
  }
  else
    hh->m=NULL;
  return hh;
}

void idInitChoise	(	int	r,
		int	beg,
		int	end,
		BOOLEAN *	endch,
		int *	choise
	)

Definition at line 797 of file simpleideals.cc.

{
  /*returns the first choise of r numbers between beg and end*/
  int i;
  for (i=0; i<r; i++)
  {
    choise[i] = 0;
  }
  if (r <= end-beg+1)
    for (i=0; i<r; i++)
    {
      choise[i] = beg+i;
    }
  if (r > end-beg+1)
    *endch = TRUE;
  else
    *endch = FALSE;
}

BOOLEAN idInsertPoly	(	ideal	h1,
		poly	h2
	)

Definition at line 607 of file simpleideals.cc.

{
  if (h2==NULL) return FALSE;
  int j = IDELEMS(h1)-1;
  while ((j >= 0) && (h1->m[j] == NULL)) j--;
  j++;
  if (j==IDELEMS(h1))
  {
    pEnlargeSet(&(h1->m),IDELEMS(h1),16);
    IDELEMS(h1)+=16;
  }
  h1->m[j]=h2;
  return TRUE;
}

BOOLEAN idIs0

(

ideal

h

)

Definition at line 709 of file simpleideals.cc.

{
  int i;

  if (h == NULL) return TRUE;
  i = IDELEMS(h)-1;
  while ((i >= 0) && (h->m[i] == NULL))
  {
    i--;
  }
  if (i < 0)
    return TRUE;
  else
    return FALSE;
}

BOOLEAN idIsModule	(	ideal	id,
		ring	r
	)

Definition at line 752 of file simpleideals.cc.

{
  if (id != NULL && rRing_has_Comp(r))
  {
    int j, l = IDELEMS(id);
    for (j=0; j<l; j++)
    {
      if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE;
    }
  }
  return FALSE;
}

void idShow	(	const ideal	id,
		const ring	lmRing,
		const ring	tailRing,
		const int	debugPrint
	)

Definition at line 58 of file simpleideals.cc.

{
  assume( debugPrint >= 0 );

  if( id == NULL )
    PrintS("(NULL)");
  else
  {
    Print("Module of rank %ld,real rank %ld and %d generators.\n",
          id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id));

    int j = (id->ncols*id->nrows) - 1;
    while ((j > 0) && (id->m[j]==NULL)) j--;
    for (int i = 0; i <= j; i++)
    {
      Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint);
    }
  }
}

void idSkipZeroes

(

ideal

ide

)

Definition at line 166 of file simpleideals.cc.

{
  int k;
  int j = -1;
  BOOLEAN change=FALSE;
  for (k=0; k<IDELEMS(ide); k++)
  {
    if (ide->m[k] != NULL)
    {
      j++;
      if (change)
      {
        ide->m[j] = ide->m[k];
      }
    }
    else
    {
      change=TRUE;
    }
  }
  if (change)
  {
    if (j == -1)
      j = 0;
    else
    {
      for (k=j+1; k<IDELEMS(ide); k++)
        ide->m[k] = NULL;
    }
    pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide));
    IDELEMS(ide) = j+1;
  }
}

static void makemonoms ( int  vars, int  actvar, int  deg, int  monomdeg, const ring  r  )

static

Definition at line 927 of file simpleideals.cc.

{
  poly p;
  int i=0;

  if ((idpowerpoint == 0) && (actvar ==1))
  {
    idpower[idpowerpoint] = p_One(r);
    monomdeg = 0;
  }
  while (i<=deg)
  {
    if (deg == monomdeg)
    {
      p_Setm(idpower[idpowerpoint],r);
      idpowerpoint++;
      return;
    }
    if (actvar == vars)
    {
      p_SetExp(idpower[idpowerpoint],actvar,deg-monomdeg,r);
      p_Setm(idpower[idpowerpoint],r);
      p_Test(idpower[idpowerpoint],r);
      idpowerpoint++;
      return;
    }
    else
    {
      p = p_Copy(idpower[idpowerpoint],r);
      makemonoms(vars,actvar+1,deg,monomdeg,r);
      idpower[idpowerpoint] = p;
    }
    monomdeg++;
    p_SetExp(idpower[idpowerpoint],actvar,p_GetExp(idpower[idpowerpoint],actvar,r)+1,r);
    p_Setm(idpower[idpowerpoint],r);
    p_Test(idpower[idpowerpoint],r);
    i++;
  }
}

static int p_Comp_RevLex ( poly  a, poly  b, BOOLEAN  nolex, const ring  R  )

static

3 for idSort: compare a and b revlex inclusive module comp.

Definition at line 446 of file simpleideals.cc.

{
  if (b==NULL) return 1;
  if (a==NULL) return -1;

  if (nolex)
  {
    int r=p_LmCmp(a,b,R);
    if (r!=0) return r;
    number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf);
    r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */
    n_Delete(&h, R->cf);
    return r;
  }
  int l=rVar(R);
  while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--;
  if (l==0)
  {
    if (p_GetComp(a,R)==p_GetComp(b,R))
    {
      number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf);
      int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */
      n_Delete(&h,R->cf);
      return r;
    }
    if (p_GetComp(a,R)>p_GetComp(b,R)) return 1;
  }
  else if (p_GetExp(a,l,R)>p_GetExp(b,l,R))
    return 1;
  return -1;
}

Variable Documentation

poly* idpower

static

Definition at line 32 of file simpleideals.cc.

int idpowerpoint

static

Definition at line 34 of file simpleideals.cc.

omBin sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal))

Definition at line 30 of file simpleideals.cc.