kutil.cc

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/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/*
* ABSTRACT: kernel: utils for kStd
*/
 
// #define PDEBUG 2
// #define PDIV_DEBUG
#define KUTIL_CC
 
#define MYTEST 0
 
//All vs Just strategy over rings:
// 1 - Just
// 0 - All
#define ALL_VS_JUST 0
//Extended Spoly Strategy:
// 0 - new gen sig
// 1 - ann*old sig
#define EXT_POLY_NEW 0
 
#include "kernel/mod2.h"
 
#include "misc/mylimits.h"
#include "misc/options.h"
#include "polys/nc/nc.h"
#include "polys/nc/sca.h"
#include "polys/weight.h" /* for kDebugPrint: maxdegreeWecart*/
 
#include <stdlib.h>
#include <string.h>
 
#ifdef KDEBUG
#undef KDEBUG
#define KDEBUG 2
#endif
 
#ifdef DEBUGF5
#undef DEBUGF5
//#define DEBUGF5 1
#endif
 
// define if enterL, enterT should use memmove instead of doing it manually
// on topgun, this is slightly faster (see monodromy_l.tst, homog_gonnet.sing)
#ifndef SunOS_4
#define ENTER_USE_MEMMOVE
#endif
 
// define, if the my_memmove inlines should be used instead of
// system memmove -- it does not seem to pay off, though
// #define ENTER_USE_MYMEMMOVE
 
#include "kernel/GBEngine/kutil.h"
#include "polys/kbuckets.h"
#include "coeffs/numbers.h"
#include "kernel/polys.h"
#include "polys/monomials/ring.h"
#include "kernel/ideals.h"
#include "kernel/combinatorics/stairc.h"
#include "kernel/GBEngine/kstd1.h"
#include "polys/operations/pShallowCopyDelete.h"
 
#ifdef HAVE_SHIFTBBA
#include "polys/shiftop.h"
#endif
 
#include "polys/prCopy.h"
 
#ifdef HAVE_RATGRING
#include "kernel/GBEngine/ratgring.h"
#endif
 
#ifdef DEBUGF5
#undef DEBUGF5
#define DEBUGF5 2
#endif
 
VAR denominator_list DENOMINATOR_LIST=NULL;
 
 
#ifdef ENTER_USE_MYMEMMOVE
inline void _my_memmove_d_gt_s(unsigned long* d, unsigned long* s, long l)
{
  REGISTER unsigned long* _dl = (unsigned long*) d;
  REGISTER unsigned long* _sl = (unsigned long*) s;
  REGISTER long _i = l - 1;
 
  do
  {
    _dl[_i] = _sl[_i];
    _i--;
  }
  while (_i >= 0);
}
 
inline void _my_memmove_d_lt_s(unsigned long* d, unsigned long* s, long l)
{
  REGISTER long _ll = l;
  REGISTER unsigned long* _dl = (unsigned long*) d;
  REGISTER unsigned long* _sl = (unsigned long*) s;
  REGISTER long _i = 0;
 
  do
  {
    _dl[_i] = _sl[_i];
    _i++;
  }
  while (_i < _ll);
}
 
inline void _my_memmove(void* d, void* s, long l)
{
  unsigned long _d = (unsigned long) d;
  unsigned long _s = (unsigned long) s;
  unsigned long _l = ((l) + SIZEOF_LONG - 1) >> LOG_SIZEOF_LONG;
 
  if (_d > _s) _my_memmove_d_gt_s(_d, _s, _l);
  else _my_memmove_d_lt_s(_d, _s, _l);
}
 
#undef memmove
#define memmove(d,s,l) _my_memmove(d, s, l)
#endif
 
static poly redMora (poly h,int maxIndex,kStrategy strat);
static poly redBba (poly h,int maxIndex,kStrategy strat);
 
#define pDivComp_EQUAL 2
#define pDivComp_LESS 1
#define pDivComp_GREATER -1
#define pDivComp_INCOMP 0
/* Checks the relation of LM(p) and LM(q)
     LM(p) = LM(q) => return pDivComp_EQUAL
     LM(p) | LM(q) => return pDivComp_LESS
     LM(q) | LM(p) => return pDivComp_GREATER
     else return pDivComp_INCOMP */
static inline int pDivCompRing(poly p, poly q)
{
  if ((currRing->pCompIndex < 0)
  || (__p_GetComp(p,currRing) == __p_GetComp(q,currRing)))
  {
    BOOLEAN a=FALSE, b=FALSE;
    int i;
    unsigned long la, lb;
    unsigned long divmask = currRing->divmask;
    for (i=0; i<currRing->VarL_Size; i++)
    {
      la = p->exp[currRing->VarL_Offset[i]];
      lb = q->exp[currRing->VarL_Offset[i]];
      if (la != lb)
      {
        if (la < lb)
        {
          if (b) return pDivComp_INCOMP;
          if (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))
            return pDivComp_INCOMP;
          a = TRUE;
        }
        else
        {
          if (a) return pDivComp_INCOMP;
          if (((la & divmask) ^ (lb & divmask)) != ((la - lb) & divmask))
            return pDivComp_INCOMP;
          b = TRUE;
        }
      }
    }
    if (a) return pDivComp_LESS;
    if (b) return pDivComp_GREATER;
    if (!a & !b) return pDivComp_EQUAL;
  }
  return pDivComp_INCOMP;
}
 
static inline int pDivComp(poly p, poly q)
{
  if ((currRing->pCompIndex < 0)
  || (__p_GetComp(p,currRing) == __p_GetComp(q,currRing)))
  {
#ifdef HAVE_RATGRING
    if (rIsRatGRing(currRing))
    {
      if (_p_LmDivisibleByPart(p,currRing,
                           q,currRing,
                           currRing->real_var_start, currRing->real_var_end))
        return 0;
      return pLmCmp(q,p); // ONLY FOR GLOBAL ORDER!
    }
#endif
    BOOLEAN a=FALSE, b=FALSE;
    int i;
    unsigned long la, lb;
    unsigned long divmask = currRing->divmask;
    for (i=0; i<currRing->VarL_Size; i++)
    {
      la = p->exp[currRing->VarL_Offset[i]];
      lb = q->exp[currRing->VarL_Offset[i]];
      if (la != lb)
      {
        if (la < lb)
        {
          if (b) return 0;
          if (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))
            return 0;
          a = TRUE;
        }
        else
        {
          if (a) return 0;
          if (((la & divmask) ^ (lb & divmask)) != ((la - lb) & divmask))
            return 0;
          b = TRUE;
        }
      }
    }
    if (a) { /*assume(pLmCmp(q,p)==1);*/ return 1; }
    if (b) { /*assume(pLmCmp(q,p)==-1);*/return -1; }
    /*assume(pLmCmp(q,p)==0);*/
  }
  return 0;
}
 
#ifdef HAVE_SHIFTBBA
static inline int pLPDivComp(poly p, poly q)
{
  if ((currRing->pCompIndex < 0) || (__p_GetComp(p,currRing) == __p_GetComp(q,currRing)))
  {
    // maybe there is a more performant way to do this? This will get called quite often in bba.
    if (_p_LPLmDivisibleByNoComp(p, q, currRing)) return 1;
    if (_p_LPLmDivisibleByNoComp(q, p, currRing)) return -1;
  }
 
  return 0;
}
#endif
 
 
VAR int     HCord;
VAR int     Kstd1_deg;
VAR int     Kstd1_mu=INT_MAX;
 
static void deleteHCBucket(LObject *L, kStrategy strat)
{
  if ((strat->kNoether!=NULL)
  && (L->bucket != NULL))
  {
    for (int i=1; i<= (int) L->bucket->buckets_used; i++)
    {
      poly p=L->bucket->buckets[i];
      if(p!=NULL)
      {
        if (p_Cmp(p,strat->kNoetherTail(), L->tailRing) == -1)
        {
          L->bucket->buckets[i]=NULL;
          L->bucket->buckets_length[i]=0;
        }
        else
        {
          do
          {
            if (p_Cmp(pNext(p),strat->kNoetherTail(), L->tailRing) == -1)
            {
              p_Delete(&pNext(p), L->tailRing);
              L->bucket->buckets_length[i]=pLength(L->bucket->buckets[i]);
              break;
            }
            pIter(p);
          } while(p!=NULL);
        }
      }
    }
    int i=L->bucket->buckets_used;
    while ((i>0)&&(L->bucket->buckets[i]==NULL))
    {
      i--;
      L->bucket->buckets_used=i;
    }
  }
}
 
/*2
*deletes higher monomial of p, re-compute ecart and length
*works only for orderings with ecart =pFDeg(end)-pFDeg(start)
*/
void deleteHC(LObject *L, kStrategy strat, BOOLEAN fromNext)
{
  if (strat->kNoether!=NULL)
  {
    kTest_L(L,strat);
    poly p1;
    poly p = L->GetLmTailRing();
    int l = 1;
 
    if (!fromNext && p_Cmp(p,strat->kNoetherTail(), L->tailRing) == -1)
    {
      if (L->bucket != NULL) kBucketDestroy(&L->bucket);
      L->Delete();
      L->Clear();
      L->ecart = -1;
      return;
    }
    if (L->bucket != NULL)
    {
      deleteHCBucket(L,strat);
      return;
    }
    BOOLEAN cut=FALSE;
    p1 = p;
    while (pNext(p1)!=NULL)
    {
      if (p_LmCmp(pNext(p1), strat->kNoetherTail(), L->tailRing) == -1)
      {
        cut=(pNext(p1)!=NULL);
        if (cut)
        {
          p_Delete(&pNext(p1), L->tailRing);
 
          if (p1 == p)
          {
            if (L->t_p != NULL)
            {
              assume(L->p != NULL && p == L->t_p);
              pNext(L->p) = NULL;
            }
            L->max_exp  = NULL;
          }
          else if (fromNext)
            L->max_exp  = p_GetMaxExpP(pNext(L->p), L->tailRing ); // p1;
          //if (L->pLength != 0)
          L->pLength = l;
          // Hmmm when called from updateT, then only
          // reset ecart when cut
          if (fromNext)
            L->ecart = L->pLDeg() - L->GetpFDeg();
        }
        break;
      }
      l++;
      pIter(p1);
    }
    if ((!fromNext) && cut)
    {
      L->SetpFDeg();
      L->ecart = L->pLDeg(strat->LDegLast) - L->GetpFDeg();
    }
    kTest_L(L,strat);
  }
}
 
void deleteHC(poly* p, int* e, int* l,kStrategy strat)
{
  LObject L(*p, currRing, strat->tailRing);
 
  deleteHC(&L, strat);
  *p = L.p;
  *e = L.ecart;
  *l = L.length;
  if (L.t_p != NULL) p_LmFree(L.t_p, strat->tailRing);
}
 
/*2
*tests if p.p=monomial*unit and cancels the unit
*/
void cancelunit (LObject* L,BOOLEAN inNF)
{
  if(rHasGlobalOrdering (currRing)) return;
  if(TEST_OPT_CANCELUNIT) return;
 
  ring r = L->tailRing;
  poly p = L->GetLmTailRing();
  if(p_GetComp(p, r) != 0 && !p_OneComp(p, r)) return;
 
  number lc=NULL; /*dummy, is always set if rField_is_Ring(r) */
  if (rField_is_Ring(r) /*&& (rHasLocalOrMixedOrdering(r))*/)
    lc = pGetCoeff(p);
 
  // Leading coef have to be a unit
  // example 2x+4x2 should be simplified to 2x*(1+2x)
  // and 2 is not a unit in Z
  //if ( !(n_IsUnit(pGetCoeff(p), r->cf)) ) return;
 
  poly h = pNext(p);
  int  i;
 
  if(rField_is_Ring(currRing))
  {
    loop
    {
      if (h==NULL)
      {
        p_Delete(&pNext(p), r);
        if (!inNF)
        {
          number eins= nCopy(lc);
          if (L->p != NULL)
          {
            pSetCoeff(L->p,eins);
            if (L->t_p != NULL)
              pSetCoeff0(L->t_p,eins);
          }
          else
            pSetCoeff(L->t_p,eins);
          /* p and t_p share the same coeff, if both are !=NULL */
          /* p==NULL==t_p cannot happen here */
        }
        L->ecart = 0;
        L->length = 1;
        //if (L->pLength > 0)
        L->pLength = 1;
        L->max_exp = NULL;
 
        if (L->t_p != NULL && pNext(L->t_p) != NULL)
          p_Delete(&pNext(L->t_p),r);
        if (L->p != NULL && pNext(L->p) != NULL)
          pNext(L->p) = NULL;
        return;
      }
      i = rVar(r);
      loop
      {
        if (p_GetExp(p,i,r) > p_GetExp(h,i,r)) return; // does not divide
        i--;
        if (i == 0) break; // does divide, try next monom
      }
      //wrp(p); PrintS(" divide ");wrp(h); PrintLn();
      // Note: As long as qring j forbidden if j contains integer (i.e. ground rings are
      //       domains), no zerodivisor test needed  CAUTION
      if (!n_DivBy(pGetCoeff(h),lc,r->cf))
      {
        return;
      }
      pIter(h);
    }
  }
  else
  {
    loop
    {
      if (h==NULL)
      {
        p_Delete(&pNext(p), r);
        if (!inNF)
        {
          number eins=nInit(1);
          if (L->p != NULL)
          {
            pSetCoeff(L->p,eins);
            if (L->t_p != NULL)
              pSetCoeff0(L->t_p,eins);
          }
          else
            pSetCoeff(L->t_p,eins);
          /* p and t_p share the same coeff, if both are !=NULL */
          /* p==NULL==t_p cannot happen here */
        }
        L->ecart = 0;
        L->length = 1;
        //if (L->pLength > 0)
        L->pLength = 1;
        L->max_exp = NULL;
 
        if (L->t_p != NULL && pNext(L->t_p) != NULL)
          p_Delete(&pNext(L->t_p),r);
        if (L->p != NULL && pNext(L->p) != NULL)
          pNext(L->p) = NULL;
 
        return;
      }
      i = rVar(r);
      loop
      {
        if (p_GetExp(p,i,r) > p_GetExp(h,i,r)) return; // does not divide
        i--;
        if (i == 0) break; // does divide, try next monom
      }
      //wrp(p); PrintS(" divide ");wrp(h); PrintLn();
      pIter(h);
    }
  }
}
 
/*2
*pp is the new element in s
*returns TRUE (in strat->kAllAxis) if
*-HEcke is allowed
*-we are in the last componente of the vector
*-on all axis are monomials (all elements in NotUsedAxis are FALSE)
*returns FALSE for pLexOrderings,
*assumes in module case an ordering of type c* !!
* HEckeTest is only called with strat->kAllAxis==FALSE !
*/
void HEckeTest (poly pp,kStrategy strat)
{
  int   j,p;
 
  if (currRing->pLexOrder
  || rHasMixedOrdering(currRing)
  || (strat->ak >1)
  || (rField_is_Ring(currRing) && (!n_IsUnit(pGetCoeff(pp),currRing->cf))))
  {
    return;
  }
  p=pIsPurePower(pp);
  if (p!=0)
    strat->NotUsedAxis[p] = FALSE;
  /*- the leading term of pp is a power of the p-th variable -*/
  for (j=(currRing->N);j>0; j--)
  {
    if (strat->NotUsedAxis[j])
    {
      strat->kAllAxis=FALSE;
      return;
    }
  }
  strat->kAllAxis=TRUE;
}
 
/*2
*utilities for TSet, LSet
*/
inline static intset initec (const int maxnr)
{
  return (intset)omAlloc(maxnr*sizeof(int));
}
 
inline static unsigned long* initsevS (const int maxnr)
{
  return (unsigned long*)omAlloc0(maxnr*sizeof(unsigned long));
}
inline static int* initS_2_R (const int maxnr)
{
  return (int*)omAlloc0(maxnr*sizeof(int));
}
 
static inline void enlargeT (TSet &T, TObject** &R, unsigned long* &sevT,
                             int &length, const int incr)
{
  assume(T!=NULL);
  assume(sevT!=NULL);
  assume(R!=NULL);
  assume((length+incr) > 0);
 
  int i;
  T = (TSet)omRealloc0Size(T, length*sizeof(TObject),
                           (length+incr)*sizeof(TObject));
 
  sevT = (unsigned long*) omReallocSize(sevT, length*sizeof(long*),
                           (length+incr)*sizeof(long*));
 
  R = (TObject**)omRealloc0Size(R,length*sizeof(TObject*),
                                (length+incr)*sizeof(TObject*));
  for (i=length-1;i>=0;i--) R[T[i].i_r] = &(T[i]);
  length += incr;
}
 
void cleanT (kStrategy strat)
{
  int i,j;
  poly  p;
  assume(currRing == strat->tailRing || strat->tailRing != NULL);
 
  pShallowCopyDeleteProc p_shallow_copy_delete =
    (strat->tailRing != currRing ?
     pGetShallowCopyDeleteProc(strat->tailRing, currRing) :
     NULL);
  for (j=0; j<=strat->tl; j++)
  {
    p = strat->T[j].p;
    strat->T[j].p=NULL;
    if (strat->T[j].max_exp != NULL)
    {
      p_LmFree(strat->T[j].max_exp, strat->tailRing);
    }
    i = -1;
    loop
    {
      i++;
      if (i>strat->sl)
      {
        if (strat->T[j].t_p != NULL)
        {
          p_Delete(&(strat->T[j].t_p), strat->tailRing);
          p_LmFree(p, currRing);
        }
        else
        {
#ifdef HAVE_SHIFTBBA
          if (currRing->isLPring && strat->T[j].shift > 0)
          {
            pNext(p) = NULL; // pNext(p) points to the unshifted tail, don't try to delete it here
          }
#endif
          pDelete(&p);
        }
        break;
      }
      if (p == strat->S[i])
      {
        if (strat->T[j].t_p != NULL)
        {
          if (p_shallow_copy_delete!=NULL)
          {
            pNext(p) = p_shallow_copy_delete(pNext(p),strat->tailRing,currRing,
                                           currRing->PolyBin);
          }
          p_LmFree(strat->T[j].t_p, strat->tailRing);
        }
        break;
      }
    }
  }
  strat->tl=-1;
}
 
void cleanTSbaRing (kStrategy strat)
{
  int i,j;
  poly  p;
  assume(currRing == strat->tailRing || strat->tailRing != NULL);
 
  pShallowCopyDeleteProc p_shallow_copy_delete =
    (strat->tailRing != currRing ?
     pGetShallowCopyDeleteProc(strat->tailRing, currRing) :
     NULL);
  for (j=0; j<=strat->tl; j++)
  {
    p = strat->T[j].p;
    strat->T[j].p=NULL;
    if (strat->T[j].max_exp != NULL)
    {
      p_LmFree(strat->T[j].max_exp, strat->tailRing);
    }
    i = -1;
    loop
    {
      i++;
      if (i>strat->sl)
      {
        if (strat->T[j].t_p != NULL)
        {
          p_Delete(&(strat->T[j].t_p), strat->tailRing);
          p_LmFree(p, currRing);
        }
        else
        {
          //pDelete(&p);
          p = NULL;
        }
        break;
      }
      if (p == strat->S[i])
      {
        if (strat->T[j].t_p != NULL)
        {
          assume(p_shallow_copy_delete != NULL);
          pNext(p) = p_shallow_copy_delete(pNext(p),strat->tailRing,currRing,
                                           currRing->PolyBin);
          p_LmFree(strat->T[j].t_p, strat->tailRing);
        }
        break;
      }
    }
  }
  strat->tl=-1;
}
 
static inline void enlargeL (LSet* L,int* length,const int incr)
{
  assume((*L)!=NULL);
  assume(((*length)+incr)>0);
 
  *L = (LSet)omReallocSize((*L),(*length)*sizeof(LObject),
                                   ((*length)+incr)*sizeof(LObject));
  (*length) += incr;
}
 
void initPairtest(kStrategy strat)
{
  strat->pairtest = (BOOLEAN *)omAlloc0((strat->sl+2)*sizeof(BOOLEAN));
}
 
/*2
*test whether (p1,p2) or (p2,p1) is in L up position length
*it returns TRUE if yes and the position k
*/
BOOLEAN isInPairsetL(int length,poly p1,poly p2,int*  k,kStrategy strat)
{
  LObject *p=&(strat->L[length]);
 
  *k = length;
  loop
  {
    if ((*k) < 0) return FALSE;
    if (((p1 == (*p).p1) && (p2 == (*p).p2))
    ||  ((p1 == (*p).p2) && (p2 == (*p).p1)))
      return TRUE;
    (*k)--;
    p--;
  }
}
 
int kFindInT(poly p, TSet T, int tlength)
{
  int i;
 
  for (i=0; i<=tlength; i++)
  {
    if (T[i].p == p) return i;
  }
  return -1;
}
 
int kFindInT(poly p, kStrategy strat)
{
  int i;
  do
  {
    i = kFindInT(p, strat->T, strat->tl);
    if (i >= 0) return i;
    strat = strat->next;
  }
  while (strat != NULL);
  return -1;
}
 
#ifdef HAVE_SHIFTBBA
int kFindInTShift(poly p, TSet T, int tlength)
{
  int i;
 
  for (i=0; i<=tlength; i++)
  {
    // in the Letterplace ring the LMs in T and L are copies thus we have to use pEqualPolys() instead of ==
    if (pEqualPolys(T[i].p, p)) return i;
  }
  return -1;
}
#endif
 
#ifdef HAVE_SHIFTBBA
int kFindInTShift(poly p, kStrategy strat)
{
  int i;
  do
  {
    i = kFindInTShift(p, strat->T, strat->tl);
    if (i >= 0) return i;
    strat = strat->next;
  }
  while (strat != NULL);
  return -1;
}
#endif
 
#ifdef KDEBUG
void sTObject::wrp()
{
  if (t_p != NULL) p_wrp(t_p, tailRing);
  else if (p != NULL) p_wrp(p, currRing, tailRing);
  else ::wrp(NULL);
}
#endif
 
#define kFalseReturn(x) do { if (!x) return FALSE;} while (0)
 
#ifdef KDEBUG
// check that Lm's of a poly from T are "equal"
static const char* kTest_LmEqual(poly p, poly t_p, ring tailRing)
{
  int i;
  for (i=1; i<=tailRing->N; i++)
  {
    if (p_GetExp(p, i, currRing) != p_GetExp(t_p, i, tailRing))
      return "Lm[i] different";
  }
  if (p_GetComp(p, currRing) != p_GetComp(t_p, tailRing))
    return "Lm[0] different";
  if (pNext(p) != pNext(t_p))
    return "Lm.next different";
  if (pGetCoeff(p) != pGetCoeff(t_p))
    return "Lm.coeff different";
  return NULL;
}
#endif
 
#ifdef KDEBUG
STATIC_VAR BOOLEAN sloppy_max = FALSE;
BOOLEAN kTest_T(TObject * T, kStrategy strat, int i, char TN)
{
  ring tailRing = T->tailRing;
  ring strat_tailRing = strat->tailRing;
  if (strat_tailRing == NULL) strat_tailRing = tailRing;
  r_assume(strat_tailRing == tailRing);
 
  poly p = T->p;
  // ring r = currRing;
 
  if (T->p == NULL && T->t_p == NULL && i >= 0)
    return dReportError("%c[%d].poly is NULL", TN, i);
 
  if (T->p!=NULL)
  {
    nTest(pGetCoeff(T->p));
    if ((T->t_p==NULL)&&(pNext(T->p)!=NULL)) p_Test(pNext(T->p),currRing);
  }
  if (T->t_p!=NULL)
  {
    nTest(pGetCoeff(T->t_p));
    if (pNext(T->t_p)!=NULL) p_Test(pNext(T->t_p),strat_tailRing);
  }
  if ((T->p!=NULL)&&(T->t_p!=NULL)) assume(pGetCoeff(T->p)==pGetCoeff(T->t_p));
 
  if (T->tailRing != currRing)
  {
    if (T->t_p == NULL && i > 0)
      return dReportError("%c[%d].t_p is NULL", TN, i);
    pFalseReturn(p_Test(T->t_p, T->tailRing));
    if (T->p != NULL) pFalseReturn(p_LmTest(T->p, currRing));
    if ((T->p != NULL) && (T->t_p != NULL))
    {
      const char* msg = kTest_LmEqual(T->p, T->t_p, T->tailRing);
      if (msg != NULL)
        return dReportError("%c[%d] %s", TN, i, msg);
      // r = T->tailRing;
      p = T->t_p;
    }
    if (T->p == NULL)
    {
      p = T->t_p;
      // r = T->tailRing;
    }
    if (T->t_p != NULL && i >= 0 && TN == 'T')
    {
      if (pNext(T->t_p) == NULL)
      {
        if (T->max_exp != NULL)
          return dReportError("%c[%d].max_exp is not NULL as it should be", TN, i);
      }
      else
      {
        if (T->max_exp == NULL)
          return dReportError("%c[%d].max_exp is NULL", TN, i);
        if (pNext(T->max_exp) != NULL)
          return dReportError("pNext(%c[%d].max_exp) != NULL", TN, i);
 
        pFalseReturn(p_CheckPolyRing(T->max_exp, tailRing));
        omCheckBinAddrSize(T->max_exp, (omSizeWOfBin(tailRing->PolyBin))*SIZEOF_LONG);
#if KDEBUG > 0
        if (! sloppy_max)
        {
          poly test_max = p_GetMaxExpP(pNext(T->t_p), tailRing);
          p_Setm(T->max_exp, tailRing);
          p_Setm(test_max, tailRing);
          BOOLEAN equal = p_ExpVectorEqual(T->max_exp, test_max, tailRing);
          if (! equal)
            return dReportError("%c[%d].max out of sync", TN, i);
          p_LmFree(test_max, tailRing);
        }
#endif
      }
    }
  }
  else
  {
    if (T->p == NULL && i > 0)
      return dReportError("%c[%d].p is NULL", TN, i);
#ifdef HAVE_SHIFTBBA
    if (currRing->isLPring && T->shift > 0)
    {
      // in this case, the order is not correct. test LM and tail separately
      pFalseReturn(p_LmTest(T->p, currRing));
      pFalseReturn(p_Test(pNext(T->p), currRing));
    }
    else
#endif
    {
      pFalseReturn(p_Test(T->p, currRing));
    }
  }
 
  if ((i >= 0) && (T->pLength != 0)
  && (! rIsSyzIndexRing(currRing)) && (T->pLength != pLength(p)))
  {
    int l=T->pLength;
    T->pLength=pLength(p);
    return dReportError("%c[%d] pLength error: has %d, specified to have %d",
                        TN, i , pLength(p), l);
  }
 
  // check FDeg,  for elements in L and T
  if (i >= 0 && (TN == 'T' || TN == 'L'))
  {
    // FDeg has ir element from T of L set
    if (strat->homog && (T->FDeg  != T->pFDeg()))
    {
      int d=T->FDeg;
      T->FDeg=T->pFDeg();
      return dReportError("%c[%d] FDeg error: has %d, specified to have %d",
                          TN, i , T->pFDeg(), d);
    }
  }
 
  // check is_normalized for elements in T
  if (i >= 0 && TN == 'T')
  {
    if (T->is_normalized && ! nIsOne(pGetCoeff(p)))
      return dReportError("T[%d] is_normalized error", i);
 
  }
  return TRUE;
}
#endif
 
#ifdef KDEBUG
BOOLEAN kTest_L(LObject *L, kStrategy strat,
                BOOLEAN testp, int lpos, TSet T, int tlength)
{
  ring strat_tailRing=strat->tailRing;
  if (L->p!=NULL)
  {
    if ((L->t_p==NULL)
    &&(pNext(L->p)!=NULL)
    &&(pGetCoeff(pNext(L->p))!=NULL)) /* !=strat->tail*/
    {
      p_Test(pNext(L->p),currRing);
      nTest(pGetCoeff(L->p));
    }
  }
  if (L->t_p!=NULL)
  {
    if ((pNext(L->t_p)!=NULL)
    &&(pGetCoeff(pNext(L->t_p))!=NULL)) /* !=strat->tail*/
    {
      p_Test(pNext(L->t_p),strat_tailRing);
      nTest(pGetCoeff(L->t_p));
    }
  }
  if ((L->p!=NULL)&&(L->t_p!=NULL)) assume(pGetCoeff(L->p)==pGetCoeff(L->t_p));
 
  if (testp)
  {
    poly pn = NULL;
    if (L->bucket != NULL)
    {
      kFalseReturn(kbTest(L->bucket));
      r_assume(L->bucket->bucket_ring == L->tailRing);
      if (L->p != NULL && pNext(L->p) != NULL)
      {
        pn = pNext(L->p);
        pNext(L->p) = NULL;
      }
    }
    kFalseReturn(kTest_T(L, strat, lpos, 'L'));
    if (pn != NULL)
      pNext(L->p) = pn;
 
    ring r;
    poly p;
    L->GetLm(p, r);
    if (L->sev != 0L)
    {
      if (p_GetShortExpVector(p, r) != L->sev)
      {
        return dReportError("L[%d] wrong sev: has %lo, specified to have %lo",
                          lpos, p_GetShortExpVector(p, r), L->sev);
      }
    }
  }
  if (L->p1 == NULL)
  {
    // L->p2 either NULL or "normal" poly
    pFalseReturn(pp_Test(L->p2, currRing, L->tailRing));
  }
  else if (tlength > 0 && T != NULL && (lpos >=0))
  {
    // now p1 and p2 must be != NULL and must be contained in T
    int i;
#ifdef HAVE_SHIFTBBA
    if (rIsLPRing(currRing))
      i = kFindInTShift(L->p1, T, tlength);
    else
#endif
      i = kFindInT(L->p1, T, tlength);
    if (i < 0)
      return dReportError("L[%d].p1 not in T",lpos);
#ifdef HAVE_SHIFTBBA
    if (rIsLPRing(currRing))
    {
      if (rField_is_Ring(currRing)) return TRUE; // m*shift(q) is not in T
      i = kFindInTShift(L->p2, T, tlength);
    }
    else
#endif
      i = kFindInT(L->p2, T, tlength);
    if (i < 0)
      return dReportError("L[%d].p2 not in T",lpos);
  }
  return TRUE;
}
#endif
 
#ifdef KDEBUG
BOOLEAN kTest (kStrategy strat)
{
  int i;
  // test P
  kFalseReturn(kTest_L(&(strat->P), strat,
                       (strat->P.p != NULL && pNext(strat->P.p)!=strat->tail),
                       -1, strat->T, strat->tl));
 
  // test T
  if (strat->T != NULL)
  {
    for (i=0; i<=strat->tl; i++)
    {
      kFalseReturn(kTest_T(&(strat->T[i]), strat, i, 'T'));
      if (strat->sevT[i] != pGetShortExpVector(strat->T[i].p))
        return dReportError("strat->sevT[%d] out of sync", i);
    }
  }
 
  // test L
  if (strat->L != NULL)
  {
    for (i=0; i<=strat->Ll; i++)
    {
      kFalseReturn(kTest_L(&(strat->L[i]), strat,
                           strat->L[i].Next() != strat->tail, i,
                           strat->T, strat->tl));
      // may be unused
      //if (strat->use_buckets && strat->L[i].Next() != strat->tail &&
      //    strat->L[i].Next() != NULL && strat->L[i].p1 != NULL)
      //{
      //  assume(strat->L[i].bucket != NULL);
      //}
    }
  }
 
  // test S
  if (strat->S != NULL)
    kFalseReturn(kTest_S(strat));
 
  return TRUE;
}
#endif
 
#ifdef KDEBUG
BOOLEAN kTest_S(kStrategy strat)
{
  int i;
  BOOLEAN ret = TRUE;
  for (i=0; i<=strat->sl; i++)
  {
    if (strat->S[i] != NULL &&
        strat->sevS[i] != pGetShortExpVector(strat->S[i]))
    {
      return dReportError("S[%d] wrong sev: has %o, specified to have %o",
                          i , pGetShortExpVector(strat->S[i]), strat->sevS[i]);
    }
  }
  return ret;
}
#endif
 
#ifdef KDEBUG
BOOLEAN kTest_TS(kStrategy strat)
{
  int i, j;
  // BOOLEAN ret = TRUE;
  kFalseReturn(kTest(strat));
 
  // test strat->R, strat->T[i].i_r
  for (i=0; i<=strat->tl; i++)
  {
    if (strat->T[i].i_r < 0 || strat->T[i].i_r > strat->tl)
      return dReportError("strat->T[%d].i_r == %d out of bounds", i,
                          strat->T[i].i_r);
    if (strat->R[strat->T[i].i_r] != &(strat->T[i]))
      return dReportError("T[%d].i_r with R out of sync", i);
  }
  // test containment of S inT
  if ((strat->S != NULL)&&(strat->tl>=0))
  {
    for (i=0; i<=strat->sl; i++)
    {
      j = kFindInT(strat->S[i], strat->T, strat->tl);
      if (j < 0)
        return dReportError("S[%d] not in T", i);
      if (strat->S_2_R[i] != strat->T[j].i_r)
        return dReportError("S_2_R[%d]=%d != T[%d].i_r=%d\n",
                            i, strat->S_2_R[i], j, strat->T[j].i_r);
    }
  }
  // test strat->L[i].i_r1
  #ifdef HAVE_SHIFTBBA
  if (!rIsLPRing(currRing)) // in the Letterplace ring we currently don't set/use i_r1 and i_r2
  #endif
  if (strat->L!=NULL)
  {
   for (i=0; i<=strat->Ll; i++)
   {
    if (strat->L[i].p1 != NULL && strat->L[i].p2)
    {
      if (strat->L[i].i_r1 < 0 ||
          strat->L[i].i_r1 > strat->tl ||
          strat->L[i].T_1(strat)->p != strat->L[i].p1)
        return dReportError("L[%d].i_r1 out of sync", i);
      if (strat->L[i].i_r2 < 0 ||
          strat->L[i].i_r2 > strat->tl ||
          strat->L[i].T_2(strat)->p != strat->L[i].p2)
        return dReportError("L[%d].i_r2 out of sync", i);
    }
    else
    {
      if (strat->L[i].i_r1 != -1)
        return dReportError("L[%d].i_r1 out of sync", i);
      if (strat->L[i].i_r2 != -1)
        return dReportError("L[%d].i_r2 out of sync", i);
    }
    if (strat->L[i].i_r != -1)
      return dReportError("L[%d].i_r out of sync", i);
  }
  }
  return TRUE;
}
#endif // KDEBUG
 
/*2
*cancels the i-th polynomial in the standardbase s
*/
void deleteInS (int i,kStrategy strat)
{
#ifdef ENTER_USE_MEMMOVE
  memmove(&(strat->S[i]), &(strat->S[i+1]), (strat->sl - i)*sizeof(poly));
  memmove(&(strat->ecartS[i]),&(strat->ecartS[i+1]),(strat->sl - i)*sizeof(int));
  memmove(&(strat->sevS[i]),&(strat->sevS[i+1]),(strat->sl - i)*sizeof(unsigned long));
  memmove(&(strat->S_2_R[i]),&(strat->S_2_R[i+1]),(strat->sl - i)*sizeof(int));
#else
  int j;
  for (j=i; j<strat->sl; j++)
  {
    strat->S[j] = strat->S[j+1];
    strat->ecartS[j] = strat->ecartS[j+1];
    strat->sevS[j] = strat->sevS[j+1];
    strat->S_2_R[j] = strat->S_2_R[j+1];
  }
#endif
  if (strat->lenS!=NULL)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->lenS[i]),&(strat->lenS[i+1]),(strat->sl - i)*sizeof(int));
#else
    for (j=i; j<strat->sl; j++) strat->lenS[j] = strat->lenS[j+1];
#endif
  }
  if (strat->lenSw!=NULL)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->lenSw[i]),&(strat->lenSw[i+1]),(strat->sl - i)*sizeof(wlen_type));
#else
    for (j=i; j<strat->sl; j++) strat->lenSw[j] = strat->lenSw[j+1];
#endif
  }
  if (strat->fromQ!=NULL)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->fromQ[i]),&(strat->fromQ[i+1]),(strat->sl - i)*sizeof(int));
#else
    for (j=i; j<strat->sl; j++)
    {
      strat->fromQ[j] = strat->fromQ[j+1];
    }
#endif
  }
  strat->S[strat->sl] = NULL;
  strat->sl--;
}
 
#ifdef HAVE_SHIFTBBA
static BOOLEAN is_shifted_p1(const kStrategy strat)
{
  if (rIsLPRing(currRing)
  && (strat->P.p1!=NULL))
  {
    // clean up strat->P.p1: may be shifted
    poly p=strat->P.p1;
    int lv=currRing->isLPring;
    BOOLEAN is_shifted=TRUE;
    for (int i=lv;i>0;i--)
    {
      if (pGetExp(p,i)!=0) { is_shifted=FALSE; break;}
    }
    if (is_shifted
    && (kFindInL1(p, strat)<0)
    && (kFindInT(p, strat->T, strat->tl) < 0)
    )
    {
      return TRUE;
    }
  }
  return FALSE;
}
#endif
/*2
*cancels the j-th polynomial in the set
*/
void deleteInL (LSet set, int *length, int j,kStrategy strat)
{
  if (set[j].lcm!=NULL)
  {
    kDeleteLcm(&set[j]);
  }
  if (set[j].sig!=NULL)
  {
    if (pGetCoeff(set[j].sig) != NULL)
      pLmDelete(set[j].sig);
    else
      pLmFree(set[j].sig);
  }
  if (set[j].p!=NULL)
  {
    if (pNext(set[j].p) == strat->tail)
    {
      if (pGetCoeff(set[j].p) != NULL)
        pLmDelete(set[j].p);
      else
        pLmFree(set[j].p);
      /*- tail belongs to several int spolys -*/
    }
    else
    {
      // search p in T, if it is there, do not delete it
      if (rHasGlobalOrdering(currRing) || (kFindInT(set[j].p, strat) < 0))
      {
        // assure that for global orderings kFindInT fails
        //assume((rHasLocalOrMixedOrdering(currRing)) && (kFindInT(set[j].p, strat) >= 0));
        set[j].Delete();
      }
    }
  }
  #ifdef HAVE_SHIFTBBA
  if (is_shifted_p1(/*strat->P.p1,*/strat))
  {
    // clean up strat->P.p1: may be shifted
    pLmDelete(strat->P.p1);
    strat->P.p1=NULL;
  }
  #endif
  if (*length > 0 && j < *length)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(set[j]), &(set[j+1]), (*length - j)*sizeof(LObject));
#else
    int i;
    for (i=j; i < (*length); i++)
      set[i] = set[i+1];
#endif
  }
#ifdef KDEBUG
  set[*length].Init();
#endif
  (*length)--;
}
 
/*2
*enters p at position at in L
*/
void enterL (LSet *set,int *length, int *LSetmax, LObject p,int at)
{
  // this should be corrected
  assume(p.FDeg == p.pFDeg());
 
  if ((*length)>=0)
  {
    if ((*length) == (*LSetmax)-1) enlargeL(set,LSetmax,*LSetmax);
    if (at <= (*length))
#ifdef ENTER_USE_MEMMOVE
      memmove(&((*set)[at+1]), &((*set)[at]), ((*length)-at+1)*sizeof(LObject));
#else
    for (i=(*length)+1; i>=at+1; i--) (*set)[i] = (*set)[i-1];
#endif
  }
  else at = 0;
  (*set)[at] = p;
  (*length)++;
}
 
/*2
* computes the normal ecart;
* used in mora case and if pLexOrder & sugar in bba case
*/
void initEcartNormal (TObject* h)
{
  h->FDeg = h->pFDeg();
  h->ecart = h->pLDeg() - h->FDeg;
  // h->length is set by h->pLDeg
  h->length=h->pLength=pLength(h->p);
}
 
void initEcartBBA (TObject* h)
{
  h->FDeg = h->pFDeg();
  (*h).ecart = 0;
  h->length=h->pLength=pLength(h->p);
}
 
void initEcartPairBba (LObject* Lp,poly /*f*/,poly /*g*/,int /*ecartF*/,int /*ecartG*/)
{
  Lp->FDeg = Lp->pFDeg();
  (*Lp).ecart = 0;
  (*Lp).length = 0;
}
 
void initEcartPairMora (LObject* Lp,poly /*f*/,poly /*g*/,int ecartF,int ecartG)
{
  Lp->FDeg = Lp->pFDeg();
  (*Lp).ecart = si_max(ecartF,ecartG);
  (*Lp).ecart = (*Lp).ecart- (Lp->FDeg -p_FDeg((*Lp).lcm,currRing));
  (*Lp).length = 0;
}
 
/*2
*if ecart1<=ecart2 it returns TRUE
*/
static inline BOOLEAN sugarDivisibleBy(int ecart1, int ecart2)
{
  return (ecart1 <= ecart2);
}
 
/*2
* put the pair (s[i],p)  into the set B, ecart=ecart(p) (ring case)
*/
static void enterOnePairRing (int i,poly p,int /*ecart*/, int isFromQ,kStrategy strat, int atR)
{
  assume(atR >= 0);
  assume(i<=strat->sl);
  assume(p!=NULL);
  assume(rField_is_Ring(currRing));
  #if ALL_VS_JUST
  //Over rings, if we construct the strong pair, do not add the spair
  if(rField_is_Ring(currRing))
  {
    number s,t,d;
    d = n_ExtGcd(pGetCoeff(p), pGetCoeff(strat->S[i]), &s, &t, currRing->cf);
 
    if (!nIsZero(s) && !nIsZero(t))  // evtl. durch divBy tests ersetzen
    {
      nDelete(&d);
      nDelete(&s);
      nDelete(&t);
      return;
    }
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
  }
  #endif
  int      j,compare,compareCoeff;
  LObject  h;
 
#ifdef KDEBUG
  h.ecart=0; h.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  if(pHasNotCFRing(p,strat->S[i]))
  {
      strat->cp++;
      return;
  }
  h.lcm = p_Lcm(p,strat->S[i],currRing);
  pSetCoeff0(h.lcm, n_Lcm(pGetCoeff(p), pGetCoeff(strat->S[i]), currRing->cf));
  if (nIsZero(pGetCoeff(h.lcm)))
  {
      strat->cp++;
      pLmDelete(h.lcm);
      return;
  }
  // basic chain criterion
  /*
  *the set B collects the pairs of type (S[j],p)
  *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p) != lcm(r,p)
  *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
  *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
  */
 
  for(j = strat->Bl;j>=0;j--)
  {
    compare=pDivCompRing(strat->B[j].lcm,h.lcm);
    compareCoeff = n_DivComp(pGetCoeff(strat->B[j].lcm), pGetCoeff(h.lcm), currRing->cf);
    if(compare == pDivComp_EQUAL)
    {
      //They have the same LM
      if(compareCoeff == pDivComp_LESS)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
      if(compareCoeff == pDivComp_GREATER)
      {
        deleteInL(strat->B,&strat->Bl,j,strat);
        strat->c3++;
      }
      if(compareCoeff == pDivComp_EQUAL)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
    }
    if(compareCoeff == compare || compareCoeff == pDivComp_EQUAL)
    {
      if(compare == pDivComp_LESS)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
      if(compare == pDivComp_GREATER)
      {
        deleteInL(strat->B,&strat->Bl,j,strat);
        strat->c3++;
      }
    }
  }
  number s, t;
  poly m1, m2, gcd = NULL;
  s = pGetCoeff(strat->S[i]);
  t = pGetCoeff(p);
  k_GetLeadTerms(p,strat->S[i],currRing,m1,m2,currRing);
  ksCheckCoeff(&s, &t, currRing->cf);
  pSetCoeff0(m1, s);
  pSetCoeff0(m2, t);
  m2 = pNeg(m2);
  p_Test(m1,strat->tailRing);
  p_Test(m2,strat->tailRing);
  poly si = pCopy(strat->S[i]);
  poly pm1 = pp_Mult_mm(pNext(p), m1, strat->tailRing);
  poly sim2 = pp_Mult_mm(pNext(si), m2, strat->tailRing);
  pDelete(&si);
  p_LmDelete(m1, currRing);
  p_LmDelete(m2, currRing);
  if(sim2 == NULL)
  {
    if(pm1 == NULL)
    {
      if(h.lcm != NULL)
      {
        pLmDelete(h.lcm);
        h.lcm=NULL;
      }
      h.Clear();
      if (strat->pairtest==NULL) initPairtest(strat);
      strat->pairtest[i] = TRUE;
      strat->pairtest[strat->sl+1] = TRUE;
      return;
    }
    else
    {
      gcd = pm1;
      pm1 = NULL;
    }
  }
  else
  {
    if((pGetComp(strat->S[i]) == 0) && (0 != pGetComp(p)))
    {
      p_SetCompP(sim2, pGetComp(p), strat->tailRing);
      pSetmComp(sim2);
    }
    //p_Write(pm1,strat->tailRing);p_Write(sim2,strat->tailRing);
    gcd = p_Add_q(pm1, sim2, strat->tailRing);
  }
  p_Test(gcd, strat->tailRing);
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    wrp(gcd);
    PrintLn();
  }
#endif
  h.p = gcd;
  h.i_r = -1;
  if(h.p == NULL)
  {
    if (strat->pairtest==NULL) initPairtest(strat);
    strat->pairtest[i] = TRUE;
    strat->pairtest[strat->sl+1] = TRUE;
    return;
  }
  h.tailRing = strat->tailRing;
  int posx;
  //h.pCleardenom();
  //pSetm(h.p);
  h.i_r1 = -1;h.i_r2 = -1;
  strat->initEcart(&h);
  #if 1
  h.p2 = strat->S[i];
  h.p1 = p;
  #endif
  #if 1
  if (atR >= 0)
  {
    h.i_r1 = atR;
    h.i_r2 = strat->S_2_R[i];
  }
  #endif
  if (strat->Bl==-1)
    posx =0;
  else
    posx = strat->posInL(strat->B,strat->Bl,&h,strat);
  h.sev = pGetShortExpVector(h.p);
  if (currRing!=strat->tailRing)
    h.t_p = k_LmInit_currRing_2_tailRing(h.p, strat->tailRing);
  if (strat->P.p!=NULL) strat->P.sev = pGetShortExpVector(strat->P.p);
  else strat->P.sev=0L;
  enterL(&strat->B,&strat->Bl,&strat->Bmax,h,posx);
  kTest_TS(strat);
}
 
/*2
* put the  lcm(s[i],p)  into the set B
*/
 
static BOOLEAN enterOneStrongPoly (int i,poly p,int /*ecart*/, int /*isFromQ*/,kStrategy strat, int atR, bool enterTstrong)
{
  number d, s, t;
  assume(atR >= 0);
  assume(rField_is_Ring(currRing));
  poly m1, m2, gcd,si;
  if(!enterTstrong)
  {
    assume(i<=strat->sl);
    si = strat->S[i];
  }
  else
  {
    assume(i<=strat->tl);
    si = strat->T[i].p;
  }
  //printf("\n--------------------------------\n");
  //pWrite(p);pWrite(si);
  d = n_ExtGcd(pGetCoeff(p), pGetCoeff(si), &s, &t, currRing->cf);
 
  if (nIsZero(s) || nIsZero(t))  // evtl. durch divBy tests ersetzen
  {
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
    return FALSE;
  }
 
  k_GetStrongLeadTerms(p, si, currRing, m1, m2, gcd, strat->tailRing);
 
  if (!rHasLocalOrMixedOrdering(currRing))
  {
    unsigned long sev = pGetShortExpVector(gcd);
 
    for (int j = 0; j < strat->sl; j++)
    {
      if (j == i)
        continue;
 
      if (n_DivBy(d, pGetCoeff(strat->S[j]), currRing->cf)
      && !(strat->sevS[j] & ~sev)
      && p_LmDivisibleBy(strat->S[j], gcd, currRing))
      {
        nDelete(&d);
        nDelete(&s);
        nDelete(&t);
        return FALSE;
      }
    }
  }
 
  //p_Test(m1,strat->tailRing);
  //p_Test(m2,strat->tailRing);
  /*if(!enterTstrong)
  {
    while (! kCheckStrongCreation(atR, m1, i, m2, strat) )
    {
      memset(&(strat->P), 0, sizeof(strat->P));
      kStratChangeTailRing(strat);
      strat->P = *(strat->R[atR]);
      p_LmFree(m1, strat->tailRing);
      p_LmFree(m2, strat->tailRing);
      p_LmFree(gcd, currRing);
      k_GetStrongLeadTerms(p, si, currRing, m1, m2, gcd, strat->tailRing);
    }
  }*/
  pSetCoeff0(m1, s);
  pSetCoeff0(m2, t);
  pSetCoeff0(gcd, d);
  p_Test(m1,strat->tailRing);
  p_Test(m2,strat->tailRing);
  //printf("\n===================================\n");
  //pWrite(m1);pWrite(m2);pWrite(gcd);
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    // Print("t = %d; s = %d; d = %d\n", nInt(t), nInt(s), nInt(d));
    PrintS("m1 = ");
    p_wrp(m1, strat->tailRing);
    PrintS(" ; m2 = ");
    p_wrp(m2, strat->tailRing);
    PrintS(" ; gcd = ");
    wrp(gcd);
    PrintS("\n--- create strong gcd poly: ");
    Print("\n p: %d", i);
    wrp(p);
    Print("\n strat->S[%d]: ", i);
    wrp(si);
    PrintS(" ---> ");
  }
#endif
 
  pNext(gcd) = p_Add_q(pp_Mult_mm(pNext(p), m1, strat->tailRing), pp_Mult_mm(pNext(si), m2, strat->tailRing), strat->tailRing);
  p_LmDelete(m1, strat->tailRing);
  p_LmDelete(m2, strat->tailRing);
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    wrp(gcd);
    PrintLn();
  }
#endif
 
  LObject h;
  h.p = gcd;
  h.tailRing = strat->tailRing;
  int posx;
  strat->initEcart(&h);
  h.sev = pGetShortExpVector(h.p);
  h.i_r1 = -1;h.i_r2 = -1;
  if (currRing!=strat->tailRing)
    h.t_p = k_LmInit_currRing_2_tailRing(h.p, strat->tailRing);
  if(!enterTstrong)
  {
    #if 1
    h.p1 = p;h.p2 = strat->S[i];
    #endif
    if (atR >= 0)
    {
      h.i_r2 = strat->S_2_R[i];
      h.i_r1 = atR;
    }
    else
    {
      h.i_r1 = -1;
      h.i_r2 = -1;
    }
    if (strat->Ll==-1)
      posx =0;
    else
      posx = strat->posInL(strat->L,strat->Ll,&h,strat);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,h,posx);
  }
  else
  {
    if(h.IsNull()) return FALSE;
    //int red_result;
    //reduzieren ist teur!!!
    //if(strat->L != NULL)
      //red_result = strat->red(&h,strat);
    if(!h.IsNull())
    {
      enterT(h, strat,-1);
      //int pos = posInS(strat,strat->sl,h.p,h.ecart);
      //strat->enterS(h,pos,strat,-1);
    }
  }
  return TRUE;
}
 
BOOLEAN sbaCheckGcdPair (LObject* h,kStrategy strat)
{
  if(strat->sl < 0) return FALSE;
  int i;
  for(i=0;i<strat->sl;i++)
  {
    //Construct the gcd pair between h and S[i]
    number d, s, t;
    poly m1, m2, gcd;
    d = n_ExtGcd(pGetCoeff(h->p), pGetCoeff(strat->S[i]), &s, &t, currRing->cf);
    if (nIsZero(s) || nIsZero(t))  // evtl. durch divBy tests ersetzen
    {
      nDelete(&d);
      nDelete(&s);
      nDelete(&t);
    }
    else
    {
      k_GetStrongLeadTerms(h->p, strat->S[i], currRing, m1, m2, gcd, strat->tailRing);
      pSetCoeff0(m1, s);
      pSetCoeff0(m2, t);
      pSetCoeff0(gcd, d);
      pNext(gcd) = p_Add_q(pp_Mult_mm(pNext(h->p), m1, strat->tailRing), pp_Mult_mm(pNext(strat->S[i]), m2, strat->tailRing), strat->tailRing);
      poly pSigMult = p_Copy(h->sig,currRing);
      poly sSigMult = p_Copy(strat->sig[i],currRing);
      pSigMult = p_Mult_mm(pSigMult,m1,currRing);
      sSigMult = p_Mult_mm(sSigMult,m2,currRing);
      p_LmDelete(m1, strat->tailRing);
      p_LmDelete(m2, strat->tailRing);
      poly pairsig = p_Add_q(pSigMult,sSigMult,currRing);
      if(pairsig!= NULL && pLtCmp(pairsig,h->sig) == 0)
      {
        pDelete(&h->p);
        h->p = gcd;
        pDelete(&h->sig);
        h->sig = pairsig;
        pNext(h->sig) = NULL;
        strat->initEcart(h);
        h->sev = pGetShortExpVector(h->p);
        h->sevSig = pGetShortExpVector(h->sig);
        h->i_r1 = -1;h->i_r2 = -1;
        if(h->lcm != NULL)
        {
          pLmDelete(h->lcm);
          h->lcm = NULL;
        }
        if (currRing!=strat->tailRing)
          h->t_p = k_LmInit_currRing_2_tailRing(h->p, strat->tailRing);
        return TRUE;
      }
      //Delete what you didn't use
      pDelete(&gcd);
      pDelete(&pairsig);
    }
  }
  return FALSE;
}
 
static BOOLEAN enterOneStrongPolySig (int i,poly p,poly sig,int /*ecart*/, int /*isFromQ*/,kStrategy strat, int atR)
{
  number d, s, t;
  assume(atR >= 0);
  poly m1, m2, gcd,si;
  assume(i<=strat->sl);
  si = strat->S[i];
  //printf("\n--------------------------------\n");
  //pWrite(p);pWrite(si);
  d = n_ExtGcd(pGetCoeff(p), pGetCoeff(si), &s, &t, currRing->cf);
 
  if (nIsZero(s) || nIsZero(t))  // evtl. durch divBy tests ersetzen
  {
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
    return FALSE;
  }
 
  k_GetStrongLeadTerms(p, si, currRing, m1, m2, gcd, strat->tailRing);
  //p_Test(m1,strat->tailRing);
  //p_Test(m2,strat->tailRing);
  /*if(!enterTstrong)
  {
    while (! kCheckStrongCreation(atR, m1, i, m2, strat) )
    {
      memset(&(strat->P), 0, sizeof(strat->P));
      kStratChangeTailRing(strat);
      strat->P = *(strat->R[atR]);
      p_LmFree(m1, strat->tailRing);
      p_LmFree(m2, strat->tailRing);
      p_LmFree(gcd, currRing);
      k_GetStrongLeadTerms(p, si, currRing, m1, m2, gcd, strat->tailRing);
    }
  }*/
  pSetCoeff0(m1, s);
  pSetCoeff0(m2, t);
  pSetCoeff0(gcd, d);
  p_Test(m1,strat->tailRing);
  p_Test(m2,strat->tailRing);
  //printf("\n===================================\n");
  //pWrite(m1);pWrite(m2);pWrite(gcd);
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    // Print("t = %d; s = %d; d = %d\n", nInt(t), nInt(s), nInt(d));
    PrintS("m1 = ");
    p_wrp(m1, strat->tailRing);
    PrintS(" ; m2 = ");
    p_wrp(m2, strat->tailRing);
    PrintS(" ; gcd = ");
    wrp(gcd);
    PrintS("\n--- create strong gcd poly: ");
    Print("\n p: %d", i);
    wrp(p);
    Print("\n strat->S[%d]: ", i);
    wrp(si);
    PrintS(" ---> ");
  }
#endif
 
  pNext(gcd) = p_Add_q(pp_Mult_mm(pNext(p), m1, strat->tailRing), pp_Mult_mm(pNext(si), m2, strat->tailRing), strat->tailRing);
 
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    wrp(gcd);
    PrintLn();
  }
#endif
 
  //Check and set the signatures
  poly pSigMult = p_Copy(sig,currRing);
  poly sSigMult = p_Copy(strat->sig[i],currRing);
  pSigMult = p_Mult_mm(pSigMult,m1,currRing);
  sSigMult = p_Mult_mm(sSigMult,m2,currRing);
  p_LmDelete(m1, strat->tailRing);
  p_LmDelete(m2, strat->tailRing);
  poly pairsig;
  if(pLmCmp(pSigMult,sSigMult) == 0)
  {
    //Same lm, have to add them
    pairsig = p_Add_q(pSigMult,sSigMult,currRing);
    //This might be zero
  }
  else
  {
    //Set the sig to either pSigMult or sSigMult
    if(pLtCmp(pSigMult,sSigMult)==1)
    {
      pairsig = pSigMult;
      pDelete(&sSigMult);
    }
    else
    {
      pairsig = sSigMult;
      pDelete(&pSigMult);
    }
  }
 
  LObject h;
  h.p = gcd;
  h.tailRing = strat->tailRing;
  h.sig = pairsig;
  int posx;
  strat->initEcart(&h);
  h.sev = pGetShortExpVector(h.p);
  h.i_r1 = -1;h.i_r2 = -1;
  if (currRing!=strat->tailRing)
    h.t_p = k_LmInit_currRing_2_tailRing(h.p, strat->tailRing);
  if(h.sig == NULL)
    {
      //sigdrop since we loose the signature
      strat->sigdrop = TRUE;
      //Try to reduce it as far as we can via redRing
      int red_result = redRing(&h,strat);
      if(red_result == 0)
      {
        // Cancel the sigdrop
        p_Delete(&h.sig,currRing);h.sig = NULL;
        strat->sigdrop = FALSE;
        return FALSE;
      }
      else
      {
        strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
        #if 1
        strat->enterS(h,0,strat,strat->tl);
        #endif
        return FALSE;
      }
    }
  if(!nGreaterZero(pGetCoeff(h.sig)))
  {
    h.sig = pNeg(h.sig);
    h.p = pNeg(h.p);
  }
 
    if(rField_is_Ring(currRing) &&  pLtCmp(h.sig,sig) == -1)
    {
      strat->sigdrop = TRUE;
      // Completely reduce it
      int red_result = redRing(&h,strat);
      if(red_result == 0)
      {
        // Reduced to 0
        strat->sigdrop = FALSE;
        p_Delete(&h.sig,currRing);h.sig = NULL;
        return FALSE;
      }
      else
      {
        strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
        // 0 - add just the original poly causing the sigdrop, 1 - add also this
        #if 1
        strat->enterS(h,0,strat, strat->tl+1);
        #endif
        return FALSE;
      }
    }
  //Check for sigdrop
  if(gcd != NULL && pLtCmp(sig,pairsig) > 0 && pLtCmp(strat->sig[i],pairsig) > 0)
  {
    strat->sigdrop = TRUE;
    //Enter this element to S
    strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
    strat->enterS(h,strat->sl+1,strat,strat->tl+1);
  }
  #if 1
  h.p1 = p;h.p2 = strat->S[i];
  #endif
  if (atR >= 0)
  {
    h.i_r2 = strat->S_2_R[i];
    h.i_r1 = atR;
  }
  else
  {
    h.i_r1 = -1;
    h.i_r2 = -1;
  }
  if (strat->Ll==-1)
    posx =0;
  else
    posx = strat->posInLSba(strat->L,strat->Ll,&h,strat);
  enterL(&strat->L,&strat->Ll,&strat->Lmax,h,posx);
  return TRUE;
}
 
/*2
* put the pair (s[i],p)  into the set B, ecart=ecart(p)
*/
 
void enterOnePairNormal (int i,poly p,int ecart, int isFromQ,kStrategy strat, int atR = -1)
{
  assume(i<=strat->sl);
 
  int      l,j,compare;
  LObject  Lp;
  Lp.i_r = -1;
 
#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = pInit();
 
#ifndef HAVE_RATGRING
  pLcm(p,strat->S[i],Lp.lcm);
#elif defined(HAVE_RATGRING)
  if (rIsRatGRing(currRing))
    pLcmRat(p,strat->S[i],Lp.lcm, currRing->real_var_start); // int rat_shift
  else
    pLcm(p,strat->S[i],Lp.lcm);
#endif
  pSetm(Lp.lcm);
 
 
  if (strat->sugarCrit && ALLOW_PROD_CRIT(strat))
  {
    if (strat->fromT && (strat->ecartS[i]>ecart))
    {
      pLmFree(Lp.lcm);
      return;
      /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
    }
    if((!((strat->ecartS[i]>0)&&(ecart>0)))
    && pHasNotCF(p,strat->S[i]))
    {
    /*
    *the product criterion has applied for (s,p),
    *i.e. lcm(s,p)=product of the leading terms of s and p.
    *Suppose (s,r) is in L and the leading term
    *of p divides lcm(s,r)
    *(==> the leading term of p divides the leading term of r)
    *but the leading term of s does not divide the leading term of r
    *(notice that tis condition is automatically satisfied if r is still
    *in S), then (s,r) can be cancelled.
    *This should be done here because the
    *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
    *
    *Moreover, skipping (s,r) holds also for the noncommutative case.
    */
      strat->cp++;
      pLmFree(Lp.lcm);
      return;
    }
    Lp.ecart = si_max(ecart,strat->ecartS[i]);
    /*
    *the set B collects the pairs of type (S[j],p)
    *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
    *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
    */
    {
      j = strat->Bl;
      loop
      {
        if (j < 0)  break;
        compare=pDivComp(strat->B[j].lcm,Lp.lcm);
        if ((compare==1)
        &&(sugarDivisibleBy(strat->B[j].ecart,Lp.ecart)))
        {
          strat->c3++;
          if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
          {
            pLmFree(Lp.lcm);
            return;
          }
          break;
        }
        else
        if ((compare ==-1)
        && sugarDivisibleBy(Lp.ecart,strat->B[j].ecart))
        {
          deleteInL(strat->B,&strat->Bl,j,strat);
          strat->c3++;
        }
        j--;
      }
    }
  }
  else /*sugarcrit*/
  {
    if (ALLOW_PROD_CRIT(strat))
    {
      if (strat->fromT && (strat->ecartS[i]>ecart))
      {
        pLmFree(Lp.lcm);
        return;
        /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
      }
      // if currRing->nc_type!=quasi (or skew)
      // TODO: enable productCrit for super commutative algebras...
      if(/*(strat->ak==0) && productCrit(p,strat->S[i])*/
      pHasNotCF(p,strat->S[i]))
      {
      /*
      *the product criterion has applied for (s,p),
      *i.e. lcm(s,p)=product of the leading terms of s and p.
      *Suppose (s,r) is in L and the leading term
      *of p divides lcm(s,r)
      *(==> the leading term of p divides the leading term of r)
      *but the leading term of s does not divide the leading term of r
      *(notice that tis condition is automatically satisfied if r is still
      *in S), then (s,r) can be canceled.
      *This should be done here because the
      *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
      */
          strat->cp++;
          pLmFree(Lp.lcm);
          return;
      }
      /*
      *the set B collects the pairs of type (S[j],p)
      *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
      *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
      *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
      */
      for(j = strat->Bl;j>=0;j--)
      {
        compare=pDivComp(strat->B[j].lcm,Lp.lcm);
        if (compare==1)
        {
          strat->c3++;
          if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
          {
            pLmFree(Lp.lcm);
            return;
          }
          break;
        }
        else
        if (compare ==-1)
        {
          deleteInL(strat->B,&strat->Bl,j,strat);
          strat->c3++;
        }
      }
    }
  }
  /*
  *the pair (S[i],p) enters B if the spoly != 0
  */
  /*-  compute the short s-polynomial -*/
  if (strat->fromT && !TEST_OPT_INTSTRATEGY)
    pNorm(p);
 
  if ((strat->S[i]==NULL) || (p==NULL))
    return;
 
  if ((strat->fromQ!=NULL) && (isFromQ!=0) && (strat->fromQ[i]!=0))
    Lp.p=NULL;
  else
  {
    #ifdef HAVE_PLURAL
    if ( rIsPluralRing(currRing) )
    {
      if(pHasNotCF(p, strat->S[i]))
      {
        if(ncRingType(currRing) == nc_lie)
        {
          // generalized prod-crit for lie-type
          strat->cp++;
          Lp.p = nc_p_Bracket_qq(pCopy(p),strat->S[i], currRing);
        }
        else
        if( ALLOW_PROD_CRIT(strat) )
        {
          // product criterion for homogeneous case in SCA
          strat->cp++;
          Lp.p = NULL;
        }
        else
        {
          Lp.p = // nc_CreateSpoly(strat->S[i],p,currRing);
               nc_CreateShortSpoly(strat->S[i], p, currRing);
          assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
          pNext(Lp.p) = strat->tail; // !!!
        }
      }
      else
      {
        Lp.p = // nc_CreateSpoly(strat->S[i],p,currRing);
              nc_CreateShortSpoly(strat->S[i], p, currRing);
 
        assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
        pNext(Lp.p) = strat->tail; // !!!
      }
    }
    else
    #endif
    {
      assume(!rIsPluralRing(currRing));
      Lp.p = ksCreateShortSpoly(strat->S[i], p, strat->tailRing);
    }
  }
  if (Lp.p == NULL)
  {
    /*- the case that the s-poly is 0 -*/
    if (strat->pairtest==NULL) initPairtest(strat);
    strat->pairtest[i] = TRUE;/*- hint for spoly(S^[i],p)=0 -*/
    strat->pairtest[strat->sl+1] = TRUE;
    /*hint for spoly(S[i],p) == 0 for some i,0 <= i <= sl*/
    /*
    *suppose we have (s,r),(r,p),(s,p) and spoly(s,p) == 0 and (r,p) is
    *still in B (i.e. lcm(r,p) == lcm(s,p) or the leading term of s does not
    *divide lcm(r,p)). In the last case (s,r) can be canceled if the leading
    *term of p divides the lcm(s,r)
    *(this canceling should be done here because
    *the case lcm(s,p) == lcm(s,r) is not covered in chainCrit)
    *the first case is handled in chainCrit
    */
    if (Lp.lcm!=NULL) pLmFree(Lp.lcm);
  }
  else
  {
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
 
    if (
        (!rIsPluralRing(currRing))
//      ||  (rIsPluralRing(currRing) && (ncRingType(currRing) != nc_lie))
       )
    {
      assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
      pNext(Lp.p) = strat->tail; // !!!
    }
 
    if (atR >= 0)
    {
      Lp.i_r1 = strat->S_2_R[i];
      Lp.i_r2 = atR;
    }
    else
    {
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
    }
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
 
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
 
    l = strat->posInL(strat->B,strat->Bl,&Lp,strat);
    enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
  }
}
 
/// p_HasNotCF for the IDLIFT case and syzComp==1: ignore component
static inline BOOLEAN p_HasNotCF_Lift(poly p1, poly p2, const ring r)
{
  int i = rVar(r);
  loop
  {
    if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0))
      return FALSE;
    i--;
    if (i == 0)
      return TRUE;
  }
}
 
/*2
* put the pair (s[i],p)  into the set B, ecart=ecart(p) for idLift(I,T)
*  (in the special case: idLift for ideals, i.e. strat->syzComp==1)
*  (prod.crit applies)
*/
 
static void enterOnePairLift (int i,poly p,int ecart, int isFromQ,kStrategy strat, int atR = -1)
{
  assume(ALLOW_PROD_CRIT(strat));
  assume(!rIsPluralRing(currRing));
  assume(i<=strat->sl);
  assume(strat->syzComp==1);
 
  if ((strat->S[i]==NULL) || (p==NULL))
    return;
 
  int      l,j,compare;
  LObject  Lp;
  Lp.i_r = -1;
 
#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = p_Lcm(p,strat->S[i],currRing);
 
  if (strat->sugarCrit)
  {
    if((!((strat->ecartS[i]>0)&&(ecart>0)))
    && p_HasNotCF_Lift(p,strat->S[i],currRing))
    {
    /*
    *the product criterion has applied for (s,p),
    *i.e. lcm(s,p)=product of the leading terms of s and p.
    *Suppose (s,r) is in L and the leading term
    *of p divides lcm(s,r)
    *(==> the leading term of p divides the leading term of r)
    *but the leading term of s does not divide the leading term of r
    *(notice that tis condition is automatically satisfied if r is still
    *in S), then (s,r) can be cancelled.
    *This should be done here because the
    *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
    *
    *Moreover, skipping (s,r) holds also for the noncommutative case.
    */
      strat->cp++;
      pLmFree(Lp.lcm);
      return;
    }
    else
      Lp.ecart = si_max(ecart,strat->ecartS[i]);
    if (strat->fromT && (strat->ecartS[i]>ecart))
    {
      pLmFree(Lp.lcm);
      return;
      /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
    }
    /*
    *the set B collects the pairs of type (S[j],p)
    *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
    *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
    */
    {
      j = strat->Bl;
      loop
      {
        if (j < 0)  break;
        compare=pDivComp(strat->B[j].lcm,Lp.lcm);
        if ((compare==1)
        &&(sugarDivisibleBy(strat->B[j].ecart,Lp.ecart)))
        {
          strat->c3++;
          if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
          {
            pLmFree(Lp.lcm);
            return;
          }
          break;
        }
        else
        if ((compare ==-1)
        && sugarDivisibleBy(Lp.ecart,strat->B[j].ecart))
        {
          deleteInL(strat->B,&strat->Bl,j,strat);
          strat->c3++;
        }
        j--;
      }
    }
  }
  else /*sugarcrit*/
  {
    if(/*(strat->ak==0) && productCrit(p,strat->S[i])*/
    p_HasNotCF_Lift(p,strat->S[i],currRing))
    {
    /*
    *the product criterion has applied for (s,p),
    *i.e. lcm(s,p)=product of the leading terms of s and p.
    *Suppose (s,r) is in L and the leading term
    *of p divides lcm(s,r)
    *(==> the leading term of p divides the leading term of r)
    *but the leading term of s does not divide the leading term of r
    *(notice that tis condition is automatically satisfied if r is still
    *in S), then (s,r) can be canceled.
    *This should be done here because the
    *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
    */
      strat->cp++;
      pLmFree(Lp.lcm);
      return;
    }
    if (strat->fromT && (strat->ecartS[i]>ecart))
    {
      pLmFree(Lp.lcm);
      return;
      /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
    }
    /*
    *the set B collects the pairs of type (S[j],p)
    *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
    *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
    */
    for(j = strat->Bl;j>=0;j--)
    {
      compare=pDivComp(strat->B[j].lcm,Lp.lcm);
      if (compare==1)
      {
        strat->c3++;
        if ((strat->fromQ==NULL) || (isFromQ==0) || (strat->fromQ[i]==0))
        {
          pLmFree(Lp.lcm);
          return;
        }
        break;
      }
      else
      if (compare ==-1)
      {
        deleteInL(strat->B,&strat->Bl,j,strat);
        strat->c3++;
      }
    }
  }
  /*
  *the pair (S[i],p) enters B if the spoly != 0
  */
  /*-  compute the short s-polynomial -*/
  if (strat->fromT && !TEST_OPT_INTSTRATEGY)
    pNorm(p);
 
  if ((strat->fromQ!=NULL) && (isFromQ!=0) && (strat->fromQ[i]!=0))
    Lp.p=NULL;
  else
  {
    assume(!rIsPluralRing(currRing));
    Lp.p = ksCreateShortSpoly(strat->S[i], p, strat->tailRing);
  }
  if (Lp.p == NULL)
  {
    /*- the case that the s-poly is 0 -*/
    if (strat->pairtest==NULL) initPairtest(strat);
    strat->pairtest[i] = TRUE;/*- hint for spoly(S^[i],p)=0 -*/
    strat->pairtest[strat->sl+1] = TRUE;
    /*hint for spoly(S[i],p) == 0 for some i,0 <= i <= sl*/
    /*
    *suppose we have (s,r),(r,p),(s,p) and spoly(s,p) == 0 and (r,p) is
    *still in B (i.e. lcm(r,p) == lcm(s,p) or the leading term of s does not
    *divide lcm(r,p)). In the last case (s,r) can be canceled if the leading
    *term of p divides the lcm(s,r)
    *(this canceling should be done here because
    *the case lcm(s,p) == lcm(s,r) is not covered in chainCrit)
    *the first case is handled in chainCrit
    */
    if (Lp.lcm!=NULL) pLmFree(Lp.lcm);
  }
  else
  {
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
 
    pNext(Lp.p) = strat->tail; // !!!
 
    if (atR >= 0)
    {
      Lp.i_r1 = strat->S_2_R[i];
      Lp.i_r2 = atR;
    }
    else
    {
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
    }
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
 
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
 
    l = strat->posInL(strat->B,strat->Bl,&Lp,strat);
    enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
  }
}
 
/*2
* put the pair (s[i],p)  into the set B, ecart=ecart(p)
* NOTE: here we need to add the signature-based criteria
*/
 
#ifdef DEBUGF5
static void enterOnePairSig (int i, poly p, poly pSig, int from, int ecart, int isFromQ, kStrategy strat, int atR = -1)
#else
static void enterOnePairSig (int i, poly p, poly pSig, int, int ecart, int isFromQ, kStrategy strat, int atR = -1)
#endif
{
  assume(i<=strat->sl);
 
  int      l;
  poly m1 = NULL,m2 = NULL; // we need the multipliers for the s-polynomial to compute
              // the corresponding signatures for criteria checks
  LObject  Lp;
  poly pSigMult = p_Copy(pSig,currRing);
  poly sSigMult = p_Copy(strat->sig[i],currRing);
  unsigned long pSigMultNegSev,sSigMultNegSev;
  Lp.i_r = -1;
 
#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = pInit();
  k_GetLeadTerms(p,strat->S[i],currRing,m1,m2,currRing);
#ifndef HAVE_RATGRING
  pLcm(p,strat->S[i],Lp.lcm);
#elif defined(HAVE_RATGRING)
  if (rIsRatGRing(currRing))
    pLcmRat(p,strat->S[i],Lp.lcm, currRing->real_var_start); // int rat_shift
  else
    pLcm(p,strat->S[i],Lp.lcm);
#endif
  pSetm(Lp.lcm);
 
  // set coeffs of multipliers m1 and m2
  pSetCoeff0(m1, nInit(1));
  pSetCoeff0(m2, nInit(1));
//#if 1
#ifdef DEBUGF5
  PrintS("P1  ");
  pWrite(pHead(p));
  PrintS("P2  ");
  pWrite(pHead(strat->S[i]));
  PrintS("M1  ");
  pWrite(m1);
  PrintS("M2  ");
  pWrite(m2);
#endif
  // get multiplied signatures for testing
  pSigMult = currRing->p_Procs->pp_Mult_mm(pSigMult,m1,currRing);
  pSigMultNegSev = ~p_GetShortExpVector(pSigMult,currRing);
  sSigMult = currRing->p_Procs->pp_Mult_mm(sSigMult,m2,currRing);
  sSigMultNegSev = ~p_GetShortExpVector(sSigMult,currRing);
 
//#if 1
#ifdef DEBUGF5
  PrintS("----------------\n");
  pWrite(pSigMult);
  pWrite(sSigMult);
  PrintS("----------------\n");
  Lp.checked  = 0;
#endif
  int sigCmp = p_LmCmp(pSigMult,sSigMult,currRing);
//#if 1
#if DEBUGF5
  Print("IN PAIR GENERATION - COMPARING SIGS: %d\n",sigCmp);
  pWrite(pSigMult);
  pWrite(sSigMult);
#endif
  if(sigCmp==0)
  {
    // printf("!!!!   EQUAL SIGS   !!!!\n");
    // pSig = sSig, delete element due to Rewritten Criterion
    pDelete(&pSigMult);
    pDelete(&sSigMult);
    if (rField_is_Ring(currRing))
      pLmDelete(Lp.lcm);
    else
      pLmFree(Lp.lcm);
    pDelete (&m1);
    pDelete (&m2);
    return;
  }
  // testing by syzCrit = F5 Criterion
  // testing by rewCrit1 = Rewritten Criterion
  // NOTE: Arri's Rewritten Criterion is tested below, we need Lp.p for it!
  if  ( strat->syzCrit(pSigMult,pSigMultNegSev,strat) ||
        strat->syzCrit(sSigMult,sSigMultNegSev,strat)
        || strat->rewCrit1(sSigMult,sSigMultNegSev,Lp.lcm,strat,i+1)
      )
  {
    pDelete(&pSigMult);
    pDelete(&sSigMult);
    if (rField_is_Ring(currRing))
      pLmDelete(Lp.lcm);
    else
      pLmFree(Lp.lcm);
    pDelete (&m1);
    pDelete (&m2);
    return;
  }
  /*
  *the pair (S[i],p) enters B if the spoly != 0
  */
  /*-  compute the short s-polynomial -*/
  if (strat->fromT && !TEST_OPT_INTSTRATEGY)
    pNorm(p);
 
  if ((strat->S[i]==NULL) || (p==NULL))
    return;
 
  if ((strat->fromQ!=NULL) && (isFromQ!=0) && (strat->fromQ[i]!=0))
    Lp.p=NULL;
  else
  {
    #ifdef HAVE_PLURAL
    if ( rIsPluralRing(currRing) )
    {
      if(pHasNotCF(p, strat->S[i]))
      {
        if(ncRingType(currRing) == nc_lie)
        {
          // generalized prod-crit for lie-type
          strat->cp++;
          Lp.p = nc_p_Bracket_qq(pCopy(p),strat->S[i], currRing);
        }
        else
        if( ALLOW_PROD_CRIT(strat) )
        {
          // product criterion for homogeneous case in SCA
          strat->cp++;
          Lp.p = NULL;
        }
        else
        {
          Lp.p = // nc_CreateSpoly(strat->S[i],p,currRing);
                nc_CreateShortSpoly(strat->S[i], p, currRing);
 
          assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
          pNext(Lp.p) = strat->tail; // !!!
        }
      }
      else
      {
        Lp.p = // nc_CreateSpoly(strat->S[i],p,currRing);
              nc_CreateShortSpoly(strat->S[i], p, currRing);
 
        assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
        pNext(Lp.p) = strat->tail; // !!!
      }
    }
    else
    #endif
    {
      assume(!rIsPluralRing(currRing));
      Lp.p = ksCreateShortSpoly(strat->S[i], p, strat->tailRing);
    }
  }
  // store from which element this pair comes from for further tests
  //Lp.from = strat->sl+1;
  if(sigCmp==currRing->OrdSgn)
  {
    // pSig > sSig
    pDelete (&sSigMult);
    Lp.sig    = pSigMult;
    Lp.sevSig = ~pSigMultNegSev;
  }
  else
  {
    // pSig < sSig
    pDelete (&pSigMult);
    Lp.sig    = sSigMult;
    Lp.sevSig = ~sSigMultNegSev;
  }
  if (Lp.p == NULL)
  {
    if (Lp.lcm!=NULL) pLmFree(Lp.lcm);
    int pos = posInSyz(strat, Lp.sig);
    enterSyz(Lp, strat, pos);
  }
  else
  {
    // testing by rewCrit3 = Arris Rewritten Criterion (for F5 nothing happens!)
    if (strat->rewCrit3(Lp.sig,~Lp.sevSig,Lp.p,strat,strat->sl+1))
    {
      pLmFree(Lp.lcm);
      pDelete(&Lp.sig);
      pDelete (&m1);
      pDelete (&m2);
      return;
    }
    // in any case Lp is checked up to the next strat->P which is added
    // to S right after this critical pair creation.
    // NOTE: this even holds if the 2nd generator gives the bigger signature
    //       moreover, this improves rewCriterion,
    //       i.e. strat->checked > strat->from if and only if the 2nd generator
    //       gives the bigger signature.
    Lp.checked = strat->sl+1;
    // at this point it is clear that the pair will be added to L, since it has
    // passed all tests up to now
 
  // adds buchberger's first criterion
    if (pLmCmp(m2,pHead(p)) == 0)
    {
      Lp.prod_crit = TRUE; // Product Criterion
#if 0
      int pos = posInSyz(strat, Lp.sig);
      enterSyz(Lp, strat, pos);
      pDelete (&m1);
      pDelete (&m2);
      return;
#endif
    }
    pDelete (&m1);
    pDelete (&m2);
#if DEBUGF5
    PrintS("SIGNATURE OF PAIR:  ");
    pWrite(Lp.sig);
#endif
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
 
    if (
        (!rIsPluralRing(currRing))
//      ||  (rIsPluralRing(currRing) && (ncRingType(currRing) != nc_lie))
       )
    {
      assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
      pNext(Lp.p) = strat->tail; // !!!
    }
 
    if (atR >= 0)
    {
      Lp.i_r1 = strat->S_2_R[i];
      Lp.i_r2 = atR;
    }
    else
    {
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
    }
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
 
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
 
    l = strat->posInLSba(strat->B,strat->Bl,&Lp,strat);
    enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
  }
}
 
 
#ifdef DEBUGF5
static void enterOnePairSigRing (int i, poly p, poly pSig, int from, int ecart, int isFromQ, kStrategy strat, int atR = -1)
#else
static void enterOnePairSigRing (int i, poly p, poly pSig, int, int ecart, int isFromQ, kStrategy strat, int atR = -1)
#endif
{
  #if ALL_VS_JUST
  //Over rings, if we construct the strong pair, do not add the spair
  if(rField_is_Ring(currRing))
  {
    number s,t,d;
    d = n_ExtGcd(pGetCoeff(p), pGetCoeff(strat->S[i]), &s, &t, currRing->cf);
 
    if (!nIsZero(s) && !nIsZero(t))  // evtl. durch divBy tests ersetzen
    {
      nDelete(&d);
      nDelete(&s);
      nDelete(&t);
      return;
    }
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
  }
  #endif
  assume(i<=strat->sl);
  int      l;
  poly m1 = NULL,m2 = NULL; // we need the multipliers for the s-polynomial to compute
              // the corresponding signatures for criteria checks
  LObject  Lp;
  poly pSigMult = p_Copy(pSig,currRing);
  poly sSigMult = p_Copy(strat->sig[i],currRing);
  unsigned long pSigMultNegSev,sSigMultNegSev;
  Lp.i_r = -1;
 
#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = pInit();
  k_GetLeadTerms(p,strat->S[i],currRing,m1,m2,currRing);
#ifndef HAVE_RATGRING
  pLcm(p,strat->S[i],Lp.lcm);
#elif defined(HAVE_RATGRING)
  if (rIsRatGRing(currRing))
    pLcmRat(p,strat->S[i],Lp.lcm, currRing->real_var_start); // int rat_shift
  else
    pLcm(p,strat->S[i],Lp.lcm);
#endif
  pSetm(Lp.lcm);
 
  // set coeffs of multipliers m1 and m2
  if(rField_is_Ring(currRing))
  {
    number s = nCopy(pGetCoeff(strat->S[i]));
    number t = nCopy(pGetCoeff(p));
    pSetCoeff0(Lp.lcm, n_Lcm(s, t, currRing->cf));
    ksCheckCoeff(&s, &t, currRing->cf);
    pSetCoeff0(m1,s);
    pSetCoeff0(m2,t);
  }
  else
  {
    pSetCoeff0(m1, nInit(1));
    pSetCoeff0(m2, nInit(1));
  }
#ifdef DEBUGF5
  Print("P1  ");
  pWrite(pHead(p));
  Print("P2  ");
  pWrite(pHead(strat->S[i]));
  Print("M1  ");
  pWrite(m1);
  Print("M2  ");
  pWrite(m2);
#endif
 
  // get multiplied signatures for testing
  pSigMult = pp_Mult_mm(pSigMult,m1,currRing);
  if(pSigMult != NULL)
    pSigMultNegSev = ~p_GetShortExpVector(pSigMult,currRing);
  sSigMult = pp_Mult_mm(sSigMult,m2,currRing);
  if(sSigMult != NULL)
    sSigMultNegSev = ~p_GetShortExpVector(sSigMult,currRing);
//#if 1
#ifdef DEBUGF5
  Print("----------------\n");
  pWrite(pSigMult);
  pWrite(sSigMult);
  Print("----------------\n");
  Lp.checked  = 0;
#endif
  int sigCmp;
  if(pSigMult != NULL && sSigMult != NULL)
  {
    if(rField_is_Ring(currRing))
      sigCmp = p_LtCmpNoAbs(pSigMult,sSigMult,currRing);
    else
      sigCmp = p_LmCmp(pSigMult,sSigMult,currRing);
  }
  else
  {
    if(pSigMult == NULL)
    {
      if(sSigMult == NULL)
        sigCmp = 0;
      else
        sigCmp = -1;
    }
    else
      sigCmp = 1;
  }
//#if 1
#if DEBUGF5
  Print("IN PAIR GENERATION - COMPARING SIGS: %d\n",sigCmp);
  pWrite(pSigMult);
  pWrite(sSigMult);
#endif
  //In the ring case we already build the sig
  if(rField_is_Ring(currRing))
  {
    if(sigCmp == 0)
    {
      //sigdrop since we loose the signature
      strat->sigdrop = TRUE;
      //Try to reduce it as far as we can via redRing
      if(rField_is_Ring(currRing))
      {
        poly p1 = p_Copy(p,currRing);
        poly p2 = p_Copy(strat->S[i],currRing);
        p1 = p_Mult_mm(p1,m1,currRing);
        p2 = p_Mult_mm(p2,m2,currRing);
        Lp.p = p_Sub(p1,p2,currRing);
        if(Lp.p != NULL)
          Lp.sev = p_GetShortExpVector(Lp.p,currRing);
      }
      int red_result = redRing(&Lp,strat);
      if(red_result == 0)
      {
        // Cancel the sigdrop
        p_Delete(&Lp.sig,currRing);Lp.sig = NULL;
        strat->sigdrop = FALSE;
        return;
      }
      else
      {
        strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
        #if 1
        strat->enterS(Lp,0,strat,strat->tl);
        #endif
        return;
      }
    }
    if(pSigMult != NULL && sSigMult != NULL && p_LmCmp(pSigMult,sSigMult,currRing) == 0)
    {
      //Same lm, have to subtract
      Lp.sig = p_Sub(pCopy(pSigMult),pCopy(sSigMult),currRing);
    }
    else
    {
      if(sigCmp == 1)
      {
        Lp.sig = pCopy(pSigMult);
      }
      if(sigCmp == -1)
      {
        Lp.sig = pNeg(pCopy(sSigMult));
      }
    }
    Lp.sevSig = p_GetShortExpVector(Lp.sig,currRing);
  }
 
  #if 0
  if(sigCmp==0)
  {
    // printf("!!!!   EQUAL SIGS   !!!!\n");
    // pSig = sSig, delete element due to Rewritten Criterion
    pDelete(&pSigMult);
    pDelete(&sSigMult);
    if (rField_is_Ring(currRing))
      pLmDelete(Lp.lcm);
    else
      pLmFree(Lp.lcm);
    pDelete (&m1);
    pDelete (&m2);
    return;
  }
  #endif
  // testing by syzCrit = F5 Criterion
  // testing by rewCrit1 = Rewritten Criterion
  // NOTE: Arri's Rewritten Criterion is tested below, we need Lp.p for it!
  if  ( strat->syzCrit(pSigMult,pSigMultNegSev,strat) ||
        strat->syzCrit(sSigMult,sSigMultNegSev,strat)
        // With this rewCrit activated i get a wrong deletion in sba_int_56.tst
        //|| strat->rewCrit1(sSigMult,sSigMultNegSev,Lp.lcm,strat,i+1)
      )
  {
    pDelete(&pSigMult);
    pDelete(&sSigMult);
    if (rField_is_Ring(currRing))
      pLmDelete(Lp.lcm);
    else
      pLmFree(Lp.lcm);
    pDelete (&m1);
    pDelete (&m2);
    return;
  }
  /*
  *the pair (S[i],p) enters B if the spoly != 0
  */
  /*-  compute the short s-polynomial -*/
  if (strat->fromT && !TEST_OPT_INTSTRATEGY)
    pNorm(p);
 
  if ((strat->S[i]==NULL) || (p==NULL))
    return;
 
  if ((strat->fromQ!=NULL) && (isFromQ!=0) && (strat->fromQ[i]!=0))
    Lp.p=NULL;
  else
  {
    //Build p
    if(rField_is_Ring(currRing))
    {
      poly p1 = p_Copy(p,currRing);
      poly p2 = p_Copy(strat->S[i],currRing);
      p1 = p_Mult_mm(p1,m1,currRing);
      p2 = p_Mult_mm(p2,m2,currRing);
      Lp.p = p_Sub(p1,p2,currRing);
      if(Lp.p != NULL)
        Lp.sev = p_GetShortExpVector(Lp.p,currRing);
    }
    else
    {
      #ifdef HAVE_PLURAL
      if ( rIsPluralRing(currRing) )
      {
        if(ncRingType(currRing) == nc_lie)
        {
          // generalized prod-crit for lie-type
          strat->cp++;
          Lp.p = nc_p_Bracket_qq(pCopy(p),strat->S[i], currRing);
        }
        else
        if( ALLOW_PROD_CRIT(strat) )
        {
          // product criterion for homogeneous case in SCA
          strat->cp++;
          Lp.p = NULL;
        }
        else
        {
          Lp.p = // nc_CreateSpoly(strat->S[i],p,currRing);
                nc_CreateShortSpoly(strat->S[i], p, currRing);
 
          assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
          pNext(Lp.p) = strat->tail; // !!!
        }
      }
      else
      #endif
      {
        assume(!rIsPluralRing(currRing));
        Lp.p = ksCreateShortSpoly(strat->S[i], p, strat->tailRing);
      }
    }
  }
  // store from which element this pair comes from for further tests
  //Lp.from = strat->sl+1;
  if(rField_is_Ring(currRing))
  {
    //Put the sig to be > 0
    if(!nGreaterZero(pGetCoeff(Lp.sig)))
    {
      Lp.sig = pNeg(Lp.sig);
      Lp.p = pNeg(Lp.p);
    }
  }
  else
  {
    if(sigCmp==currRing->OrdSgn)
    {
      // pSig > sSig
      pDelete (&sSigMult);
      Lp.sig    = pSigMult;
      Lp.sevSig = ~pSigMultNegSev;
    }
    else
    {
      // pSig < sSig
      pDelete (&pSigMult);
      Lp.sig    = sSigMult;
      Lp.sevSig = ~sSigMultNegSev;
    }
  }
  if (Lp.p == NULL)
  {
    if (Lp.lcm!=NULL) pLmFree(Lp.lcm);
    int pos = posInSyz(strat, Lp.sig);
    enterSyz(Lp, strat, pos);
  }
  else
  {
    // testing by rewCrit3 = Arris Rewritten Criterion (for F5 nothing happens!)
    if (strat->rewCrit3(Lp.sig,~Lp.sevSig,Lp.p,strat,strat->sl+1))
    {
      pLmFree(Lp.lcm);
      pDelete(&Lp.sig);
      pDelete (&m1);
      pDelete (&m2);
      return;
    }
    // in any case Lp is checked up to the next strat->P which is added
    // to S right after this critical pair creation.
    // NOTE: this even holds if the 2nd generator gives the bigger signature
    //       moreover, this improves rewCriterion,
    //       i.e. strat->checked > strat->from if and only if the 2nd generator
    //       gives the bigger signature.
    Lp.checked = strat->sl+1;
    // at this point it is clear that the pair will be added to L, since it has
    // passed all tests up to now
 
  // adds buchberger's first criterion
    if (pLmCmp(m2,pHead(p)) == 0)
    {
      Lp.prod_crit = TRUE; // Product Criterion
#if 0
      int pos = posInSyz(strat, Lp.sig);
      enterSyz(Lp, strat, pos);
      pDelete (&m1);
      pDelete (&m2);
      return;
#endif
    }
    pDelete (&m1);
    pDelete (&m2);
#if DEBUGF5
    PrintS("SIGNATURE OF PAIR:  ");
    pWrite(Lp.sig);
#endif
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
 
    if (
        (!rIsPluralRing(currRing))
//      ||  (rIsPluralRing(currRing) && (ncRingType(currRing) != nc_lie))
      && !rField_is_Ring(currRing)
       )
    {
      assume(pNext(Lp.p)==NULL); // TODO: this may be violated whenever ext.prod.crit. for Lie alg. is used
      pNext(Lp.p) = strat->tail; // !!!
    }
 
    if (atR >= 0)
    {
      Lp.i_r1 = strat->S_2_R[i];
      Lp.i_r2 = atR;
    }
    else
    {
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
    }
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
 
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
    // Check for sigdrop
    if(rField_is_Ring(currRing) && pLtCmp(Lp.sig,pSig) == -1)
    {
      strat->sigdrop = TRUE;
      // Completely reduce it
      int red_result = redRing(&Lp,strat);
      if(red_result == 0)
      {
        // Reduced to 0
        strat->sigdrop = FALSE;
        p_Delete(&Lp.sig,currRing);Lp.sig = NULL;
        return;
      }
      else
      {
        strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
        // 0 - add just the original poly causing the sigdrop, 1 - add also this
        #if 1
        strat->enterS(Lp,0,strat, strat->tl+1);
        #endif
        return;
      }
    }
    l = strat->posInLSba(strat->L,strat->Ll,&Lp,strat);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,Lp,l);
  }
}
 
/*2
* put the pair (s[i],p) into the set L, ecart=ecart(p)
* in the case that s forms a SB of (s)
*/
void enterOnePairSpecial (int i,poly p,int ecart,kStrategy strat, int atR = -1)
{
  //PrintS("try ");wrp(strat->S[i]);PrintS(" and ");wrp(p);PrintLn();
  if(pHasNotCF(p,strat->S[i]))
  {
    //PrintS("prod-crit\n");
    if(ALLOW_PROD_CRIT(strat))
    {
      //PrintS("prod-crit\n");
      strat->cp++;
      return;
    }
  }
 
  int      l;
  LObject  Lp;
  Lp.i_r = -1;
 
  Lp.lcm = p_Lcm(p,strat->S[i],currRing);
  /*-  compute the short s-polynomial -*/
 
  #ifdef HAVE_PLURAL
  if (rIsPluralRing(currRing))
  {
    Lp.p = nc_CreateShortSpoly(strat->S[i],p, currRing); // ??? strat->tailRing?
  }
  else
  #endif
    Lp.p = ksCreateShortSpoly(strat->S[i],p,strat->tailRing);
 
  if (Lp.p == NULL)
  {
     //PrintS("short spoly==NULL\n");
     pLmFree(Lp.lcm);
  }
  else
  {
    /*- the pair (S[i],p) enters L -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
    if (atR >= 0)
    {
      Lp.i_r1 = strat->S_2_R[i];
      Lp.i_r2 = atR;
    }
    else
    {
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
    }
    assume(pNext(Lp.p) == NULL);
    pNext(Lp.p) = strat->tail;
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
    l = strat->posInL(strat->L,strat->Ll,&Lp,strat);
    //Print("-> L[%d]\n",l);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,Lp,l);
  }
}
 
/*2
* merge set B into L
*/
void kMergeBintoL(kStrategy strat)
{
  int j=strat->Ll+strat->Bl+1;
  if (j>strat->Lmax)
  {
    j=((j+setmaxLinc-1)/setmaxLinc)*setmaxLinc-strat->Lmax;
    enlargeL(&(strat->L),&(strat->Lmax),j);
  }
  j = strat->Ll;
  int i;
  for (i=strat->Bl; i>=0; i--)
  {
    j = strat->posInL(strat->L,j,&(strat->B[i]),strat);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,strat->B[i],j);
  }
  strat->Bl = -1;
}
 
/*2
* merge set B into L
*/
void kMergeBintoLSba(kStrategy strat)
{
  int j=strat->Ll+strat->Bl+1;
  if (j>strat->Lmax)
  {
    j=((j+setmaxLinc-1)/setmaxLinc)*setmaxLinc-strat->Lmax;
    enlargeL(&(strat->L),&(strat->Lmax),j);
  }
  j = strat->Ll;
  int i;
  for (i=strat->Bl; i>=0; i--)
  {
    j = strat->posInLSba(strat->L,j,&(strat->B[i]),strat);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,strat->B[i],j);
  }
  strat->Bl = -1;
}
 
/*2
*the pairset B of pairs of type (s[i],p) is complete now. It will be updated
*using the chain-criterion in B and L and enters B to L
*/
void chainCritNormal (poly p,int ecart,kStrategy strat)
{
  int i,j,l;
 
  /*
  *pairtest[i] is TRUE if spoly(S[i],p) == 0.
  *In this case all elements in B such
  *that their lcm is divisible by the leading term of S[i] can be canceled
  */
  if (strat->pairtest!=NULL)
  {
#ifdef HAVE_SHIFTBBA
    // only difference is pLPDivisibleBy instead of pDivisibleBy
    if (rIsLPRing(currRing))
    {
      for (j=0; j<=strat->sl; j++)
      {
        if (strat->pairtest[j])
        {
          for (i=strat->Bl; i>=0; i--)
          {
            if (pLPDivisibleBy(strat->S[j],strat->B[i].lcm))
            {
              deleteInL(strat->B,&strat->Bl,i,strat);
              strat->c3++;
            }
          }
        }
      }
    }
    else
#endif
    {
      /*- i.e. there is an i with pairtest[i]==TRUE -*/
      for (j=0; j<=strat->sl; j++)
      {
        if (strat->pairtest[j])
        {
          for (i=strat->Bl; i>=0; i--)
          {
            if (pDivisibleBy(strat->S[j],strat->B[i].lcm))
            {
              deleteInL(strat->B,&strat->Bl,i,strat);
              strat->c3++;
            }
          }
        }
      }
    }
    omFreeSize(strat->pairtest,(strat->sl+2)*sizeof(BOOLEAN));
    strat->pairtest=NULL;
  }
  if (strat->Gebauer || strat->fromT)
  {
    if (strat->sugarCrit)
    {
    /*
    *suppose L[j] == (s,r) and p/lcm(s,r)
    *and lcm(s,r)#lcm(s,p) and lcm(s,r)#lcm(r,p)
    *and in case the sugar is o.k. then L[j] can be canceled
    */
      for (j=strat->Ll; j>=0; j--)
      {
        if (sugarDivisibleBy(ecart,strat->L[j].ecart)
        && ((pNext(strat->L[j].p) == strat->tail) || (rHasGlobalOrdering(currRing)))
        && pCompareChain(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
        {
          if (strat->L[j].p == strat->tail)
          {
            deleteInL(strat->L,&strat->Ll,j,strat);
            strat->c3++;
          }
        }
      }
      /*
      *this is GEBAUER-MOELLER:
      *in B all elements with the same lcm except the "best"
      *(i.e. the last one in B with this property) will be canceled
      */
      j = strat->Bl;
      loop /*cannot be changed into a for !!! */
      {
        if (j <= 0) break;
        i = j-1;
        loop
        {
          if (i <  0) break;
          if (pLmEqual(strat->B[j].lcm,strat->B[i].lcm))
          {
            strat->c3++;
            if (sugarDivisibleBy(strat->B[j].ecart,strat->B[i].ecart))
            {
              deleteInL(strat->B,&strat->Bl,i,strat);
              j--;
            }
            else
            {
              deleteInL(strat->B,&strat->Bl,j,strat);
              break;
            }
          }
          i--;
        }
        j--;
      }
    }
    else /*sugarCrit*/
    {
      /*
      *suppose L[j] == (s,r) and p/lcm(s,r)
      *and lcm(s,r)#lcm(s,p) and lcm(s,r)#lcm(r,p)
      *and in case the sugar is o.k. then L[j] can be canceled
      */
      for (j=strat->Ll; j>=0; j--)
      {
        if (pCompareChain(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
        {
          if ((pNext(strat->L[j].p) == strat->tail)||(rHasGlobalOrdering(currRing)))
          {
            deleteInL(strat->L,&strat->Ll,j,strat);
            strat->c3++;
          }
        }
      }
      /*
      *this is GEBAUER-MOELLER:
      *in B all elements with the same lcm except the "best"
      *(i.e. the last one in B with this property) will be canceled
      */
      j = strat->Bl;
      loop   /*cannot be changed into a for !!! */
      {
        if (j <= 0) break;
        for(i=j-1; i>=0; i--)
        {
          if (pLmEqual(strat->B[j].lcm,strat->B[i].lcm))
          {
            strat->c3++;
            deleteInL(strat->B,&strat->Bl,i,strat);
            j--;
          }
        }
        j--;
      }
    }
    /*
    *the elements of B enter L
    */
    kMergeBintoL(strat);
  }
  else
  {
    for (j=strat->Ll; j>=0; j--)
    {
      #ifdef HAVE_SHIFTBBA
      if ((strat->L[j].p1!=NULL) &&
      pCompareChain(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
      #else
      if (pCompareChain(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
      #endif
      {
        if ((pNext(strat->L[j].p) == strat->tail)||(rHasGlobalOrdering(currRing)))
        {
          deleteInL(strat->L,&strat->Ll,j,strat);
          strat->c3++;
        }
      }
    }
    /*
    *this is our MODIFICATION of GEBAUER-MOELLER:
    *First the elements of B enter L,
    *then we fix a lcm and the "best" element in L
    *(i.e the last in L with this lcm and of type (s,p))
    *and cancel all the other elements of type (r,p) with this lcm
    *except the case the element (s,r) has also the same lcm
    *and is on the worst position with respect to (s,p) and (r,p)
    */
    /*
    *B enters to L/their order with respect to B is permutated for elements
    *B[i].p with the same leading term
    */
    kMergeBintoL(strat);
    j = strat->Ll;
    loop  /*cannot be changed into a for !!! */
    {
      if (j <= 0)
      {
        /*now L[0] cannot be canceled any more and the tail can be removed*/
        if (strat->L[0].p2 == strat->tail) strat->L[0].p2 = p;
        break;
      }
      if (strat->L[j].p2 == p)
      {
        i = j-1;
        loop
        {
          if (i < 0)  break;
          if ((strat->L[i].p2 == p) && pLmEqual(strat->L[j].lcm,strat->L[i].lcm))
          {
            /*L[i] could be canceled but we search for a better one to cancel*/
            strat->c3++;
            if (isInPairsetL(i-1,strat->L[j].p1,strat->L[i].p1,&l,strat)
            && (pNext(strat->L[l].p) == strat->tail)
            && (!pLmEqual(strat->L[i].p,strat->L[l].p))
            && pDivisibleBy(p,strat->L[l].lcm))
            {
              /*
              *"NOT equal(...)" because in case of "equal" the element L[l]
              *is "older" and has to be from theoretical point of view behind
              *L[i], but we do not want to reorder L
              */
              strat->L[i].p2 = strat->tail;
              /*
              *L[l] will be canceled, we cannot cancel L[i] later on,
              *so we mark it with "tail"
              */
              deleteInL(strat->L,&strat->Ll,l,strat);
              i--;
            }
            else
            {
              deleteInL(strat->L,&strat->Ll,i,strat);
            }
            j--;
          }
          i--;
        }
      }
      else if (strat->L[j].p2 == strat->tail)
      {
        /*now L[j] cannot be canceled any more and the tail can be removed*/
        strat->L[j].p2 = p;
      }
      j--;
    }
  }
}
/*2
*the pairset B of pairs of type (s[i],p) is complete now. It will be updated
*without the chain-criterion in B and L and enters B to L
*/
void chainCritOpt_1 (poly,int,kStrategy strat)
{
  if (strat->pairtest!=NULL)
  {
    omFreeSize(strat->pairtest,(strat->sl+2)*sizeof(BOOLEAN));
    strat->pairtest=NULL;
  }
  /*
  *the elements of B enter L
  */
  kMergeBintoL(strat);
}
/*2
*the pairset B of pairs of type (s[i],p) is complete now. It will be updated
*using the chain-criterion in B and L and enters B to L
*/
void chainCritSig (poly p,int /*ecart*/,kStrategy strat)
{
  int i,j,l;
  kMergeBintoLSba(strat);
  j = strat->Ll;
  loop  /*cannot be changed into a for !!! */
  {
    if (j <= 0)
    {
      /*now L[0] cannot be canceled any more and the tail can be removed*/
      if (strat->L[0].p2 == strat->tail) strat->L[0].p2 = p;
      break;
    }
    if (strat->L[j].p2 == p)
    {
      i = j-1;
      loop
      {
        if (i < 0)  break;
        if ((strat->L[i].p2 == p) && pLmEqual(strat->L[j].lcm,strat->L[i].lcm))
        {
          /*L[i] could be canceled but we search for a better one to cancel*/
          strat->c3++;
          if (isInPairsetL(i-1,strat->L[j].p1,strat->L[i].p1,&l,strat)
              && (pNext(strat->L[l].p) == strat->tail)
              && (!pLmEqual(strat->L[i].p,strat->L[l].p))
              && pDivisibleBy(p,strat->L[l].lcm))
          {
            /*
             *"NOT equal(...)" because in case of "equal" the element L[l]
             *is "older" and has to be from theoretical point of view behind
             *L[i], but we do not want to reorder L
             */
            strat->L[i].p2 = strat->tail;
            /*
             *L[l] will be canceled, we cannot cancel L[i] later on,
             *so we mark it with "tail"
             */
            deleteInL(strat->L,&strat->Ll,l,strat);
            i--;
          }
          else
          {
            deleteInL(strat->L,&strat->Ll,i,strat);
          }
          j--;
        }
        i--;
      }
    }
    else if (strat->L[j].p2 == strat->tail)
    {
      /*now L[j] cannot be canceled any more and the tail can be removed*/
      strat->L[j].p2 = p;
    }
    j--;
  }
}
#ifdef HAVE_RATGRING
void chainCritPart (poly p,int ecart,kStrategy strat)
{
  int i,j,l;
 
  /*
  *pairtest[i] is TRUE if spoly(S[i],p) == 0.
  *In this case all elements in B such
  *that their lcm is divisible by the leading term of S[i] can be canceled
  */
  if (strat->pairtest!=NULL)
  {
    /*- i.e. there is an i with pairtest[i]==TRUE -*/
    for (j=0; j<=strat->sl; j++)
    {
      if (strat->pairtest[j])
      {
        for (i=strat->Bl; i>=0; i--)
        {
          if (_p_LmDivisibleByPart(strat->S[j],currRing,
             strat->B[i].lcm,currRing,
             currRing->real_var_start,currRing->real_var_end))
          {
            if(TEST_OPT_DEBUG)
            {
               Print("chain-crit-part: S[%d]=",j);
               p_wrp(strat->S[j],currRing);
               Print(" divide B[%d].lcm=",i);
               p_wrp(strat->B[i].lcm,currRing);
               PrintLn();
            }
            deleteInL(strat->B,&strat->Bl,i,strat);
            strat->c3++;
          }
        }
      }
    }
    omFreeSize(strat->pairtest,(strat->sl+2)*sizeof(BOOLEAN));
    strat->pairtest=NULL;
  }
  if (strat->Gebauer || strat->fromT)
  {
    if (strat->sugarCrit)
    {
    /*
    *suppose L[j] == (s,r) and p/lcm(s,r)
    *and lcm(s,r)#lcm(s,p) and lcm(s,r)#lcm(r,p)
    *and in case the sugar is o.k. then L[j] can be canceled
    */
      for (j=strat->Ll; j>=0; j--)
      {
        if (sugarDivisibleBy(ecart,strat->L[j].ecart)
        && ((pNext(strat->L[j].p) == strat->tail) || (rHasGlobalOrdering(currRing)))
        && pCompareChainPart(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
        {
          if (strat->L[j].p == strat->tail)
          {
            if(TEST_OPT_DEBUG)
            {
               PrintS("chain-crit-part: pCompareChainPart p=");
               p_wrp(p,currRing);
               Print(" delete L[%d]",j);
               p_wrp(strat->L[j].lcm,currRing);
               PrintLn();
            }
            deleteInL(strat->L,&strat->Ll,j,strat);
            strat->c3++;
          }
        }
      }
      /*
      *this is GEBAUER-MOELLER:
      *in B all elements with the same lcm except the "best"
      *(i.e. the last one in B with this property) will be canceled
      */
      j = strat->Bl;
      loop /*cannot be changed into a for !!! */
      {
        if (j <= 0) break;
        i = j-1;
        loop
        {
          if (i <  0) break;
          if (pLmEqual(strat->B[j].lcm,strat->B[i].lcm))
          {
            strat->c3++;
            if (sugarDivisibleBy(strat->B[j].ecart,strat->B[i].ecart))
            {
              if(TEST_OPT_DEBUG)
              {
                Print("chain-crit-part: sugar B[%d].lcm=",j);
                p_wrp(strat->B[j].lcm,currRing);
                Print(" delete B[%d]",i);
                p_wrp(strat->B[i].lcm,currRing);
                PrintLn();
              }
              deleteInL(strat->B,&strat->Bl,i,strat);
              j--;
            }
            else
            {
              if(TEST_OPT_DEBUG)
              {
                Print("chain-crit-part: sugar B[%d].lcm=",i);
                p_wrp(strat->B[i].lcm,currRing);
                Print(" delete B[%d]",j);
                p_wrp(strat->B[j].lcm,currRing);
                PrintLn();
              }
              deleteInL(strat->B,&strat->Bl,j,strat);
              break;
            }
          }
          i--;
        }
        j--;
      }
    }
    else /*sugarCrit*/
    {
      /*
      *suppose L[j] == (s,r) and p/lcm(s,r)
      *and lcm(s,r)#lcm(s,p) and lcm(s,r)#lcm(r,p)
      *and in case the sugar is o.k. then L[j] can be canceled
      */
      for (j=strat->Ll; j>=0; j--)
      {
        if (pCompareChainPart(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
        {
          if ((pNext(strat->L[j].p) == strat->tail)||(rHasGlobalOrdering(currRing)))
          {
            if(TEST_OPT_DEBUG)
            {
              PrintS("chain-crit-part: sugar:pCompareChainPart p=");
              p_wrp(p,currRing);
              Print(" delete L[%d]",j);
              p_wrp(strat->L[j].lcm,currRing);
              PrintLn();
            }
            deleteInL(strat->L,&strat->Ll,j,strat);
            strat->c3++;
          }
        }
      }
      /*
      *this is GEBAUER-MOELLER:
      *in B all elements with the same lcm except the "best"
      *(i.e. the last one in B with this property) will be canceled
      */
      j = strat->Bl;
      loop   /*cannot be changed into a for !!! */
      {
        if (j <= 0) break;
        for(i=j-1; i>=0; i--)
        {
          if (pLmEqual(strat->B[j].lcm,strat->B[i].lcm))
          {
            if(TEST_OPT_DEBUG)
            {
              Print("chain-crit-part: equal lcm B[%d].lcm=",j);
              p_wrp(strat->B[j].lcm,currRing);
              Print(" delete B[%d]\n",i);
            }
            strat->c3++;
            deleteInL(strat->B,&strat->Bl,i,strat);
            j--;
          }
        }
        j--;
      }
    }
    /*
    *the elements of B enter L
    */
    kMergeBintoL(strat);
  }
  else
  {
    for (j=strat->Ll; j>=0; j--)
    {
      if (pCompareChainPart(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
      {
        if ((pNext(strat->L[j].p) == strat->tail)||(rHasGlobalOrdering(currRing)))
        {
          if(TEST_OPT_DEBUG)
          {
            PrintS("chain-crit-part: pCompareChainPart p=");
            p_wrp(p,currRing);
            Print(" delete L[%d]",j);
            p_wrp(strat->L[j].lcm,currRing);
            PrintLn();
          }
          deleteInL(strat->L,&strat->Ll,j,strat);
          strat->c3++;
        }
      }
    }
    /*
    *this is our MODIFICATION of GEBAUER-MOELLER:
    *First the elements of B enter L,
    *then we fix a lcm and the "best" element in L
    *(i.e the last in L with this lcm and of type (s,p))
    *and cancel all the other elements of type (r,p) with this lcm
    *except the case the element (s,r) has also the same lcm
    *and is on the worst position with respect to (s,p) and (r,p)
    */
    /*
    *B enters to L/their order with respect to B is permutated for elements
    *B[i].p with the same leading term
    */
    kMergeBintoL(strat);
    j = strat->Ll;
    loop  /*cannot be changed into a for !!! */
    {
      if (j <= 0)
      {
        /*now L[0] cannot be canceled any more and the tail can be removed*/
        if (strat->L[0].p2 == strat->tail) strat->L[0].p2 = p;
        break;
      }
      if (strat->L[j].p2 == p)
      {
        i = j-1;
        loop
        {
          if (i < 0)  break;
          if ((strat->L[i].p2 == p) && pLmEqual(strat->L[j].lcm,strat->L[i].lcm))
          {
            /*L[i] could be canceled but we search for a better one to cancel*/
            strat->c3++;
            if (isInPairsetL(i-1,strat->L[j].p1,strat->L[i].p1,&l,strat)
            && (pNext(strat->L[l].p) == strat->tail)
            && (!pLmEqual(strat->L[i].p,strat->L[l].p))
            && _p_LmDivisibleByPart(p,currRing,
                           strat->L[l].lcm,currRing,
                           currRing->real_var_start, currRing->real_var_end))
 
            {
              /*
              *"NOT equal(...)" because in case of "equal" the element L[l]
              *is "older" and has to be from theoretical point of view behind
              *L[i], but we do not want to reorder L
              */
              strat->L[i].p2 = strat->tail;
              /*
              *L[l] will be canceled, we cannot cancel L[i] later on,
              *so we mark it with "tail"
              */
              if(TEST_OPT_DEBUG)
              {
                PrintS("chain-crit-part: divisible_by p=");
                p_wrp(p,currRing);
                Print(" delete L[%d]",l);
                p_wrp(strat->L[l].lcm,currRing);
                PrintLn();
              }
              deleteInL(strat->L,&strat->Ll,l,strat);
              i--;
            }
            else
            {
              if(TEST_OPT_DEBUG)
              {
                PrintS("chain-crit-part: divisible_by(2) p=");
                p_wrp(p,currRing);
                Print(" delete L[%d]",i);
                p_wrp(strat->L[i].lcm,currRing);
                PrintLn();
              }
              deleteInL(strat->L,&strat->Ll,i,strat);
            }
            j--;
          }
          i--;
        }
      }
      else if (strat->L[j].p2 == strat->tail)
      {
        /*now L[j] cannot be canceled any more and the tail can be removed*/
        strat->L[j].p2 = p;
      }
      j--;
    }
  }
}
#endif
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L
*/
void initenterpairs (poly h,int k,int ecart,int isFromQ,kStrategy strat, int atR/* = -1*/)
{
 
  if ((strat->syzComp==0)
  || (pGetComp(h)<=strat->syzComp))
  {
    int j;
    BOOLEAN new_pair=FALSE;
 
    if (pGetComp(h)==0)
    {
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        for (j=0; j<=k; j++)
        {
          if (!strat->fromQ[j])
          {
            new_pair=TRUE;
            strat->enterOnePair(j,h,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
          }
        }
      }
      else
      {
        new_pair=TRUE;
        for (j=0; j<=k; j++)
        {
          strat->enterOnePair(j,h,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
    else
    {
      for (j=0; j<=k; j++)
      {
        if ((pGetComp(h)==pGetComp(strat->S[j]))
        || (pGetComp(strat->S[j])==0))
        {
          new_pair=TRUE;
          strat->enterOnePair(j,h,ecart,isFromQ,strat, atR);
        //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
    if (new_pair)
    {
    #ifdef HAVE_RATGRING
      if (currRing->real_var_start>0)
        chainCritPart(h,ecart,strat);
      else
    #endif
      strat->chainCrit(h,ecart,strat);
    }
    kMergeBintoL(strat);
  }
}
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L
*using signatures <= only for signature-based standard basis algorithms
*/
 
void initenterpairsSig (poly h,poly hSig,int hFrom,int k,int ecart,int isFromQ,kStrategy strat, int atR = -1)
{
 
  if ((strat->syzComp==0)
  || (pGetComp(h)<=strat->syzComp))
  {
    int j;
    BOOLEAN new_pair=FALSE;
 
    if (pGetComp(h)==0)
    {
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        for (j=0; j<=k; j++)
        {
          if (!strat->fromQ[j])
          {
            new_pair=TRUE;
            enterOnePairSig(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
          }
        }
      }
      else
      {
        new_pair=TRUE;
        for (j=0; j<=k; j++)
        {
          enterOnePairSig(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
    else
    {
      for (j=0; j<=k; j++)
      {
        if ((pGetComp(h)==pGetComp(strat->S[j]))
        || (pGetComp(strat->S[j])==0))
        {
          new_pair=TRUE;
          enterOnePairSig(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
        //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
 
    if (new_pair)
    {
#ifdef HAVE_RATGRING
      if (currRing->real_var_start>0)
        chainCritPart(h,ecart,strat);
      else
#endif
      strat->chainCrit(h,ecart,strat);
    }
  }
}
 
void initenterpairsSigRing (poly h,poly hSig,int hFrom,int k,int ecart,int isFromQ,kStrategy strat, int atR = -1)
{
 
  if ((strat->syzComp==0)
  || (pGetComp(h)<=strat->syzComp))
  {
    int j;
 
    if (pGetComp(h)==0)
    {
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        for (j=0; j<=k && !strat->sigdrop; j++)
        {
          if (!strat->fromQ[j])
          {
            enterOnePairSigRing(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
          }
        }
      }
      else
      {
        for (j=0; j<=k && !strat->sigdrop; j++)
        {
          enterOnePairSigRing(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
    else
    {
      for (j=0; j<=k && !strat->sigdrop; j++)
      {
        if ((pGetComp(h)==pGetComp(strat->S[j]))
        || (pGetComp(strat->S[j])==0))
        {
          enterOnePairSigRing(j,h,hSig,hFrom,ecart,isFromQ,strat, atR);
        //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
 
#if 0
    if (new_pair)
    {
#ifdef HAVE_RATGRING
      if (currRing->real_var_start>0)
        chainCritPart(h,ecart,strat);
      else
#endif
      strat->chainCrit(h,ecart,strat);
    }
#endif
  }
}
 
/*2
*the pairset B of pairs of type (s[i],p) is complete now. It will be updated
*using the chain-criterion in B and L and enters B to L
*/
void chainCritRing (poly p,int, kStrategy strat)
{
  int i,j,l;
  /*
  *pairtest[i] is TRUE if spoly(S[i],p) == 0.
  *In this case all elements in B such
  *that their lcm is divisible by the leading term of S[i] can be canceled
  */
  if (strat->pairtest!=NULL)
  {
    {
      /*- i.e. there is an i with pairtest[i]==TRUE -*/
      for (j=0; j<=strat->sl; j++)
      {
        if (strat->pairtest[j])
        {
          for (i=strat->Bl; i>=0; i--)
          {
            if (pDivisibleBy(strat->S[j],strat->B[i].lcm) && n_DivBy(pGetCoeff(strat->B[i].lcm), pGetCoeff(strat->S[j]),currRing->cf))
            {
#ifdef KDEBUG
              if (TEST_OPT_DEBUG)
              {
                PrintS("--- chain criterion func chainCritRing type 1\n");
                PrintS("strat->S[j]:");
                wrp(strat->S[j]);
                PrintS("  strat->B[i].lcm:");
                wrp(strat->B[i].lcm);PrintLn();
                pWrite(strat->B[i].p);
                pWrite(strat->B[i].p1);
                pWrite(strat->B[i].p2);
                wrp(strat->B[i].lcm);
                PrintLn();
              }
#endif
              deleteInL(strat->B,&strat->Bl,i,strat);
              strat->c3++;
            }
          }
        }
      }
    }
    omFreeSize(strat->pairtest,(strat->sl+2)*sizeof(BOOLEAN));
    strat->pairtest=NULL;
  }
  assume(!(strat->Gebauer || strat->fromT));
  for (j=strat->Ll; j>=0; j--)
  {
    if ((strat->L[j].lcm != NULL) && n_DivBy(pGetCoeff(strat->L[j].lcm), pGetCoeff(p), currRing->cf))
    {
      if (pCompareChain(p,strat->L[j].p1,strat->L[j].p2,strat->L[j].lcm))
      {
        if ((pNext(strat->L[j].p) == strat->tail) || (rHasGlobalOrdering(currRing)))
        {
          deleteInL(strat->L,&strat->Ll,j,strat);
          strat->c3++;
#ifdef KDEBUG
          if (TEST_OPT_DEBUG)
          {
            PrintS("--- chain criterion func chainCritRing type 2\n");
            PrintS("strat->L[j].p:");
            wrp(strat->L[j].p);
            PrintS("  p:");
            wrp(p);
            PrintLn();
          }
#endif
        }
      }
    }
  }
  /*
  *this is our MODIFICATION of GEBAUER-MOELLER:
  *First the elements of B enter L,
  *then we fix a lcm and the "best" element in L
  *(i.e the last in L with this lcm and of type (s,p))
  *and cancel all the other elements of type (r,p) with this lcm
  *except the case the element (s,r) has also the same lcm
  *and is on the worst position with respect to (s,p) and (r,p)
  */
  /*
  *B enters to L/their order with respect to B is permutated for elements
  *B[i].p with the same leading term
  */
  kMergeBintoL(strat);
  j = strat->Ll;
  loop  /*cannot be changed into a for !!! */
  {
    if (j <= 0)
    {
      /*now L[0] cannot be canceled any more and the tail can be removed*/
      if (strat->L[0].p2 == strat->tail) strat->L[0].p2 = p;
      break;
    }
    if (strat->L[j].p2 == p) // Was the element added from B?
    {
      i = j-1;
      loop
      {
        if (i < 0)  break;
        // Element is from B and has the same lcm as L[j]
        if ((strat->L[i].p2 == p) && n_DivBy(pGetCoeff(strat->L[j].lcm), pGetCoeff(strat->L[i].lcm), currRing->cf)
             && pLmEqual(strat->L[j].lcm,strat->L[i].lcm))
        {
          /*L[i] could be canceled but we search for a better one to cancel*/
          strat->c3++;
#ifdef KDEBUG
          if (TEST_OPT_DEBUG)
          {
            PrintS("--- chain criterion func chainCritRing type 3\n");
            PrintS("strat->L[j].lcm:");
            wrp(strat->L[j].lcm);
            PrintS("  strat->L[i].lcm:");
            wrp(strat->L[i].lcm);
            PrintLn();
          }
#endif
          if (isInPairsetL(i-1,strat->L[j].p1,strat->L[i].p1,&l,strat)
          && (pNext(strat->L[l].p) == strat->tail)
          && (!pLmEqual(strat->L[i].p,strat->L[l].p))
          && pDivisibleBy(p,strat->L[l].lcm))
          {
            /*
            *"NOT equal(...)" because in case of "equal" the element L[l]
            *is "older" and has to be from theoretical point of view behind
            *L[i], but we do not want to reorder L
            */
            strat->L[i].p2 = strat->tail;
            /*
            *L[l] will be canceled, we cannot cancel L[i] later on,
            *so we mark it with "tail"
            */
            deleteInL(strat->L,&strat->Ll,l,strat);
            i--;
          }
          else
          {
            deleteInL(strat->L,&strat->Ll,i,strat);
          }
          j--;
        }
        i--;
      }
    }
    else if (strat->L[j].p2 == strat->tail)
    {
      /*now L[j] cannot be canceled any more and the tail can be removed*/
      strat->L[j].p2 = p;
    }
    j--;
  }
}
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L
*/
void initenterstrongPairs (poly h,int k,int ecart,int isFromQ,kStrategy strat, int atR = -1)
{
  if (!nIsOne(pGetCoeff(h)))
  {
    int j;
    BOOLEAN new_pair=FALSE;
 
    if (pGetComp(h)==0)
    {
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        for (j=0; j<=k; j++)
        {
          if (!strat->fromQ[j])
          {
            new_pair=TRUE;
            enterOneStrongPoly(j,h,ecart,isFromQ,strat, atR, FALSE);
          }
        }
      }
      else
      {
        new_pair=TRUE;
        for (j=0; j<=k; j++)
        {
          enterOneStrongPoly(j,h,ecart,isFromQ,strat, atR, FALSE);
        }
      }
    }
    else
    {
      for (j=0; j<=k; j++)
      {
        if ((pGetComp(h)==pGetComp(strat->S[j]))
        || (pGetComp(strat->S[j])==0))
        {
          new_pair=TRUE;
          enterOneStrongPoly(j,h,ecart,isFromQ,strat, atR, FALSE);
        }
      }
    }
    if (new_pair)
    {
    #ifdef HAVE_RATGRING
      if (currRing->real_var_start>0)
        chainCritPart(h,ecart,strat);
      else
    #endif
      strat->chainCrit(h,ecart,strat);
    }
    kMergeBintoL(strat);
  }
}
 
static void initenterstrongPairsSig (poly h,poly hSig, int k,int ecart,int isFromQ,kStrategy strat, int atR = -1)
{
  const int iCompH = pGetComp(h);
  if (!nIsOne(pGetCoeff(h)))
  {
    int j;
 
    for (j=0; j<=k && !strat->sigdrop; j++)
    {
      // Print("j:%d, Ll:%d\n",j,strat->Ll);
//      if (((unsigned long) pGetCoeff(h) % (unsigned long) pGetCoeff(strat->S[j]) != 0) &&
//         ((unsigned long) pGetCoeff(strat->S[j]) % (unsigned long) pGetCoeff(h) != 0))
      if (((iCompH == pGetComp(strat->S[j]))
      || (0 == pGetComp(strat->S[j])))
      && ((iCompH<=strat->syzComp)||(strat->syzComp==0)))
      {
        enterOneStrongPolySig(j,h,hSig,ecart,isFromQ,strat, atR);
      }
    }
  }
}
 
/*2
* Generates spoly(0, h) if applicable. Assumes ring has zero divisors
*/
void enterExtendedSpoly(poly h,kStrategy strat)
{
  if (nIsOne(pGetCoeff(h))) return;
  number gcd;
  number zero=n_Init(0,currRing->cf);
  bool go = false;
  if (n_DivBy(zero, pGetCoeff(h), currRing->cf))
  {
    gcd = n_Ann(pGetCoeff(h),currRing->cf);
    go = true;
  }
  else
    gcd = n_Gcd(zero, pGetCoeff(h), strat->tailRing->cf);
  if (go || !nIsOne(gcd))
  {
    poly p = h->next;
    if (!go)
    {
      number tmp = gcd;
      gcd = n_Ann(gcd,currRing->cf);
      nDelete(&tmp);
    }
    p_Test(p,strat->tailRing);
    p = __pp_Mult_nn(p, gcd, strat->tailRing);
 
    if (p != NULL)
    {
      if (TEST_OPT_PROT)
      {
        PrintS("Z");
      }
#ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        PrintS("--- create zero spoly: ");
        p_wrp(h,currRing,strat->tailRing);
        PrintS(" ---> ");
      }
#endif
      poly tmp = pInit();
      pSetCoeff0(tmp, pGetCoeff(p));
      for (int i = 1; i <= rVar(currRing); i++)
      {
        pSetExp(tmp, i, p_GetExp(p, i, strat->tailRing));
      }
      if (rRing_has_Comp(currRing) && rRing_has_Comp(strat->tailRing))
      {
        p_SetComp(tmp, __p_GetComp(p, strat->tailRing), currRing);
      }
      p_Setm(tmp, currRing);
      p = p_LmFreeAndNext(p, strat->tailRing);
      pNext(tmp) = p;
      LObject Lp;
      Lp.Init();
      Lp.p = tmp;
      Lp.tailRing = strat->tailRing;
      int posx;
      if (Lp.p!=NULL)
      {
        strat->initEcart(&Lp);
        if (strat->Ll==-1)
          posx =0;
        else
          posx = strat->posInL(strat->L,strat->Ll,&Lp,strat);
        Lp.sev = pGetShortExpVector(Lp.p);
        if (strat->tailRing != currRing)
        {
          Lp.t_p = k_LmInit_currRing_2_tailRing(Lp.p, strat->tailRing);
        }
#ifdef KDEBUG
        if (TEST_OPT_DEBUG)
        {
          p_wrp(tmp,currRing,strat->tailRing);
          PrintLn();
        }
#endif
        enterL(&strat->L,&strat->Ll,&strat->Lmax,Lp,posx);
      }
    }
  }
  nDelete(&zero);
  nDelete(&gcd);
}
 
void enterExtendedSpolySig(poly h,poly hSig,kStrategy strat)
{
  if (nIsOne(pGetCoeff(h))) return;
  number gcd;
  number zero=n_Init(0,currRing->cf);
  bool go = false;
  if (n_DivBy(zero, pGetCoeff(h), currRing->cf))
  {
    gcd = n_Ann(pGetCoeff(h),currRing->cf);
    go = true;
  }
  else
    gcd = n_Gcd(zero, pGetCoeff(h), strat->tailRing->cf);
  if (go || !nIsOne(gcd))
  {
    poly p = h->next;
    if (!go)
    {
      number tmp = gcd;
      gcd = n_Ann(gcd,currRing->cf);
      nDelete(&tmp);
    }
    p_Test(p,strat->tailRing);
    p = __pp_Mult_nn(p, gcd, strat->tailRing);
 
    if (p != NULL)
    {
      if (TEST_OPT_PROT)
      {
        PrintS("Z");
      }
#ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        PrintS("--- create zero spoly: ");
        p_wrp(h,currRing,strat->tailRing);
        PrintS(" ---> ");
      }
#endif
      poly tmp = pInit();
      pSetCoeff0(tmp, pGetCoeff(p));
      for (int i = 1; i <= rVar(currRing); i++)
      {
        pSetExp(tmp, i, p_GetExp(p, i, strat->tailRing));
      }
      if (rRing_has_Comp(currRing) && rRing_has_Comp(strat->tailRing))
      {
        p_SetComp(tmp, __p_GetComp(p, strat->tailRing), currRing);
      }
      p_Setm(tmp, currRing);
      p = p_LmFreeAndNext(p, strat->tailRing);
      pNext(tmp) = p;
      LObject Lp;
      Lp.Init();
      Lp.p = tmp;
      //printf("\nOld\n");pWrite(h);pWrite(hSig);
      #if EXT_POLY_NEW
      Lp.sig = __pp_Mult_nn(hSig, gcd, currRing);
      if(Lp.sig == NULL || nIsZero(pGetCoeff(Lp.sig)))
      {
        strat->sigdrop = TRUE;
        //Try to reduce it as far as we can via redRing
        int red_result = redRing(&Lp,strat);
        if(red_result == 0)
        {
          // Cancel the sigdrop
          p_Delete(&Lp.sig,currRing);Lp.sig = NULL;
          strat->sigdrop = FALSE;
        }
        else
        {
          strat->enterS(strat->P,strat->sl+1,strat, strat->tl+1);
          #if 1
          strat->enterS(Lp,0,strat,strat->tl);
          #endif
        }
        nDelete(&zero);
        nDelete(&gcd);
        return;
      }
      #else
      Lp.sig = pOne();
      if(strat->Ll >= 0)
        p_SetComp(Lp.sig,pGetComp(strat->L[0].sig)+1,currRing);
      else
        p_SetComp(Lp.sig,pGetComp(hSig)+1,currRing);
      #endif
      Lp.tailRing = strat->tailRing;
      int posx;
      if (Lp.p!=NULL)
      {
        strat->initEcart(&Lp);
        if (strat->Ll==-1)
          posx =0;
        else
          posx = strat->posInLSba(strat->L,strat->Ll,&Lp,strat);
        Lp.sev = pGetShortExpVector(Lp.p);
        if (strat->tailRing != currRing)
        {
          Lp.t_p = k_LmInit_currRing_2_tailRing(Lp.p, strat->tailRing);
        }
#ifdef KDEBUG
        if (TEST_OPT_DEBUG)
        {
          p_wrp(tmp,currRing,strat->tailRing);
          PrintLn();
        }
#endif
  //pWrite(h);pWrite(hSig);pWrite(Lp.p);pWrite(Lp.sig);printf("\n------------------\n");getchar();
        enterL(&strat->L,&strat->Ll,&strat->Lmax,Lp,posx);
      }
    }
  }
  nDelete(&gcd);
  nDelete(&zero);
}
 
void clearSbatch (poly h,int k,int pos,kStrategy strat)
{
  int j = pos;
  if ( (!strat->fromT)
  && ((strat->syzComp==0)
    ||(pGetComp(h)<=strat->syzComp)
  ))
  {
    // Print("start clearS k=%d, pos=%d, sl=%d\n",k,pos,strat->sl);
    unsigned long h_sev = pGetShortExpVector(h);
    loop
    {
      if (j > k) break;
      clearS(h,h_sev, &j,&k,strat);
      j++;
    }
    // Print("end clearS sl=%d\n",strat->sl);
  }
}
 
/*2
* Generates a sufficient set of spolys (maybe just a finite generating
* set of the syzygys)
*/
void superenterpairs (poly h,int k,int ecart,int pos,kStrategy strat, int atR)
{
  assume (rField_is_Ring(currRing));
#if HAVE_SHIFTBBA
  assume(!rIsLPRing(currRing)); /* LP should use enterpairsShift */
#endif
  // enter also zero divisor * poly, if this is non zero and of smaller degree
  if (!(rField_is_Domain(currRing))) enterExtendedSpoly(h, strat);
  initenterstrongPairs(h, k, ecart, 0, strat, atR);
  initenterpairs(h, k, ecart, 0, strat, atR);
  clearSbatch(h, k, pos, strat);
}
 
void superenterpairsSig (poly h,poly hSig,int hFrom,int k,int ecart,int pos,kStrategy strat, int atR)
{
  assume (rField_is_Ring(currRing));
  // enter also zero divisor * poly, if this is non zero and of smaller degree
  if (!(rField_is_Domain(currRing))) enterExtendedSpolySig(h, hSig, strat);
  if(strat->sigdrop) return;
  initenterpairsSigRing(h, hSig, hFrom, k, ecart, 0, strat, atR);
  if(strat->sigdrop) return;
  initenterstrongPairsSig(h, hSig, k, ecart, 0, strat, atR);
  if(strat->sigdrop) return;
  clearSbatch(h, k, pos, strat);
}
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L(via initenterpairs)
*superfluous elements in S will be deleted
*/
void enterpairs (poly h,int k,int ecart,int pos,kStrategy strat, int atR)
{
  int j=pos;
 
  assume (!rField_is_Ring(currRing));
  initenterpairs(h,k,ecart,0,strat, atR);
  if ( (!strat->fromT)
  && ((strat->syzComp==0)
    ||(pGetComp(h)<=strat->syzComp)))
  {
    unsigned long h_sev = pGetShortExpVector(h);
    loop
    {
      if (j > k) break;
      clearS(h,h_sev, &j,&k,strat);
      j++;
    }
  }
}
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L(via initenterpairs)
*superfluous elements in S will be deleted
*this is a special variant of signature-based algorithms including the
*signatures for criteria checks
*/
void enterpairsSig (poly h,poly hSig,int hFrom,int k,int ecart,int pos,kStrategy strat, int atR)
{
  int j=pos;
  assume (!rField_is_Ring(currRing));
  initenterpairsSig(h,hSig,hFrom,k,ecart,0,strat, atR);
  if ( (!strat->fromT)
  && ((strat->syzComp==0)
    ||(pGetComp(h)<=strat->syzComp)))
  {
    unsigned long h_sev = pGetShortExpVector(h);
    loop
    {
      if (j > k) break;
      clearS(h,h_sev, &j,&k,strat);
      j++;
    }
  }
}
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L(via initenterpairs)
*superfluous elements in S will be deleted
*/
void enterpairsSpecial (poly h,int k,int ecart,int pos,kStrategy strat, int atR = -1)
{
  int j;
  const int iCompH = pGetComp(h);
 
  if (rField_is_Ring(currRing))
  {
    for (j=0; j<=k; j++)
    {
      const int iCompSj = pGetComp(strat->S[j]);
      if ((iCompH==iCompSj)
          //|| (0==iCompH) // can only happen,if iCompSj==0
          || (0==iCompSj))
      {
        enterOnePairRing(j,h,ecart,FALSE,strat, atR);
      }
    }
    kMergeBintoL(strat);
  }
  else
  {
    for (j=0; j<=k; j++)
    {
      const int iCompSj = pGetComp(strat->S[j]);
      if ((iCompH==iCompSj)
          //|| (0==iCompH) // can only happen,if iCompSj==0
          || (0==iCompSj))
      {
        enterOnePairSpecial(j,h,ecart,strat, atR);
      }
    }
  }
 
  if (strat->noClearS) return;
 
//   #ifdef HAVE_PLURAL
/*
  if (rIsPluralRing(currRing))
  {
    j=pos;
    loop
    {
      if (j > k) break;
 
      if (pLmDivisibleBy(h, strat->S[j]))
      {
        deleteInS(j, strat);
        j--;
        k--;
      }
 
      j++;
    }
  }
  else
*/
//   #endif // ??? Why was the following cancellation disabled for non-commutative rings?
  {
    j=pos;
    loop
    {
      unsigned long h_sev = pGetShortExpVector(h);
      if (j > k) break;
      clearS(h,h_sev,&j,&k,strat);
      j++;
    }
  }
}
 
/*2
*reorders  s with respect to posInS,
*suc is the first changed index or zero
*/
 
void reorderS (int* suc,kStrategy strat)
{
  int i,j,at,ecart, s2r;
  int fq=0;
  unsigned long sev;
  poly  p;
  int new_suc=strat->sl+1;
  i= *suc;
  if (i<0) i=0;
 
  for (; i<=strat->sl; i++)
  {
    at = posInS(strat,i-1,strat->S[i],strat->ecartS[i]);
    if (at != i)
    {
      if (new_suc > at) new_suc = at;
      p = strat->S[i];
      ecart = strat->ecartS[i];
      sev = strat->sevS[i];
      s2r = strat->S_2_R[i];
      if (strat->fromQ!=NULL) fq=strat->fromQ[i];
      for (j=i; j>=at+1; j--)
      {
        strat->S[j] = strat->S[j-1];
        strat->ecartS[j] = strat->ecartS[j-1];
        strat->sevS[j] = strat->sevS[j-1];
        strat->S_2_R[j] = strat->S_2_R[j-1];
      }
      strat->S[at] = p;
      strat->ecartS[at] = ecart;
      strat->sevS[at] = sev;
      strat->S_2_R[at] = s2r;
      if (strat->fromQ!=NULL)
      {
        for (j=i; j>=at+1; j--)
        {
          strat->fromQ[j] = strat->fromQ[j-1];
        }
        strat->fromQ[at]=fq;
      }
    }
  }
  if (new_suc <= strat->sl) *suc=new_suc;
  else                      *suc=-1;
}
 
 
/*2
*looks up the position of p in set
*set[0] is the smallest with respect to the ordering-procedure deg/pComp
* Assumption: posInS only depends on the leading term
*             otherwise, bba has to be changed
*/
int posInS (const kStrategy strat, const int length,const poly p,
            const int ecart_p)
{
  if(length==-1) return 0;
  polyset set=strat->S;
  int i;
  int an = 0;
  int en = length;
  int cmp_int = currRing->OrdSgn;
  if ((rHasMixedOrdering(currRing))
#ifdef HAVE_PLURAL
  && (currRing->real_var_start==0)
#endif
#if 0
  || ((strat->ak>0) && ((currRing->order[0]==ringorder_c)||((currRing->order[0]==ringorder_C))))
#endif
  )
  {
    int o=p_Deg(p,currRing);
    int oo=p_Deg(set[length],currRing);
 
    if ((oo<o)
    || ((o==oo) && (pLmCmp(set[length],p)!= cmp_int)))
      return length+1;
 
    loop
    {
      if (an >= en-1)
      {
        if ((p_Deg(set[an],currRing)>=o) && (pLmCmp(set[an],p) == cmp_int))
        {
          return an;
        }
        return en;
      }
      i=(an+en) / 2;
      if ((p_Deg(set[i],currRing)>=o) && (pLmCmp(set[i],p) == cmp_int)) en=i;
      else                              an=i;
    }
  }
  else
  {
    if (rField_is_Ring(currRing))
    {
      if (pLmCmp(set[length],p)== -cmp_int)
        return length+1;
      int cmp;
      loop
      {
        if (an >= en-1)
        {
          cmp = pLmCmp(set[an],p);
          if (cmp == cmp_int)  return an;
          if (cmp == -cmp_int) return en;
          if (n_DivBy(pGetCoeff(p), pGetCoeff(set[an]), currRing->cf)) return en;
          return an;
        }
        i = (an+en) / 2;
        cmp = pLmCmp(set[i],p);
        if (cmp == cmp_int)         en = i;
        else if (cmp == -cmp_int)   an = i;
        else
        {
          if (n_DivBy(pGetCoeff(p), pGetCoeff(set[i]), currRing->cf)) an = i;
          else en = i;
        }
      }
    }
    else
    if (pLmCmp(set[length],p)== -cmp_int)
      return length+1;
 
    loop
    {
      if (an >= en-1)
      {
        if (pLmCmp(set[an],p) == cmp_int) return an;
        if (pLmCmp(set[an],p) == -cmp_int) return en;
        if ((cmp_int!=1)
        && ((strat->ecartS[an])>ecart_p))
          return an;
        return en;
      }
      i=(an+en) / 2;
      if (pLmCmp(set[i],p) == cmp_int) en=i;
      else if (pLmCmp(set[i],p) == -cmp_int) an=i;
      else
      {
        if ((cmp_int!=1)
        &&((strat->ecartS[i])<ecart_p))
          en=i;
        else
          an=i;
      }
    }
  }
}
 
 
// sorts by degree and pLtCmp
// but puts pure monomials at the beginning
int posInSMonFirst (const kStrategy strat, const int length,const poly p)
{
  if (length<0) return 0;
  polyset set=strat->S;
  if(pNext(p) == NULL)
  {
    int mon = 0;
    for(int i = 0;i<=length;i++)
    {
      if(set[i] != NULL && pNext(set[i]) == NULL)
        mon++;
    }
    int o = p_Deg(p,currRing);
    int op = p_Deg(set[mon],currRing);
 
    if ((op < o)
    || ((op == o) && (pLtCmp(set[mon],p) == -1)))
      return length+1;
    int i;
    int an = 0;
    int en= mon;
    loop
    {
      if (an >= en-1)
      {
        op = p_Deg(set[an],currRing);
        if ((op < o)
        || ((op == o) && (pLtCmp(set[an],p) == -1)))
          return en;
        return an;
      }
      i=(an+en) / 2;
      op = p_Deg(set[i],currRing);
      if ((op < o)
      || ((op == o) && (pLtCmp(set[i],p) == -1)))
        an=i;
      else
        en=i;
    }
  }
  else /*if(pNext(p) != NULL)*/
  {
    int o = p_Deg(p,currRing);
    int op = p_Deg(set[length],currRing);
 
    if ((op < o)
    || ((op == o) && (pLtCmp(set[length],p) == -1)))
      return length+1;
    int i;
    int an = 0;
    for(i=0;i<=length;i++)
      if(set[i] != NULL && pNext(set[i]) == NULL)
        an++;
    int en= length;
    loop
    {
      if (an >= en-1)
      {
        op = p_Deg(set[an],currRing);
        if ((op < o)
        || ((op == o) && (pLtCmp(set[an],p) == -1)))
          return en;
        return an;
      }
      i=(an+en) / 2;
      op = p_Deg(set[i],currRing);
      if ((op < o)
      || ((op == o) && (pLtCmp(set[i],p) == -1)))
        an=i;
      else
        en=i;
    }
  }
}
 
// sorts by degree and pLtCmp in the block between start,end;
// but puts pure monomials at the beginning
int posInIdealMonFirst (const ideal F, const poly p,int start,int end)
{
  if(end < 0 || end >= IDELEMS(F))
    end = IDELEMS(F);
  if (end<0) return 0;
  if(pNext(p) == NULL) return start;
  polyset set=F->m;
  int o = p_Deg(p,currRing);
  int op;
  int i;
  int an = start;
  for(i=start;i<end;i++)
    if(set[i] != NULL && pNext(set[i]) == NULL)
      an++;
  if(an == end-1)
    return end;
  int en= end;
  loop
  {
    if(an>=en)
      return en;
    if (an == en-1)
    {
      op = p_Deg(set[an],currRing);
      if ((op < o)
      || ((op == o) && (pLtCmp(set[an],p) == -1)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = p_Deg(set[i],currRing);
    if ((op < o)
    || ((op == o) && (pLtCmp(set[i],p) == -1)))
      an=i;
    else
      en=i;
  }
}
 
 
/*2
* looks up the position of p in set
* the position is the last one
*/
int posInT0 (const TSet,const int length,LObject &)
{
  return (length+1);
}
 
 
/*2
* looks up the position of p in T
* set[0] is the smallest with respect to the ordering-procedure
* pComp
*/
int posInT1 (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  if (pLmCmp(set[length].p,p.p)!= currRing->OrdSgn) return length+1;
 
  int i;
  int an = 0;
  int en= length;
  int cmp_int=currRing->OrdSgn;
 
  loop
  {
    if (an >= en-1)
    {
      if (pLmCmp(set[an].p,p.p) == cmp_int) return an;
      return en;
    }
    i=(an+en) / 2;
    if (pLmCmp(set[i].p,p.p) == cmp_int) en=i;
    else                                 an=i;
  }
}
 
/*2
* looks up the position of p in T
* set[0] is the smallest with respect to the ordering-procedure
* length
*/
int posInT2 (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
  p.GetpLength();
  if (set[length].length<p.length) return length+1;
 
  int i;
  int an = 0;
  int en= length;
 
  loop
  {
    if (an >= en-1)
    {
      if (set[an].length>p.length) return an;
      return en;
    }
    i=(an+en) / 2;
    if (set[i].length>p.length) en=i;
    else                        an=i;
  }
}
 
/*2
* looks up the position of p in T
* set[0] is the smallest with respect to the ordering-procedure
* totaldegree,pComp
*/
int posInT11 (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg();
  int op = set[length].GetpFDeg();
  int cmp_int=currRing->OrdSgn;
 
  if ((op < o)
  || ((op == o) && (pLmCmp(set[length].p,p.p) != cmp_int)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
 
  loop
  {
    if (an >= en-1)
    {
      op= set[an].GetpFDeg();
      if ((op > o)
      || (( op == o) && (pLmCmp(set[an].p,p.p) == cmp_int)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if (( op > o)
    || (( op == o) && (pLmCmp(set[i].p,p.p) == cmp_int)))
      en=i;
    else
      an=i;
  }
}
 
int posInT11Ring (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg();
  int op = set[length].GetpFDeg();
 
  if ((op < o)
  || ((op == o) && (pLtCmpOrdSgnDiffP(set[length].p,p.p))))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
 
  loop
  {
    if (an >= en-1)
    {
      op= set[an].GetpFDeg();
      if ((op > o)
      || (( op == o) && (pLtCmpOrdSgnEqP(set[an].p,p.p))))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if (( op > o)
    || (( op == o) && (pLtCmpOrdSgnEqP(set[i].p,p.p))))
      en=i;
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in T
* set[0] is the smallest with respect to the ordering-procedure
* totaldegree,pComp
*/
int posInT110 (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
  p.GetpLength();
 
  int o = p.GetpFDeg();
  int op = set[length].GetpFDeg();
  int cmp_int=currRing->OrdSgn;
 
  if (( op < o)
  || (( op == o) && (set[length].length<p.length))
  || (( op == o) && (set[length].length == p.length)
     && (pLmCmp(set[length].p,p.p) != cmp_int)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if (( op > o)
      || (( op == o) && (set[an].length > p.length))
      || (( op == o) && (set[an].length == p.length)
         && (pLmCmp(set[an].p,p.p) == cmp_int)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if (( op > o)
    || (( op == o) && (set[i].length > p.length))
    || (( op == o) && (set[i].length == p.length)
       && (pLmCmp(set[i].p,p.p) == cmp_int)))
      en=i;
    else
      an=i;
  }
}
 
int posInT110Ring (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
  p.GetpLength();
 
  int o = p.GetpFDeg();
  int op = set[length].GetpFDeg();
 
  if (( op < o)
  || (( op == o) && (set[length].length<p.length))
  || (( op == o) && (set[length].length == p.length)
     && (pLtCmpOrdSgnDiffP(set[length].p,p.p))))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if (( op > o)
      || (( op == o) && (set[an].length > p.length))
      || (( op == o) && (set[an].length == p.length)
         && (pLtCmpOrdSgnEqP(set[an].p,p.p))))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if (( op > o)
    || (( op == o) && (set[i].length > p.length))
    || (( op == o) && (set[i].length == p.length)
       && (pLtCmpOrdSgnEqP(set[i].p,p.p))))
      en=i;
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in set
* set[0] is the smallest with respect to the ordering-procedure
* pFDeg
*/
int posInT13 (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg();
 
  if (set[length].GetpFDeg() <= o)
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (set[an].GetpFDeg() > o)
        return an;
      return en;
    }
    i=(an+en) / 2;
    if (set[i].GetpFDeg() > o)
      en=i;
    else
      an=i;
  }
}
 
// determines the position based on: 1.) Ecart 2.) pLength
int posInT_EcartpLength(const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
  int ol = p.GetpLength();
  int op=p.ecart;
  int oo=set[length].ecart;
 
  if ((oo < op) || ((oo==op) && (set[length].length <= ol)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      int oo=set[an].ecart;
      if((oo > op)
         || ((oo==op) && (set[an].pLength > ol)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    int oo=set[i].ecart;
    if ((oo > op)
        || ((oo == op) && (set[i].pLength > ol)))
      en=i;
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in set
* set[0] is the smallest with respect to the ordering-procedure
* maximaldegree, pComp
*/
int posInT15 (const TSet set,const int length,LObject &p)
/*{
 *int j=0;
 * int o;
 *
 * o = p.GetpFDeg()+p.ecart;
 * loop
 * {
 *   if ((set[j].GetpFDeg()+set[j].ecart > o)
 *   || ((set[j].GetpFDeg()+set[j].ecart == o)
 *     && (pLmCmp(set[j].p,p.p) == currRing->OrdSgn)))
 *   {
 *     return j;
 *   }
 *   j++;
 *   if (j > length) return j;
 * }
 *}
 */
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg() + p.ecart;
  int op = set[length].GetpFDeg()+set[length].ecart;
  int cmp_int=currRing->OrdSgn;
 
  if ((op < o)
  || ((op == o)
     && (pLmCmp(set[length].p,p.p) != cmp_int)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg()+set[an].ecart;
      if (( op > o)
      || (( op  == o) && (pLmCmp(set[an].p,p.p) == cmp_int)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg()+set[i].ecart;
    if (( op > o)
    || (( op == o) && (pLmCmp(set[i].p,p.p) == cmp_int)))
      en=i;
    else
      an=i;
  }
}
 
int posInT15Ring (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg() + p.ecart;
  int op = set[length].GetpFDeg()+set[length].ecart;
 
  if ((op < o)
  || ((op == o)
     && (pLtCmpOrdSgnDiffP(set[length].p,p.p))))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg()+set[an].ecart;
      if (( op > o)
      || (( op  == o) && (pLtCmpOrdSgnEqP(set[an].p,p.p))))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg()+set[i].ecart;
    if (( op > o)
    || (( op == o) && (pLtCmpOrdSgnEqP(set[i].p,p.p))))
      en=i;
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in set
* set[0] is the smallest with respect to the ordering-procedure
* pFDeg+ecart, ecart, pComp
*/
int posInT17 (const TSet set,const int length,LObject &p)
/*
*{
* int j=0;
* int  o;
*
*  o = p.GetpFDeg()+p.ecart;
*  loop
*  {
*    if ((pFDeg(set[j].p)+set[j].ecart > o)
*    || (((pFDeg(set[j].p)+set[j].ecart == o)
*      && (set[j].ecart < p.ecart)))
*    || ((pFDeg(set[j].p)+set[j].ecart == o)
*      && (set[j].ecart==p.ecart)
*      && (pLmCmp(set[j].p,p.p)==currRing->OrdSgn)))
*      return j;
*    j++;
*    if (j > length) return j;
*  }
* }
*/
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg() + p.ecart;
  int op = set[length].GetpFDeg()+set[length].ecart;
  int cmp_int=currRing->OrdSgn;
 
  if ((op < o)
  || (( op == o) && (set[length].ecart > p.ecart))
  || (( op == o) && (set[length].ecart==p.ecart)
     && (pLmCmp(set[length].p,p.p) != cmp_int)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg()+set[an].ecart;
      if (( op > o)
      || (( op == o) && (set[an].ecart < p.ecart))
      || (( op  == o) && (set[an].ecart==p.ecart)
         && (pLmCmp(set[an].p,p.p) == cmp_int)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg()+set[i].ecart;
    if ((op > o)
    || (( op == o) && (set[i].ecart < p.ecart))
    || (( op == o) && (set[i].ecart == p.ecart)
       && (pLmCmp(set[i].p,p.p) == cmp_int)))
      en=i;
    else
      an=i;
  }
}
 
int posInT17Ring (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int o = p.GetpFDeg() + p.ecart;
  int op = set[length].GetpFDeg()+set[length].ecart;
 
  if ((op < o)
  || (( op == o) && (set[length].ecart > p.ecart))
  || (( op == o) && (set[length].ecart==p.ecart)
     && (pLtCmpOrdSgnDiffP(set[length].p,p.p))))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg()+set[an].ecart;
      if (( op > o)
      || (( op == o) && (set[an].ecart < p.ecart))
      || (( op  == o) && (set[an].ecart==p.ecart)
         && (pLtCmpOrdSgnEqP(set[an].p,p.p))))
        return an;
      return en;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg()+set[i].ecart;
    if ((op > o)
    || (( op == o) && (set[i].ecart < p.ecart))
    || (( op == o) && (set[i].ecart == p.ecart)
       && (pLtCmpOrdSgnEqP(set[i].p,p.p))))
      en=i;
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in set
* set[0] is the smallest with respect to the ordering-procedure
* pGetComp, pFDeg+ecart, ecart, pComp
*/
int posInT17_c (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int cc = (-1+2*currRing->order[0]==ringorder_c);
  /* cc==1 for (c,..), cc==-1 for (C,..) */
  int o = p.GetpFDeg() + p.ecart;
  int c = pGetComp(p.p)*cc;
  int cmp_int=currRing->OrdSgn;
 
  if (pGetComp(set[length].p)*cc < c)
    return length+1;
  if (pGetComp(set[length].p)*cc == c)
  {
    int op = set[length].GetpFDeg()+set[length].ecart;
    if ((op < o)
    || ((op == o) && (set[length].ecart > p.ecart))
    || ((op == o) && (set[length].ecart==p.ecart)
       && (pLmCmp(set[length].p,p.p) != cmp_int)))
      return length+1;
  }
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pGetComp(set[an].p)*cc < c)
        return en;
      if (pGetComp(set[an].p)*cc == c)
      {
        int op = set[an].GetpFDeg()+set[an].ecart;
        if ((op > o)
        || ((op == o) && (set[an].ecart < p.ecart))
        || ((op == o) && (set[an].ecart==p.ecart)
           && (pLmCmp(set[an].p,p.p) == cmp_int)))
          return an;
      }
      return en;
    }
    i=(an+en) / 2;
    if (pGetComp(set[i].p)*cc > c)
      en=i;
    else if (pGetComp(set[i].p)*cc == c)
    {
      int op = set[i].GetpFDeg()+set[i].ecart;
      if ((op > o)
      || ((op == o) && (set[i].ecart < p.ecart))
      || ((op == o) && (set[i].ecart == p.ecart)
         && (pLmCmp(set[i].p,p.p) == cmp_int)))
        en=i;
      else
        an=i;
    }
    else
      an=i;
  }
}
 
int posInT17_cRing (const TSet set,const int length,LObject &p)
{
  if (length==-1) return 0;
 
  int cc = (-1+2*currRing->order[0]==ringorder_c);
  /* cc==1 for (c,..), cc==-1 for (C,..) */
  int o = p.GetpFDeg() + p.ecart;
  int c = pGetComp(p.p)*cc;
 
  if (pGetComp(set[length].p)*cc < c)
    return length+1;
  if (pGetComp(set[length].p)*cc == c)
  {
    int op = set[length].GetpFDeg()+set[length].ecart;
    if ((op < o)
    || ((op == o) && (set[length].ecart > p.ecart))
    || ((op == o) && (set[length].ecart==p.ecart)
       && (pLtCmpOrdSgnDiffP(set[length].p,p.p))))
      return length+1;
  }
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pGetComp(set[an].p)*cc < c)
        return en;
      if (pGetComp(set[an].p)*cc == c)
      {
        int op = set[an].GetpFDeg()+set[an].ecart;
        if ((op > o)
        || ((op == o) && (set[an].ecart < p.ecart))
        || ((op == o) && (set[an].ecart==p.ecart)
           && (pLtCmpOrdSgnEqP(set[an].p,p.p))))
          return an;
      }
      return en;
    }
    i=(an+en) / 2;
    if (pGetComp(set[i].p)*cc > c)
      en=i;
    else if (pGetComp(set[i].p)*cc == c)
    {
      int op = set[i].GetpFDeg()+set[i].ecart;
      if ((op > o)
      || ((op == o) && (set[i].ecart < p.ecart))
      || ((op == o) && (set[i].ecart == p.ecart)
         && (pLtCmpOrdSgnEqP(set[i].p,p.p))))
        en=i;
      else
        an=i;
    }
    else
      an=i;
  }
}
 
/*2
* looks up the position of p in set
* set[0] is the smallest with respect to
* ecart, pFDeg, length
*/
int posInT19 (const TSet set,const int length,LObject &p)
{
  p.GetpLength();
  if (length==-1) return 0;
 
  int o = p.ecart;
  int op=p.GetpFDeg();
 
  if (set[length].ecart < o)
    return length+1;
  if (set[length].ecart == o)
  {
    int oo=set[length].GetpFDeg();
    if ((oo < op) || ((oo==op) && (set[length].length < p.length)))
      return length+1;
  }
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (set[an].ecart > o)
        return an;
      if (set[an].ecart == o)
      {
        int oo=set[an].GetpFDeg();
        if((oo > op)
        || ((oo==op) && (set[an].length > p.length)))
          return an;
      }
      return en;
    }
    i=(an+en) / 2;
    if (set[i].ecart > o)
      en=i;
    else if (set[i].ecart == o)
    {
      int oo=set[i].GetpFDeg();
      if ((oo > op)
      || ((oo == op) && (set[i].length > p.length)))
        en=i;
      else
       an=i;
    }
    else
      an=i;
  }
}
 
/*2
*looks up the position of polynomial p in set
*set[length] is the smallest element in set with respect
*to the ordering-procedure pComp
*/
int posInLSpecial (const LSet set, const int length,
                   LObject *p,const kStrategy)
{
  if (length<0) return 0;
 
  int d=p->GetpFDeg();
  int op=set[length].GetpFDeg();
  int cmp_int=currRing->OrdSgn;
 
  if ((op > d)
  || ((op == d) && (p->p1!=NULL)&&(set[length].p1==NULL))
  || (pLmCmp(set[length].p,p->p)== cmp_int))
     return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op=set[an].GetpFDeg();
      if ((op > d)
      || ((op == d) && (p->p1!=NULL) && (set[an].p1==NULL))
      || (pLmCmp(set[an].p,p->p)== cmp_int))
         return en;
      return an;
    }
    i=(an+en) / 2;
    op=set[i].GetpFDeg();
    if ((op>d)
    || ((op==d) && (p->p1!=NULL) && (set[i].p1==NULL))
    || (pLmCmp(set[i].p,p->p) == cmp_int))
      an=i;
    else
      en=i;
  }
}
 
/*2
*looks up the position of polynomial p in set
*set[length] is the smallest element in set with respect
*to the ordering-procedure pComp
*/
int posInL0 (const LSet set, const int length,
             LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int cmp_int=currRing->OrdSgn;
 
  if (pLmCmp(set[length].p,p->p)== cmp_int)
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pLmCmp(set[an].p,p->p) == cmp_int) return en;
      return an;
    }
    i=(an+en) / 2;
    if (pLmCmp(set[i].p,p->p) == cmp_int) an=i;
    else                                 en=i;
    /*aend. fuer lazy == in !=- machen */
  }
}
 
int posInL0Ring (const LSet set, const int length,
             LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  if (pLtCmpOrdSgnEqP(set[length].p,p->p))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pLtCmpOrdSgnEqP(set[an].p,p->p)) return en;
      return an;
    }
    i=(an+en) / 2;
    if (pLtCmpOrdSgnEqP(set[i].p,p->p)) an=i;
    else                                 en=i;
    /*aend. fuer lazy == in !=- machen */
  }
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the signature order
*/
int posInLSig (const LSet set, const int length,
               LObject* p,const kStrategy /*strat*/)
{
  if (length<0) return 0;
  int cmp_int=currRing->OrdSgn;
  if (pLtCmp(set[length].sig,p->sig)==cmp_int)
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pLtCmp(set[an].sig,p->sig) == cmp_int) return en;
      return an;
    }
    i=(an+en) / 2;
    if (pLtCmp(set[i].sig,p->sig) == cmp_int) an=i;
    else                                      en=i;
    /*aend. fuer lazy == in !=- machen */
  }
}
//sorts the pair list in this order: pLtCmp on the sigs, FDeg, pLtCmp on the polys
int posInLSigRing (const LSet set, const int length,
               LObject* p,const kStrategy /*strat*/)
{
  assume(currRing->OrdSgn == 1 && rField_is_Ring(currRing));
  if (length<0) return 0;
  if (pLtCmp(set[length].sig,p->sig)== 1)
    return length+1;
 
  int an,en,i;
  an = 0;
  en = length+1;
  int cmp;
  loop
  {
    if (an >= en-1)
    {
      if(an == en)
        return en;
      cmp = pLtCmp(set[an].sig,p->sig);
      if (cmp == 1)
        return en;
      if (cmp == -1)
        return an;
      if (cmp == 0)
      {
         if (set[an].FDeg > p->FDeg)
          return en;
         if (set[an].FDeg < p->FDeg)
          return an;
         if (set[an].FDeg == p->FDeg)
         {
            cmp = pLtCmp(set[an].p,p->p);
            if(cmp == 1)
              return en;
            else
              return an;
         }
      }
    }
    i=(an+en) / 2;
    cmp = pLtCmp(set[i].sig,p->sig);
    if (cmp == 1)
      an = i;
    if (cmp == -1)
      en = i;
    if (cmp == 0)
    {
       if (set[i].FDeg > p->FDeg)
        an = i;
       if (set[i].FDeg < p->FDeg)
        en = i;
       if (set[i].FDeg == p->FDeg)
       {
          cmp = pLtCmp(set[i].p,p->p);
          if(cmp == 1)
            an = i;
          else
            en = i;
       }
    }
  }
}
 
// for sba, sorting syzygies
int posInSyz (const kStrategy strat, poly sig)
{
  if (strat->syzl==0) return 0;
  int cmp_int=currRing->OrdSgn;
  if (pLtCmp(strat->syz[strat->syzl-1],sig) != cmp_int)
    return strat->syzl;
  int i;
  int an = 0;
  int en= strat->syzl-1;
  loop
  {
    if (an >= en-1)
    {
      if (pLtCmp(strat->syz[an],sig) != cmp_int) return en;
      return an;
    }
    i=(an+en) / 2;
    if (pLtCmp(strat->syz[i],sig) != cmp_int) an=i;
    else                                      en=i;
    /*aend. fuer lazy == in !=- machen */
  }
}
 
/*2
*
* is only used in F5C, must ensure that the interreduction process does add new
* critical pairs to strat->L only behind all other critical pairs which are
* still in strat->L!
*/
int posInLF5C (const LSet /*set*/, const int /*length*/,
               LObject* /*p*/,const kStrategy strat)
{
  return strat->Ll+1;
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure totaldegree,pComp
*/
int posInL11 (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
  int cmp_int= -currRing->OrdSgn;
 
  if ((op > o)
  || ((op == o) && (pLmCmp(set[length].p,p->p) != cmp_int)))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((op > o)
      || ((op == o) && (pLmCmp(set[an].p,p->p) != cmp_int)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if ((op > o)
    || ((op == o) && (pLmCmp(set[i].p,p->p) != cmp_int)))
      an=i;
    else
      en=i;
  }
}
 
/*2
* looks up the position of polynomial p in set
* set[length] is the smallest element in set with respect
* to the ordering-procedure pLmCmp,totaldegree,coefficient
* For the same totaldegree, original pairs (from F) will
* be put at the end and smallest coefficients
*/
int posInL11Ring (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
 
  if ((op > o)
  || ((op == o) && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((op > o)
      || ((op == o) && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if ((op > o)
    || ((op == o) && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
      an=i;
    else
      en=i;
  }
}
 
int posInLF5CRing (const LSet set, int start,const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
  if(start == (length +1)) return (length+1);
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
 
  if ((op > o)
  || ((op == o) && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
    return length+1;
  int i;
  int an = start;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((op > o)
      || ((op == o) && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if ((op > o)
    || ((op == o) && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
      an=i;
    else
      en=i;
  }
}
 
int posInL11Ringls (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length < 0) return 0;
  int an,en,i;
  an = 0;
  en = length+1;
  loop
  {
    if (an >= en-1)
    {
      if(an == en)
        return en;
      if (set[an].FDeg > p->FDeg)
        return en;
      if (set[an].FDeg < p->FDeg)
        return an;
      if (set[an].FDeg == p->FDeg)
      {
        number lcset,lcp;
        lcset = pGetCoeff(set[an].p);
        lcp = pGetCoeff(p->p);
        if(!nGreaterZero(lcset))
        {
          set[an].p=p_Neg(set[an].p,currRing);
          if (set[an].t_p!=NULL)
            pSetCoeff0(set[an].t_p,pGetCoeff(set[an].p));
          lcset=pGetCoeff(set[an].p);
        }
        if(!nGreaterZero(lcp))
        {
          p->p=p_Neg(p->p,currRing);
          if (p->t_p!=NULL)
            pSetCoeff0(p->t_p,pGetCoeff(p->p));
          lcp=pGetCoeff(p->p);
        }
        if(nGreater(lcset, lcp))
        {
          return en;
        }
        else
        {
          return an;
        }
      }
    }
    i=(an+en) / 2;
    if (set[i].FDeg > p->FDeg)
      an=i;
    if (set[i].FDeg < p->FDeg)
      en=i;
    if (set[i].FDeg == p->FDeg)
    {
      number lcset,lcp;
      lcset = pGetCoeff(set[i].p);
      lcp = pGetCoeff(p->p);
      if(!nGreaterZero(lcset))
      {
        set[i].p=p_Neg(set[i].p,currRing);
        if (set[i].t_p!=NULL)
          pSetCoeff0(set[i].t_p,pGetCoeff(set[i].p));
        lcset=pGetCoeff(set[i].p);
      }
      if(!nGreaterZero(lcp))
      {
        p->p=p_Neg(p->p,currRing);
        if (p->t_p!=NULL)
          pSetCoeff0(p->t_p,pGetCoeff(p->p));
        lcp=pGetCoeff(p->p);
      }
      if(nGreater(lcset, lcp))
      {
        an = i;
      }
      else
      {
        en = i;
      }
    }
  }
}
 
/*2 Position for rings L: Here I am
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure totaldegree,pComp
*/
inline int getIndexRng(long coeff)
{
  if (coeff == 0) return -1;
  long tmp = coeff;
  int ind = 0;
  while (tmp % 2 == 0)
  {
    tmp = tmp / 2;
    ind++;
  }
  return ind;
}
 
/*{
  if (length < 0) return 0;
 
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
 
  int inde = getIndexRng((unsigned long) pGetCoeff(set[length].p));
  int indp = getIndexRng((unsigned long) pGetCoeff(p->p));
  int inda;
  int indi;
 
  if ((inda > indp) || ((inda == inde) && ((op > o) || ((op == o) && (pLmCmp(set[length].p,p->p) != -currRing->OrdSgn)))))
    return length + 1;
  int i;
  int an = 0;
  inda = getIndexRng((unsigned long) pGetCoeff(set[an].p));
  int en = length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((indp > inda) || ((indp == inda) && ((op > o) || ((op == o) && (pLmCmp(set[an].p,p->p) != -currRing->OrdSgn)))))
        return en;
      return an;
    }
    i = (an + en) / 2;
    indi = getIndexRng((unsigned long) pGetCoeff(set[i].p));
    op = set[i].GetpFDeg();
    if ((indi > indp) || ((indi == indp) && ((op > o) || ((op == o) && (pLmCmp(set[i].p,p->p) != -currRing->OrdSgn)))))
    // if ((op > o) || ((op == o) && (pLmCmp(set[i].p,p->p) != -currRing->OrdSgn)))
    {
      an = i;
      inda = getIndexRng((unsigned long) pGetCoeff(set[an].p));
    }
    else
      en = i;
  }
} */
 
/*2
* looks up the position of polynomial p in set
* set[length] is the smallest element in set with respect
* to the ordering-procedure totaldegree,pLength0
*/
int posInL110 (const LSet set, const int length,
               LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
  int cmp_int= -currRing->OrdSgn;
 
  if ((op > o)
  || ((op == o) && (set[length].length >p->length))
  || ((op == o) && (set[length].length <= p->length)
     && (pLmCmp(set[length].p,p->p) != cmp_int)))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((op > o)
      || ((op == o) && (set[an].length >p->length))
      || ((op == o) && (set[an].length <=p->length)
         && (pLmCmp(set[an].p,p->p) != cmp_int)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if ((op > o)
    || ((op == o) && (set[i].length > p->length))
    || ((op == o) && (set[i].length <= p->length)
       && (pLmCmp(set[i].p,p->p) != cmp_int)))
      an=i;
    else
      en=i;
  }
}
 
int posInL110Ring (const LSet set, const int length,
               LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg();
  int op = set[length].GetpFDeg();
 
  if ((op > o)
  || ((op == o) && (set[length].length >p->length))
  || ((op == o) && (set[length].length <= p->length)
     && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg();
      if ((op > o)
      || ((op == o) && (set[an].length >p->length))
      || ((op == o) && (set[an].length <=p->length)
         && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg();
    if ((op > o)
    || ((op == o) && (set[i].length > p->length))
    || ((op == o) && (set[i].length <= p->length)
       && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
      an=i;
    else
      en=i;
  }
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure totaldegree
*/
int posInL13 (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg();
 
  if (set[length].GetpFDeg() > o)
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (set[an].GetpFDeg() >= o)
        return en;
      return an;
    }
    i=(an+en) / 2;
    if (set[i].GetpFDeg() >= o)
      an=i;
    else
      en=i;
  }
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure maximaldegree,pComp
*/
int posInL15 (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg() + p->ecart;
  int op = set[length].GetpFDeg() + set[length].ecart;
  int cmp_int= -currRing->OrdSgn;
 
  if ((op > o)
  || ((op == o) && (pLmCmp(set[length].p,p->p) != cmp_int)))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg() + set[an].ecart;
      if ((op > o)
      || ((op == o) && (pLmCmp(set[an].p,p->p) != cmp_int)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg() + set[i].ecart;
    if ((op > o)
    || ((op == o) && (pLmCmp(set[i].p,p->p) != cmp_int)))
      an=i;
    else
      en=i;
  }
}
 
int posInL15Ring (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg() + p->ecart;
  int op = set[length].GetpFDeg() + set[length].ecart;
 
  if ((op > o)
  || ((op == o) && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      op = set[an].GetpFDeg() + set[an].ecart;
      if ((op > o)
      || ((op == o) && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
        return en;
      return an;
    }
    i=(an+en) / 2;
    op = set[i].GetpFDeg() + set[i].ecart;
    if ((op > o)
    || ((op == o) && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
      an=i;
    else
      en=i;
  }
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure totaldegree
*/
int posInL17 (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg() + p->ecart;
  int cmp_int= -currRing->OrdSgn;
 
  if ((set[length].GetpFDeg() + set[length].ecart > o)
  || ((set[length].GetpFDeg() + set[length].ecart == o)
     && (set[length].ecart > p->ecart))
  || ((set[length].GetpFDeg() + set[length].ecart == o)
     && (set[length].ecart == p->ecart)
     && (pLmCmp(set[length].p,p->p) != cmp_int)))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if ((set[an].GetpFDeg() + set[an].ecart > o)
      || ((set[an].GetpFDeg() + set[an].ecart == o)
         && (set[an].ecart > p->ecart))
      || ((set[an].GetpFDeg() + set[an].ecart == o)
         && (set[an].ecart == p->ecart)
         && (pLmCmp(set[an].p,p->p) != cmp_int)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((set[i].GetpFDeg() + set[i].ecart > o)
    || ((set[i].GetpFDeg() + set[i].ecart == o)
       && (set[i].ecart > p->ecart))
    || ((set[i].GetpFDeg() +set[i].ecart == o)
       && (set[i].ecart == p->ecart)
       && (pLmCmp(set[i].p,p->p) != cmp_int)))
      an=i;
    else
      en=i;
  }
}
 
int posInL17Ring (const LSet set, const int length,
              LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int o = p->GetpFDeg() + p->ecart;
 
  if ((set[length].GetpFDeg() + set[length].ecart > o)
  || ((set[length].GetpFDeg() + set[length].ecart == o)
     && (set[length].ecart > p->ecart))
  || ((set[length].GetpFDeg() + set[length].ecart == o)
     && (set[length].ecart == p->ecart)
     && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
    return length+1;
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if ((set[an].GetpFDeg() + set[an].ecart > o)
      || ((set[an].GetpFDeg() + set[an].ecart == o)
         && (set[an].ecart > p->ecart))
      || ((set[an].GetpFDeg() + set[an].ecart == o)
         && (set[an].ecart == p->ecart)
         && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((set[i].GetpFDeg() + set[i].ecart > o)
    || ((set[i].GetpFDeg() + set[i].ecart == o)
       && (set[i].ecart > p->ecart))
    || ((set[i].GetpFDeg() +set[i].ecart == o)
       && (set[i].ecart == p->ecart)
       && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
      an=i;
    else
      en=i;
  }
}
 
/*2
* looks up the position of polynomial p in set
* e is the ecart of p
* set[length] is the smallest element in set with respect
* to the ordering-procedure pComp
*/
int posInL17_c (const LSet set, const int length,
                LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int cc = (-1+2*currRing->order[0]==ringorder_c);
  /* cc==1 for (c,..), cc==-1 for (C,..) */
  long c = pGetComp(p->p)*cc;
  int o = p->GetpFDeg() + p->ecart;
  int cmp_int= -currRing->OrdSgn;
 
  if (pGetComp(set[length].p)*cc > c)
    return length+1;
  if (pGetComp(set[length].p)*cc == c)
  {
    if ((set[length].GetpFDeg() + set[length].ecart > o)
    || ((set[length].GetpFDeg() + set[length].ecart == o)
       && (set[length].ecart > p->ecart))
    || ((set[length].GetpFDeg() + set[length].ecart == o)
       && (set[length].ecart == p->ecart)
       && (pLmCmp(set[length].p,p->p) != cmp_int)))
      return length+1;
  }
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pGetComp(set[an].p)*cc > c)
        return en;
      if (pGetComp(set[an].p)*cc == c)
      {
        if ((set[an].GetpFDeg() + set[an].ecart > o)
        || ((set[an].GetpFDeg() + set[an].ecart == o)
           && (set[an].ecart > p->ecart))
        || ((set[an].GetpFDeg() + set[an].ecart == o)
           && (set[an].ecart == p->ecart)
           && (pLmCmp(set[an].p,p->p) != cmp_int)))
          return en;
      }
      return an;
    }
    i=(an+en) / 2;
    if (pGetComp(set[i].p)*cc > c)
      an=i;
    else if (pGetComp(set[i].p)*cc == c)
    {
      if ((set[i].GetpFDeg() + set[i].ecart > o)
      || ((set[i].GetpFDeg() + set[i].ecart == o)
         && (set[i].ecart > p->ecart))
      || ((set[i].GetpFDeg() +set[i].ecart == o)
         && (set[i].ecart == p->ecart)
         && (pLmCmp(set[i].p,p->p) != cmp_int)))
        an=i;
      else
        en=i;
    }
    else
      en=i;
  }
}
 
int posInL17_cRing (const LSet set, const int length,
                LObject* p,const kStrategy)
{
  if (length<0) return 0;
 
  int cc = (-1+2*currRing->order[0]==ringorder_c);
  /* cc==1 for (c,..), cc==-1 for (C,..) */
  long c = pGetComp(p->p)*cc;
  int o = p->GetpFDeg() + p->ecart;
 
  if (pGetComp(set[length].p)*cc > c)
    return length+1;
  if (pGetComp(set[length].p)*cc == c)
  {
    if ((set[length].GetpFDeg() + set[length].ecart > o)
    || ((set[length].GetpFDeg() + set[length].ecart == o)
       && (set[length].ecart > p->ecart))
    || ((set[length].GetpFDeg() + set[length].ecart == o)
       && (set[length].ecart == p->ecart)
       && (pLtCmpOrdSgnDiffM(set[length].p,p->p))))
      return length+1;
  }
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (pGetComp(set[an].p)*cc > c)
        return en;
      if (pGetComp(set[an].p)*cc == c)
      {
        if ((set[an].GetpFDeg() + set[an].ecart > o)
        || ((set[an].GetpFDeg() + set[an].ecart == o)
           && (set[an].ecart > p->ecart))
        || ((set[an].GetpFDeg() + set[an].ecart == o)
           && (set[an].ecart == p->ecart)
           && (pLtCmpOrdSgnDiffM(set[an].p,p->p))))
          return en;
      }
      return an;
    }
    i=(an+en) / 2;
    if (pGetComp(set[i].p)*cc > c)
      an=i;
    else if (pGetComp(set[i].p)*cc == c)
    {
      if ((set[i].GetpFDeg() + set[i].ecart > o)
      || ((set[i].GetpFDeg() + set[i].ecart == o)
         && (set[i].ecart > p->ecart))
      || ((set[i].GetpFDeg() +set[i].ecart == o)
         && (set[i].ecart == p->ecart)
         && (pLtCmpOrdSgnDiffM(set[i].p,p->p))))
        an=i;
      else
        en=i;
    }
    else
      en=i;
  }
}
 
/*
 * SYZYGY CRITERION for signature-based standard basis algorithms
 */
BOOLEAN syzCriterion(poly sig, unsigned long not_sevSig, kStrategy strat)
{
//#if 1
#ifdef DEBUGF5
  PrintS("syzygy criterion checks:  ");
  pWrite(sig);
#endif
  for (int k=0; k<strat->syzl; k++)
  {
    //printf("-%d",k);
//#if 1
#ifdef DEBUGF5
    Print("checking with: %d / %d --  \n",k,strat->syzl);
    pWrite(pHead(strat->syz[k]));
#endif
    if (p_LmShortDivisibleBy(strat->syz[k], strat->sevSyz[k], sig, not_sevSig, currRing)
    && (!rField_is_Ring(currRing) ||
    (n_DivBy(pGetCoeff(sig), pGetCoeff(strat->syz[k]),currRing->cf) && pLtCmp(sig,strat->syz[k]) == 1)))
    {
//#if 1
#ifdef DEBUGF5
      PrintS("DELETE!\n");
#endif
      strat->nrsyzcrit++;
      //printf("- T -\n\n");
      return TRUE;
    }
  }
  //printf("- F -\n\n");
  return FALSE;
}
 
/*
 * SYZYGY CRITERION for signature-based standard basis algorithms
 */
BOOLEAN syzCriterionInc(poly sig, unsigned long not_sevSig, kStrategy strat)
{
//#if 1
  if(sig == NULL)
    return FALSE;
#ifdef DEBUGF5
  PrintS("--- syzygy criterion checks:  ");
  pWrite(sig);
#endif
  int comp = (int)__p_GetComp(sig, currRing);
  int min, max;
  if (comp<=1)
    return FALSE;
  else
  {
    min = strat->syzIdx[comp-2];
    //printf("SYZIDX %d/%d\n",strat->syzIdx[comp-2],comp-2);
    //printf("SYZIDX %d/%d\n",strat->syzIdx[comp-1],comp-1);
    //printf("SYZIDX %d/%d\n",strat->syzIdx[comp],comp);
    if (comp == strat->currIdx)
    {
      max = strat->syzl;
    }
    else
    {
      max = strat->syzIdx[comp-1];
    }
    for (int k=min; k<max; k++)
    {
#ifdef F5DEBUG
      Print("COMP %d/%d - MIN %d - MAX %d - SYZL %ld\n",comp,strat->currIdx,min,max,strat->syzl);
      Print("checking with: %d --  ",k);
      pWrite(pHead(strat->syz[k]));
#endif
      if (p_LmShortDivisibleBy(strat->syz[k], strat->sevSyz[k], sig, not_sevSig, currRing)
      && (!rField_is_Ring(currRing) ||
      (n_DivBy(pGetCoeff(sig), pGetCoeff(strat->syz[k]),currRing->cf) && pLtCmp(sig,strat->syz[k]) == 1)))
      {
        strat->nrsyzcrit++;
        return TRUE;
      }
    }
    return FALSE;
  }
}
 
/*
 * REWRITTEN CRITERION for signature-based standard basis algorithms
 */
BOOLEAN faugereRewCriterion(poly sig, unsigned long not_sevSig, poly /*lm*/, kStrategy strat, int start=0)
{
  //printf("Faugere Rewritten Criterion\n");
  if(rField_is_Ring(currRing))
    return FALSE;
//#if 1
#ifdef DEBUGF5
  PrintS("rewritten criterion checks:  ");
  pWrite(sig);
#endif
  for(int k = strat->sl; k>=start; k--)
  {
//#if 1
#ifdef DEBUGF5
    PrintS("checking with:  ");
    pWrite(strat->sig[k]);
    pWrite(pHead(strat->S[k]));
#endif
    if (p_LmShortDivisibleBy(strat->sig[k], strat->sevSig[k], sig, not_sevSig, currRing))
    {
//#if 1
#ifdef DEBUGF5
      PrintS("DELETE!\n");
#endif
      strat->nrrewcrit++;
      return TRUE;
    }
    //k--;
  }
#ifdef DEBUGF5
  PrintS("ALL ELEMENTS OF S\n----------------------------------------\n");
  for(int kk = 0; kk<strat->sl+1; kk++)
  {
    pWrite(pHead(strat->S[kk]));
  }
  PrintS("------------------------------\n");
#endif
  return FALSE;
}
 
/*
 * REWRITTEN CRITERION for signature-based standard basis algorithms
 ***************************************************************************
 * TODO:This should become the version of Arri/Perry resp. Bjarke/Stillman *
 ***************************************************************************
 */
 
// real implementation of arri's rewritten criterion, only called once in
// kstd2.cc, right before starting reduction
// IDEA:  Arri says that it is enough to consider 1 polynomial for each unique
//        signature appearing during the computations. Thus we first of all go
//        through strat->L and delete all other pairs of the same signature,
//        keeping only the one with least possible leading monomial. After this
//        we check if we really need to compute this critical pair at all: There
//        can be elements already in strat->S whose signatures divide the
//        signature of the critical pair in question and whose multiplied
//        leading monomials are smaller than the leading monomial of the
//        critical pair. In this situation we can discard the critical pair
//        completely.
BOOLEAN arriRewCriterion(poly /*sig*/, unsigned long /*not_sevSig*/, poly /*lm*/, kStrategy strat, int start=0)
{
  if(rField_is_Ring(currRing))
    return FALSE;
  poly p1 = pOne();
  poly p2 = pOne();
  for (int ii=strat->sl; ii>start; ii--)
  {
    if (p_LmShortDivisibleBy(strat->sig[ii], strat->sevSig[ii], strat->P.sig, ~strat->P.sevSig, currRing))
    {
      p_ExpVectorSum(p1,strat->P.sig,strat->S[ii],currRing);
      p_ExpVectorSum(p2,strat->sig[ii],strat->P.p,currRing);
      if (!(pLmCmp(p1,p2) == 1))
      {
        pDelete(&p1);
        pDelete(&p2);
        return TRUE;
      }
    }
  }
  pDelete(&p1);
  pDelete(&p2);
  return FALSE;
}
 
BOOLEAN arriRewCriterionPre(poly sig, unsigned long not_sevSig, poly lm, kStrategy strat, int /*start=0*/)
{
  //Over Rings, there are still some changes to do: considering coeffs
  if(rField_is_Ring(currRing))
    return FALSE;
  int found = -1;
  for (int i=strat->Bl; i>-1; i--)
  {
    if (pLmEqual(strat->B[i].sig,sig))
    {
      found = i;
      break;
    }
  }
  if (found != -1)
  {
    if (pLmCmp(lm,strat->B[found].GetLmCurrRing()) == -1)
    {
      deleteInL(strat->B,&strat->Bl,found,strat);
    }
    else
    {
      return TRUE;
    }
  }
  poly p1 = pOne();
  poly p2 = pOne();
  for (int ii=strat->sl; ii>-1; ii--)
  {
    if (p_LmShortDivisibleBy(strat->sig[ii], strat->sevSig[ii], sig, not_sevSig, currRing))
    {
      p_ExpVectorSum(p1,sig,strat->S[ii],currRing);
      p_ExpVectorSum(p2,strat->sig[ii],lm,currRing);
      if (!(pLmCmp(p1,p2) == 1))
      {
        pDelete(&p1);
        pDelete(&p2);
        return TRUE;
      }
    }
  }
  pDelete(&p1);
  pDelete(&p2);
  return FALSE;
}
 
/***************************************************************
 *
 * Tail reductions
 *
 ***************************************************************/
TObject* kFindDivisibleByInS_T(kStrategy strat, int end_pos, LObject* L, TObject *T, long ecart)
{
  int j = 0;
  const unsigned long not_sev = ~L->sev;
  const unsigned long* sev = strat->sevS;
  poly p;
  ring r;
  L->GetLm(p, r);
 
  assume(~not_sev == p_GetShortExpVector(p, r));
 
  if (r == currRing)
  {
    if(!rField_is_Ring(r))
    {
      loop
      {
        if (j > end_pos) return NULL;
  #if defined(PDEBUG) || defined(PDIV_DEBUG)
        if (strat->S[j]!= NULL && p_LmShortDivisibleBy(strat->S[j], sev[j], p, not_sev, r) &&
            (ecart== LONG_MAX || ecart>= strat->ecartS[j]))
  #else
        if (!(sev[j] & not_sev) &&
            (ecart== LONG_MAX || ecart>= strat->ecartS[j]) &&
            p_LmDivisibleBy(strat->S[j], p, r))
  #endif
        {
            break;
        }
        j++;
      }
    }
    else
    {
      loop
      {
        if (j > end_pos) return NULL;
  #if defined(PDEBUG) || defined(PDIV_DEBUG)
        if (strat->S[j]!= NULL
        && p_LmShortDivisibleBy(strat->S[j], sev[j], p, not_sev, r)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j])
        && n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), r->cf))
  #else
        if (!(sev[j] & not_sev)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j])
        && p_LmDivisibleBy(strat->S[j], p, r)
        && n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), r->cf))
  #endif
        {
          break; // found
        }
        j++;
      }
    }
    // if called from NF, T objects do not exist:
    if (strat->tl < 0 || strat->S_2_R[j] == -1)
    {
      T->Set(strat->S[j], r, strat->tailRing);
      assume(T->GetpLength()==pLength(T->p != __null ? T->p : T->t_p));
      return T;
    }
    else
    {
/////      assume (j >= 0 && j <= strat->tl && strat->S_2_T(j) != NULL
/////      && strat->S_2_T(j)->p == strat->S[j]); // wrong?
//      assume (j >= 0 && j <= strat->sl && strat->S_2_T(j) != NULL && strat->S_2_T(j)->p == strat->S[j]);
      return strat->S_2_T(j);
    }
  }
  else
  {
    TObject* t;
    if(!rField_is_Ring(r))
    {
      loop
      {
        if (j > end_pos) return NULL;
        assume(strat->S_2_R[j] != -1);
  #if defined(PDEBUG) || defined(PDIV_DEBUG)
        t = strat->S_2_T(j);
        assume(t != NULL && t->t_p != NULL && t->tailRing == r);
        if (p_LmShortDivisibleBy(t->t_p, sev[j], p, not_sev, r)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j]))
        {
          t->pLength=pLength(t->t_p);
          return t;
        }
  #else
        if (! (sev[j] & not_sev)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j]))
        {
          t = strat->S_2_T(j);
          assume(t != NULL && t->t_p != NULL && t->tailRing == r && t->p == strat->S[j]);
          if (p_LmDivisibleBy(t->t_p, p, r))
          {
            t->pLength=pLength(t->t_p);
            return t;
          }
        }
  #endif
        j++;
      }
    }
    else
    {
      loop
      {
        if (j > end_pos) return NULL;
        assume(strat->S_2_R[j] != -1);
  #if defined(PDEBUG) || defined(PDIV_DEBUG)
        t = strat->S_2_T(j);
        assume(t != NULL && t->t_p != NULL && t->tailRing == r);
        if (p_LmShortDivisibleBy(t->t_p, sev[j], p, not_sev, r)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j])
        && n_DivBy(pGetCoeff(p), pGetCoeff(t->t_p), r->cf))
        {
          t->pLength=pLength(t->t_p);
          return t;
        }
  #else
        if (! (sev[j] & not_sev)
        && (ecart== LONG_MAX || ecart>= strat->ecartS[j]))
        {
          t = strat->S_2_T(j);
          assume(t != NULL && t->t_p != NULL && t->tailRing == r && t->p == strat->S[j]);
          if (p_LmDivisibleBy(t->t_p, p, r)
          && n_DivBy(pGetCoeff(p), pGetCoeff(t->t_p), r->cf))
          {
            t->pLength=pLength(t->t_p);
            return t;
          }
        }
  #endif
        j++;
      }
    }
  }
}
 
poly redtail (LObject* L, int end_pos, kStrategy strat)
{
  poly h, hn;
  strat->redTailChange=FALSE;
 
  L->GetP();
  poly p = L->p;
  if (strat->noTailReduction || pNext(p) == NULL)
    return p;
 
  LObject Ln(strat->tailRing);
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
  h = p;
  hn = pNext(h);
  long op = strat->tailRing->pFDeg(hn, strat->tailRing);
  long e;
  int l;
  BOOLEAN save_HE=strat->kAllAxis;
  strat->kAllAxis |=
    ((Kstd1_deg>0) && (op<=Kstd1_deg)) || TEST_OPT_INFREDTAIL;
 
  while(hn != NULL)
  {
    op = strat->tailRing->pFDeg(hn, strat->tailRing);
    if ((Kstd1_deg>0)&&(op>Kstd1_deg)) goto all_done;
    e = strat->tailRing->pLDeg(hn, &l, strat->tailRing) - op;
    loop
    {
      Ln.Set(hn, strat->tailRing);
      Ln.sev = p_GetShortExpVector(hn, strat->tailRing);
      if (strat->kAllAxis)
        With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s);
      else
        With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s, e);
      if (With == NULL) break;
      With->length=0;
      With->pLength=0;
      strat->redTailChange=TRUE;
      if (ksReducePolyTail(L, With, h, strat->kNoetherTail()))
      {
        // reducing the tail would violate the exp bound
        if (kStratChangeTailRing(strat, L))
        {
          strat->kAllAxis = save_HE;
          return redtail(L, end_pos, strat);
        }
        else
          return NULL;
      }
      hn = pNext(h);
      if (hn == NULL) goto all_done;
      op = strat->tailRing->pFDeg(hn, strat->tailRing);
      if ((Kstd1_deg>0)&&(op>Kstd1_deg)) goto all_done;
      e = strat->tailRing->pLDeg(hn, &l, strat->tailRing) - op;
    }
    h = hn;
    hn = pNext(h);
  }
 
  all_done:
  if (strat->redTailChange)
  {
    L->pLength = 0;
  }
  strat->kAllAxis = save_HE;
  return p;
}
 
poly redtail (poly p, int end_pos, kStrategy strat)
{
  LObject L(p, currRing);
  return redtail(&L, end_pos, strat);
}
 
poly redtailBba (LObject* L, int end_pos, kStrategy strat, BOOLEAN withT, BOOLEAN normalize)
{
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return L->GetLmCurrRing();
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return L->GetLmCurrRing();
 
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
 
  LObject Ln(pNext(h), strat->tailRing);
  Ln.GetpLength();
 
  pNext(h) = NULL;
  if (L->p != NULL)
  {
    pNext(L->p) = NULL;
    if (L->t_p != NULL) pNext(L->t_p) = NULL;
  }
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  int cnt=REDTAIL_CANONICALIZE;
  while(!Ln.IsNull())
  {
    loop
    {
      if (TEST_OPT_IDLIFT)
      {
        if (Ln.p!=NULL)
        {
          if ((int)__p_GetComp(Ln.p,currRing)> strat->syzComp) break;
        }
        else
        {
          if ((int)__p_GetComp(Ln.t_p,strat->tailRing)> strat->syzComp) break;
        }
      }
      Ln.SetShortExpVector();
      if (withT)
      {
        int j;
        j = kFindDivisibleByInT(strat, &Ln);
        if (j < 0) break;
        With = &(strat->T[j]);
        assume(With->GetpLength()==pLength(With->p != __null ? With->p : With->t_p));
      }
      else
      {
        With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s);
        if (With == NULL) break;
        assume(With->GetpLength()==pLength(With->p != __null ? With->p : With->t_p));
      }
      cnt--;
      if (cnt==0)
      {
        cnt=REDTAIL_CANONICALIZE;
        /*poly tmp=*/Ln.CanonicalizeP();
        if (normalize)
        {
          Ln.Normalize();
          //pNormalize(tmp);
          //if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
        }
      }
      if (normalize && (!TEST_OPT_INTSTRATEGY) && (!nIsOne(pGetCoeff(With->p))))
      {
        With->pNorm();
      }
      strat->redTailChange=TRUE;
      if (ksReducePolyTail(L, With, &Ln))
      {
        // reducing the tail would violate the exp bound
        //  set a flag and hope for a retry (in bba)
        strat->completeReduce_retry=TRUE;
        if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
        do
        {
          pNext(h) = Ln.LmExtractAndIter();
          pIter(h);
          L->pLength++;
        } while (!Ln.IsNull());
        goto all_done;
      }
      if (Ln.IsNull()) goto all_done;
      if (! withT) With_s.Init(currRing);
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    pNormalize(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
    L->pLength = 0;
  }
 
  //if (TEST_OPT_PROT) { PrintS("N"); mflush(); }
  //L->Normalize(); // HANNES: should have a test
  kTest_L(L,strat);
  return L->GetLmCurrRing();
}
 
poly redtailBbaBound (LObject* L, int end_pos, kStrategy strat, int bound, BOOLEAN withT, BOOLEAN normalize)
{
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return L->GetLmCurrRing();
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return L->GetLmCurrRing();
 
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
 
  LObject Ln(pNext(h), strat->tailRing);
  Ln.pLength = L->GetpLength() - 1;
 
  pNext(h) = NULL;
  if (L->p != NULL) pNext(L->p) = NULL;
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  int cnt=REDTAIL_CANONICALIZE;
  while(!Ln.IsNull())
  {
    loop
    {
      if (TEST_OPT_IDLIFT)
      {
        if (Ln.p!=NULL)
        {
          if ((int)__p_GetComp(Ln.p,currRing)> strat->syzComp) break;
        }
        else
        {
          if ((int)__p_GetComp(Ln.t_p,strat->tailRing)> strat->syzComp) break;
        }
      }
      Ln.SetShortExpVector();
      if (withT)
      {
        int j;
        j = kFindDivisibleByInT(strat, &Ln);
        if (j < 0) break;
        With = &(strat->T[j]);
      }
      else
      {
        With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s);
        if (With == NULL) break;
      }
      cnt--;
      if (cnt==0)
      {
        cnt=REDTAIL_CANONICALIZE;
        /*poly tmp=*/Ln.CanonicalizeP();
        if (normalize)
        {
          Ln.Normalize();
          //pNormalize(tmp);
          //if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
        }
      }
      if (normalize && (!TEST_OPT_INTSTRATEGY) && (!nIsOne(pGetCoeff(With->p))))
      {
        With->pNorm();
      }
      strat->redTailChange=TRUE;
      if (ksReducePolyTail(L, With, &Ln))
      {
        // reducing the tail would violate the exp bound
        //  set a flag and hope for a retry (in bba)
        strat->completeReduce_retry=TRUE;
        if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
        do
        {
          pNext(h) = Ln.LmExtractAndIter();
          pIter(h);
          L->pLength++;
        } while (!Ln.IsNull());
        goto all_done;
      }
      if(!Ln.IsNull())
      {
        Ln.GetP();
        Ln.p = pJet(Ln.p,bound);
      }
      if (Ln.IsNull())
      {
        goto all_done;
      }
      if (! withT) With_s.Init(currRing);
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    pNormalize(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
    L->pLength = 0;
  }
 
  //if (TEST_OPT_PROT) { PrintS("N"); mflush(); }
  //L->Normalize(); // HANNES: should have a test
  kTest_L(L,strat);
  return L->GetLmCurrRing();
}
 
void redtailBbaAlsoLC_Z (LObject* L, int end_pos, kStrategy strat )
// normalize=FALSE, withT=FALSE, coeff=Z
{
  strat->redTailChange=FALSE;
 
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return;
 
  TObject* With;
  LObject Ln(pNext(h), strat->tailRing);
  Ln.GetpLength();
 
  pNext(h) = NULL;
  if (L->p != NULL)
  {
    pNext(L->p) = NULL;
    if (L->t_p != NULL) pNext(L->t_p) = NULL;
  }
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  int cnt=REDTAIL_CANONICALIZE;
 
  while(!Ln.IsNull())
  {
    loop
    {
      if (TEST_OPT_IDLIFT)
      {
        if (Ln.p!=NULL)
        {
          if ((int)__p_GetComp(Ln.p,currRing)> strat->syzComp) break;
        }
        else
        {
          if ((int)__p_GetComp(Ln.t_p,strat->tailRing)> strat->syzComp) break;
        }
      }
      Ln.SetShortExpVector();
      int j;
      j = kFindDivisibleByInT(strat, &Ln);
      if (j < 0)
      {
        j = kFindDivisibleByInT_Z(strat, &Ln);
        if (j < 0)
        {
          break;
        }
        else
        {
          /* reduction not cancelling a tail term, but reducing its coefficient */
          With = &(strat->T[j]);
          assume(With->GetpLength()==pLength(With->p != __null ? With->p : With->t_p));
          cnt--;
          if (cnt==0)
          {
            cnt=REDTAIL_CANONICALIZE;
            /*poly tmp=*/Ln.CanonicalizeP();
          }
          strat->redTailChange=TRUE;
          /* reduction cancelling a tail term */
          if (ksReducePolyTailLC_Z(L, With, &Ln))
          {
            // reducing the tail would violate the exp bound
            //  set a flag and hope for a retry (in bba)
            strat->completeReduce_retry=TRUE;
            if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
            do
            {
              pNext(h) = Ln.LmExtractAndIter();
              pIter(h);
              L->pLength++;
            } while (!Ln.IsNull());
            goto all_done;
          }
          /* we have to break since we did not cancel the term, but only decreased
           * its coefficient. */
          break;
        }
      } else {
        With = &(strat->T[j]);
        assume(With->GetpLength()==pLength(With->p != __null ? With->p : With->t_p));
        cnt--;
        if (cnt==0)
        {
          cnt=REDTAIL_CANONICALIZE;
          /*poly tmp=*/Ln.CanonicalizeP();
        }
        strat->redTailChange=TRUE;
        /* reduction cancelling a tail term */
        if (ksReducePolyTail_Z(L, With, &Ln))
        {
          // reducing the tail would violate the exp bound
          //  set a flag and hope for a retry (in bba)
          strat->completeReduce_retry=TRUE;
          if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
          do
          {
            pNext(h) = Ln.LmExtractAndIter();
            pIter(h);
            L->pLength++;
          } while (!Ln.IsNull());
          goto all_done;
        }
      }
      if (Ln.IsNull()) goto all_done;
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
    L->pLength = 0;
  }
 
  kTest_L(L, strat);
  return;
}
 
poly redtailBba_Z (LObject* L, int end_pos, kStrategy strat )
// normalize=FALSE, withT=FALSE, coeff=Z
{
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return L->GetLmCurrRing();
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return L->GetLmCurrRing();
 
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
 
  LObject Ln(pNext(h), strat->tailRing);
  Ln.pLength = L->GetpLength() - 1;
 
  pNext(h) = NULL;
  if (L->p != NULL) pNext(L->p) = NULL;
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  int cnt=REDTAIL_CANONICALIZE;
  while(!Ln.IsNull())
  {
    loop
    {
      Ln.SetShortExpVector();
      With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s);
      if (With == NULL) break;
      cnt--;
      if (cnt==0)
      {
        cnt=REDTAIL_CANONICALIZE;
        /*poly tmp=*/Ln.CanonicalizeP();
      }
      // we are in Z, do not call pNorm
      strat->redTailChange=TRUE;
      // test divisibility of coefs:
      Ln.GetLmCurrRing();
      With->GetLmCurrRing();
 
      if (ksReducePolyTail_Z(L, With, &Ln))
      {
        // reducing the tail would violate the exp bound
        //  set a flag and hope for a retry (in bba)
        strat->completeReduce_retry=TRUE;
        if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
        do
        {
          pNext(h) = Ln.LmExtractAndIter();
          pIter(h);
          L->pLength++;
        } while (!Ln.IsNull());
        goto all_done;
      }
      if (Ln.IsNull()) goto all_done;
      With_s.Init(currRing);
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    pNormalize(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
  }
 
  //if (TEST_OPT_PROT) { PrintS("N"); mflush(); }
  //L->Normalize(); // HANNES: should have a test
  kTest_L(L,strat);
  return L->GetLmCurrRing();
}
 
poly redtailBba_NF (poly p, kStrategy strat )
{
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return p;
  if ((p==NULL) || (pNext(p)==NULL))
    return p;
 
  int max_ind;
  poly h=p;
  p=pNext(p);
  pNext(h)=NULL;
  while(p!=NULL)
  {
    p=redNF(p,max_ind,1,strat);
    if (p!=NULL)
    {
      poly hh=p;
      p=pNext(p);
      pNext(hh)=NULL;
      h=p_Add_q(h,hh,currRing);
    }
  }
  return h;
}
 
poly redtailBba_Ring (LObject* L, int end_pos, kStrategy strat )
// normalize=FALSE, withT=FALSE, coeff=Ring
{
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return L->GetLmCurrRing();
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return L->GetLmCurrRing();
 
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
 
  LObject Ln(pNext(h), strat->tailRing);
  Ln.pLength = L->GetpLength() - 1;
 
  pNext(h) = NULL;
  if (L->p != NULL) pNext(L->p) = NULL;
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  int cnt=REDTAIL_CANONICALIZE;
  while(!Ln.IsNull())
  {
    loop
    {
      Ln.SetShortExpVector();
      With_s.Init(currRing);
      With = kFindDivisibleByInS_T(strat, end_pos, &Ln, &With_s);
      if (With == NULL) break;
      cnt--;
      if (cnt==0)
      {
        cnt=REDTAIL_CANONICALIZE;
        /*poly tmp=*/Ln.CanonicalizeP();
      }
      // we are in a ring, do not call pNorm
      // test divisibility of coefs:
      poly p_Ln=Ln.GetLmCurrRing();
      poly p_With=With->GetLmCurrRing();
      if (n_DivBy(pGetCoeff(p_Ln),pGetCoeff(p_With), currRing->cf))
      {
        strat->redTailChange=TRUE;
 
        if (ksReducePolyTail_Z(L, With, &Ln))
        {
          // reducing the tail would violate the exp bound
          //  set a flag and hope for a retry (in bba)
          strat->completeReduce_retry=TRUE;
          if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
          do
          {
            pNext(h) = Ln.LmExtractAndIter();
            pIter(h);
            L->pLength++;
          } while (!Ln.IsNull());
          goto all_done;
        }
      }
      else break; /*proceed to next monomial*/
      if (Ln.IsNull()) goto all_done;
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    pNormalize(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
  }
 
  //if (TEST_OPT_PROT) { PrintS("N"); mflush(); }
  //L->Normalize(); // HANNES: should have a test
  kTest_L(L,strat);
  return L->GetLmCurrRing();
}
 
/*2
*checks the change degree and write progress report
*/
void message (int i,int* olddeg,int* reduc,kStrategy strat, int red_result)
{
  if (i != *olddeg)
  {
    Print("%d",i);
    *olddeg = i;
  }
  if (TEST_OPT_OLDSTD)
  {
    if (strat->Ll != *reduc)
    {
      if (strat->Ll != *reduc-1)
        Print("(%d)",strat->Ll+1);
      else
        PrintS("-");
      *reduc = strat->Ll;
    }
    else
      PrintS(".");
    mflush();
  }
  else
  {
    if (red_result == 0)
      PrintS("-");
    else if (red_result < 0)
      PrintS(".");
    if ((red_result > 0) || ((strat->Ll % 100)==99))
    {
      if (strat->Ll != *reduc && strat->Ll > 0)
      {
        Print("(%d)",strat->Ll+1);
        *reduc = strat->Ll;
      }
    }
  }
}
 
/*2
*statistics
*/
void messageStat (int hilbcount,kStrategy strat)
{
  //PrintS("\nUsage/Allocation of temporary storage:\n");
  //Print("%d/%d polynomials in standard base\n",srmax,IDELEMS(Shdl));
  //Print("%d/%d polynomials in set L (for lazy alg.)",lrmax+1,strat->Lmax);
  Print("product criterion:%d chain criterion:%d\n",strat->cp,strat->c3);
  if (hilbcount!=0) Print("hilbert series criterion:%d\n",hilbcount);
  #ifdef HAVE_SHIFTBBA
  /* in usual case strat->cv is 0, it gets changed only in shift routines */
  if (strat->cv!=0) Print("shift V criterion:%d\n",strat->cv);
  #endif
}
 
void messageStatSBA (int hilbcount,kStrategy strat)
{
  //PrintS("\nUsage/Allocation of temporary storage:\n");
  //Print("%d/%d polynomials in standard base\n",srmax,IDELEMS(Shdl));
  //Print("%d/%d polynomials in set L (for lazy alg.)",lrmax+1,strat->Lmax);
  Print("syz criterion:%d rew criterion:%d\n",strat->nrsyzcrit,strat->nrrewcrit);
  //Print("product criterion:%d chain criterion:%d\n",strat->cp,strat->c3);
  if (hilbcount!=0) Print("hilbert series criterion:%d\n",hilbcount);
  #ifdef HAVE_SHIFTBBA
  /* in usual case strat->cv is 0, it gets changed only in shift routines */
  if (strat->cv!=0) Print("shift V criterion:%d\n",strat->cv);
  #endif
}
 
#ifdef KDEBUG
/*2
*debugging output: all internal sets, if changed
*for testing purpose only/has to be changed for later use
*/
void messageSets (kStrategy strat)
{
  int i;
  if (strat->news)
  {
    PrintS("set S");
    for (i=0; i<=strat->sl; i++)
    {
      Print("\n  %d:",i);
      p_wrp(strat->S[i], currRing, strat->tailRing);
      if (strat->fromQ!=NULL && strat->fromQ[i])
        Print(" (from Q)");
    }
    strat->news = FALSE;
  }
  if (strat->newt)
  {
    PrintS("\nset T");
    for (i=0; i<=strat->tl; i++)
    {
      Print("\n  %d:",i);
      strat->T[i].wrp();
      if (strat->T[i].length==0) strat->T[i].length=pLength(strat->T[i].p);
      Print(" o:%ld e:%d l:%d",
        strat->T[i].pFDeg(),strat->T[i].ecart,strat->T[i].length);
    }
    strat->newt = FALSE;
  }
  PrintS("\nset L");
  for (i=strat->Ll; i>=0; i--)
  {
    Print("\n%d:",i);
    p_wrp(strat->L[i].p1, currRing, strat->tailRing);
    PrintS("  ");
    p_wrp(strat->L[i].p2, currRing, strat->tailRing);
    PrintS(" lcm: ");p_wrp(strat->L[i].lcm, currRing);
    PrintS("\n  p : ");
    strat->L[i].wrp();
    Print("  o:%ld e:%d l:%d",
          strat->L[i].pFDeg(),strat->L[i].ecart,strat->L[i].length);
  }
  PrintLn();
}
 
#endif
 
 
/*2
*construct the set s from F
*/
void initS (ideal F, ideal Q, kStrategy strat)
{
  int   i,pos;
 
  if (Q!=NULL) i=((IDELEMS(F)+IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
  else         i=((IDELEMS(F)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
  if (i<setmaxTinc) i=setmaxT;
  strat->ecartS=initec(i);
  strat->sevS=initsevS(i);
  strat->S_2_R=initS_2_R(i);
  strat->fromQ=NULL;
  strat->Shdl=idInit(i,F->rank);
  strat->S=strat->Shdl->m;
  /*- put polys into S -*/
  if (Q!=NULL)
  {
    strat->fromQ=initec(i);
    memset(strat->fromQ,0,i*sizeof(int));
    for (i=0; i<IDELEMS(Q); i++)
    {
      if (Q->m[i]!=NULL)
      {
        LObject h;
        h.p = pCopy(Q->m[i]);
        if (TEST_OPT_INTSTRATEGY)
        {
          h.pCleardenom(); // also does remove Content
        }
        else
        {
          h.pNorm();
        }
        if (rHasLocalOrMixedOrdering(currRing))
        {
          deleteHC(&h, strat);
        }
        if (h.p!=NULL)
        {
          strat->initEcart(&h);
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat,strat->sl,h.p,h.ecart);
          }
          h.sev = pGetShortExpVector(h.p);
          strat->enterS(h,pos,strat,-1);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      LObject h;
      h.p = pCopy(F->m[i]);
      if (rHasLocalOrMixedOrdering(currRing))
      {
        cancelunit(&h);  /*- tries to cancel a unit -*/
        deleteHC(&h, strat);
      }
      if (h.p!=NULL)
      // do not rely on the input being a SB!
      {
        if (TEST_OPT_INTSTRATEGY)
        {
          h.pCleardenom(); // also does remove Content
        }
        else
        {
          h.pNorm();
        }
        strat->initEcart(&h);
        if (strat->sl==-1)
          pos =0;
        else
          pos = posInS(strat,strat->sl,h.p,h.ecart);
        h.sev = pGetShortExpVector(h.p);
        strat->enterS(h,pos,strat,-1);
      }
    }
  }
  /*- test, if a unit is in F -*/
  if ((strat->sl>=0)
       && n_IsUnit(pGetCoeff(strat->S[0]),currRing->cf)
       && pIsConstant(strat->S[0]))
  {
    while (strat->sl>0) deleteInS(strat->sl,strat);
  }
}
 
void initSL (ideal F, ideal Q,kStrategy strat)
{
  int   i,pos;
 
  if (Q!=NULL)
  {
    i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
    if (i<setmaxTinc) i=setmaxT;
  }
  else i=setmaxT;
  strat->ecartS=initec(i);
  strat->sevS=initsevS(i);
  strat->S_2_R=initS_2_R(i);
  strat->fromQ=NULL;
  strat->Shdl=idInit(i,F->rank);
  strat->S=strat->Shdl->m;
  /*- put polys into S -*/
  if (Q!=NULL)
  {
    strat->fromQ=initec(i);
    memset(strat->fromQ,0,i*sizeof(int));
    for (i=0; i<IDELEMS(Q); i++)
    {
      if (Q->m[i]!=NULL)
      {
        LObject h;
        h.p = pCopy(Q->m[i]);
        if (rHasLocalOrMixedOrdering(currRing))
        {
          deleteHC(&h,strat);
          cancelunit(&h);  /*- tries to cancel a unit -*/
        }
        if (TEST_OPT_INTSTRATEGY)
        {
          h.pCleardenom(); // also does remove Content
        }
        else
        {
          h.pNorm();
        }
        if (h.p!=NULL)
        {
          strat->initEcart(&h);
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat,strat->sl,h.p,h.ecart);
          }
          h.sev = pGetShortExpVector(h.p);
          strat->enterS(h,pos,strat,-1);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      LObject h;
      h.p = pCopy(F->m[i]);
      if (h.p!=NULL)
      {
        if (rHasLocalOrMixedOrdering(currRing))
        {
          cancelunit(&h);  /*- tries to cancel a unit -*/
          deleteHC(&h, strat);
        }
        if (h.p!=NULL)
        {
          if (TEST_OPT_INTSTRATEGY)
          {
            h.pCleardenom(); // also does remove Content
          }
          else
          {
            h.pNorm();
          }
          strat->initEcart(&h);
          if (strat->Ll==-1)
            pos =0;
          else
            pos = strat->posInL(strat->L,strat->Ll,&h,strat);
          h.sev = pGetShortExpVector(h.p);
          enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos);
        }
      }
    }
  }
  /*- test, if a unit is in F -*/
 
  if ((strat->Ll>=0)
       && n_IsUnit(pGetCoeff(strat->L[strat->Ll].p), currRing->cf)
       && pIsConstant(strat->L[strat->Ll].p))
  {
    while (strat->Ll>0) deleteInL(strat->L,&strat->Ll,strat->Ll-1,strat);
  }
}
 
void initSLSba (ideal F, ideal Q,kStrategy strat)
{
  int   i,pos;
  if (Q!=NULL)
  {
    i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
    if (i<setmaxTinc) i=setmaxT;
  }
  else i=setmaxT;
  strat->ecartS =   initec(i);
  strat->sevS   =   initsevS(i);
  strat->sevSig =   initsevS(i);
  strat->S_2_R  =   initS_2_R(i);
  strat->fromQ  =   NULL;
  strat->Shdl   =   idInit(i,F->rank);
  strat->S      =   strat->Shdl->m;
  strat->sig    =   (poly *)omAlloc0(i*sizeof(poly));
  if (strat->sbaOrder != 1)
  {
    strat->syz    = (poly *)omAlloc0(i*sizeof(poly));
    strat->sevSyz = initsevS(i);
    strat->syzmax = i;
    strat->syzl   = 0;
  }
  /*- put polys into S -*/
  if (Q!=NULL)
  {
    strat->fromQ=initec(i);
    memset(strat->fromQ,0,i*sizeof(int));
    for (i=0; i<IDELEMS(Q); i++)
    {
      if (Q->m[i]!=NULL)
      {
        LObject h;
        h.p = pCopy(Q->m[i]);
        if (rHasLocalOrMixedOrdering(currRing))
        {
          deleteHC(&h,strat);
        }
        if (TEST_OPT_INTSTRATEGY)
        {
          h.pCleardenom(); // also does remove Content
        }
        else
        {
          h.pNorm();
        }
        if (h.p!=NULL)
        {
          strat->initEcart(&h);
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat,strat->sl,h.p,h.ecart);
          }
          h.sev = pGetShortExpVector(h.p);
          strat->enterS(h,pos,strat,-1);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      LObject h;
      h.p = pCopy(F->m[i]);
      h.sig = pOne();
      //h.sig = pInit();
      //p_SetCoeff(h.sig,nInit(1),currRing);
      p_SetComp(h.sig,i+1,currRing);
      // if we are working with the Schreyer order we generate it
      // by multiplying the initial signatures with the leading monomial
      // of the corresponding initial polynomials generating the ideal
      // => we can keep the underlying monomial order and get a Schreyer
      //    order without any bigger overhead
      if (strat->sbaOrder == 0 || strat->sbaOrder == 3)
      {
        p_ExpVectorAdd (h.sig,F->m[i],currRing);
      }
      h.sevSig = pGetShortExpVector(h.sig);
#ifdef DEBUGF5
      pWrite(h.p);
      pWrite(h.sig);
#endif
      if (h.p!=NULL)
      {
        if (rHasLocalOrMixedOrdering(currRing))
        {
          cancelunit(&h);  /*- tries to cancel a unit -*/
          deleteHC(&h, strat);
        }
        if (h.p!=NULL)
        {
          if (TEST_OPT_INTSTRATEGY)
          {
            h.pCleardenom(); // also does remove Content
          }
          else
          {
            h.pNorm();
          }
          strat->initEcart(&h);
          if (strat->Ll==-1)
            pos =0;
          else
            pos = strat->posInLSba(strat->L,strat->Ll,&h,strat);
          h.sev = pGetShortExpVector(h.p);
          enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos);
        }
      }
      /*
      if (strat->sbaOrder != 1)
      {
        for(j=0;j<i;j++)
        {
          strat->syz[ctr] = pCopy(F->m[j]);
          p_SetCompP(strat->syz[ctr],i+1,currRing);
          // add LM(F->m[i]) to the signature to get a Schreyer order
          // without changing the underlying polynomial ring at all
          p_ExpVectorAdd (strat->syz[ctr],F->m[i],currRing);
          // since p_Add_q() destroys all input
          // data we need to recreate help
          // each time
          poly help = pCopy(F->m[i]);
          p_SetCompP(help,j+1,currRing);
          pWrite(strat->syz[ctr]);
          pWrite(help);
          printf("%d\n",pLmCmp(strat->syz[ctr],help));
          strat->syz[ctr] = p_Add_q(strat->syz[ctr],help,currRing);
          printf("%d. SYZ  ",ctr);
          pWrite(strat->syz[ctr]);
          strat->sevSyz[ctr] = p_GetShortExpVector(strat->syz[ctr],currRing);
          ctr++;
        }
        strat->syzl = ps;
      }
      */
    }
  }
  /*- test, if a unit is in F -*/
 
  if ((strat->Ll>=0)
       && n_IsUnit(pGetCoeff(strat->L[strat->Ll].p), currRing->cf)
       && pIsConstant(strat->L[strat->Ll].p))
  {
    while (strat->Ll>0) deleteInL(strat->L,&strat->Ll,strat->Ll-1,strat);
  }
}
 
void initSyzRules (kStrategy strat)
{
  if( strat->S[0] )
  {
    if( strat->S[1] && !rField_is_Ring(currRing))
    {
      omFreeSize(strat->syzIdx,(strat->syzidxmax)*sizeof(int));
      omFreeSize(strat->sevSyz,(strat->syzmax)*sizeof(unsigned long));
      omFreeSize(strat->syz,(strat->syzmax)*sizeof(poly));
    }
    int i, j, k, diff, comp, comp_old, ps=0, ctr=0;
    /************************************************************
     * computing the length of the syzygy array needed
     ***********************************************************/
    for(i=1; i<=strat->sl; i++)
    {
      if (pGetComp(strat->sig[i-1]) != pGetComp(strat->sig[i]))
      {
        ps += i;
      }
    }
    ps += strat->sl+1;
    //comp              = pGetComp (strat->P.sig);
    comp              = strat->currIdx;
    strat->syzIdx     = initec(comp);
    strat->sevSyz     = initsevS(ps);
    strat->syz        = (poly *)omAlloc(ps*sizeof(poly));
    strat->syzmax     = ps;
    strat->syzl       = 0;
    strat->syzidxmax  = comp;
#if defined(DEBUGF5) || defined(DEBUGF51)
    PrintS("------------- GENERATING SYZ RULES NEW ---------------\n");
#endif
    i = 1;
    j = 0;
    /************************************************************
     * generating the leading terms of the principal syzygies
     ***********************************************************/
    while (i <= strat->sl)
    {
      /**********************************************************
       * principal syzygies start with component index 2
       * the array syzIdx starts with index 0
       * => the rules for a signature with component comp start
       *    at strat->syz[strat->syzIdx[comp-2]] !
       *********************************************************/
      if (pGetComp(strat->sig[i-1]) != pGetComp(strat->sig[i]))
      {
        comp      = pGetComp(strat->sig[i]);
        comp_old  = pGetComp(strat->sig[i-1]);
        diff      = comp - comp_old - 1;
        // diff should be zero, but sometimes also the initial generating
        // elements of the input ideal reduce to zero. then there is an
        // index-gap between the signatures. for these in-between signatures we
        // can safely set syzIdx[j] = 0 as no such element will be ever computed
        // in the following.
        // doing this, we keep the relation "j = comp - 2" alive, which makes
        // jumps way easier when checking criteria
        while (diff>0)
        {
          strat->syzIdx[j]  = 0;
          diff--;
          j++;
        }
        strat->syzIdx[j]  = ctr;
        j++;
        LObject Q;
        int pos;
        for (k = 0; k<i; k++)
        {
          Q.sig          = pOne();
          if(rField_is_Ring(currRing))
            p_SetCoeff(Q.sig,nCopy(p_GetCoeff(strat->S[k],currRing)),currRing);
          p_ExpVectorCopy(Q.sig,strat->S[k],currRing);
          p_SetCompP (Q.sig, comp, currRing);
          poly q          = p_One(currRing);
          if(rField_is_Ring(currRing))
            p_SetCoeff(q,nCopy(p_GetCoeff(strat->S[i],currRing)),currRing);
          p_ExpVectorCopy(q,strat->S[i],currRing);
          q               = p_Neg (q, currRing);
          p_SetCompP (q, __p_GetComp(strat->sig[k], currRing), currRing);
          Q.sig = p_Add_q (Q.sig, q, currRing);
          Q.sevSig  = p_GetShortExpVector(Q.sig,currRing);
          pos = posInSyz(strat, Q.sig);
          enterSyz(Q, strat, pos);
          ctr++;
        }
      }
      i++;
    }
    /**************************************************************
    * add syzygies for upcoming first element of new iteration step
    **************************************************************/
    comp      = strat->currIdx;
    comp_old  = pGetComp(strat->sig[i-1]);
    diff      = comp - comp_old - 1;
    // diff should be zero, but sometimes also the initial generating
    // elements of the input ideal reduce to zero. then there is an
    // index-gap between the signatures. for these in-between signatures we
    // can safely set syzIdx[j] = 0 as no such element will be ever computed
    // in the following.
    // doing this, we keep the relation "j = comp - 2" alive, which makes
    // jumps way easier when checking criteria
    while (diff>0)
    {
      strat->syzIdx[j]  = 0;
      diff--;
      j++;
    }
    strat->syzIdx[j]  = ctr;
    LObject Q;
    int pos;
    for (k = 0; k<strat->sl+1; k++)
    {
      Q.sig          = pOne();
      if(rField_is_Ring(currRing))
        p_SetCoeff(Q.sig,nCopy(p_GetCoeff(strat->S[k],currRing)),currRing);
      p_ExpVectorCopy(Q.sig,strat->S[k],currRing);
      p_SetCompP (Q.sig, comp, currRing);
      poly q          = p_One(currRing);
      if(rField_is_Ring(currRing))
        p_SetCoeff(q,nCopy(p_GetCoeff(strat->L[strat->Ll].p,currRing)),currRing);
      p_ExpVectorCopy(q,strat->L[strat->Ll].p,currRing);
      q               = p_Neg (q, currRing);
      p_SetCompP (q, __p_GetComp(strat->sig[k], currRing), currRing);
      Q.sig = p_Add_q (Q.sig, q, currRing);
      Q.sevSig = p_GetShortExpVector(Q.sig,currRing);
      pos = posInSyz(strat, Q.sig);
      enterSyz(Q, strat, pos);
      ctr++;
    }
//#if 1
#ifdef DEBUGF5
    PrintS("Principal syzygies:\n");
    Print("syzl   %d\n",strat->syzl);
    Print("syzmax %d\n",strat->syzmax);
    Print("ps     %d\n",ps);
    PrintS("--------------------------------\n");
    for(i=0;i<=strat->syzl-1;i++)
    {
      Print("%d - ",i);
      pWrite(strat->syz[i]);
    }
    for(i=0;i<strat->currIdx;i++)
    {
      Print("%d - %d\n",i,strat->syzIdx[i]);
    }
    PrintS("--------------------------------\n");
#endif
  }
}
 
/*2
*construct the set s from F and {P}
*/
void initSSpecial (ideal F, ideal Q, ideal P,kStrategy strat)
{
  int   i,pos;
 
  if (Q!=NULL)
  {
    i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
    if (i<setmaxTinc) i=setmaxT;
  }
  else i=setmaxT;
  i=((i+IDELEMS(F)+IDELEMS(P)+setmax-1)/setmax)*setmax;
  strat->ecartS=initec(i);
  strat->sevS=initsevS(i);
  strat->S_2_R=initS_2_R(i);
  strat->fromQ=NULL;
  strat->Shdl=idInit(i,F->rank);
  strat->S=strat->Shdl->m;
 
  /*- put polys into S -*/
  if (Q!=NULL)
  {
    strat->fromQ=initec(i);
    memset(strat->fromQ,0,i*sizeof(int));
    for (i=0; i<IDELEMS(Q); i++)
    {
      if (Q->m[i]!=NULL)
      {
        LObject h;
        h.p = pCopy(Q->m[i]);
        //if (TEST_OPT_INTSTRATEGY)
        //{
        //  h.pCleardenom(); // also does remove Content
        //}
        //else
        //{
        //  h.pNorm();
        //}
        if (rHasLocalOrMixedOrdering(currRing))
        {
          deleteHC(&h,strat);
        }
        if (h.p!=NULL)
        {
          strat->initEcart(&h);
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat,strat->sl,h.p,h.ecart);
          }
          h.sev = pGetShortExpVector(h.p);
          strat->enterS(h,pos,strat, strat->tl+1);
          enterT(h, strat);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  /*- put polys into S -*/
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      LObject h;
      h.p = pCopy(F->m[i]);
      if (rHasLocalOrMixedOrdering(currRing))
      {
        deleteHC(&h,strat);
      }
      else if (TEST_OPT_REDTAIL || TEST_OPT_REDSB)
      {
        h.p=redtailBba(h.p,strat->sl,strat);
      }
      if (h.p!=NULL)
      {
        strat->initEcart(&h);
        if (strat->sl==-1)
          pos =0;
        else
          pos = posInS(strat,strat->sl,h.p,h.ecart);
        h.sev = pGetShortExpVector(h.p);
        strat->enterS(h,pos,strat, strat->tl+1);
        enterT(h,strat);
      }
    }
  }
  for (i=0; i<IDELEMS(P); i++)
  {
    if (P->m[i]!=NULL)
    {
      LObject h;
      h.p=pCopy(P->m[i]);
      if (TEST_OPT_INTSTRATEGY)
      {
        h.pCleardenom();
      }
      else
      {
        h.pNorm();
      }
      if(strat->sl>=0)
      {
        if (rHasGlobalOrdering(currRing))
        {
          h.p=redBba(h.p,strat->sl,strat);
          if ((h.p!=NULL)&&(TEST_OPT_REDTAIL || TEST_OPT_REDSB))
          {
            h.p=redtailBba(h.p,strat->sl,strat);
          }
        }
        else
        {
          h.p=redMora(h.p,strat->sl,strat);
        }
        if(h.p!=NULL)
        {
          strat->initEcart(&h);
          if (TEST_OPT_INTSTRATEGY)
          {
            h.pCleardenom();
          }
          else
          {
            h.is_normalized = 0;
            h.pNorm();
          }
          h.sev = pGetShortExpVector(h.p);
          h.SetpFDeg();
          pos = posInS(strat,strat->sl,h.p,h.ecart);
          enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat,strat->tl+1);
          strat->enterS(h,pos,strat, strat->tl+1);
          enterT(h,strat);
        }
      }
      else
      {
        h.sev = pGetShortExpVector(h.p);
        strat->initEcart(&h);
        strat->enterS(h,0,strat, strat->tl+1);
        enterT(h,strat);
      }
    }
  }
}
/*2
*construct the set s from F and {P}
*/
 
void initSSpecialSba (ideal F, ideal Q, ideal P,kStrategy strat)
{
  int   i,pos;
 
  if (Q!=NULL)
  {
    i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc;
    if (i<setmaxTinc) i=setmaxT;
  }
  else i=setmaxT;
  i=((i+IDELEMS(F)+IDELEMS(P)+setmax-1)/setmax)*setmax;
  strat->sevS=initsevS(i);
  strat->sevSig=initsevS(i);
  strat->S_2_R=initS_2_R(i);
  strat->fromQ=NULL;
  strat->Shdl=idInit(i,F->rank);
  strat->S=strat->Shdl->m;
  strat->sig=(poly *)omAlloc0(i*sizeof(poly));
  /*- put polys into S -*/
  if (Q!=NULL)
  {
    strat->fromQ=initec(i);
    memset(strat->fromQ,0,i*sizeof(int));
    for (i=0; i<IDELEMS(Q); i++)
    {
      if (Q->m[i]!=NULL)
      {
        LObject h;
        h.p = pCopy(Q->m[i]);
        //if (TEST_OPT_INTSTRATEGY)
        //{
        //  h.pCleardenom(); // also does remove Content
        //}
        //else
        //{
        //  h.pNorm();
        //}
        if (rHasLocalOrMixedOrdering(currRing))
        {
          deleteHC(&h,strat);
        }
        if (h.p!=NULL)
        {
          strat->initEcart(&h);
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat,strat->sl,h.p,h.ecart);
          }
          h.sev = pGetShortExpVector(h.p);
          strat->enterS(h,pos,strat, strat->tl+1);
          enterT(h, strat);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  /*- put polys into S -*/
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      LObject h;
      h.p = pCopy(F->m[i]);
      if (rHasLocalOrMixedOrdering(currRing))
      {
        deleteHC(&h,strat);
      }
      else if (TEST_OPT_REDTAIL || TEST_OPT_REDSB)
      {
        h.p=redtailBba(h.p,strat->sl,strat);
      }
      if (h.p!=NULL)
      {
        strat->initEcart(&h);
        if (strat->sl==-1)
          pos =0;
        else
          pos = posInS(strat,strat->sl,h.p,h.ecart);
        h.sev = pGetShortExpVector(h.p);
        strat->enterS(h,pos,strat, strat->tl+1);
        enterT(h,strat);
      }
    }
  }
  for (i=0; i<IDELEMS(P); i++)
  {
    if (P->m[i]!=NULL)
    {
      LObject h;
      h.p=pCopy(P->m[i]);
      if (TEST_OPT_INTSTRATEGY)
      {
        h.pCleardenom();
      }
      else
      {
        h.pNorm();
      }
      if(strat->sl>=0)
      {
        if (rHasGlobalOrdering(currRing))
        {
          h.p=redBba(h.p,strat->sl,strat);
          if ((h.p!=NULL)&&(TEST_OPT_REDTAIL || TEST_OPT_REDSB))
          {
            h.p=redtailBba(h.p,strat->sl,strat);
          }
        }
        else
        {
          h.p=redMora(h.p,strat->sl,strat);
        }
        if(h.p!=NULL)
        {
          strat->initEcart(&h);
          if (TEST_OPT_INTSTRATEGY)
          {
            h.pCleardenom();
          }
          else
          {
            h.is_normalized = 0;
            h.pNorm();
          }
          h.sev = pGetShortExpVector(h.p);
          h.SetpFDeg();
          pos = posInS(strat,strat->sl,h.p,h.ecart);
          enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat,strat->tl+1);
          strat->enterS(h,pos,strat, strat->tl+1);
          enterT(h,strat);
        }
      }
      else
      {
        h.sev = pGetShortExpVector(h.p);
        strat->initEcart(&h);
        strat->enterS(h,0,strat, strat->tl+1);
        enterT(h,strat);
      }
    }
  }
}
 
/*2
* reduces h using the set S
* procedure used in cancelunit1
*/
static poly redBba1 (poly h,int maxIndex,kStrategy strat)
{
  int j = 0;
  unsigned long not_sev = ~ pGetShortExpVector(h);
 
  while (j <= maxIndex)
  {
    if (pLmShortDivisibleBy(strat->S[j],strat->sevS[j],h, not_sev))
       return ksOldSpolyRedNew(strat->S[j],h,strat->kNoetherTail());
    else j++;
  }
  return h;
}
 
/*2
*tests if p.p=monomial*unit and cancels the unit
*/
void cancelunit1 (LObject* p,int *suc, int index,kStrategy strat )
{
  int k;
  poly r,h,h1,q;
 
  if (!pIsVector((*p).p) && ((*p).ecart != 0))
  {
    // Leading coef have to be a unit: no
    // example 2x+4x2 should be simplified to 2x*(1+2x)
    // and 2 is not a unit in Z
    //if ( !(n_IsUnit(pGetCoeff((*p).p), currRing->cf)) ) return;
    k = 0;
    h1 = r = pCopy((*p).p);
    h =pNext(r);
    loop
    {
      if (h==NULL)
      {
        pDelete(&r);
        pDelete(&(pNext((*p).p)));
        (*p).ecart = 0;
        (*p).length = 1;
        (*p).pLength = 1;
        (*suc)=0;
        return;
      }
      if (!pDivisibleBy(r,h))
      {
        q=redBba1(h,index ,strat);
        if (q != h)
        {
          k++;
          pDelete(&h);
          pNext(h1) = h = q;
        }
        else
        {
          pDelete(&r);
          return;
        }
      }
      else
      {
        h1 = h;
        pIter(h);
      }
      if (k > 10)
      {
        pDelete(&r);
        return;
      }
    }
  }
}
 
#if 0
/*2
* reduces h using the elements from Q in the set S
* procedure used in updateS
* must not be used for elements of Q or elements of an ideal !
*/
static poly redQ (poly h, int j, kStrategy strat)
{
  int start;
  unsigned long not_sev = ~ pGetShortExpVector(h);
  while ((j <= strat->sl) && (pGetComp(strat->S[j])!=0)) j++;
  start=j;
  while (j<=strat->sl)
  {
    if (pLmShortDivisibleBy(strat->S[j],strat->sevS[j], h, not_sev))
    {
      h = ksOldSpolyRed(strat->S[j],h,strat->kNoetherTail());
      if (h==NULL) return NULL;
      j = start;
      not_sev = ~ pGetShortExpVector(h);
    }
    else j++;
  }
  return h;
}
#endif
 
/*2
* reduces h using the set S
* procedure used in updateS
*/
static poly redBba (poly h,int maxIndex,kStrategy strat)
{
  int j = 0;
  unsigned long not_sev = ~ pGetShortExpVector(h);
 
  while (j <= maxIndex)
  {
    if (pLmShortDivisibleBy(strat->S[j],strat->sevS[j], h, not_sev))
    {
      h = ksOldSpolyRed(strat->S[j],h,strat->kNoetherTail());
      if (h==NULL) return NULL;
      j = 0;
      not_sev = ~ pGetShortExpVector(h);
    }
    else j++;
  }
  return h;
}
 
/*2
* reduces h using the set S
*e is the ecart of h
*procedure used in updateS
*/
static poly redMora (poly h,int maxIndex,kStrategy strat)
{
  int  j=0;
  int  e,l;
  unsigned long not_sev = ~ pGetShortExpVector(h);
 
  if (maxIndex >= 0)
  {
    e = currRing->pLDeg(h,&l,currRing)-p_FDeg(h,currRing);
    do
    {
      if (pLmShortDivisibleBy(strat->S[j],strat->sevS[j], h, not_sev)
      && ((e >= strat->ecartS[j]) || (strat->kNoether!=NULL)))
      {
#ifdef KDEBUG
        if (TEST_OPT_DEBUG)
        {
          PrintS("reduce ");wrp(h);Print(" with S[%d] (",j);wrp(strat->S[j]);
        }
#endif
        h = ksOldSpolyRed(strat->S[j],h,strat->kNoetherTail());
#ifdef KDEBUG
        if(TEST_OPT_DEBUG)
        {
          PrintS(")\nto "); wrp(h); PrintLn();
        }
#endif
        // pDelete(&h);
        if (h == NULL) return NULL;
        e = currRing->pLDeg(h,&l,currRing)-p_FDeg(h,currRing);
        j = 0;
        not_sev = ~ pGetShortExpVector(h);
      }
      else j++;
    }
    while (j <= maxIndex);
  }
  return h;
}
 
/*2
*updates S:
*the result is a set of polynomials which are in
*normalform with respect to S
*/
void updateS(BOOLEAN toT,kStrategy strat)
{
  LObject h;
  int i, suc=0;
  poly redSi=NULL;
  BOOLEAN change,any_change;
//  Print("nach initS: updateS start mit sl=%d\n",(strat->sl));
//  for (i=0; i<=(strat->sl); i++)
//  {
//    Print("s%d:",i);
//    if (strat->fromQ!=NULL) Print("(Q:%d) ",strat->fromQ[i]);
//    pWrite(strat->S[i]);
//  }
//  Print("currRing->OrdSgn=%d\n", currRing->OrdSgn);
  any_change=FALSE;
  if (rHasGlobalOrdering(currRing))
  {
    while (suc != -1)
    {
      i=suc+1;
      while (i<=strat->sl)
      {
        change=FALSE;
        if(rField_is_Ring(currRing))
            any_change = FALSE;
        if (((strat->fromQ==NULL) || (strat->fromQ[i]==0)) && (i>0))
        {
          redSi = pHead(strat->S[i]);
          strat->S[i] = redBba(strat->S[i],i-1,strat);
          //if ((strat->ak!=0)&&(strat->S[i]!=NULL))
          //  strat->S[i]=redQ(strat->S[i],i+1,strat); /*reduce S[i] mod Q*/
          if (pCmp(redSi,strat->S[i])!=0)
          {
            change=TRUE;
            any_change=TRUE;
            #ifdef KDEBUG
            if (TEST_OPT_DEBUG)
            {
              PrintS("reduce:");
              wrp(redSi);PrintS(" to ");p_wrp(strat->S[i], currRing, strat->tailRing);PrintLn();
            }
            #endif
            if (TEST_OPT_PROT)
            {
              if (strat->S[i]==NULL)
                PrintS("V");
              else
                PrintS("v");
              mflush();
            }
          }
          pLmDelete(&redSi);
          if (strat->S[i]==NULL)
          {
            deleteInS(i,strat);
            i--;
          }
          else if (change)
          {
            if (TEST_OPT_INTSTRATEGY)
            {
              if (TEST_OPT_CONTENTSB)
              {
                number n;
                p_Cleardenom_n(strat->S[i], currRing, n);// also does remove Content
                if (!nIsOne(n))
                {
                  denominator_list denom=(denominator_list)omAlloc(sizeof(denominator_list_s));
                  denom->n=nInvers(n);
                  denom->next=DENOMINATOR_LIST;
                  DENOMINATOR_LIST=denom;
                }
                nDelete(&n);
              }
              else
              {
                strat->S[i]=p_Cleardenom(strat->S[i], currRing);// also does remove Content
              }
            }
            else
            {
              pNorm(strat->S[i]);
            }
            strat->sevS[i] = pGetShortExpVector(strat->S[i]);
          }
        }
        i++;
      }
      if (any_change) reorderS(&suc,strat);
      else break;
    }
    if (toT)
    {
      for (i=0; i<=strat->sl; i++)
      {
        if ((strat->fromQ==NULL) || (strat->fromQ[i]==0))
        {
          h.p = redtailBba(strat->S[i],i-1,strat);
          if (TEST_OPT_INTSTRATEGY)
          {
            h.pCleardenom();// also does remove Content
          }
        }
        else
        {
          h.p = strat->S[i];
        }
        strat->initEcart(&h);
        if (strat->honey)
        {
          strat->ecartS[i] = h.ecart;
        }
        if (strat->sevS[i] == 0) {strat->sevS[i] = pGetShortExpVector(h.p);}
        else assume(strat->sevS[i] == pGetShortExpVector(h.p));
        h.sev = strat->sevS[i];
        /*puts the elements of S also to T*/
        strat->initEcart(&h);
        /*if (toT) - already checked*/ enterT(h,strat);
        strat->S_2_R[i] = strat->tl;
#ifdef HAVE_SHIFTBBA
        if (/*(toT) && */(currRing->isLPring))
          enterTShift(h, strat);
#endif
      }
    }
  }
  else
  {
    while (suc != -1)
    {
      i=suc;
      while (i<=strat->sl)
      {
        change=FALSE;
        if (((strat->fromQ==NULL) || (strat->fromQ[i]==0)) && (i>0))
        {
          redSi=pHead((strat->S)[i]);
          (strat->S)[i] = redMora((strat->S)[i],i-1,strat);
          if ((strat->S)[i]==NULL)
          {
            deleteInS(i,strat);
            i--;
          }
          else if (pCmp((strat->S)[i],redSi)!=0)
          {
            any_change=TRUE;
            h.p = strat->S[i];
            strat->initEcart(&h);
            strat->ecartS[i] = h.ecart;
            if (TEST_OPT_INTSTRATEGY)
            {
              if (TEST_OPT_CONTENTSB)
              {
                number n;
                p_Cleardenom_n(strat->S[i], currRing, n);// also does remove Content
                if (!nIsOne(n))
                {
                  denominator_list denom=(denominator_list)omAlloc(sizeof(denominator_list_s));
                  denom->n=nInvers(n);
                  denom->next=DENOMINATOR_LIST;
                  DENOMINATOR_LIST=denom;
                }
                nDelete(&n);
              }
              else
              {
                strat->S[i]=p_Cleardenom(strat->S[i], currRing);// also does remove Content
              }
            }
            else
            {
              pNorm(strat->S[i]); // == h.p
            }
            h.sev =  pGetShortExpVector(h.p);
            strat->sevS[i] = h.sev;
          }
          pLmDelete(&redSi);
          kTest(strat);
        }
        i++;
      }
#ifdef KDEBUG
      kTest(strat);
#endif
      if (any_change) reorderS(&suc,strat);
      else { suc=-1; break; }
      if (h.p!=NULL)
      {
        if (!strat->kAllAxis)
        {
          /*strat->kAllAxis =*/ HEckeTest(h.p,strat);
        }
        if (strat->kAllAxis)
          newHEdge(strat);
      }
    }
    for (i=0; i<=strat->sl; i++)
    {
      if ((strat->fromQ==NULL) || (strat->fromQ[i]==0))
      {
        strat->S[i] = h.p = redtail(strat->S[i],strat->sl,strat);
        strat->initEcart(&h);
        strat->ecartS[i] = h.ecart;
        h.sev = pGetShortExpVector(h.p);
        strat->sevS[i] = h.sev;
      }
      else
      {
        h.p = strat->S[i];
        h.ecart=strat->ecartS[i];
        h.sev = strat->sevS[i];
        h.length = h.pLength = pLength(h.p);
      }
      if ((strat->fromQ==NULL) || (strat->fromQ[i]==0))
        cancelunit1(&h,&suc,strat->sl,strat);
      h.SetpFDeg();
      /*puts the elements of S also to T*/
      enterT(h,strat);
      strat->S_2_R[i] = strat->tl;
#ifdef HAVE_SHIFTBBA
      if (currRing->isLPring)
        enterTShift(h, strat);
#endif
    }
    if (suc!= -1) updateS(toT,strat);
  }
#ifdef KDEBUG
  kTest(strat);
#endif
}
 
/*2
* -puts p to the standardbasis s at position at
* -saves the result in S
*/
void enterSBba (LObject &p,int atS,kStrategy strat, int atR)
{
  strat->news = TRUE;
  /*- puts p to the standardbasis s at position at -*/
  if (strat->sl == IDELEMS(strat->Shdl)-1)
  {
    strat->sevS = (unsigned long*) omRealloc0Size(strat->sevS,
                                    IDELEMS(strat->Shdl)*sizeof(unsigned long),
                                    (IDELEMS(strat->Shdl)+setmaxTinc)
                                                  *sizeof(unsigned long));
    strat->ecartS = (intset)omReallocSize(strat->ecartS,
                                          IDELEMS(strat->Shdl)*sizeof(int),
                                          (IDELEMS(strat->Shdl)+setmaxTinc)
                                                  *sizeof(int));
    strat->S_2_R = (int*) omRealloc0Size(strat->S_2_R,
                                         IDELEMS(strat->Shdl)*sizeof(int),
                                         (IDELEMS(strat->Shdl)+setmaxTinc)
                                                  *sizeof(int));
    if (strat->lenS!=NULL)
      strat->lenS=(int*)omRealloc0Size(strat->lenS,
                                       IDELEMS(strat->Shdl)*sizeof(int),
                                       (IDELEMS(strat->Shdl)+setmaxTinc)
                                                 *sizeof(int));
    if (strat->lenSw!=NULL)
      strat->lenSw=(wlen_type*)omRealloc0Size(strat->lenSw,
                                       IDELEMS(strat->Shdl)*sizeof(wlen_type),
                                       (IDELEMS(strat->Shdl)+setmaxTinc)
                                                 *sizeof(wlen_type));
    if (strat->fromQ!=NULL)
    {
      strat->fromQ = (intset)omReallocSize(strat->fromQ,
                                    IDELEMS(strat->Shdl)*sizeof(int),
                                    (IDELEMS(strat->Shdl)+setmaxTinc)*sizeof(int));
    }
    pEnlargeSet(&strat->S,IDELEMS(strat->Shdl),setmaxTinc);
    IDELEMS(strat->Shdl)+=setmaxTinc;
    strat->Shdl->m=strat->S;
  }
  if (atS <= strat->sl)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->S[atS+1]), &(strat->S[atS]),
            (strat->sl - atS + 1)*sizeof(poly));
    memmove(&(strat->ecartS[atS+1]), &(strat->ecartS[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    memmove(&(strat->sevS[atS+1]), &(strat->sevS[atS]),
            (strat->sl - atS + 1)*sizeof(unsigned long));
    memmove(&(strat->S_2_R[atS+1]), &(strat->S_2_R[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    if (strat->lenS!=NULL)
    memmove(&(strat->lenS[atS+1]), &(strat->lenS[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    if (strat->lenSw!=NULL)
    memmove(&(strat->lenSw[atS+1]), &(strat->lenSw[atS]),
            (strat->sl - atS + 1)*sizeof(wlen_type));
#else
    for (i=strat->sl+1; i>=atS+1; i--)
    {
      strat->S[i] = strat->S[i-1];
      strat->ecartS[i] = strat->ecartS[i-1];
      strat->sevS[i] = strat->sevS[i-1];
      strat->S_2_R[i] = strat->S_2_R[i-1];
    }
    if (strat->lenS!=NULL)
    for (i=strat->sl+1; i>=atS+1; i--)
      strat->lenS[i] = strat->lenS[i-1];
    if (strat->lenSw!=NULL)
    for (i=strat->sl+1; i>=atS+1; i--)
      strat->lenSw[i] = strat->lenSw[i-1];
#endif
  }
  if (strat->fromQ!=NULL)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->fromQ[atS+1]), &(strat->fromQ[atS]),
                  (strat->sl - atS + 1)*sizeof(int));
#else
    for (i=strat->sl+1; i>=atS+1; i--)
    {
      strat->fromQ[i] = strat->fromQ[i-1];
    }
#endif
    strat->fromQ[atS]=0;
  }
 
  /*- save result -*/
  poly pp=p.p;
  strat->S[atS] = pp;
  if (strat->honey) strat->ecartS[atS] = p.ecart;
  if (p.sev == 0)
    p.sev = pGetShortExpVector(pp);
  else
    assume(p.sev == pGetShortExpVector(pp));
  strat->sevS[atS] = p.sev;
  strat->ecartS[atS] = p.ecart;
  strat->S_2_R[atS] = atR;
  strat->sl++;
}
 
#ifdef HAVE_SHIFTBBA
void enterSBbaShift (LObject &p,int atS,kStrategy strat, int atR)
{
  enterSBba(p, atS, strat, atR);
 
  int maxPossibleShift = p_mLPmaxPossibleShift(p.p, strat->tailRing);
  for (int i = maxPossibleShift; i > 0; i--)
  {
    // NOTE: don't use "shared tails" here. In rare cases it can cause problems
    // in `kNF2` because of lazy poly normalizations.
    LObject qq(p_Copy(p.p, strat->tailRing));
    p_mLPshift(qq.p, i, strat->tailRing);
    qq.shift = i;
    strat->initEcart(&qq); // initEcartBBA sets length, pLength, FDeg and ecart
    int atS = posInS(strat, strat->sl, qq.p, qq.ecart); // S needs to stay sorted because this is for example assumed when searching S later
    enterSBba(qq, atS, strat, -1);
  }
}
#endif
 
/*2
* -puts p to the standardbasis s at position at
* -saves the result in S
*/
void enterSSba (LObject &p,int atS,kStrategy strat, int atR)
{
  strat->news = TRUE;
  /*- puts p to the standardbasis s at position at -*/
  if (strat->sl == IDELEMS(strat->Shdl)-1)
  {
    strat->sevS = (unsigned long*) omRealloc0Size(strat->sevS,
                                    IDELEMS(strat->Shdl)*sizeof(unsigned long),
                                    (IDELEMS(strat->Shdl)+setmax)
                                                  *sizeof(unsigned long));
    strat->sevSig = (unsigned long*) omRealloc0Size(strat->sevSig,
                                    IDELEMS(strat->Shdl)*sizeof(unsigned long),
                                    (IDELEMS(strat->Shdl)+setmax)
                                                  *sizeof(unsigned long));
    strat->ecartS = (intset)omReallocSize(strat->ecartS,
                                          IDELEMS(strat->Shdl)*sizeof(int),
                                          (IDELEMS(strat->Shdl)+setmax)
                                                  *sizeof(int));
    strat->S_2_R = (int*) omRealloc0Size(strat->S_2_R,
                                         IDELEMS(strat->Shdl)*sizeof(int),
                                         (IDELEMS(strat->Shdl)+setmax)
                                                  *sizeof(int));
    if (strat->lenS!=NULL)
      strat->lenS=(int*)omRealloc0Size(strat->lenS,
                                       IDELEMS(strat->Shdl)*sizeof(int),
                                       (IDELEMS(strat->Shdl)+setmax)
                                                 *sizeof(int));
    if (strat->lenSw!=NULL)
      strat->lenSw=(wlen_type*)omRealloc0Size(strat->lenSw,
                                       IDELEMS(strat->Shdl)*sizeof(wlen_type),
                                       (IDELEMS(strat->Shdl)+setmax)
                                                 *sizeof(wlen_type));
    if (strat->fromQ!=NULL)
    {
      strat->fromQ = (intset)omReallocSize(strat->fromQ,
                                    IDELEMS(strat->Shdl)*sizeof(int),
                                    (IDELEMS(strat->Shdl)+setmax)*sizeof(int));
    }
    pEnlargeSet(&strat->S,IDELEMS(strat->Shdl),setmax);
    pEnlargeSet(&strat->sig,IDELEMS(strat->Shdl),setmax);
    IDELEMS(strat->Shdl)+=setmax;
    strat->Shdl->m=strat->S;
  }
  // in a signature-based algorithm the following situation will never
  // appear due to the fact that the critical pairs are already sorted
  // by increasing signature.
  // True. However, in the case of integers we need to put the element
  // that caused the signature drop on the first position
  if (atS <= strat->sl)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->S[atS+1]), &(strat->S[atS]),
            (strat->sl - atS + 1)*sizeof(poly));
    memmove(&(strat->sig[atS+1]), &(strat->sig[atS]),
            (strat->sl - atS + 1)*sizeof(poly));
    memmove(&(strat->sevSig[atS+1]), &(strat->sevSig[atS]),
            (strat->sl - atS + 1)*sizeof(unsigned long));
    memmove(&(strat->ecartS[atS+1]), &(strat->ecartS[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    memmove(&(strat->sevS[atS+1]), &(strat->sevS[atS]),
            (strat->sl - atS + 1)*sizeof(unsigned long));
    memmove(&(strat->S_2_R[atS+1]), &(strat->S_2_R[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    if (strat->lenS!=NULL)
      memmove(&(strat->lenS[atS+1]), &(strat->lenS[atS]),
            (strat->sl - atS + 1)*sizeof(int));
    if (strat->lenSw!=NULL)
      memmove(&(strat->lenSw[atS+1]), &(strat->lenSw[atS]),
            (strat->sl - atS + 1)*sizeof(wlen_type));
#else
    for (i=strat->sl+1; i>=atS+1; i--)
    {
      strat->S[i] = strat->S[i-1];
      strat->ecartS[i] = strat->ecartS[i-1];
      strat->sevS[i] = strat->sevS[i-1];
      strat->S_2_R[i] = strat->S_2_R[i-1];
      strat->sig[i] = strat->sig[i-1];
      strat->sevSig[i] = strat->sevSig[i-1];
    }
    if (strat->lenS!=NULL)
      for (i=strat->sl+1; i>=atS+1; i--)
        strat->lenS[i] = strat->lenS[i-1];
    if (strat->lenSw!=NULL)
      for (i=strat->sl+1; i>=atS+1; i--)
        strat->lenSw[i] = strat->lenSw[i-1];
#endif
  }
  if (strat->fromQ!=NULL)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->fromQ[atS+1]), &(strat->fromQ[atS]),
                  (strat->sl - atS + 1)*sizeof(int));
#else
    for (i=strat->sl+1; i>=atS+1; i--)
    {
      strat->fromQ[i] = strat->fromQ[i-1];
    }
#endif
    strat->fromQ[atS]=0;
  }
 
  /*- save result -*/
  strat->S[atS] = p.p;
  strat->sig[atS] = p.sig; // TODO: get the correct signature in here!
  if (strat->honey) strat->ecartS[atS] = p.ecart;
  if (p.sev == 0)
    p.sev = pGetShortExpVector(p.p);
  else
    assume(p.sev == pGetShortExpVector(p.p));
  strat->sevS[atS] = p.sev;
  // during the interreduction process of a signature-based algorithm we do not
  // compute the signature at this point, but when the whole interreduction
  // process finishes, i.e. f5c terminates!
  if (p.sig != NULL)
  {
    if (p.sevSig == 0)
      p.sevSig = pGetShortExpVector(p.sig);
    else
      assume(p.sevSig == pGetShortExpVector(p.sig));
    strat->sevSig[atS] = p.sevSig; // TODO: get the correct signature in here!
  }
  strat->ecartS[atS] = p.ecart;
  strat->S_2_R[atS] = atR;
  strat->sl++;
#ifdef DEBUGF5
  int k;
  Print("--- LIST S: %d ---\n",strat->sl);
  for(k=0;k<=strat->sl;k++)
  {
    pWrite(strat->sig[k]);
  }
  PrintS("--- LIST S END ---\n");
#endif
}
 
void replaceInLAndSAndT(LObject &p, int tj, kStrategy strat)
{
  p.GetP(strat->lmBin);
  if (strat->homog) strat->initEcart(&p);
      strat->redTailChange=FALSE;
  if (TEST_OPT_INTSTRATEGY)
  {
    p.pCleardenom();
    if ((TEST_OPT_REDSB)||(TEST_OPT_REDTAIL))
    {
#ifdef HAVE_SHIFTBBA
      if (rIsLPRing(currRing))
        p.p = redtailBba(&p,strat->tl,strat, TRUE,!TEST_OPT_CONTENTSB);
      else
#endif
      {
        p.p = redtailBba(&p,strat->sl,strat, FALSE,!TEST_OPT_CONTENTSB);
      }
      p.pCleardenom();
      if (strat->redTailChange)
        p.t_p=NULL;
      if (strat->P.p!=NULL) strat->P.sev=p_GetShortExpVector(strat->P.p,currRing);
      else strat->P.sev=0;
    }
  }
 
  assume(strat->tailRing == p.tailRing);
  assume(p.pLength == 0 || pLength(p.p) == p.pLength || rIsSyzIndexRing(currRing)); // modulo syzring
 
  int i, j, pos;
  poly tp = strat->T[tj].p;
 
  /* enter p to T set */
  enterT(p, strat);
 
  for (j = 0; j <= strat->sl; ++j)
  {
    if (pLtCmp(tp, strat->S[j]) == 0)
    {
      break;
    }
  }
  /* it may be that the exchanged element
   * is until now only in T and not in S */
  if (j <= strat->sl)
  {
    deleteInS(j, strat);
  }
 
  pos = posInS(strat, strat->sl, p.p, p.ecart);
 
  pp_Test(p.p, currRing, p.tailRing);
  assume(p.FDeg == p.pFDeg());
 
  /* remove useless pairs from L set */
  for (i = 0; i <= strat->Ll; ++i)
  {
    if (strat->L[i].p1 != NULL && pLtCmp(tp, strat->L[i].p1) == 0)
    {
      deleteInL(strat->L, &(strat->Ll), i, strat);
      i--;
      continue;
    }
    if (strat->L[i].p2 != NULL && pLtCmp(tp, strat->L[i].p2) == 0)
    {
      deleteInL(strat->L, &(strat->Ll), i, strat);
      i--;
    }
  }
#ifdef HAVE_SHIFTBBA
  if (rIsLPRing(currRing))
    enterpairsShift(p.p, strat->sl, p.ecart, pos, strat, strat->tl); // TODO LP
  else
#endif
  {
    /* generate new pairs with p, probably removing older, now useless pairs */
    superenterpairs(p.p, strat->sl, p.ecart, pos, strat, strat->tl);
  }
  /* enter p to S set */
  strat->enterS(p, pos, strat, strat->tl);
 
#ifdef HAVE_SHIFTBBA
  /* do this after enterS so that the index in R (which is strat->tl) is correct */
  if (rIsLPRing(currRing) && !strat->rightGB)
    enterTShift(p,strat);
#endif
}
 
/*2
* puts p to the set T at position atT
*/
void enterT(LObject &p, kStrategy strat, int atT)
{
  int i;
 
#ifdef PDEBUG
#ifdef HAVE_SHIFTBBA
  if (currRing->isLPring && p.shift > 0)
  {
    // in this case, the order is not correct. test LM and tail separately
    p_LmTest(p.p, currRing);
    p_Test(pNext(p.p), currRing);
  }
  else
#endif
  {
    pp_Test(p.p, currRing, p.tailRing);
  }
#endif
  assume(strat->tailRing == p.tailRing);
  // redMoraNF complains about this -- but, we don't really
  // need this so far
  assume(p.pLength == 0 || pLength(p.p) == p.pLength || rIsSyzIndexRing(currRing)); // modulo syzring
  assume(!strat->homog || (p.FDeg == p.pFDeg()));
  assume(!p.is_normalized || nIsOne(pGetCoeff(p.p)));
 
#ifdef KDEBUG
  // do not put an LObject twice into T:
  for(i=strat->tl;i>=0;i--)
  {
    if (p.p==strat->T[i].p)
    {
      printf("already in T at pos %d of %d, atT=%d\n",i,strat->tl,atT);
      return;
    }
  }
#endif
 
#ifdef HAVE_TAIL_RING
  if (currRing!=strat->tailRing)
  {
    p.t_p=p.GetLmTailRing();
  }
#endif
  strat->newt = TRUE;
  if (atT < 0)
    atT = strat->posInT(strat->T, strat->tl, p);
  if (strat->tl == strat->tmax-1)
    enlargeT(strat->T,strat->R,strat->sevT,strat->tmax,strat->tmax);
  if (atT <= strat->tl)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->T[atT+1]), &(strat->T[atT]),
            (strat->tl-atT+1)*sizeof(TObject));
    memmove(&(strat->sevT[atT+1]), &(strat->sevT[atT]),
            (strat->tl-atT+1)*sizeof(unsigned long));
#endif
    for (i=strat->tl+1; i>=atT+1; i--)
    {
#ifndef ENTER_USE_MEMMOVE
      strat->T[i] = strat->T[i-1];
      strat->sevT[i] = strat->sevT[i-1];
#endif
      strat->R[strat->T[i].i_r] = &(strat->T[i]);
    }
  }
 
  if ((strat->tailBin != NULL) && (pNext(p.p) != NULL))
  {
#ifdef HAVE_SHIFTBBA
    // letterplace: if p.shift > 0 then pNext(p.p) is already in the tailBin
    if (!(currRing->isLPring && p.shift > 0))
#endif
    {
      pNext(p.p)=p_ShallowCopyDelete(pNext(p.p),
          (strat->tailRing != NULL ?
           strat->tailRing : currRing),
          strat->tailBin);
      if (p.t_p != NULL) pNext(p.t_p) = pNext(p.p);
    }
  }
  strat->T[atT] = (TObject) p;
  //printf("\nenterT: add new: length = %i, ecart = %i\n",p.length,p.ecart);
 
  if ((pNext(p.p) != NULL) && (!rIsLPRing(currRing)))
    strat->T[atT].max_exp = p_GetMaxExpP(pNext(p.p), strat->tailRing);
  else
    strat->T[atT].max_exp = NULL;
 
  strat->tl++;
  strat->R[strat->tl] = &(strat->T[atT]);
  strat->T[atT].i_r = strat->tl;
  assume((p.sev == 0) || (pGetShortExpVector(p.p) == p.sev));
  strat->sevT[atT] = (p.sev == 0 ? pGetShortExpVector(p.p) : p.sev);
  kTest_T(&(strat->T[atT]),strat);
}
 
/*2
* puts p to the set T at position atT
*/
void enterT_strong(LObject &p, kStrategy strat, int atT)
{
  assume(rField_is_Ring(currRing));
  int i;
 
  pp_Test(p.p, currRing, p.tailRing);
  assume(strat->tailRing == p.tailRing);
  // redMoraNF complains about this -- but, we don't really
  // need this so far
  assume(p.pLength == 0 || (int)pLength(p.p) == p.pLength || rIsSyzIndexRing(currRing)); // modulo syzring
  assume(p.FDeg == p.pFDeg());
  assume(!p.is_normalized || nIsOne(pGetCoeff(p.p)));
 
#ifdef KDEBUG
  // do not put an LObject twice into T:
  for(i=strat->tl;i>=0;i--)
  {
    if (p.p==strat->T[i].p)
    {
      printf("already in T at pos %d of %d, atT=%d\n",i,strat->tl,atT);
      return;
    }
  }
#endif
 
#ifdef HAVE_TAIL_RING
  if (currRing!=strat->tailRing)
  {
    p.t_p=p.GetLmTailRing();
  }
#endif
  strat->newt = TRUE;
  if (atT < 0)
    atT = strat->posInT(strat->T, strat->tl, p);
  if (strat->tl == strat->tmax-1)
    enlargeT(strat->T,strat->R,strat->sevT,strat->tmax,strat->tmax);
  if (atT <= strat->tl)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->T[atT+1]), &(strat->T[atT]),
            (strat->tl-atT+1)*sizeof(TObject));
    memmove(&(strat->sevT[atT+1]), &(strat->sevT[atT]),
            (strat->tl-atT+1)*sizeof(unsigned long));
#endif
    for (i=strat->tl+1; i>=atT+1; i--)
    {
#ifndef ENTER_USE_MEMMOVE
      strat->T[i] = strat->T[i-1];
      strat->sevT[i] = strat->sevT[i-1];
#endif
      strat->R[strat->T[i].i_r] = &(strat->T[i]);
    }
  }
 
  if ((strat->tailBin != NULL) && (pNext(p.p) != NULL))
  {
    pNext(p.p)=p_ShallowCopyDelete(pNext(p.p),
                                   (strat->tailRing != NULL ?
                                    strat->tailRing : currRing),
                                   strat->tailBin);
    if (p.t_p != NULL) pNext(p.t_p) = pNext(p.p);
  }
  strat->T[atT] = (TObject) p;
  //printf("\nenterT_strong: add new: length = %i, ecart = %i\n",p.length,p.ecart);
 
  if (pNext(p.p) != NULL)
    strat->T[atT].max_exp = p_GetMaxExpP(pNext(p.p), strat->tailRing);
  else
    strat->T[atT].max_exp = NULL;
 
  strat->tl++;
  strat->R[strat->tl] = &(strat->T[atT]);
  strat->T[atT].i_r = strat->tl;
  assume(p.sev == 0 || pGetShortExpVector(p.p) == p.sev);
  strat->sevT[atT] = (p.sev == 0 ? pGetShortExpVector(p.p) : p.sev);
  #if 1
  if(rHasLocalOrMixedOrdering(currRing)
  && !n_IsUnit(p.p->coef, currRing->cf))
  {
    for(i=strat->tl;i>=0;i--)
    {
      if(strat->T[i].ecart <= p.ecart && pLmDivisibleBy(strat->T[i].p,p.p))
      {
        enterOneStrongPoly(i,p.p,p.ecart,0,strat,0 , TRUE);
      }
    }
  }
  /*
  printf("\nThis is T:\n");
  for(i=strat->tl;i>=0;i--)
  {
    pWrite(strat->T[i].p);
  }
  //getchar();*/
  #endif
  kTest_T(&(strat->T[atT]),strat);
}
 
/*2
* puts signature p.sig to the set syz
*/
void enterSyz(LObject &p, kStrategy strat, int atT)
{
  int i;
  strat->newt = TRUE;
  if (strat->syzl == strat->syzmax-1)
  {
    pEnlargeSet(&strat->syz,strat->syzmax,setmax);
    strat->sevSyz = (unsigned long*) omRealloc0Size(strat->sevSyz,
                                    (strat->syzmax)*sizeof(unsigned long),
                                    ((strat->syzmax)+setmax)
                                                  *sizeof(unsigned long));
    strat->syzmax += setmax;
  }
  if (atT < strat->syzl)
  {
#ifdef ENTER_USE_MEMMOVE
    memmove(&(strat->syz[atT+1]), &(strat->syz[atT]),
            (strat->syzl-atT+1)*sizeof(poly));
    memmove(&(strat->sevSyz[atT+1]), &(strat->sevSyz[atT]),
            (strat->syzl-atT+1)*sizeof(unsigned long));
#endif
    for (i=strat->syzl; i>=atT+1; i--)
    {
#ifndef ENTER_USE_MEMMOVE
      strat->syz[i] = strat->syz[i-1];
      strat->sevSyz[i] = strat->sevSyz[i-1];
#endif
    }
  }
  //i = strat->syzl;
  i = atT;
  //Makes sure the syz saves just the signature
  if(rField_is_Ring(currRing))
    pNext(p.sig) = NULL;
  strat->syz[atT] = p.sig;
  strat->sevSyz[atT] = p.sevSig;
  strat->syzl++;
#if F5DEBUG
  Print("element in strat->syz: %d--%d  ",atT+1,strat->syzmax);
  pWrite(strat->syz[atT]);
#endif
  // recheck pairs in strat->L with new rule and delete correspondingly
  int cc = strat->Ll;
  while (cc>-1)
  {
    //printf("\nCheck if syz is div by L\n");pWrite(strat->syz[atT]);pWrite(strat->L[cc].sig);
    //printf("\npLmShDivBy(syz,L) = %i\nn_DivBy(L,syz) = %i\n pLtCmp(L,syz) = %i",p_LmShortDivisibleBy( strat->syz[atT], strat->sevSyz[atT],strat->L[cc].sig, ~strat->L[cc].sevSig, currRing), n_DivBy(pGetCoeff(strat->L[cc].sig),pGetCoeff(strat->syz[atT]),currRing), pLtCmp(strat->L[cc].sig,strat->syz[atT])==1);
    if (p_LmShortDivisibleBy( strat->syz[atT], strat->sevSyz[atT],
                              strat->L[cc].sig, ~strat->L[cc].sevSig, currRing)
                              &&((!rField_is_Ring(currRing))
                              || (n_DivBy(pGetCoeff(strat->L[cc].sig),pGetCoeff(strat->syz[atT]),currRing->cf) && (pLtCmp(strat->L[cc].sig,strat->syz[atT])==1)))
                              )
    {
      //printf("\nYES!\n");
      deleteInL(strat->L,&strat->Ll,cc,strat);
    }
    cc--;
  }
//#if 1
#ifdef DEBUGF5
    PrintS("--- Syzygies ---\n");
    Print("syzl   %d\n",strat->syzl);
    Print("syzmax %d\n",strat->syzmax);
    PrintS("--------------------------------\n");
    for(i=0;i<=strat->syzl-1;i++)
    {
      Print("%d - ",i);
      pWrite(strat->syz[i]);
    }
    PrintS("--------------------------------\n");
#endif
}
 
 
void initHilbCrit(ideal/*F*/, ideal /*Q*/, bigintmat **hilb,kStrategy strat)
{
 
  //if the ordering is local, then hilb criterion
  //can be used also if the ideal is not homogeneous
  if((rHasLocalOrMixedOrdering(currRing)) && (rHasMixedOrdering(currRing)==FALSE))
  {
    if(rField_is_Ring(currRing))
      *hilb=NULL;
    else
      return;
  }
  if (strat->homog!=isHomog)
  {
    *hilb=NULL;
  }
}
 
void initBuchMoraCrit(kStrategy strat)
{
  strat->enterOnePair=enterOnePairNormal;
  strat->chainCrit=chainCritNormal;
  if (TEST_OPT_SB_1)
    strat->chainCrit=chainCritOpt_1;
  if (rField_is_Ring(currRing))
  {
    strat->enterOnePair=enterOnePairRing;
    strat->chainCrit=chainCritRing;
  }
#ifdef HAVE_RATGRING
  if (rIsRatGRing(currRing))
  {
     strat->chainCrit=chainCritPart;
     /* enterOnePairNormal get rational part in it */
  }
#endif
  if (TEST_OPT_IDLIFT
  && (strat->syzComp==1)
  && (!rIsPluralRing(currRing)))
    strat->enterOnePair=enterOnePairLift;
 
  strat->sugarCrit =        TEST_OPT_SUGARCRIT;
  strat->Gebauer =          strat->homog || strat->sugarCrit;
  strat->honey =            !strat->homog || strat->sugarCrit || TEST_OPT_WEIGHTM;
  if (TEST_OPT_NOT_SUGAR) strat->honey = FALSE;
  strat->pairtest = NULL;
  /* always use tailreduction, except:
  * - in local rings, - in lex order case, -in ring over extensions */
  strat->noTailReduction = !TEST_OPT_REDTAIL;
  //if(rHasMixedOrdering(currRing)==2)
  //{
  // strat->noTailReduction =TRUE;
  //}
 
#ifdef HAVE_PLURAL
  // and r is plural_ring
  //  hence this holds for r a rational_plural_ring
  if( rIsPluralRing(currRing) || (rIsSCA(currRing) && !strat->z2homog) )
  {    //or it has non-quasi-comm type... later
    strat->sugarCrit = FALSE;
    strat->Gebauer = FALSE;
    strat->honey = FALSE;
  }
#endif
 
  // Coefficient ring?
  if (rField_is_Ring(currRing))
  {
    strat->sugarCrit = FALSE;
    strat->Gebauer = FALSE;
    strat->honey = FALSE;
  }
  #ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    if (strat->homog) PrintS("ideal/module is homogeneous\n");
    else              PrintS("ideal/module is not homogeneous\n");
  }
  #endif
}
 
void initSbaCrit(kStrategy strat)
{
  //strat->enterOnePair=enterOnePairNormal;
  strat->enterOnePair = enterOnePairNormal;
  //strat->chainCrit=chainCritNormal;
  strat->chainCrit    = chainCritSig;
  /******************************************
   * rewCrit1 and rewCrit2 are already set in
   * kSba() in kstd1.cc
   *****************************************/
  //strat->rewCrit1     = faugereRewCriterion;
  if (strat->sbaOrder == 1)
  {
    strat->syzCrit  = syzCriterionInc;
  }
  else
  {
    strat->syzCrit  = syzCriterion;
  }
  if (rField_is_Ring(currRing))
  {
    strat->enterOnePair=enterOnePairRing;
    strat->chainCrit=chainCritRing;
  }
#ifdef HAVE_RATGRING
  if (rIsRatGRing(currRing))
  {
     strat->chainCrit=chainCritPart;
     /* enterOnePairNormal get rational part in it */
  }
#endif
 
  strat->sugarCrit =        TEST_OPT_SUGARCRIT;
  strat->Gebauer =          strat->homog || strat->sugarCrit;
  strat->honey =            !strat->homog || strat->sugarCrit || TEST_OPT_WEIGHTM;
  if (TEST_OPT_NOT_SUGAR) strat->honey = FALSE;
  strat->pairtest = NULL;
  /* always use tailreduction, except:
  * - in local rings, - in lex order case, -in ring over extensions */
  strat->noTailReduction = !TEST_OPT_REDTAIL;
  if(rHasMixedOrdering(currRing)) strat->noTailReduction =TRUE;
 
#ifdef HAVE_PLURAL
  // and r is plural_ring
  //  hence this holds for r a rational_plural_ring
  if( rIsPluralRing(currRing) || (rIsSCA(currRing) && !strat->z2homog) )
  {    //or it has non-quasi-comm type... later
    strat->sugarCrit = FALSE;
    strat->Gebauer = FALSE;
    strat->honey = FALSE;
  }
#endif
 
  // Coefficient ring?
  if (rField_is_Ring(currRing))
  {
    strat->sugarCrit = FALSE;
    strat->Gebauer = FALSE ;
    strat->honey = FALSE;
  }
  #ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    if (strat->homog) PrintS("ideal/module is homogeneous\n");
    else              PrintS("ideal/module is not homogeneous\n");
  }
  #endif
}
 
BOOLEAN kPosInLDependsOnLength(int (*pos_in_l)
                               (const LSet set, const int length,
                                LObject* L,const kStrategy strat))
{
  if (pos_in_l == posInL110
  ||  pos_in_l == posInL10
  ||  pos_in_l == posInL110Ring
  )
    return TRUE;
 
  return FALSE;
}
 
void initBuchMoraPos (kStrategy strat)
{
  if (rHasGlobalOrdering(currRing))
  {
    if (strat->honey)
    {
      strat->posInL = posInL15;
      // ok -- here is the deal: from my experiments for Singular-2-0
      // I conclude that that posInT_EcartpLength is the best of
      // posInT15, posInT_EcartFDegpLength, posInT_FDegLength, posInT_pLength
      // see the table at the end of this file
      if (TEST_OPT_OLDSTD)
        strat->posInT = posInT15;
      else
        strat->posInT = posInT_EcartpLength;
    }
    else if (currRing->pLexOrder && !TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else if (TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else
    {
      strat->posInL = posInL0;
      strat->posInT = posInT0;
    }
    //if (strat->minim>0) strat->posInL =posInLSpecial;
    if (strat->homog)
    {
      strat->posInL = posInL110;
      strat->posInT = posInT110;
    }
  }
  else /* local/mixed ordering */
  {
    if (strat->homog)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else
    {
      if ((currRing->order[0]==ringorder_c)
      ||(currRing->order[0]==ringorder_C))
      {
        strat->posInL = posInL17_c;
        strat->posInT = posInT17_c;
      }
      else
      {
        strat->posInL = posInL17;
        strat->posInT = posInT17;
      }
    }
  }
  if (strat->minim>0) strat->posInL =posInLSpecial;
  // for further tests only
  if ((BTEST1(11)) || (BTEST1(12)))
    strat->posInL = posInL11;
  else if ((BTEST1(13)) || (BTEST1(14)))
    strat->posInL = posInL13;
  else if ((BTEST1(15)) || (BTEST1(16)))
    strat->posInL = posInL15;
  else if ((BTEST1(17)) || (BTEST1(18)))
    strat->posInL = posInL17;
  if (BTEST1(11))
    strat->posInT = posInT11;
  else if (BTEST1(13))
    strat->posInT = posInT13;
  else if (BTEST1(15))
    strat->posInT = posInT15;
  else if ((BTEST1(17)))
    strat->posInT = posInT17;
  else if ((BTEST1(19)))
    strat->posInT = posInT19;
  else if (BTEST1(12) || BTEST1(14) || BTEST1(16) || BTEST1(18))
    strat->posInT = posInT1;
  strat->posInLDependsOnLength = kPosInLDependsOnLength(strat->posInL);
}
 
void initBuchMoraPosRing (kStrategy strat)
{
  if (rHasGlobalOrdering(currRing))
  {
    if (strat->honey)
    {
      strat->posInL = posInL15Ring;
      // ok -- here is the deal: from my experiments for Singular-2-0
      // I conclude that that posInT_EcartpLength is the best of
      // posInT15, posInT_EcartFDegpLength, posInT_FDegLength, posInT_pLength
      // see the table at the end of this file
      if (TEST_OPT_OLDSTD)
        strat->posInT = posInT15Ring;
      else
        strat->posInT = posInT_EcartpLength;
    }
    else if (currRing->pLexOrder && !TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11Ring;
      strat->posInT = posInT11;
    }
    else if (TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11Ring;
      strat->posInT = posInT11;
    }
    else
    {
      strat->posInL = posInL0Ring;
      strat->posInT = posInT0;
    }
    //if (strat->minim>0) strat->posInL =posInLSpecial;
    if (strat->homog)
    {
      strat->posInL = posInL110Ring;
      strat->posInT = posInT110Ring;
    }
  }
  else
  {
    if (strat->homog)
    {
      //printf("\nHere 3\n");
      strat->posInL = posInL11Ring;
      strat->posInT = posInT11Ring;
    }
    else
    {
      if ((currRing->order[0]==ringorder_c)
      ||(currRing->order[0]==ringorder_C))
      {
        strat->posInL = posInL17_cRing;
        strat->posInT = posInT17_cRing;
      }
      else
      {
        strat->posInL = posInL11Ringls;
        strat->posInT = posInT17Ring;
      }
    }
  }
  if (strat->minim>0) strat->posInL =posInLSpecial;
  // for further tests only
  if ((BTEST1(11)) || (BTEST1(12)))
    strat->posInL = posInL11Ring;
  else if ((BTEST1(13)) || (BTEST1(14)))
    strat->posInL = posInL13;
  else if ((BTEST1(15)) || (BTEST1(16)))
    strat->posInL = posInL15Ring;
  else if ((BTEST1(17)) || (BTEST1(18)))
    strat->posInL = posInL17Ring;
  if (BTEST1(11))
    strat->posInT = posInT11Ring;
  else if (BTEST1(13))
    strat->posInT = posInT13;
  else if (BTEST1(15))
    strat->posInT = posInT15Ring;
  else if ((BTEST1(17)))
    strat->posInT = posInT17Ring;
  else if ((BTEST1(19)))
    strat->posInT = posInT19;
  else if (BTEST1(12) || BTEST1(14) || BTEST1(16) || BTEST1(18))
    strat->posInT = posInT1;
  strat->posInLDependsOnLength = kPosInLDependsOnLength(strat->posInL);
}
 
void initBuchMora (ideal F,ideal Q,kStrategy strat)
{
  strat->interpt = BTEST1(OPT_INTERRUPT);
  /*- creating temp data structures------------------- -*/
  //strat->cp = 0; // already by skStragy()
  //strat->c3 = 0; // already by skStragy()
#ifdef HAVE_SHIFTBBA
  strat->cv = 0; // already by skStragy()
#endif
  strat->tail = pInit();
  /*- set s -*/
  strat->sl = -1;
  /*- set L -*/
  strat->Lmax = ((IDELEMS(F)+setmaxLinc-1)/setmaxLinc)*setmaxLinc;
  strat->Ll = -1;
  strat->L = initL(strat->Lmax);
  /*- set B -*/
  strat->Bmax = setmaxL;
  strat->Bl = -1;
  strat->B = initL();
  /*- set T -*/
  strat->tl = -1;
  strat->tmax = setmaxT;
  strat->T = initT();
  strat->R = initR();
  strat->sevT = initsevT();
  /*- init local data struct.---------------------------------------- -*/
  //strat->P.ecart=0; // already by skStragy()
  //strat->P.length=0; // already by skStragy()
  //strat->P.pLength=0; // already by skStragy()
  if (rHasLocalOrMixedOrdering(currRing))
  {
    if (strat->kNoether!=NULL)
    {
      pSetComp(strat->kNoether, strat->ak);
      pSetComp(strat->kNoetherTail(), strat->ak);
    }
  }
  if(rField_is_Ring(currRing))
  {
    /*Shdl=*/initSL(F, Q,strat); /*sets also S, ecartS, fromQ */
  }
  else
  {
    if(TEST_OPT_SB_1)
    {
      int i;
      ideal P=idInit(IDELEMS(F)-strat->newIdeal,F->rank);
      for (i=strat->newIdeal;i<IDELEMS(F);i++)
      {
        P->m[i-strat->newIdeal] = F->m[i];
        F->m[i] = NULL;
      }
      initSSpecial(F,Q,P,strat);
      for (i=strat->newIdeal;i<IDELEMS(F);i++)
      {
        F->m[i] = P->m[i-strat->newIdeal];
        P->m[i-strat->newIdeal] = NULL;
      }
      idDelete(&P);
    }
    else
    {
      /*Shdl=*/initSL(F, Q,strat); /*sets also S, ecartS, fromQ */
      // /*Shdl=*/initS(F, Q,strat); /*sets also S, ecartS, fromQ */
    }
  }
  strat->fromT = FALSE;
  strat->noTailReduction = !TEST_OPT_REDTAIL;
  if ((!TEST_OPT_SB_1)
  || (rField_is_Ring(currRing))
  )
  {
    updateS(TRUE,strat);
  }
#ifdef HAVE_SHIFTBBA
  if (!(rIsLPRing(currRing) && strat->rightGB)) // for right GB, we need to check later whether a poly is from Q
#endif
  {
    if (strat->fromQ!=NULL) omFreeSize(strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int));
    strat->fromQ=NULL;
  }
  #ifdef KDEBUG
  assume(kTest_TS(strat));
  #endif
}
 
void exitBuchMora (kStrategy strat)
{
  /*- release temp data -*/
  cleanT(strat);
  omFreeSize(strat->T,(strat->tmax)*sizeof(TObject));
  omFreeSize(strat->R,(strat->tmax)*sizeof(TObject*));
  omFreeSize(strat->sevT, (strat->tmax)*sizeof(unsigned long));
  omFreeSize(strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int));
  omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long));
  omFreeSize(strat->S_2_R,IDELEMS(strat->Shdl)*sizeof(int));
  /*- set L: should be empty -*/
  omFreeSize(strat->L,(strat->Lmax)*sizeof(LObject));
  /*- set B: should be empty -*/
  omFreeSize(strat->B,(strat->Bmax)*sizeof(LObject));
  pLmFree(&strat->tail);
  strat->syzComp=0;
 
#ifdef HAVE_SHIFTBBA
  if (rIsLPRing(currRing) && strat->rightGB)
  {
    if (strat->fromQ!=NULL) omFreeSize(strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int));
    strat->fromQ=NULL;
  }
#endif
}
 
void initSbaPos (kStrategy strat)
{
  if (rHasGlobalOrdering(currRing))
  {
    if (strat->honey)
    {
      strat->posInL = posInL15;
      // ok -- here is the deal: from my experiments for Singular-2-0
      // I conclude that that posInT_EcartpLength is the best of
      // posInT15, posInT_EcartFDegpLength, posInT_FDegLength, posInT_pLength
      // see the table at the end of this file
      if (TEST_OPT_OLDSTD)
        strat->posInT = posInT15;
      else
        strat->posInT = posInT_EcartpLength;
    }
    else if (currRing->pLexOrder && !TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else if (TEST_OPT_INTSTRATEGY)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else
    {
      strat->posInL = posInL0;
      strat->posInT = posInT0;
    }
    //if (strat->minim>0) strat->posInL =posInLSpecial;
    if (strat->homog)
    {
      strat->posInL = posInL110;
      strat->posInT = posInT110;
    }
  }
  else
  {
    if (strat->homog)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else
    {
      if ((currRing->order[0]==ringorder_c)
      ||(currRing->order[0]==ringorder_C))
      {
        strat->posInL = posInL17_c;
        strat->posInT = posInT17_c;
      }
      else
      {
        strat->posInL = posInL17;
        strat->posInT = posInT17;
      }
    }
  }
  if (strat->minim>0) strat->posInL =posInLSpecial;
  // for further tests only
  if ((BTEST1(11)) || (BTEST1(12)))
    strat->posInL = posInL11;
  else if ((BTEST1(13)) || (BTEST1(14)))
    strat->posInL = posInL13;
  else if ((BTEST1(15)) || (BTEST1(16)))
    strat->posInL = posInL15;
  else if ((BTEST1(17)) || (BTEST1(18)))
    strat->posInL = posInL17;
  if (BTEST1(11))
    strat->posInT = posInT11;
  else if (BTEST1(13))
    strat->posInT = posInT13;
  else if (BTEST1(15))
    strat->posInT = posInT15;
  else if ((BTEST1(17)))
    strat->posInT = posInT17;
  else if ((BTEST1(19)))
    strat->posInT = posInT19;
  else if (BTEST1(12) || BTEST1(14) || BTEST1(16) || BTEST1(18))
    strat->posInT = posInT1;
  if (rField_is_Ring(currRing))
  {
    strat->posInL = posInL11Ring;
    if(rHasLocalOrMixedOrdering(currRing) && currRing->pLexOrder == TRUE)
      strat->posInL = posInL11Ringls;
    strat->posInT = posInT11;
  }
  strat->posInLDependsOnLength = FALSE;
  strat->posInLSba  = posInLSig;
  //strat->posInL     = posInLSig;
  strat->posInL     = posInLF5C;
  /*
  if (rField_is_Ring(currRing))
  {
    strat->posInLSba  = posInLSigRing;
    strat->posInL     = posInL11Ring;
  }*/
  //strat->posInT     = posInTSig;
}
 
void initSbaBuchMora (ideal F,ideal Q,kStrategy strat)
{
  strat->interpt = BTEST1(OPT_INTERRUPT);
  //strat->kNoether=NULL; // done by skStrategy
  /*- creating temp data structures------------------- -*/
  //strat->cp = 0; // done by skStrategy
  //strat->c3 = 0; // done by skStrategy
  strat->tail = pInit();
  /*- set s -*/
  strat->sl = -1;
  /*- set ps -*/
  strat->syzl = -1;
  /*- set L -*/
  strat->Lmax = ((IDELEMS(F)+setmaxLinc-1)/setmaxLinc)*setmaxLinc;
  strat->Ll = -1;
  strat->L = initL(strat->Lmax);
  /*- set B -*/
  strat->Bmax = setmaxL;
  strat->Bl = -1;
  strat->B = initL();
  /*- set T -*/
  strat->tl = -1;
  strat->tmax = setmaxT;
  strat->T = initT();
  strat->R = initR();
  strat->sevT = initsevT();
  /*- init local data struct.---------------------------------------- -*/
  //strat->P.ecart=0;  // done by skStrategy
  //strat->P.length=0;  // done by skStrategy
  if (rHasLocalOrMixedOrdering(currRing))
  {
    if (strat->kNoether!=NULL)
    {
      pSetComp(strat->kNoether, strat->ak);
      pSetComp(strat->kNoetherTail(), strat->ak);
    }
  }
  if(rField_is_Ring(currRing))
  {
    /*Shdl=*/initSLSba(F, Q,strat); /*sets also S, ecartS, fromQ */
  }
  else
  {
    if(TEST_OPT_SB_1)
    {
      int i;
      ideal P=idInit(IDELEMS(F)-strat->newIdeal,F->rank);
      for (i=strat->newIdeal;i<IDELEMS(F);i++)
      {
        P->m[i-strat->newIdeal] = F->m[i];
        F->m[i] = NULL;
      }
      initSSpecialSba(F,Q,P,strat);
      for (i=strat->newIdeal;i<IDELEMS(F);i++)
      {
        F->m[i] = P->m[i-strat->newIdeal];
        P->m[i-strat->newIdeal] = NULL;
      }
      idDelete(&P);
    }
    else
    {
      initSLSba(F, Q,strat); /*sets also S, ecartS, fromQ */
    }
  }
  //strat->fromT = FALSE;  // done by skStrategy
  if (!TEST_OPT_SB_1)
  {
    if(!rField_is_Ring(currRing)) updateS(TRUE,strat);
  }
  //if (strat->fromQ!=NULL) omFreeSize(strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int));
  //strat->fromQ=NULL;
  assume(kTest_TS(strat));
}
 
void exitSba (kStrategy strat)
{
  /*- release temp data -*/
  if(rField_is_Ring(currRing))
    cleanTSbaRing(strat);
  else
    cleanT(strat);
  omFreeSize(strat->T,(strat->tmax)*sizeof(TObject));
  omFreeSize(strat->R,(strat->tmax)*sizeof(TObject*));
  omFreeSize(strat->sevT, (strat->tmax)*sizeof(unsigned long));
  omFreeSize(strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int));
  omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long));
  omFreeSize((ADDRESS)strat->sevSig,IDELEMS(strat->Shdl)*sizeof(unsigned long));
  if(strat->syzmax>0)
  {
    omFreeSize((ADDRESS)strat->syz,(strat->syzmax)*sizeof(poly));
    omFreeSize((ADDRESS)strat->sevSyz,(strat->syzmax)*sizeof(unsigned long));
    if (strat->sbaOrder == 1)
    {
      omFreeSize(strat->syzIdx,(strat->syzidxmax)*sizeof(int));
    }
  }
  omFreeSize(strat->S_2_R,IDELEMS(strat->Shdl)*sizeof(int));
  /*- set L: should be empty -*/
  omFreeSize(strat->L,(strat->Lmax)*sizeof(LObject));
  /*- set B: should be empty -*/
  omFreeSize(strat->B,(strat->Bmax)*sizeof(LObject));
  /*- set sig: no need for the signatures anymore -*/
  omFreeSize(strat->sig,IDELEMS(strat->Shdl)*sizeof(poly));
  pLmDelete(&strat->tail);
  strat->syzComp=0;
}
 
/*2
* in the case of a standardbase of a module over a qring:
* replace polynomials in i by ak vectors,
* (the polynomial * unit vectors gen(1)..gen(ak)
* in every case (also for ideals:)
* deletes divisible vectors/polynomials
*/
void updateResult(ideal r,ideal Q, kStrategy strat)
{
  int l;
  if (strat->ak>0)
  {
    for (l=IDELEMS(r)-1;l>=0;l--)
    {
      if ((r->m[l]!=NULL) && (pGetComp(r->m[l])==0))
      {
        pDelete(&r->m[l]); // and set it to NULL
      }
    }
    int q;
    poly p;
    if(!rField_is_Ring(currRing))
    {
      for (l=IDELEMS(r)-1;l>=0;l--)
      {
        if ((r->m[l]!=NULL)
        //&& (strat->syzComp>0)
        //&& (pGetComp(r->m[l])<=strat->syzComp)
        )
        {
          for(q=IDELEMS(Q)-1; q>=0;q--)
          {
            if ((Q->m[q]!=NULL)
            &&(pLmDivisibleBy(Q->m[q],r->m[l])))
            {
              if (TEST_OPT_REDSB)
              {
                p=r->m[l];
                r->m[l]=kNF(Q,NULL,p);
                pDelete(&p);
              }
              else
              {
                pDelete(&r->m[l]); // and set it to NULL
              }
              break;
            }
          }
        }
      }
    }
    else
    {
      for (l=IDELEMS(r)-1;l>=0;l--)
      {
        if ((r->m[l]!=NULL)
        //&& (strat->syzComp>0)
        //&& (pGetComp(r->m[l])<=strat->syzComp)
        )
        {
          for(q=IDELEMS(Q)-1; q>=0;q--)
          {
            if ((Q->m[q]!=NULL)
            &&(pLmDivisibleBy(Q->m[q],r->m[l])))
            {
              if(n_DivBy(r->m[l]->coef, Q->m[q]->coef, currRing->cf))
              {
                if (TEST_OPT_REDSB)
                {
                  p=r->m[l];
                  r->m[l]=kNF(Q,NULL,p);
                  pDelete(&p);
                }
                else
                {
                  pDelete(&r->m[l]); // and set it to NULL
                }
                break;
              }
            }
          }
        }
      }
    }
  }
  else
  {
    int q;
    poly p;
    BOOLEAN reduction_found=FALSE;
    if (!rField_is_Ring(currRing))
    {
      for (l=IDELEMS(r)-1;l>=0;l--)
      {
        if (r->m[l]!=NULL)
        {
          for(q=IDELEMS(Q)-1; q>=0;q--)
          {
            if ((Q->m[q]!=NULL)&&(pLmEqual(Q->m[q],r->m[l])))
            {
              if (TEST_OPT_REDSB)
              {
                p=r->m[l];
                r->m[l]=kNF(Q,NULL,p);
                pDelete(&p);
                reduction_found=TRUE;
              }
              else
              {
                pDelete(&r->m[l]); // and set it to NULL
              }
              break;
            }
          }
        }
      }
    }
    //Also need divisibility of the leading coefficients
    else
    {
      for (l=IDELEMS(r)-1;l>=0;l--)
      {
        if (r->m[l]!=NULL)
        {
          for(q=IDELEMS(Q)-1; q>=0;q--)
          {
            if(n_DivBy(r->m[l]->coef, Q->m[q]->coef, currRing->cf))
            {
              if ((Q->m[q]!=NULL)&&(pLmEqual(Q->m[q],r->m[l])) && pDivisibleBy(Q->m[q],r->m[l]))
              {
                if (TEST_OPT_REDSB)
                {
                  p=r->m[l];
                  r->m[l]=kNF(Q,NULL,p);
                  pDelete(&p);
                  reduction_found=TRUE;
                }
                else
                {
                  pDelete(&r->m[l]); // and set it to NULL
                }
                break;
              }
            }
          }
        }
      }
    }
    if (/*TEST_OPT_REDSB &&*/ reduction_found)
    {
      if(rField_is_Ring(currRing))
      {
        for (l=IDELEMS(r)-1;l>=0;l--)
        {
          if (r->m[l]!=NULL)
          {
            for(q=IDELEMS(r)-1;q>=0;q--)
            {
              if ((l!=q)
              && (r->m[q]!=NULL)
              &&(pLmDivisibleBy(r->m[l],r->m[q]))
              &&(n_DivBy(r->m[q]->coef, r->m[l]->coef, currRing->cf))
              )
              {
                //If they are equal then take the one with the smallest length
                if(pLmDivisibleBy(r->m[q],r->m[l])
                && n_DivBy(r->m[q]->coef, r->m[l]->coef, currRing->cf)
                && (pLength(r->m[q]) < pLength(r->m[l]) ||
                (pLength(r->m[q]) == pLength(r->m[l]) && nGreaterZero(r->m[q]->coef))))
                {
                  pDelete(&r->m[l]);
                  break;
                }
                else
                  pDelete(&r->m[q]);
              }
            }
          }
        }
      }
      else
      {
        for (l=IDELEMS(r)-1;l>=0;l--)
        {
          if (r->m[l]!=NULL)
          {
            for(q=IDELEMS(r)-1;q>=0;q--)
            {
              if ((l!=q)
              && (r->m[q]!=NULL)
              &&(pLmDivisibleBy(r->m[l],r->m[q]))
              )
              {
                //If they are equal then take the one with the smallest length
                if(pLmDivisibleBy(r->m[q],r->m[l])
                &&(pLength(r->m[q]) < pLength(r->m[l]) ||
                (pLength(r->m[q]) == pLength(r->m[l]) && nGreaterZero(r->m[q]->coef))))
                {
                  pDelete(&r->m[l]);
                  break;
                }
                else
                  pDelete(&r->m[q]);
              }
            }
          }
        }
      }
    }
  }
  idSkipZeroes(r);
}
 
void completeReduce (kStrategy strat, BOOLEAN withT)
{
  int i;
  int low = (((rHasGlobalOrdering(currRing)) && (strat->ak==0)) ? 1 : 0);
  LObject L;
 
#ifdef KDEBUG
  // need to set this: during tailreductions of T[i], T[i].max is out of
  // sync
  sloppy_max = TRUE;
#endif
 
  strat->noTailReduction = FALSE;
  //if(rHasMixedOrdering(currRing)) strat->noTailReduction = TRUE;
  if (TEST_OPT_PROT)
  {
    PrintLn();
//    if (timerv) writeTime("standard base computed:");
  }
  if (TEST_OPT_PROT)
  {
    Print("(S:%d)",strat->sl);mflush();
  }
  for (i=strat->sl; i>=low; i--)
  {
    int end_pos=strat->sl;
    if ((strat->fromQ!=NULL) && (strat->fromQ[i])) continue; // do not reduce Q_i
    if (strat->ak==0) end_pos=i-1;
    TObject* T_j = strat->s_2_t(i);
    if ((T_j != NULL)&&(T_j->p==strat->S[i]))
    {
      L = *T_j;
      #ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        Print("test S[%d]:",i);
        p_wrp(L.p,currRing,strat->tailRing);
        PrintLn();
      }
      #endif
      if (rHasGlobalOrdering(currRing))
        strat->S[i] = redtailBba(&L, end_pos, strat, withT,FALSE /*no normalize*/);
      else
        strat->S[i] = redtail(&L, strat->sl, strat);
      #ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        Print("to (tailR) S[%d]:",i);
        p_wrp(strat->S[i],currRing,strat->tailRing);
        PrintLn();
      }
      #endif
 
      if (strat->redTailChange)
      {
        if (T_j->max_exp != NULL) p_LmFree(T_j->max_exp, strat->tailRing);
        if (pNext(T_j->p) != NULL)
          T_j->max_exp = p_GetMaxExpP(pNext(T_j->p), strat->tailRing);
        else
          T_j->max_exp = NULL;
      }
      if (TEST_OPT_INTSTRATEGY)
        T_j->pCleardenom();
    }
    else
    {
      assume(currRing == strat->tailRing);
      #ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        Print("test S[%d]:",i);
        p_wrp(strat->S[i],currRing,strat->tailRing);
        PrintLn();
      }
      #endif
      if (rHasGlobalOrdering(currRing))
        strat->S[i] = redtailBba(strat->S[i], end_pos, strat, withT);
      else
        strat->S[i] = redtail(strat->S[i], strat->sl, strat);
      if (TEST_OPT_INTSTRATEGY)
      {
        if (TEST_OPT_CONTENTSB)
        {
          number n;
          p_Cleardenom_n(strat->S[i], currRing, n);// also does remove Content
          if (!nIsOne(n))
          {
            denominator_list denom=(denominator_list)omAlloc(sizeof(denominator_list_s));
            denom->n=nInvers(n);
            denom->next=DENOMINATOR_LIST;
            DENOMINATOR_LIST=denom;
          }
          nDelete(&n);
        }
        else
        {
          strat->S[i]=p_Cleardenom(strat->S[i], currRing);// also does remove Content
        }
      }
      #ifdef KDEBUG
      if (TEST_OPT_DEBUG)
      {
        Print("to (-tailR) S[%d]:",i);
        p_wrp(strat->S[i],currRing,strat->tailRing);
        PrintLn();
      }
      #endif
    }
    if (TEST_OPT_PROT)
      PrintS("-");
  }
  if (TEST_OPT_PROT) PrintLn();
#ifdef KDEBUG
  sloppy_max = FALSE;
#endif
}
 
 
/*2
* computes the new strat->kNoether and the new pNoether,
* returns TRUE, if pNoether has changed
*/
BOOLEAN newHEdge(kStrategy strat)
{
  if (currRing->pLexOrder || rHasMixedOrdering(currRing))
    return FALSE;
  int i,j;
  poly newNoether;
 
#if 0
  if (currRing->weight_all_1)
    scComputeHC(strat->Shdl,NULL,strat->ak,strat->kNoether);
  else
    scComputeHCw(strat->Shdl,NULL,strat->ak,strat->kNoether);
#else
  scComputeHC(strat->Shdl,NULL,strat->ak,strat->kNoether);
#endif
  if (strat->kNoether==NULL) return FALSE;
  if (strat->t_kNoether != NULL)
  {
    p_LmFree(strat->t_kNoether, strat->tailRing);
    strat->t_kNoether=NULL;
  }
  if (strat->tailRing != currRing)
    strat->t_kNoether = k_LmInit_currRing_2_tailRing(strat->kNoether, strat->tailRing);
  /* compare old and new noether*/
  newNoether = pLmInit(strat->kNoether);
  pSetCoeff0(newNoether,nInit(1));
  j = p_FDeg(newNoether,currRing);
  // newNoether is now the new highest edge (on the boundary)
  // now find the next monomial after highest monomial in R/I
  // (the smallest monomial not in R/I)
  for (i=currRing->N-1;i>0; i--)
  {
    int e;
    if ((e=pGetExp(newNoether, i)) > 0)
    {
      e--;
      pSetExp(newNoether,i,e);
    }
  }
  pSetm(newNoether);
  if (j < HCord) /*- statistics -*/
  {
    if (TEST_OPT_PROT)
    {
      Print("H(%d)",j);
      mflush();
    }
    HCord=j;
    #ifdef KDEBUG
    if (TEST_OPT_DEBUG)
    {
      Print("H(%d):",j);
      wrp(strat->kNoether);
      PrintLn();
    }
    #endif
  }
  if (pCmp(strat->kNoether,newNoether)!=1)
  {
    if (strat->kNoether!=NULL) p_LmDelete0(strat->kNoether,currRing);
    strat->kNoether=newNoether;
    if (strat->t_kNoether != NULL)
    {
      p_LmFree(strat->t_kNoether, strat->tailRing);
      strat->t_kNoether=NULL;
    }
    if (strat->tailRing != currRing)
      strat->t_kNoether = k_LmInit_currRing_2_tailRing(strat->kNoether, strat->tailRing);
 
    return TRUE;
  }
  pLmDelete(newNoether);
  return FALSE;
}
 
/***************************************************************
 *
 * Routines related for ring changes during std computations
 *
 ***************************************************************/
BOOLEAN kCheckSpolyCreation(LObject *L, kStrategy strat, poly &m1, poly &m2)
{
  if (strat->overflow) return FALSE;
  assume(L->p1 != NULL && L->p2 != NULL);
  // shift changes: from 0 to -1
  assume(L->i_r1 >= -1 && L->i_r1 <= strat->tl);
  assume(L->i_r2 >= -1 && L->i_r2 <= strat->tl);
 
  if (! k_GetLeadTerms(L->p1, L->p2, currRing, m1, m2, strat->tailRing))
    return FALSE;
  // shift changes: extra case inserted
  if ((L->i_r1 == -1) || (L->i_r2 == -1) )
  {
    return TRUE;
  }
  poly p1_max=NULL;
  if ((L->i_r1>=0)&&(strat->R[L->i_r1]!=NULL)) p1_max = (strat->R[L->i_r1])->max_exp;
  poly p2_max=NULL;
  if ((L->i_r2>=0)&&(strat->R[L->i_r2]!=NULL)) p2_max = (strat->R[L->i_r2])->max_exp;
 
  if (((p1_max != NULL) && !p_LmExpVectorAddIsOk(m1, p1_max, strat->tailRing)) ||
      ((p2_max != NULL) && !p_LmExpVectorAddIsOk(m2, p2_max, strat->tailRing)))
  {
    p_LmFree(m1, strat->tailRing);
    p_LmFree(m2, strat->tailRing);
    m1 = NULL;
    m2 = NULL;
    return FALSE;
  }
  return TRUE;
}
 
/***************************************************************
 *
 * Checks, if we can compute the gcd poly / strong pair
 * gcd-poly = m1 * R[atR] + m2 * S[atS]
 *
 ***************************************************************/
BOOLEAN kCheckStrongCreation(int atR, poly m1, int atS, poly m2, kStrategy strat)
{
  assume(strat->S_2_R[atS] >= -1 && strat->S_2_R[atS] <= strat->tl);
  //assume(strat->tailRing != currRing);
 
  poly p1_max = (strat->R[atR])->max_exp;
  poly p2_max = (strat->R[strat->S_2_R[atS]])->max_exp;
 
  if (((p1_max != NULL) && !p_LmExpVectorAddIsOk(m1, p1_max, strat->tailRing)) ||
      ((p2_max != NULL) && !p_LmExpVectorAddIsOk(m2, p2_max, strat->tailRing)))
  {
    return FALSE;
  }
  return TRUE;
}
 
/*!
  used for GB over ZZ: look for constant and monomial elements in the ideal
  background: any known constant element of ideal suppresses
              intermediate coefficient swell
*/
poly preIntegerCheck(const ideal Forig, const ideal Q)
{
  assume(nCoeff_is_Z(currRing->cf));
  ideal F = idCopy(Forig);
  idSkipZeroes(F);
  poly pmon;
  ring origR = currRing;
  ideal monred = idInit(1,1);
  for(int i=0; i<idElem(F); i++)
  {
    if(pNext(F->m[i]) == NULL)
        idInsertPoly(monred, pCopy(F->m[i]));
  }
  int posconst = idPosConstant(F);
  if((posconst != -1) && (!nIsZero(F->m[posconst]->coef)))
  {
    idDelete(&F);
    idDelete(&monred);
    return NULL;
  }
  int idelemQ = 0;
  if(Q!=NULL)
  {
    idelemQ = IDELEMS(Q);
    for(int i=0; i<idelemQ; i++)
    {
      if(pNext(Q->m[i]) == NULL)
        idInsertPoly(monred, pCopy(Q->m[i]));
    }
    idSkipZeroes(monred);
    posconst = idPosConstant(monred);
    //the constant, if found, will be from Q
    if((posconst != -1) && (!nIsZero(monred->m[posconst]->coef)))
    {
      pmon = pCopy(monred->m[posconst]);
      idDelete(&F);
      idDelete(&monred);
      return pmon;
    }
  }
  ring QQ_ring = rCopy0(currRing,FALSE);
  nKillChar(QQ_ring->cf);
  QQ_ring->cf = nInitChar(n_Q, NULL);
  rComplete(QQ_ring,1);
  QQ_ring = rAssure_c_dp(QQ_ring);
  rChangeCurrRing(QQ_ring);
  nMapFunc nMap = n_SetMap(origR->cf, QQ_ring->cf);
  ideal II = idInit(IDELEMS(F)+idelemQ+2,id_RankFreeModule(F, origR));
  for(int i = 0, j = 0; i<IDELEMS(F); i++)
    II->m[j++] = prMapR(F->m[i], nMap, origR, QQ_ring);
  for(int i = 0, j = IDELEMS(F); i<idelemQ; i++)
    II->m[j++] = prMapR(Q->m[i], nMap, origR, QQ_ring);
  ideal one = kStd2(II, NULL, isNotHomog, NULL,(bigintmat*)NULL);
  idSkipZeroes(one);
  if(idIsConstant(one))
  {
    //one should be <1>
    for(int i = IDELEMS(II)-1; i>=0; i--)
      if(II->m[i] != NULL)
        II->m[i+1] = II->m[i];
    II->m[0] = pOne();
    ideal syz = idSyzygies(II, isNotHomog, NULL);
    poly integer = NULL;
    for(int i = IDELEMS(syz)-1;i>=0; i--)
    {
      if(pGetComp(syz->m[i]) == 1)
      {
        pSetComp(syz->m[i],0);
        if(pIsConstant(pHead(syz->m[i])))
        {
          integer = pHead(syz->m[i]);
          break;
        }
      }
    }
    rChangeCurrRing(origR);
    nMapFunc nMap2 = n_SetMap(QQ_ring->cf, origR->cf);
    pmon = prMapR(integer, nMap2, QQ_ring, origR);
    idDelete(&monred);
    idDelete(&F);
    id_Delete(&II,QQ_ring);
    id_Delete(&one,QQ_ring);
    id_Delete(&syz,QQ_ring);
    p_Delete(&integer,QQ_ring);
    rDelete(QQ_ring);
    return pmon;
  }
  else
  {
    if(idIs0(monred))
    {
      poly mindegmon = NULL;
      for(int i = 0; i<IDELEMS(one); i++)
      {
        if(pNext(one->m[i]) == NULL)
        {
          if(mindegmon == NULL)
            mindegmon = pCopy(one->m[i]);
          else
          {
            if(p_Deg(one->m[i], QQ_ring) < p_Deg(mindegmon, QQ_ring))
              mindegmon = pCopy(one->m[i]);
          }
        }
      }
      if(mindegmon != NULL)
      {
        for(int i = IDELEMS(II)-1; i>=0; i--)
          if(II->m[i] != NULL)
            II->m[i+1] = II->m[i];
        II->m[0] = pCopy(mindegmon);
        ideal syz = idSyzygies(II, isNotHomog, NULL);
        bool found = FALSE;
        for(int i = IDELEMS(syz)-1;i>=0; i--)
        {
          if(pGetComp(syz->m[i]) == 1)
          {
            pSetComp(syz->m[i],0);
            if(pIsConstant(pHead(syz->m[i])))
            {
              pSetCoeff(mindegmon, nCopy(syz->m[i]->coef));
              found = TRUE;
              break;
            }
          }
        }
        id_Delete(&syz,QQ_ring);
        if (found == FALSE)
        {
          rChangeCurrRing(origR);
          idDelete(&monred);
          idDelete(&F);
          id_Delete(&II,QQ_ring);
          id_Delete(&one,QQ_ring);
          rDelete(QQ_ring);
          return NULL;
        }
        rChangeCurrRing(origR);
        nMapFunc nMap2 = n_SetMap(QQ_ring->cf, origR->cf);
        pmon = prMapR(mindegmon, nMap2, QQ_ring, origR);
        idDelete(&monred);
        idDelete(&F);
        id_Delete(&II,QQ_ring);
        id_Delete(&one,QQ_ring);
        id_Delete(&syz,QQ_ring);
        rDelete(QQ_ring);
        return pmon;
      }
    }
  }
  rChangeCurrRing(origR);
  idDelete(&monred);
  idDelete(&F);
  id_Delete(&II,QQ_ring);
  id_Delete(&one,QQ_ring);
  rDelete(QQ_ring);
  return NULL;
}
 
/*!
  used for GB over ZZ: intermediate reduction by monomial elements
  background: any known constant element of ideal suppresses
              intermediate coefficient swell
*/
void postReduceByMon(LObject* h, kStrategy strat)
{
  if(!nCoeff_is_Z(currRing->cf))
      return;
  poly pH = h->GetP();
  poly p,pp;
  p = pH;
  bool deleted = FALSE, ok = FALSE;
  for(int i = 0; i<=strat->sl; i++)
  {
    p = pH;
    if(pNext(strat->S[i]) == NULL)
    {
      //pWrite(p);
      //pWrite(strat->S[i]);
      while(ok == FALSE && p != NULL)
      {
        if(pLmDivisibleBy(strat->S[i], p)
#ifdef HAVE_SHIFTBBA
            || (rIsLPRing(currRing) && pLPLmDivisibleBy(strat->S[i], p))
#endif
          )
        {
          number dummy = n_IntMod(p->coef, strat->S[i]->coef, currRing->cf);
          p_SetCoeff(p,dummy,currRing);
        }
        if(nIsZero(p->coef))
        {
          pLmDelete(&p);
          h->p = p;
          deleted = TRUE;
        }
        else
        {
          ok = TRUE;
        }
      }
      if (p!=NULL)
      {
        pp = pNext(p);
        while(pp != NULL)
        {
          if(pLmDivisibleBy(strat->S[i], pp)
#ifdef HAVE_SHIFTBBA
            || (rIsLPRing(currRing) && pLPLmDivisibleBy(strat->S[i], pp))
#endif
            )
          {
            number dummy = n_IntMod(pp->coef, strat->S[i]->coef, currRing->cf);
            p_SetCoeff(pp,dummy,currRing);
            if(nIsZero(pp->coef))
            {
              pLmDelete(&pNext(p));
              pp = pNext(p);
              deleted = TRUE;
            }
            else
            {
              p = pp;
              pp = pNext(p);
            }
          }
          else
          {
            p = pp;
            pp = pNext(p);
          }
        }
      }
    }
  }
  h->SetLmCurrRing();
  if((deleted)&&(h->p!=NULL))
    strat->initEcart(h);
}
 
void postReduceByMonSig(LObject* h, kStrategy strat)
{
  if(!nCoeff_is_Z(currRing->cf))
      return;
  poly hSig = h->sig;
  poly pH = h->GetP();
  poly p,pp;
  p = pH;
  bool deleted = FALSE, ok = FALSE;
  for(int i = 0; i<=strat->sl; i++)
  {
    p = pH;
    if(pNext(strat->S[i]) == NULL)
    {
      while(ok == FALSE && p!=NULL)
      {
        if(pLmDivisibleBy(strat->S[i], p))
        {
          poly sigMult = pDivideM(pHead(p),pHead(strat->S[i]));
          sigMult = ppMult_mm(sigMult,pCopy(strat->sig[i]));
          if(sigMult!= NULL && pLtCmp(hSig,sigMult) == 1)
          {
            number dummy = n_IntMod(p->coef, strat->S[i]->coef, currRing->cf);
            p_SetCoeff(p,dummy,currRing);
          }
          pDelete(&sigMult);
        }
        if(nIsZero(p->coef))
        {
          pLmDelete(&p);
          h->p = p;
          deleted = TRUE;
        }
        else
        {
          ok = TRUE;
        }
      }
      if(p == NULL)
        return;
      pp = pNext(p);
      while(pp != NULL)
      {
        if(pLmDivisibleBy(strat->S[i], pp))
        {
          poly sigMult = pDivideM(pHead(p),pHead(strat->S[i]));
          sigMult = ppMult_mm(sigMult,pCopy(strat->sig[i]));
          if(sigMult!= NULL && pLtCmp(hSig,sigMult) == 1)
          {
            number dummy = n_IntMod(pp->coef, strat->S[i]->coef, currRing->cf);
            p_SetCoeff(pp,dummy,currRing);
            if(nIsZero(pp->coef))
            {
              pLmDelete(&pNext(p));
              pp = pNext(p);
              deleted = TRUE;
            }
            else
            {
              p = pp;
              pp = pNext(p);
            }
          }
          else
          {
            p = pp;
            pp = pNext(p);
          }
          pDelete(&sigMult);
        }
        else
        {
          p = pp;
          pp = pNext(p);
        }
      }
    }
  }
  h->SetLmCurrRing();
  if(deleted)
    strat->initEcart(h);
 
}
 
/*!
  used for GB over ZZ: final reduction by constant elements
  background: any known constant element of ideal suppresses
              intermediate coefficient swell and beautifies output
*/
void finalReduceByMon(kStrategy strat)
{
  assume(strat->tl<0); /* can only be called with no elements in T:
                          i.e. after exitBuchMora */
  /* do not use strat->S, strat->sl as they may be out of sync*/
  if(!nCoeff_is_Z(currRing->cf))
      return;
  poly p,pp;
  for(int j = 0; j<IDELEMS(strat->Shdl); j++)
  {
    if((strat->Shdl->m[j]!=NULL)&&(pNext(strat->Shdl->m[j]) == NULL))
    {
      for(int i = 0; i<IDELEMS(strat->Shdl); i++)
      {
        if((i != j) && (strat->Shdl->m[i] != NULL))
        {
          p = strat->Shdl->m[i];
          while((p!=NULL) && (pLmDivisibleBy(strat->Shdl->m[j], p)
#if HAVE_SHIFTBBA
                || (rIsLPRing(currRing) && pLPLmDivisibleBy(strat->Shdl->m[j], p))
#endif
                ))
          {
            number dummy = n_IntMod(p->coef, strat->Shdl->m[j]->coef, currRing->cf);
            if (!nEqual(dummy,p->coef))
            {
              if (nIsZero(dummy))
              {
                nDelete(&dummy);
                pLmDelete(&strat->Shdl->m[i]);
                p=strat->Shdl->m[i];
              }
              else
              {
                p_SetCoeff(p,dummy,currRing);
                break;
              }
            }
            else
            {
              nDelete(&dummy);
              break;
            }
          }
          if (p!=NULL)
          {
            pp = pNext(p);
            while(pp != NULL)
            {
              if(pLmDivisibleBy(strat->Shdl->m[j], pp)
#if HAVE_SHIFTBBA
                  || (rIsLPRing(currRing) && pLPLmDivisibleBy(strat->Shdl->m[j], pp))
#endif
                )
              {
                number dummy = n_IntMod(pp->coef, strat->Shdl->m[j]->coef, currRing->cf);
                if (!nEqual(dummy,pp->coef))
                {
                  p_SetCoeff(pp,dummy,currRing);
                  if(nIsZero(pp->coef))
                  {
                    pLmDelete(&pNext(p));
                    pp = pNext(p);
                  }
                  else
                  {
                    p = pp;
                    pp = pNext(p);
                  }
                }
                else
                {
                  nDelete(&dummy);
                  p = pp;
                  pp = pNext(p);
                }
              }
              else
              {
                p = pp;
                pp = pNext(p);
              }
            }
          }
        }
      }
      //idPrint(strat->Shdl);
    }
  }
  idSkipZeroes(strat->Shdl);
}
 
BOOLEAN kStratChangeTailRing(kStrategy strat, LObject *L, TObject* T, unsigned long expbound)
{
  assume((strat->tailRing == currRing) || (strat->tailRing->bitmask <= currRing->bitmask));
  /* initial setup or extending */
 
  if (rIsLPRing(currRing)) return TRUE;
  if (expbound == 0) expbound = strat->tailRing->bitmask << 1;
  if (expbound >= currRing->bitmask) return FALSE;
  strat->overflow=FALSE;
  ring new_tailRing = rModifyRing(currRing,
  // Hmmm .. the condition pFDeg == p_Deg
  // might be too strong
  (strat->homog && currRing->pFDeg == p_Deg && !(rField_is_Ring(currRing))), // omit degree
  (strat->ak==0), // omit_comp if the input is an ideal
  expbound); // exp_limit
 
  if (new_tailRing == currRing) return TRUE;
 
  strat->pOrigFDeg_TailRing = new_tailRing->pFDeg;
  strat->pOrigLDeg_TailRing = new_tailRing->pLDeg;
 
  if (currRing->pFDeg != currRing->pFDegOrig)
  {
    new_tailRing->pFDeg = currRing->pFDeg;
    new_tailRing->pLDeg = currRing->pLDeg;
  }
 
  if (TEST_OPT_PROT)
    Print("[%lu:%d", (unsigned long) new_tailRing->bitmask, new_tailRing->ExpL_Size);
  #ifdef KDEBUG
  kTest_TS(strat);
  assume(new_tailRing != strat->tailRing);
  #endif
  pShallowCopyDeleteProc p_shallow_copy_delete
    = pGetShallowCopyDeleteProc(strat->tailRing, new_tailRing);
 
  omBin new_tailBin = omGetStickyBinOfBin(new_tailRing->PolyBin);
 
  int i;
  for (i=0; i<=strat->tl; i++)
  {
    strat->T[i].ShallowCopyDelete(new_tailRing, new_tailBin,
                                  p_shallow_copy_delete);
  }
  for (i=0; i<=strat->Ll; i++)
  {
    assume(strat->L[i].p != NULL);
    if (pNext(strat->L[i].p) != strat->tail)
      strat->L[i].ShallowCopyDelete(new_tailRing, p_shallow_copy_delete);
  }
  if ((strat->P.t_p != NULL) ||
      ((strat->P.p != NULL) && pNext(strat->P.p) != strat->tail))
    strat->P.ShallowCopyDelete(new_tailRing, p_shallow_copy_delete);
 
  if ((L != NULL) && (L->tailRing != new_tailRing))
  {
    if (L->i_r < 0)
      L->ShallowCopyDelete(new_tailRing, p_shallow_copy_delete);
    else
    {
      assume(L->i_r <= strat->tl);
      TObject* t_l = strat->R[L->i_r];
      assume(t_l != NULL);
      L->tailRing = new_tailRing;
      L->p = t_l->p;
      L->t_p = t_l->t_p;
      L->max_exp = t_l->max_exp;
    }
  }
 
  if ((T != NULL) && (T->tailRing != new_tailRing && T->i_r < 0))
    T->ShallowCopyDelete(new_tailRing, new_tailBin, p_shallow_copy_delete);
 
  omMergeStickyBinIntoBin(strat->tailBin, strat->tailRing->PolyBin);
  if (strat->tailRing != currRing)
    rKillModifiedRing(strat->tailRing);
 
  strat->tailRing = new_tailRing;
  strat->tailBin = new_tailBin;
  strat->p_shallow_copy_delete
    = pGetShallowCopyDeleteProc(currRing, new_tailRing);
 
  if (strat->kNoether != NULL)
  {
    if (strat->t_kNoether != NULL)
      p_LmFree(strat->t_kNoether, strat->tailRing);
    strat->t_kNoether=k_LmInit_currRing_2_tailRing(strat->kNoether, new_tailRing);
  }
 
  #ifdef KDEBUG
  kTest_TS(strat);
  #endif
  if (TEST_OPT_PROT)
    PrintS("]");
  return TRUE;
}
 
void kStratInitChangeTailRing(kStrategy strat)
{
  unsigned long l = 0;
  int i;
  long e;
 
  assume(strat->tailRing == currRing);
 
  for (i=0; i<= strat->Ll; i++)
  {
    l = p_GetMaxExpL(strat->L[i].p, currRing, l);
  }
  for (i=0; i<=strat->tl; i++)
  {
    // Hmm ... this we could do in one Step
    l = p_GetMaxExpL(strat->T[i].p, currRing, l);
  }
  if (rField_is_Ring(currRing))
  {
    l *= 2;
  }
  e = p_GetMaxExp(l, currRing);
  if (e <= 1) e = 2;
  if (rIsLPRing(currRing)) e = 1;
 
  kStratChangeTailRing(strat, NULL, NULL, e);
}
 
ring sbaRing (kStrategy strat, const ring r, BOOLEAN /*complete*/, int /*sgn*/)
{
  int n = rBlocks(r); // Including trailing zero!
  // if sbaOrder == 1 => use (C,monomial order from r)
  if (strat->sbaOrder == 1)
  {
    if (r->order[0] == ringorder_C || r->order[0] == ringorder_c)
    {
      return r;
    }
    ring res = rCopy0(r, TRUE, FALSE);
    res->order  = (rRingOrder_t *)omAlloc0((n+1)*sizeof(rRingOrder_t));
    res->block0 = (int *)omAlloc0((n+1)*sizeof(int));
    res->block1 = (int *)omAlloc0((n+1)*sizeof(int));
    int **wvhdl = (int **)omAlloc0((n+1)*sizeof(int*));
    res->wvhdl  = wvhdl;
    for (int i=1; i<n; i++)
    {
      res->order[i]   = r->order[i-1];
      res->block0[i]  = r->block0[i-1];
      res->block1[i]  = r->block1[i-1];
      res->wvhdl[i]   = r->wvhdl[i-1];
    }
 
    // new 1st block
    res->order[0]   = ringorder_C; // Prefix
    // removes useless secondary component order if defined in old ring
    for (int i=rBlocks(res); i>0; --i)
    {
      if (res->order[i] == ringorder_C || res->order[i] == ringorder_c)
      {
        res->order[i] = (rRingOrder_t)0;
      }
    }
    rComplete(res, 1);
#ifdef HAVE_PLURAL
    if (rIsPluralRing(r))
    {
      if ( nc_rComplete(r, res, false) ) // no qideal!
      {
#ifndef SING_NDEBUG
        WarnS("error in nc_rComplete");
#endif
        // cleanup?
 
        //      rDelete(res);
        //      return r;
 
        // just go on..
      }
    }
#endif
    strat->tailRing = res;
    return (res);
  }
  // if sbaOrder == 3 => degree - position - ring order
  if (strat->sbaOrder == 3)
  {
    ring res = rCopy0(r, TRUE, FALSE);
    res->order  = (rRingOrder_t*)omAlloc0((n+2)*sizeof(rRingOrder_t));
    res->block0 = (int *)omAlloc0((n+2)*sizeof(int));
    res->block1 = (int *)omAlloc0((n+2)*sizeof(int));
    int **wvhdl = (int **)omAlloc0((n+2)*sizeof(int*));
    res->wvhdl  = wvhdl;
    for (int i=2; i<n+2; i++)
    {
      res->order[i]   = r->order[i-2];
      res->block0[i]  = r->block0[i-2];
      res->block1[i]  = r->block1[i-2];
      res->wvhdl[i]   = r->wvhdl[i-2];
    }
 
    // new 1st block
    res->order[0]   = ringorder_a; // Prefix
    res->block0[0]  = 1;
    res->wvhdl[0]   = (int *)omAlloc(res->N*sizeof(int));
    for (int i=0; i<res->N; ++i)
      res->wvhdl[0][i]  = 1;
    res->block1[0]  = si_min(res->N, rVar(res));
    // new 2nd block
    res->order[1]   = ringorder_C; // Prefix
    res->wvhdl[1]   = NULL;
    // removes useless secondary component order if defined in old ring
    for (int i=rBlocks(res); i>1; --i)
    {
      if (res->order[i] == ringorder_C || res->order[i] == ringorder_c)
      {
        res->order[i] = (rRingOrder_t)0;
      }
    }
    rComplete(res, 1);
#ifdef HAVE_PLURAL
    if (rIsPluralRing(r))
    {
      if ( nc_rComplete(r, res, false) ) // no qideal!
      {
#ifndef SING_NDEBUG
        WarnS("error in nc_rComplete");
#endif
        // cleanup?
 
        //      rDelete(res);
        //      return r;
 
        // just go on..
      }
    }
#endif
    strat->tailRing = res;
    return (res);
  }
 
  // not sbaOrder == 1 => use Schreyer order
  // this is done by a trick when initializing the signatures
  // in initSLSba():
  // Instead of using the signature 1e_i for F->m[i], we start
  // with the signature LM(F->m[i])e_i for F->m[i]. Doing this we get a
  // Schreyer order w.r.t. the underlying monomial order.
  // => we do not need to change the underlying polynomial ring at all!
 
  // UPDATE/NOTE/TODO: use induced Schreyer ordering 'IS'!!!!????
 
  /*
  else
  {
    ring res = rCopy0(r, FALSE, FALSE);
    // Create 2 more blocks for prefix/suffix:
    res->order=(int *)omAlloc0((n+2)*sizeof(int)); // 0  ..  n+1
    res->block0=(int *)omAlloc0((n+2)*sizeof(int));
    res->block1=(int *)omAlloc0((n+2)*sizeof(int));
    int ** wvhdl =(int **)omAlloc0((n+2)*sizeof(int**));
 
    // Encapsulate all existing blocks between induced Schreyer ordering markers: prefix and suffix!
    // Note that prefix and suffix have the same ringorder marker and only differ in block[] parameters!
 
    // new 1st block
    int j = 0;
    res->order[j] = ringorder_IS; // Prefix
    res->block0[j] = res->block1[j] = 0;
    // wvhdl[j] = NULL;
    j++;
 
    for(int i = 0; (i < n) && (r->order[i] != 0); i++, j++) // i = [0 .. n-1] <- non-zero old blocks
    {
      res->order [j] = r->order [i];
      res->block0[j] = r->block0[i];
      res->block1[j] = r->block1[i];
 
      if (r->wvhdl[i] != NULL)
      {
        wvhdl[j] = (int*) omMemDup(r->wvhdl[i]);
      } // else wvhdl[j] = NULL;
    }
 
    // new last block
    res->order [j] = ringorder_IS; // Suffix
    res->block0[j] = res->block1[j] = sgn; // Sign of v[o]: 1 for C, -1 for c
    // wvhdl[j] = NULL;
    j++;
 
    // res->order [j] = 0; // The End!
    res->wvhdl = wvhdl;
 
    // j == the last zero block now!
    assume(j == (n+1));
    assume(res->order[0]==ringorder_IS);
    assume(res->order[j-1]==ringorder_IS);
    assume(res->order[j]==0);
 
    if (complete)
    {
      rComplete(res, 1);
 
#ifdef HAVE_PLURAL
      if (rIsPluralRing(r))
      {
        if ( nc_rComplete(r, res, false) ) // no qideal!
        {
        }
      }
      assume(rIsPluralRing(r) == rIsPluralRing(res));
#endif
 
 
#ifdef HAVE_PLURAL
      ring old_ring = r;
 
#endif
 
      if (r->qideal!=NULL)
      {
        res->qideal= idrCopyR_NoSort(r->qideal, r, res);
 
        assume(idRankFreeModule(res->qideal, res) == 0);
 
#ifdef HAVE_PLURAL
        if( rIsPluralRing(res) )
          if( nc_SetupQuotient(res, r, true) )
          {
            //          WarnS("error in nc_SetupQuotient"); // cleanup?      rDelete(res);       return r;  // just go on...?
          }
 
#endif
        assume(idRankFreeModule(res->qideal, res) == 0);
      }
 
#ifdef HAVE_PLURAL
      assume((res->qideal==NULL) == (old_ring->qideal==NULL));
      assume(rIsPluralRing(res) == rIsPluralRing(old_ring));
      assume(rIsSCA(res) == rIsSCA(old_ring));
      assume(ncRingType(res) == ncRingType(old_ring));
#endif
    }
    strat->tailRing = res;
    return res;
  }
  */
 
  assume(FALSE);
  return(NULL);
}
 
skStrategy::skStrategy()
{
  memset(this, 0, sizeof(skStrategy));
  strat_nr++;
  nr=strat_nr;
  tailRing = currRing;
  P.tailRing = currRing;
  tl = -1;
  sl = -1;
#ifdef HAVE_LM_BIN
  lmBin = omGetStickyBinOfBin(currRing->PolyBin);
#endif
#ifdef HAVE_TAIL_BIN
  tailBin = omGetStickyBinOfBin(tailRing->PolyBin);
#endif
  pOrigFDeg = currRing->pFDeg;
  pOrigLDeg = currRing->pLDeg;
}
 
 
skStrategy::~skStrategy()
{
  if(kNoether!=NULL) pLmFree(&kNoether);
  if (lmBin != NULL)
    omMergeStickyBinIntoBin(lmBin, currRing->PolyBin);
  if (tailBin != NULL)// && !rField_is_Ring(currRing))
    omMergeStickyBinIntoBin(tailBin,
                            ((tailRing != NULL) ? tailRing->PolyBin:
                             currRing->PolyBin));
  if (t_kNoether != NULL)
    p_LmFree(t_kNoether, tailRing);
 
  if (currRing != tailRing)
    rKillModifiedRing(tailRing);
  pRestoreDegProcs(currRing,pOrigFDeg, pOrigLDeg);
}
 
#if 0
Timings for the different possibilities of posInT:
            T15           EDL         DL          EL            L         1-2-3
Gonnet      43.26       42.30       38.34       41.98       38.40      100.04
Hairer_2_1   1.11        1.15        1.04        1.22        1.08        4.7
Twomat3      1.62        1.69        1.70        1.65        1.54       11.32
ahml         4.48        4.03        4.03        4.38        4.96       26.50
c7          15.02       13.98       15.16       13.24       17.31       47.89
c8         505.09      407.46      852.76      413.21      499.19        n/a
f855        12.65        9.27       14.97        8.78       14.23       33.12
gametwo6    11.47       11.35       14.57       11.20       12.02       35.07
gerhard_3    2.73        2.83        2.93        2.64        3.12        6.24
ilias13     22.89       22.46       24.62       20.60       23.34       53.86
noon8       40.68       37.02       37.99       36.82       35.59      877.16
rcyclic_19  48.22       42.29       43.99       45.35       51.51      204.29
rkat9       82.37       79.46       77.20       77.63       82.54      267.92
schwarz_11  16.46       16.81       16.76       16.81       16.72       35.56
test016     16.39       14.17       14.40       13.50       14.26       34.07
test017     34.70       36.01       33.16       35.48       32.75       71.45
test042     10.76       10.99       10.27       11.57       10.45       23.04
test058      6.78        6.75        6.51        6.95        6.22        9.47
test066     10.71       10.94       10.76       10.61       10.56       19.06
test073     10.75       11.11       10.17       10.79        8.63       58.10
test086     12.23       11.81       12.88       12.24       13.37       66.68
test103      5.05        4.80        5.47        4.64        4.89       11.90
test154     12.96       11.64       13.51       12.46       14.61       36.35
test162     65.27       64.01       67.35       59.79       67.54      196.46
test164      7.50        6.50        7.68        6.70        7.96       17.13
virasoro     3.39        3.50        3.35        3.47        3.70        7.66
#endif
 
 
//#ifdef HAVE_MORE_POS_IN_T
#if 1
// determines the position based on: 1.) Ecart 2.) FDeg 3.) pLength
int posInT_EcartFDegpLength(const TSet set,const int length,LObject &p)
{
 
  if (length==-1) return 0;
 
  int o = p.ecart;
  int op=p.GetpFDeg();
  int ol = p.GetpLength();
 
  if (set[length].ecart < o)
    return length+1;
  if (set[length].ecart == o)
  {
     int oo=set[length].GetpFDeg();
     if ((oo < op) || ((oo==op) && (set[length].length < ol)))
       return length+1;
  }
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      if (set[an].ecart > o)
        return an;
      if (set[an].ecart == o)
      {
         int oo=set[an].GetpFDeg();
         if((oo > op)
         || ((oo==op) && (set[an].pLength > ol)))
           return an;
      }
      return en;
    }
    i=(an+en) / 2;
    if (set[i].ecart > o)
      en=i;
    else if (set[i].ecart == o)
    {
       int oo=set[i].GetpFDeg();
       if ((oo > op)
       || ((oo == op) && (set[i].pLength > ol)))
         en=i;
       else
        an=i;
    }
    else
      an=i;
  }
}
 
// determines the position based on: 1.) FDeg 2.) pLength
int posInT_FDegpLength(const TSet set,const int length,LObject &p)
{
 
  if (length==-1) return 0;
 
  int op=p.GetpFDeg();
  int ol = p.GetpLength();
 
  int oo=set[length].GetpFDeg();
  if ((oo < op) || ((oo==op) && (set[length].length < ol)))
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
  loop
  {
    if (an >= en-1)
    {
      int oo=set[an].GetpFDeg();
      if((oo > op)
         || ((oo==op) && (set[an].pLength > ol)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    int oo=set[i].GetpFDeg();
    if ((oo > op)
        || ((oo == op) && (set[i].pLength > ol)))
      en=i;
    else
      an=i;
  }
}
 
 
// determines the position based on: 1.) pLength
int posInT_pLength(const TSet set,const int length,LObject &p)
{
  int ol = p.GetpLength();
  if (length==-1)
    return 0;
  if (set[length].length<p.length)
    return length+1;
 
  int i;
  int an = 0;
  int en= length;
 
  loop
  {
    if (an >= en-1)
    {
      if (set[an].pLength>ol) return an;
      return en;
    }
    i=(an+en) / 2;
    if (set[i].pLength>ol) en=i;
    else                        an=i;
  }
}
#endif
 
// ../Singular/misc.cc:
extern char *  showOption();
 
void kDebugPrint(kStrategy strat)
{
  printf("red: ");
    if (strat->red==redFirst) printf("redFirst\n");
    else if (strat->red==redHoney) printf("redHoney\n");
    else if (strat->red==redEcart) printf("redEcart\n");
    else if (strat->red==redHomog) printf("redHomog\n");
    else if (strat->red==redLazy) printf("redLazy\n");
    else if (strat->red==redLiftstd) printf("redLiftstd\n");
    else  printf("%p\n",(void*)strat->red);
  printf("posInT: ");
    if (strat->posInT==posInT0) printf("posInT0\n");
    else if (strat->posInT==posInT1) printf("posInT1\n");
    else if (strat->posInT==posInT11) printf("posInT11\n");
    else if (strat->posInT==posInT110) printf("posInT110\n");
    else if (strat->posInT==posInT13) printf("posInT13\n");
    else if (strat->posInT==posInT15) printf("posInT15\n");
    else if (strat->posInT==posInT17) printf("posInT17\n");
    else if (strat->posInT==posInT17_c) printf("posInT17_c\n");
    else if (strat->posInT==posInT19) printf("posInT19\n");
    else if (strat->posInT==posInT2) printf("posInT2\n");
    else if (strat->posInT==posInT11Ring) printf("posInT11Ring\n");
    else if (strat->posInT==posInT110Ring) printf("posInT110Ring\n");
    else if (strat->posInT==posInT15Ring) printf("posInT15Ring\n");
    else if (strat->posInT==posInT17Ring) printf("posInT17Ring\n");
    else if (strat->posInT==posInT17_cRing) printf("posInT17_cRing\n");
#ifdef HAVE_MORE_POS_IN_T
    else if (strat->posInT==posInT_EcartFDegpLength) printf("posInT_EcartFDegpLength\n");
    else if (strat->posInT==posInT_FDegpLength) printf("posInT_FDegpLength\n");
    else if (strat->posInT==posInT_pLength) printf("posInT_pLength\n");
#endif
    else if (strat->posInT==posInT_EcartpLength) printf("posInT_EcartpLength\n");
    else  printf("%p\n",(void*)strat->posInT);
  printf("posInL: ");
    if (strat->posInL==posInL0) printf("posInL0\n");
    else if (strat->posInL==posInL10) printf("posInL10\n");
    else if (strat->posInL==posInL11) printf("posInL11\n");
    else if (strat->posInL==posInL110) printf("posInL110\n");
    else if (strat->posInL==posInL13) printf("posInL13\n");
    else if (strat->posInL==posInL15) printf("posInL15\n");
    else if (strat->posInL==posInL17) printf("posInL17\n");
    else if (strat->posInL==posInL17_c) printf("posInL17_c\n");
    else if (strat->posInL==posInL0) printf("posInL0Ring\n");
    else if (strat->posInL==posInL11Ring) printf("posInL11Ring\n");
    else if (strat->posInL==posInL11Ringls) printf("posInL11Ringls\n");
    else if (strat->posInL==posInL110Ring) printf("posInL110Ring\n");
    else if (strat->posInL==posInL15Ring) printf("posInL15Ring\n");
    else if (strat->posInL==posInL17Ring) printf("posInL17Ring\n");
    else if (strat->posInL==posInL17_cRing) printf("posInL17_cRing\n");
    else if (strat->posInL==posInLSpecial) printf("posInLSpecial\n");
    else  printf("%p\n",(void*)strat->posInL);
  printf("enterS: ");
    if (strat->enterS==enterSBba) printf("enterSBba\n");
    else if (strat->enterS==enterSMora) printf("enterSMora\n");
    else if (strat->enterS==enterSMoraNF) printf("enterSMoraNF\n");
    else  printf("%p\n",(void*)strat->enterS);
  printf("initEcart: ");
    if (strat->initEcart==initEcartBBA) printf("initEcartBBA\n");
    else if (strat->initEcart==initEcartNormal) printf("initEcartNormal\n");
    else  printf("%p\n",(void*)strat->initEcart);
  printf("initEcartPair: ");
    if (strat->initEcartPair==initEcartPairBba) printf("initEcartPairBba\n");
    else if (strat->initEcartPair==initEcartPairMora) printf("initEcartPairMora\n");
    else  printf("%p\n",(void*)strat->initEcartPair);
  printf("homog=%d, LazyDegree=%d, LazyPass=%d, ak=%d,\n",
    strat->homog, strat->LazyDegree,strat->LazyPass, strat->ak);
  printf("honey=%d, sugarCrit=%d, Gebauer=%d, noTailReduction=%d, use_buckets=%d\n",
    strat->honey,strat->sugarCrit,strat->Gebauer,strat->noTailReduction,strat->use_buckets);
  printf("chainCrit: ");
    if (strat->chainCrit==chainCritNormal) printf("chainCritNormal\n");
    else if (strat->chainCrit==chainCritOpt_1) printf("chainCritOpt_1\n");
    else  printf("%p\n",(void*)strat->chainCrit);
  printf("posInLDependsOnLength=%d\n",
         strat->posInLDependsOnLength);
  printf("%s\n",showOption());
  printf("LDeg: ");
    if (currRing->pLDeg==pLDeg0) printf("pLDeg0");
    else if (currRing->pLDeg==pLDeg0c) printf("pLDeg0c");
    else if (currRing->pLDeg==pLDegb) printf("pLDegb");
    else if (currRing->pLDeg==pLDeg1) printf("pLDeg1");
    else if (currRing->pLDeg==pLDeg1c) printf("pLDeg1c");
    else if (currRing->pLDeg==pLDeg1_Deg) printf("pLDeg1_Deg");
    else if (currRing->pLDeg==pLDeg1c_Deg) printf("pLDeg1c_Deg");
    else if (currRing->pLDeg==pLDeg1_Totaldegree) printf("pLDeg1_Totaldegree");
    else if (currRing->pLDeg==pLDeg1c_Totaldegree) printf("pLDeg1c_Totaldegree");
    else if (currRing->pLDeg==pLDeg1_WFirstTotalDegree) printf("pLDeg1_WFirstTotalDegree");
    else if (currRing->pLDeg==pLDeg1c_WFirstTotalDegree) printf("pLDeg1c_WFirstTotalDegree");
    else if (currRing->pLDeg==maxdegreeWecart) printf("maxdegreeWecart");
    else printf("? (%lx)", (long)currRing->pLDeg);
    printf(" / ");
    if (strat->tailRing->pLDeg==pLDeg0) printf("pLDeg0");
    else if (strat->tailRing->pLDeg==pLDeg0c) printf("pLDeg0c");
    else if (strat->tailRing->pLDeg==pLDegb) printf("pLDegb");
    else if (strat->tailRing->pLDeg==pLDeg1) printf("pLDeg1");
    else if (strat->tailRing->pLDeg==pLDeg1c) printf("pLDeg1c");
    else if (strat->tailRing->pLDeg==pLDeg1_Deg) printf("pLDeg1_Deg");
    else if (strat->tailRing->pLDeg==pLDeg1c_Deg) printf("pLDeg1c_Deg");
    else if (strat->tailRing->pLDeg==pLDeg1_Totaldegree) printf("pLDeg1_Totaldegree");
    else if (strat->tailRing->pLDeg==pLDeg1c_Totaldegree) printf("pLDeg1c_Totaldegree");
    else if (strat->tailRing->pLDeg==pLDeg1_WFirstTotalDegree) printf("pLDeg1_WFirstTotalDegree");
    else if (strat->tailRing->pLDeg==pLDeg1c_WFirstTotalDegree) printf("pLDeg1c_WFirstTotalDegree");
    else if (strat->tailRing->pLDeg==maxdegreeWecart) printf("maxdegreeWecart");
    else printf("? (%lx)", (long)strat->tailRing->pLDeg);
    printf("\n");
  printf("currRing->pFDeg: ");
    if (currRing->pFDeg==p_Totaldegree) printf("p_Totaldegree");
    else if (currRing->pFDeg==p_WFirstTotalDegree) printf("pWFirstTotalDegree");
    else if (currRing->pFDeg==p_Deg) printf("p_Deg");
    else if (currRing->pFDeg==kHomModDeg) printf("kHomModDeg");
    else if (currRing->pFDeg==kModDeg) printf("kModDeg");
    else if (currRing->pFDeg==totaldegreeWecart) printf("totaldegreeWecart");
    else if (currRing->pFDeg==p_WTotaldegree) printf("p_WTotaldegree");
    else printf("? (%lx)", (long)currRing->pFDeg);
    printf("\n");
    printf(" syzring:%d, syzComp(strat):%d limit:%d\n",rIsSyzIndexRing(currRing),strat->syzComp,rGetCurrSyzLimit(currRing));
    if(TEST_OPT_DEGBOUND)
      printf(" degBound: %d\n", Kstd1_deg);
 
    if( ecartWeights != NULL )
    {
       printf("ecartWeights: ");
       for (int i = rVar(currRing); i > 0; i--)
         printf("%hd ", ecartWeights[i]);
       printf("\n");
       assume( TEST_OPT_WEIGHTM );
    }
 
#ifndef SING_NDEBUG
    rDebugPrint(currRing);
#endif
}
 
//LObject pCopyp2L(poly p, kStrategy strat)
//{
    /* creates LObject from the poly in currRing */
  /* actually put p into L.p and make L.t_p=NULL : does not work */
 
//}
 
/*2
* put the  lcm(q,p)  into the set B, q is the shift of some s[i]
*/
#ifdef HAVE_SHIFTBBA
static BOOLEAN enterOneStrongPolyShift (poly q, poly p, int /*ecart*/, int /*isFromQ*/, kStrategy strat, int atR, int /*ecartq*/, int /*qisFromQ*/, int shiftcount, int ifromS)
{
  number d, s, t;
  /* assume(atR >= 0); */
  assume(ifromS <= strat->sl);
  assume(rField_is_Ring(currRing));
  poly m1, m2, gcd;
  //printf("\n--------------------------------\n");
  //pWrite(p);pWrite(si);
  d = n_ExtGcd(pGetCoeff(p), pGetCoeff(q), &s, &t, currRing->cf);
 
  if (nIsZero(s) || nIsZero(t))  // evtl. durch divBy tests ersetzen
  {
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
    return FALSE;
  }
 
  assume(pIsInV(p));
 
  k_GetStrongLeadTerms(p, q, currRing, m1, m2, gcd, strat->tailRing);
 
  /* the V criterion */
  if (!pmIsInV(gcd))
  {
    strat->cv++;
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
    pLmFree(gcd);
    return FALSE;
  }
 
  // disabled for Letterplace because it is not so easy to check
  /* if (!rHasLocalOrMixedOrdering(currRing)) { */
  /*   unsigned long sev = pGetShortExpVector(gcd); */
 
  /*   for (int j = 0; j < strat->sl; j++) { */
  /*     if (j == i) */
  /*       continue; */
 
  /*     if (n_DivBy(d, pGetCoeff(strat->S[j]), currRing->cf) && */
  /*         !(strat->sevS[j] & ~sev) && */
  /*         p_LmDivisibleBy(strat->S[j], gcd, currRing)) { */
  /*       nDelete(&d); */
  /*       nDelete(&s); */
  /*       nDelete(&t); */
  /*       return FALSE; */
  /*     } */
  /*   } */
  /* } */
 
  poly m12, m22;
  assume(p_mFirstVblock(p, currRing) <= 1 || p_mFirstVblock(q, currRing) <= 1);
  k_SplitFrame(m1, m12, si_max(p_mFirstVblock(p, currRing), 1), currRing);
  k_SplitFrame(m2, m22, si_max(p_mFirstVblock(q, currRing), 1), currRing);
  // manually free the coeffs, because pSetCoeff0 is used in the next step
  n_Delete(&(m1->coef), currRing->cf);
  n_Delete(&(m2->coef), currRing->cf);
 
  //p_Test(m1,strat->tailRing);
  //p_Test(m2,strat->tailRing);
  /*if(!enterTstrong)
  {
    while (! kCheckStrongCreation(atR, m1, i, m2, strat) )
    {
      memset(&(strat->P), 0, sizeof(strat->P));
      kStratChangeTailRing(strat);
      strat->P = *(strat->R[atR]);
      p_LmFree(m1, strat->tailRing);
      p_LmFree(m2, strat->tailRing);
      p_LmFree(gcd, currRing);
      k_GetStrongLeadTerms(p, si, currRing, m1, m2, gcd, strat->tailRing);
    }
  }*/
  pSetCoeff0(m1, s);
  pSetCoeff0(m2, t);
  pSetCoeff0(gcd, d);
  p_Test(m1,strat->tailRing);
  p_Test(m2,strat->tailRing);
  p_Test(m12,strat->tailRing);
  p_Test(m22,strat->tailRing);
  assume(pmIsInV(m1));
  assume(pmIsInV(m2));
  assume(pmIsInV(m12));
  assume(pmIsInV(m22));
  //printf("\n===================================\n");
  //pWrite(m1);pWrite(m2);pWrite(gcd);
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    // Print("t = %d; s = %d; d = %d\n", nInt(t), nInt(s), nInt(d));
    PrintS("m1 = ");
    p_wrp(m1, strat->tailRing);
    PrintS("m12 = ");
    p_wrp(m12, strat->tailRing);
    PrintS(" ; m2 = ");
    p_wrp(m2, strat->tailRing);
    PrintS(" ; m22 = ");
    p_wrp(m22, strat->tailRing);
    PrintS(" ; gcd = ");
    wrp(gcd);
    PrintS("\n--- create strong gcd poly: ");
    PrintS("\n p: ");
    wrp(p);
    Print("\n q (strat->S[%d]): ", ifromS);
    wrp(q);
    PrintS(" ---> ");
  }
#endif
 
  pNext(gcd) = p_Add_q(pp_Mult_mm(pp_mm_Mult(pNext(p), m1, strat->tailRing), m12, strat->tailRing), pp_Mult_mm(pp_mm_Mult(pNext(q), m2, strat->tailRing), m22, strat->tailRing), strat->tailRing);
  p_LmDelete(m1, strat->tailRing);
  p_LmDelete(m2, strat->tailRing);
  p_LmDelete(m12, strat->tailRing);
  p_LmDelete(m22, strat->tailRing);
 
  assume(pIsInV(gcd));
 
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    wrp(gcd);
    PrintLn();
  }
#endif
 
  LObject h;
  h.p = gcd;
  h.tailRing = strat->tailRing;
  int posx;
  strat->initEcart(&h);
  h.sev = pGetShortExpVector(h.p);
  h.i_r1 = -1;h.i_r2 = -1;
  if (currRing!=strat->tailRing)
    h.t_p = k_LmInit_currRing_2_tailRing(h.p, strat->tailRing);
#if 1
  h.p1 = p;
  h.p2 = q;
#endif
  if (atR >= 0 && shiftcount == 0 && ifromS >= 0)
  {
    h.i_r2 = kFindInT(h.p1, strat);
    h.i_r1 = atR;
  }
  else
  {
    h.i_r1 = -1;
    h.i_r2 = -1;
  }
  if (strat->Ll==-1)
    posx =0;
  else
    posx = strat->posInL(strat->L,strat->Ll,&h,strat);
 
  assume(pIsInV(h.p));
  assume(pIsInV(h.p1));
 
  enterL(&strat->L,&strat->Ll,&strat->Lmax,h,posx);
  return TRUE;
}
#endif
 
 
/*2
* put the pair (q,p)  into the set B, ecart=ecart(p), q is the shift of some s[i] (ring case)
*/
#ifdef HAVE_SHIFTBBA
static void enterOnePairRingShift (poly q, poly p, int /*ecart*/, int isFromQ, kStrategy strat, int atR, int /*ecartq*/, int qisFromQ, int shiftcount, int ifromS)
{
  /* assume(atR >= 0); */
  /* assume(i<=strat->sl); */
  assume(p!=NULL);
  assume(rField_is_Ring(currRing));
  assume(pIsInV(p));
  #if ALL_VS_JUST
  //Over rings, if we construct the strong pair, do not add the spair
  if(rField_is_Ring(currRing))
  {
    number s,t,d;
    d = n_ExtGcd(pGetCoeff(p), pGetCoeff(q, &s, &t, currRing->cf);
 
    if (!nIsZero(s) && !nIsZero(t))  // evtl. durch divBy tests ersetzen
    {
      nDelete(&d);
      nDelete(&s);
      nDelete(&t);
      return;
    }
    nDelete(&d);
    nDelete(&s);
    nDelete(&t);
  }
  #endif
  int      j,compare,compareCoeff;
  LObject  h;
 
#ifdef KDEBUG
  h.ecart=0; h.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  if(pHasNotCFRing(p,q))
  {
      strat->cp++;
      return;
  }
  h.lcm = p_Lcm(p,q,currRing);
  pSetCoeff0(h.lcm, n_Lcm(pGetCoeff(p), pGetCoeff(q), currRing->cf));
  if (nIsZero(pGetCoeff(h.lcm)))
  {
      strat->cp++;
      pLmDelete(h.lcm);
      return;
  }
 
  /* the V criterion */
  if (!pmIsInV(h.lcm))
  {
    strat->cv++;
    pLmDelete(h.lcm);
    return;
  }
  // basic chain criterion
  /*
  *the set B collects the pairs of type (S[j],p)
  *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p) != lcm(r,p)
  *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
  *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
  */
 
  for(j = strat->Bl;j>=0;j--)
  {
    compare=pDivCompRing(strat->B[j].lcm,h.lcm);
    compareCoeff = n_DivComp(pGetCoeff(strat->B[j].lcm), pGetCoeff(h.lcm), currRing->cf);
    if(compare == pDivComp_EQUAL)
    {
      //They have the same LM
      if(compareCoeff == pDivComp_LESS)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (qisFromQ==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
      if(compareCoeff == pDivComp_GREATER)
      {
        deleteInL(strat->B,&strat->Bl,j,strat);
        strat->c3++;
      }
      if(compareCoeff == pDivComp_EQUAL)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (qisFromQ==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
    }
    if(compareCoeff == compare || compareCoeff == pDivComp_EQUAL)
    {
      if(compare == pDivComp_LESS)
      {
        if ((strat->fromQ==NULL) || (isFromQ==0) || (qisFromQ==0))
        {
          strat->c3++;
          pLmDelete(h.lcm);
          return;
        }
        break;
      }
      if(compare == pDivComp_GREATER)
      {
        deleteInL(strat->B,&strat->Bl,j,strat);
        strat->c3++;
      }
    }
  }
  number s, t;
  poly m1, m2, gcd = NULL;
  s = pGetCoeff(q);
  t = pGetCoeff(p);
  k_GetLeadTerms(p,q,currRing,m1,m2,currRing);
 
  poly m12, m22;
  assume(p_mFirstVblock(p, currRing) <= 1 || p_mFirstVblock(q, currRing) <= 1);
  k_SplitFrame(m1, m12, si_max(p_mFirstVblock(p, currRing), 1), currRing);
  k_SplitFrame(m2, m22, si_max(p_mFirstVblock(q, currRing), 1), currRing);
  // manually free the coeffs, because pSetCoeff0 is used in the next step
  n_Delete(&(m1->coef), currRing->cf);
  n_Delete(&(m2->coef), currRing->cf);
 
  ksCheckCoeff(&s, &t, currRing->cf);
  pSetCoeff0(m1, s);
  pSetCoeff0(m2, t);
  m2 = pNeg(m2);
  p_Test(m1,strat->tailRing);
  p_Test(m2,strat->tailRing);
  p_Test(m12,strat->tailRing);
  p_Test(m22,strat->tailRing);
  assume(pmIsInV(m1));
  assume(pmIsInV(m2));
  assume(pmIsInV(m12));
  assume(pmIsInV(m22));
  poly pm1 = pp_Mult_mm(pp_mm_Mult(pNext(p), m1, strat->tailRing), m12, strat->tailRing);
  poly sim2 = pp_Mult_mm(pp_mm_Mult(pNext(q), m2, strat->tailRing), m22, strat->tailRing);
  assume(pIsInV(pm1));
  assume(pIsInV(sim2));
  p_LmDelete(m1, currRing);
  p_LmDelete(m2, currRing);
  p_LmDelete(m12, currRing);
  p_LmDelete(m22, currRing);
  if(sim2 == NULL)
  {
    if(pm1 == NULL)
    {
      if(h.lcm != NULL)
      {
        pLmDelete(h.lcm);
        h.lcm=NULL;
      }
      h.Clear();
      /* TEMPORARILY DISABLED FOR SHIFTS because there is no i*/
      /* if (strat->pairtest==NULL) initPairtest(strat); */
      /* strat->pairtest[i] = TRUE; */
      /* strat->pairtest[strat->sl+1] = TRUE; */
      return;
    }
    else
    {
      gcd = pm1;
      pm1 = NULL;
    }
  }
  else
  {
    if((pGetComp(q) == 0) && (0 != pGetComp(p)))
    {
      p_SetCompP(sim2, pGetComp(p), strat->tailRing);
      pSetmComp(sim2);
    }
    //p_Write(pm1,strat->tailRing);p_Write(sim2,strat->tailRing);
    gcd = p_Add_q(pm1, sim2, strat->tailRing);
  }
  p_Test(gcd, strat->tailRing);
  assume(pIsInV(gcd));
#ifdef KDEBUG
  if (TEST_OPT_DEBUG)
  {
    wrp(gcd);
    PrintLn();
  }
#endif
  h.p = gcd;
  h.i_r = -1;
  if(h.p == NULL)
  {
    /* TEMPORARILY DISABLED FOR SHIFTS because there is no i*/
    /* if (strat->pairtest==NULL) initPairtest(strat); */
    /* strat->pairtest[i] = TRUE; */
    /* strat->pairtest[strat->sl+1] = TRUE; */
    return;
  }
  h.tailRing = strat->tailRing;
  int posx;
  //h.pCleardenom();
  //pSetm(h.p);
  h.i_r1 = -1;h.i_r2 = -1;
  strat->initEcart(&h);
  #if 1
  h.p1 = p;
  h.p2 = q;
  #endif
  #if 1
  /* TEMPORARILY DISABLED FOR SHIFTS because there's no i*/
  /* at the beginning we DO NOT set atR = -1 ANYMORE*/
  if (atR >= 0 && shiftcount == 0 && ifromS >= 0)
  {
    h.i_r2 = kFindInT(h.p1, strat); //strat->S_2_R[i];
    h.i_r1 = atR;
  }
  else
  {
    /* END _ TEMPORARILY DISABLED FOR SHIFTS */
    h.i_r1 = -1;
    h.i_r2 = -1;
  }
  #endif
  if (strat->Bl==-1)
    posx =0;
  else
    posx = strat->posInL(strat->B,strat->Bl,&h,strat);
  h.sev = pGetShortExpVector(h.p);
  if (currRing!=strat->tailRing)
    h.t_p = k_LmInit_currRing_2_tailRing(h.p, strat->tailRing);
 
  assume(pIsInV(h.p));
  assume(pIsInV(h.p1));
  assume(h.lcm != NULL);
  assume(pIsInV(h.lcm));
 
  enterL(&strat->B,&strat->Bl,&strat->Bmax,h,posx);
  kTest_TS(strat);
}
#endif
 
#ifdef HAVE_SHIFTBBA
// adds the strong pair and the normal pair for rings (aka gpoly and spoly)
static BOOLEAN enterOneStrongPolyAndEnterOnePairRingShift(poly q, poly p, int ecart, int isFromQ, kStrategy strat, int atR, int ecartq, int qisFromQ, int shiftcount, int ifromS)
{
  enterOneStrongPolyShift(q, p, ecart, isFromQ, strat, atR, ecartq, qisFromQ, shiftcount, ifromS); // "gpoly"
  enterOnePairRingShift(q, p, ecart, isFromQ, strat, atR, ecartq, qisFromQ, shiftcount, ifromS); // "spoly"
  return FALSE; // TODO: delete q?
}
#endif
 
#ifdef HAVE_SHIFTBBA
// creates if possible (q,p), (shifts(q),p)
static BOOLEAN enterOnePairWithShifts (int q_inS /*also i*/, poly q, poly p, int ecartp, int p_isFromQ, kStrategy strat, int /*atR*/, int p_lastVblock, int q_lastVblock)
{
  // note: ecart and isFromQ is for p
  assume(q_inS < 0 || strat->S[q_inS] == q); // if q is from S, q_inS should be the index of q in S
  assume(pmFirstVblock(p) == 1);
  assume(pmFirstVblock(q) == 1);
  assume(p_lastVblock == pmLastVblock(p));
  assume(q_lastVblock == pmLastVblock(q));
 
  // TODO: is ecartq = 0 still ok?
  int ecartq = 0; //Hans says it's ok; we're in the homog case, no ecart
 
  int q_isFromQ = 0;
  if (strat->fromQ != NULL && q_inS >= 0)
    q_isFromQ = strat->fromQ[q_inS];
 
  BOOLEAN (*enterPair)(poly, poly, int, int, kStrategy, int, int, int, int, int);
  if (rField_is_Ring(currRing))
    enterPair = enterOneStrongPolyAndEnterOnePairRingShift;
  else
    enterPair = enterOnePairShift;
 
  int degbound = currRing->N/currRing->isLPring;
  int neededShift = p_lastVblock - ((pGetComp(p) > 0 || pGetComp(q) > 0) ? 0 : 1); // in the module case, product criterion does not hold
  int maxPossibleShift = degbound - q_lastVblock;
  int maxShift = si_min(neededShift, maxPossibleShift);
  int firstShift = (q == p ? 1 : 0); // do not add (q,p) if q=p
  BOOLEAN delete_pair=TRUE;
  for (int j = firstShift; j <= maxShift; j++)
  {
    poly qq = pLPCopyAndShiftLM(q, j);
    if (enterPair(qq, p, ecartp, p_isFromQ, strat, -1, ecartq, q_isFromQ, j, q_inS))
    {
      if (j>0) pLmDelete(qq);
      // delete qq, if not it does not enter the pair set
    }
    else
      delete_pair=FALSE;
  }
 
  if (rField_is_Ring(currRing) && p_lastVblock >= firstShift && p_lastVblock <= maxPossibleShift)
  {
    // add pairs (m*shifts(q), p) where m is a monomial and the pair has no overlap
    for (int j = p_lastVblock; j <= maxPossibleShift; j++)
    {
      ideal fillers = id_MaxIdeal(j - p_lastVblock, currRing);
      for (int k = 0; k < IDELEMS(fillers); k++)
      {
        poly qq = pLPCopyAndShiftLM(pp_mm_Mult(q, fillers->m[k], currRing), p_lastVblock);
        enterPair(qq, p, ecartp, p_isFromQ, strat, -1, ecartq, q_isFromQ, p_lastVblock, q_inS);
      }
      idDelete(&fillers);
    }
  }
  return delete_pair;
}
#endif
 
#ifdef HAVE_SHIFTBBA
// creates (q,p), use it when q is already shifted
// return TRUE, if (q,p) is discarded
static BOOLEAN enterOnePairWithoutShifts (int p_inS /*also i*/, poly q, poly p, int ecartq, int q_isFromQ, kStrategy strat, int /*atR*/, int p_lastVblock, int q_shift)
{
  // note: ecart and isFromQ is for p
  assume(p_inS < 0 || strat->S[p_inS] == p); // if p is from S, p_inS should be the index of p in S
  assume(pmFirstVblock(p) == 1);
  assume(p_lastVblock == pmLastVblock(p));
  assume(q_shift == pmFirstVblock(q) - 1);
 
  // TODO: is ecartp = 0 still ok?
  int ecartp = 0; //Hans says it's ok; we're in the homog e:, no ecart
 
  int p_isFromQ = 0;
  if (strat->fromQ != NULL && p_inS >= 0)
    p_isFromQ = strat->fromQ[p_inS];
 
  if (rField_is_Ring(currRing))
  {
    assume(q_shift <= p_lastVblock); // we allow the special case where there is no overlap
    return enterOneStrongPolyAndEnterOnePairRingShift(q, p, ecartp, p_isFromQ, strat, -1, ecartq, q_isFromQ, q_shift, -1);
  }
  else
  {
    assume(q_shift <= p_lastVblock - ((pGetComp(q) > 0 || pGetComp(p) > 0) ? 0 : 1)); // there should be an overlap (in the module case epsilon overlap is also allowed)
    return enterOnePairShift(q, p, ecartp, p_isFromQ, strat, -1, ecartq, q_isFromQ, q_shift, -1);
  }
}
#endif
 
 
#ifdef KDEBUG
// enable to print which pairs are considered or discarded and why
/* #define CRITERION_DEBUG */
#endif
/*2
* put the pair (q,p)  into the set B, ecart=ecart(p), q is the shift of some s[i]
* return TRUE, if (q,p) does not enter B
*/
#ifdef HAVE_SHIFTBBA
BOOLEAN enterOnePairShift (poly q, poly p, int ecart, int isFromQ, kStrategy strat, int atR, int ecartq, int qisFromQ, int shiftcount, int ifromS)
{
#ifdef CRITERION_DEBUG
  if (TEST_OPT_DEBUG)
  {
    PrintS("Consider pair ("); wrp(q); PrintS(", "); wrp(p); PrintS(")"); PrintLn();
    // also write the LMs in separate lines:
    poly lmq = pHead(q);
    poly lmp = pHead(p);
    pSetCoeff(lmq, n_Init(1, currRing->cf));
    pSetCoeff(lmp, n_Init(1, currRing->cf));
    Print("    %s\n", pString(lmq));
    Print("    %s\n", pString(lmp));
    pLmDelete(lmq);
    pLmDelete(lmp);
  }
#endif
 
  /* Format: q and p are like strat->P.p, so lm in CR, tail in TR */
 
  /* check this Formats: */
  assume(p_LmCheckIsFromRing(q,currRing));
  assume(p_CheckIsFromRing(pNext(q),strat->tailRing));
  assume(p_LmCheckIsFromRing(p,currRing));
  assume(p_CheckIsFromRing(pNext(p),strat->tailRing));
 
  /* poly q stays for s[i], ecartq = ecart(q), qisFromQ = applies to q */
 
  int qfromQ = qisFromQ;
 
  /* need additionally: int up_to_degree, poly V0 with the variables in (0)  or just the number lV = the length of the first block */
 
  int      l,j,compare;
  LObject  Lp;
  Lp.i_r = -1;
 
#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = p_Lcm(p,q, currRing); // q is what was strat->S[i], so a poly in LM/TR presentation
 
  /* the V criterion */
  if (!pmIsInV(Lp.lcm))
  {
    strat->cv++; // counter for applying the V criterion
    pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
    if (TEST_OPT_DEBUG) PrintS("--- V crit\n");
#endif
    return TRUE;
  }
 
  if (strat->sugarCrit && ALLOW_PROD_CRIT(strat))
  {
    if((!((ecartq>0)&&(ecart>0)))
    && pHasNotCF(p,q))
    {
    /*
    *the product criterion has applied for (s,p),
    *i.e. lcm(s,p)=product of the leading terms of s and p.
    *Suppose (s,r) is in L and the leading term
    *of p divides lcm(s,r)
    *(==> the leading term of p divides the leading term of r)
    *but the leading term of s does not divide the leading term of r
    *(notice that this condition is automatically satisfied if r is still
    *in S), then (s,r) can be cancelled.
    *This should be done here because the
    *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
    *
    *Moreover, skipping (s,r) holds also for the noncommutative case.
    */
      strat->cp++;
      pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
      if (TEST_OPT_DEBUG) PrintS("--- prod crit\n");
#endif
      return TRUE;
    }
    else
      Lp.ecart = si_max(ecart,ecartq);
    if (strat->fromT && (ecartq>ecart))
    {
      pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
      if (TEST_OPT_DEBUG) PrintS("--- ecartq > ecart\n");
#endif
      return TRUE;
      /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
    }
    /*
    *the set B collects the pairs of type (S[j],p)
    *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
    *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
    */
    {
      j = strat->Bl;
      loop
      {
        if (j < 0)  break;
        compare=pLPDivComp(strat->B[j].lcm,Lp.lcm);
        if ((compare==1)
        &&(sugarDivisibleBy(strat->B[j].ecart,Lp.ecart)))
        {
          strat->c3++;
          if ((strat->fromQ==NULL) || (isFromQ==0) || (qfromQ==0))
          {
            pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
            if (TEST_OPT_DEBUG)
            {
              Print("--- chain crit using B[%d].lcm=%s\n", j, pString(strat->B[j].lcm));
            }
#endif
            return TRUE;
          }
          break;
        }
        else
        if ((compare ==-1)
        && sugarDivisibleBy(Lp.ecart,strat->B[j].ecart))
        {
#ifdef CRITERION_DEBUG
          if (TEST_OPT_DEBUG)
          {
            Print("--- chain crit using pair to remove B[%d].lcm=%s\n", j, pString(strat->B[j].lcm));
          }
#endif
          deleteInL(strat->B,&strat->Bl,j,strat);
          strat->c3++;
        }
        j--;
      }
    }
  }
  else /*sugarcrit*/
  {
    if (ALLOW_PROD_CRIT(strat))
    {
      // if currRing->nc_type!=quasi (or skew)
      // TODO: enable productCrit for super commutative algebras...
      if(/*(strat->ak==0) && productCrit(p,strat->S[i])*/
      pHasNotCF(p,q))
      {
      /*
      *the product criterion has applied for (s,p),
      *i.e. lcm(s,p)=product of the leading terms of s and p.
      *Suppose (s,r) is in L and the leading term
      *of p divides lcm(s,r)
      *(==> the leading term of p divides the leading term of r)
      *but the leading term of s does not divide the leading term of r
      *(notice that tis condition is automatically satisfied if r is still
      *in S), then (s,r) can be canceled.
      *This should be done here because the
      *case lcm(s,r)=lcm(s,p) is not covered by chainCrit.
      */
          strat->cp++;
          pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
          if (TEST_OPT_DEBUG) PrintS("--- prod crit\n");
#endif
          return TRUE;
      }
      if (strat->fromT && (ecartq>ecart))
      {
        pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
        if (TEST_OPT_DEBUG) PrintS("--- ecartq > ecart\n");
#endif
        return TRUE;
        /*the pair is (s[i],t[.]), discard it if the ecart is too big*/
      }
      /*
      *the set B collects the pairs of type (S[j],p)
      *suppose (r,p) is in B and (s,p) is the new pair and lcm(s,p)#lcm(r,p)
      *if the leading term of s divides lcm(r,p) then (r,p) will be canceled
      *if the leading term of r divides lcm(s,p) then (s,p) will not enter B
      */
      for(j = strat->Bl;j>=0;j--)
      {
        compare=pLPDivComp(strat->B[j].lcm,Lp.lcm);
        if (compare==1)
        {
          strat->c3++;
          if ((strat->fromQ==NULL) || (isFromQ==0) || (qfromQ==0))
          {
            pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
            if (TEST_OPT_DEBUG)
            {
              Print("--- chain crit using B[%d].lcm=%s\n", j, pString(strat->B[j].lcm));
            }
#endif
            return TRUE;
          }
          break;
        }
        else
        if (compare ==-1)
        {
#ifdef CRITERION_DEBUG
          if (TEST_OPT_DEBUG)
          {
            Print("--- chain crit using pair to remove B[%d].lcm=%s\n", j, pString(strat->B[j].lcm));
          }
#endif
          deleteInL(strat->B,&strat->Bl,j,strat);
          strat->c3++;
        }
      }
    }
  }
  /*
  *the pair (S[i],p) enters B if the spoly != 0
  */
  /*-  compute the short s-polynomial -*/
  if (strat->fromT && !TEST_OPT_INTSTRATEGY)
    pNorm(p);
  if ((q==NULL) || (p==NULL))
  {
#ifdef CRITERION_DEBUG
    if (TEST_OPT_DEBUG) PrintS("--- q == NULL || p == NULL\n");
#endif
    return FALSE;
  }
  if ((strat->fromQ!=NULL) && (isFromQ!=0) && (qfromQ!=0))
  {
    Lp.p=NULL;
#ifdef CRITERION_DEBUG
    if (TEST_OPT_DEBUG) PrintS("--- pair is from Q\n");
#endif
  }
  else
  {
//     if ( rIsPluralRing(currRing) )
//     {
//       if(pHasNotCF(p, q))
//       {
//         if(ncRingType(currRing) == nc_lie)
//         {
//             // generalized prod-crit for lie-type
//             strat->cp++;
//             Lp.p = nc_p_Bracket_qq(pCopy(p),q, currRing);
//         }
//         else
//         if( ALLOW_PROD_CRIT(strat) )
//         {
//             // product criterion for homogeneous case in SCA
//             strat->cp++;
//             Lp.p = NULL;
//         }
//         else
//           Lp.p = nc_CreateSpoly(q,p,currRing); // ?
//       }
//       else  Lp.p = nc_CreateSpoly(q,p,currRing);
//     }
//     else
//     {
 
    /* ksCreateShortSpoly needs two Lobject-kind presentations */
    /* p is already in this form, so convert q */
    Lp.p = ksCreateShortSpoly(q, p, strat->tailRing);
      //  }
  }
  if (Lp.p == NULL)
  {
    /*- the case that the s-poly is 0 -*/
    // TODO: currently ifromS is only > 0 if called from enterOnePairWithShifts
    if (ifromS > 0)
    {
      if (strat->pairtest==NULL) initPairtest(strat);
      strat->pairtest[ifromS] = TRUE;/*- hint for spoly(S^[i],p)=0 -*/
      strat->pairtest[strat->sl+1] = TRUE;
    }
      //if (TEST_OPT_DEBUG){Print("!");} // option teach
    /* END _ TEMPORARILY DISABLED FOR SHIFTS */
    /*hint for spoly(S[i],p) == 0 for some i,0 <= i <= sl*/
    /*
    *suppose we have (s,r),(r,p),(s,p) and spoly(s,p) == 0 and (r,p) is
    *still in B (i.e. lcm(r,p) == lcm(s,p) or the leading term of s does not
    *divide lcm(r,p)). In the last case (s,r) can be canceled if the leading
    *term of p divides the lcm(s,r)
    *(this canceling should be done here because
    *the case lcm(s,p) == lcm(s,r) is not covered in chainCrit)
    *the first case is handled in chainCrit
    */
    if (Lp.lcm!=NULL) pLmFree(Lp.lcm);
#ifdef CRITERION_DEBUG
    if (TEST_OPT_DEBUG) PrintS("--- S-poly = 0\n");
#endif
    return TRUE;
  }
  else
  {
    /*- the pair (S[i],p) enters B -*/
    /* both of them should have their LM in currRing and TAIL in tailring */
    Lp.p1 = q;  // already in the needed form
    Lp.p2 = p; // already in the needed form
 
    if ( !rIsPluralRing(currRing) )
      pNext(Lp.p) = strat->tail;
 
    /* TEMPORARILY DISABLED FOR SHIFTS because there's no i*/
    /* at the beginning we DO NOT set atR = -1 ANYMORE*/
    if ( (atR >= 0) && (shiftcount==0) && (ifromS >=0) )
    {
      Lp.i_r1 = kFindInT(Lp.p1,strat); //strat->S_2_R[ifromS];
      Lp.i_r2 = atR;
    }
    else
    {
      /* END _ TEMPORARILY DISABLED FOR SHIFTS */
      Lp.i_r1 = -1;
      Lp.i_r2 = -1;
     }
    strat->initEcartPair(&Lp,q,p,ecartq,ecart);
 
    if (TEST_OPT_INTSTRATEGY)
    {
      if (!rIsPluralRing(currRing)
      && !rField_is_Ring(currRing)
      && (Lp.p->coef!=NULL))
        nDelete(&(Lp.p->coef));
    }
 
    l = strat->posInL(strat->B,strat->Bl,&Lp,strat);
    enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
#ifdef CRITERION_DEBUG
    if (TEST_OPT_DEBUG) PrintS("+++ Entered pair\n");
#endif
  }
  return FALSE;
}
#endif
 
/*3
*(s[0], s \dot h),...,(s[k],s \dot h) will be put to the pairset L
* also the pairs (h, s\dot s[0]), ..., (h, s\dot s[k]) enter L
* additionally we put the pairs (h, s \sdot h) for s>=1 to L
*/
#ifdef HAVE_SHIFTBBA
void initenterpairsShift (poly h,int k,int ecart,int isFromQ, kStrategy strat, int atR)
{
  int h_lastVblock = pmLastVblock(h);
  assume(h_lastVblock != 0 || pLmIsConstantComp(h));
  // TODO: is it allowed to skip pairs with constants? also with constants from other components?
  if (h_lastVblock == 0) return;
  assume(pmFirstVblock(h) == 1);
  /* h comes from strat->P.p, that is LObject with LM in currRing and Tail in tailRing */
  //  atR = -1;
  if ((strat->syzComp==0)
  || (pGetComp(h)<=strat->syzComp))
  {
    int i,j;
    BOOLEAN new_pair=FALSE;
 
    int degbound = currRing->N/currRing->isLPring;
    int maxShift = degbound - h_lastVblock;
 
    if (pGetComp(h)==0)
    {
      if (strat->rightGB)
      {
        if (isFromQ)
        {
          // pairs (shifts(h),s[1..k]), (h, s[1..k])
          for (i=0; i<=maxShift; i++)
          {
            poly hh = pLPCopyAndShiftLM(h, i);
            BOOLEAN delete_hh=TRUE;
            for (j=0; j<=k; j++)
            {
              if (strat->fromQ == NULL || !strat->fromQ[j])
              {
                new_pair=TRUE;
                poly s = strat->S[j];
                if (!enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, pmLastVblock(s), i))
                  delete_hh=FALSE;
              }
            }
            if (delete_hh) pLmDelete(hh);
          }
        }
        else
        {
          new_pair=TRUE;
          for (j=0; j<=k; j++)
          {
            poly s = strat->S[j];
            if (strat->fromQ != NULL && strat->fromQ[j])
            {
              // pairs (shifts(s[j]),h), (s[j],h)
              enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
            }
            else
            {
              // pair (h, s[j])
              enterOnePairWithoutShifts(j, h, s, ecart, isFromQ, strat, atR, pmLastVblock(s), 0);
            }
          }
        }
      }
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      else if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          if (!strat->fromQ[j])
          {
            new_pair=TRUE;
            poly s = strat->S[j];
            enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
          }
        }
        // pairs (shifts(h),s[1..k])
        if (new_pair)
        {
          for (i=1; i<=maxShift; i++)
          {
            BOOLEAN delete_hh=TRUE;
            poly hh = pLPCopyAndShiftLM(h, i);
            for (j=0; j<=k; j++)
            {
              if (!strat->fromQ[j])
              {
                poly s = strat->S[j];
                int s_lastVblock = pmLastVblock(s);
                if (i < s_lastVblock || (pGetComp(s) > 0 && i == s_lastVblock)) // in the module case, product criterion does not hold (note: comp h is always zero here)
                {
                  if(!enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, s_lastVblock, i))
                    delete_hh=FALSE;
                }
                else if (rField_is_Ring(currRing))
                {
                  assume(i >= s_lastVblock); // this is always the case, but just to be very sure
                  ideal fillers = id_MaxIdeal(i - s_lastVblock, currRing);
                  for (int k = 0; k < IDELEMS(fillers); k++)
                  {
                    poly hhh = pLPCopyAndShiftLM(pp_mm_Mult(h, fillers->m[k], currRing), s_lastVblock);
                    enterOnePairWithoutShifts(j, hhh, s, ecart, isFromQ, strat, atR, s_lastVblock, s_lastVblock);
                  }
                  idDelete(&fillers);
                }
              }
            }
            if (delete_hh) p_LmDelete(hh,currRing);
          }
        }
      }
      else
      {
        new_pair=TRUE;
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          poly s = strat->S[j];
          enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
        }
        // pairs (shifts(h),s[1..k]), (shifts(h), h)
        for (i=1; i<=maxShift; i++)
        {
          poly hh = pLPCopyAndShiftLM(h, i);
          BOOLEAN delete_hh=TRUE;
          for (j=0; j<=k; j++)
          {
            poly s = strat->S[j];
            int s_lastVblock = pmLastVblock(s);
            if (i < s_lastVblock || (pGetComp(s) > 0 && i == s_lastVblock)) // in the module case, product criterion does not hold (note: comp h is always zero here)
              delete_hh=enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, s_lastVblock, i)
                && delete_hh;
            else if (rField_is_Ring(currRing))
            {
              assume(i >= s_lastVblock); // this is always the case, but just to be very sure
              ideal fillers = id_MaxIdeal(i - s_lastVblock, currRing);
              for (int k = 0; k < IDELEMS(fillers); k++)
              {
                poly hhh = pLPCopyAndShiftLM(pp_mm_Mult(h, fillers->m[k], currRing), s_lastVblock);
                enterOnePairWithoutShifts(j, hhh, s, ecart, isFromQ, strat, atR, s_lastVblock, s_lastVblock);
              }
              idDelete(&fillers);
            }
          }
          if (i < h_lastVblock) // in the module case, product criterion does not hold (note: comp h is always zero here)
            delete_hh=enterOnePairWithoutShifts(-1, hh, h, ecart, isFromQ, strat, atR, h_lastVblock, i)
              && delete_hh;
          else if (rField_is_Ring(currRing))
          {
            assume(i >= h_lastVblock); // this is always the case, but just to be very sure
            ideal fillers = id_MaxIdeal(i - h_lastVblock, currRing);
            for (int k = 0; k < IDELEMS(fillers); k++)
            {
              poly hhh = pLPCopyAndShiftLM(pp_mm_Mult(h, fillers->m[k], currRing), h_lastVblock);
              enterOnePairWithoutShifts(-1, hhh, h, ecart, isFromQ, strat, atR, h_lastVblock, h_lastVblock);
            }
            idDelete(&fillers);
          }
          if (delete_hh) pLmDelete(hh);
        }
      }
    }
    else
    {
      assume(isFromQ == 0); // an element from Q should always has 0 component
      new_pair=TRUE;
      if (strat->rightGB)
      {
        for (j=0; j<=k; j++)
        {
          if ((pGetComp(h)==pGetComp(strat->S[j]))
              || (pGetComp(strat->S[j])==0))
          {
            poly s = strat->S[j];
            if (strat->fromQ != NULL && strat->fromQ[j])
            {
              // pairs (shifts(s[j]),h), (s[j],h)
              enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
            }
            else
            {
              // pair (h, s[j])
              enterOnePairWithoutShifts(j, h, s, ecart, isFromQ, strat, atR, pmLastVblock(s), 0);
            }
          }
        }
      }
      else
      {
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          if ((pGetComp(h)==pGetComp(strat->S[j]))
              || (pGetComp(strat->S[j])==0))
          {
            poly s = strat->S[j];
            enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
          }
        }
        // pairs (shifts(h),s[1..k]), (shifts(h), h)
        for (i=1; i<=maxShift; i++)
        {
          poly hh = pLPCopyAndShiftLM(h, i);
          for (j=0; j<=k; j++)
          {
            if ((pGetComp(h)==pGetComp(strat->S[j]))
                || (pGetComp(strat->S[j])==0))
            {
              poly s = strat->S[j];
              int s_lastVblock = pmLastVblock(s);
              if (i <= s_lastVblock) // in the module case, product criterion does not hold
                enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, s_lastVblock, i);
              else if (rField_is_Ring(currRing))
              {
                assume(i >= s_lastVblock); // this is always the case, but just to be very sure
                ideal fillers = id_MaxIdeal(i - s_lastVblock, currRing);
                for (int k = 0; k < IDELEMS(fillers); k++)
                {
                  poly hhh = pLPCopyAndShiftLM(pp_mm_Mult(h, fillers->m[k], currRing), s_lastVblock);
                  enterOnePairWithoutShifts(j, hhh, s, ecart, isFromQ, strat, atR, s_lastVblock, s_lastVblock);
                }
                idDelete(&fillers);
              }
            }
          }
          if (i <= h_lastVblock) // in the module case, product criterion does not hold
            enterOnePairWithoutShifts(-1, hh, h, ecart, isFromQ, strat, atR, h_lastVblock, i);
          else if (rField_is_Ring(currRing))
          {
            assume(i >= h_lastVblock); // this is always the case, but just to be very sure
            ideal fillers = id_MaxIdeal(i - h_lastVblock, currRing);
            for (int k = 0; k < IDELEMS(fillers); k++)
            {
              BOOLEAN delete_hhh=TRUE;
              poly hhh = pLPCopyAndShiftLM(pp_mm_Mult(h, fillers->m[k], currRing), h_lastVblock);
              if(!enterOnePairWithoutShifts(-1, hhh, h, ecart, isFromQ, strat, atR, h_lastVblock, h_lastVblock))
                delete_hhh=FALSE;
              if (delete_hhh) p_LmDelete(hhh,currRing);
            }
            idDelete(&fillers);
          }
        }
      }
    }
 
    if (new_pair)
    {
      strat->chainCrit(h,ecart,strat);
    }
    kMergeBintoL(strat);
  }
}
#endif
 
/*3
*(s[0], s \dot h),...,(s[k],s \dot h) will be put to the pairset L
* also the pairs (h, s\dot s[0]), ..., (h, s\dot s[k]) enter L
* additionally we put the pairs (h, s \sdot h) for s>=1 to L
*/
#ifdef HAVE_SHIFTBBA
void initenterstrongPairsShift (poly h,int k,int ecart,int isFromQ, kStrategy strat, int atR)
{
  int h_lastVblock = pmLastVblock(h);
  assume(h_lastVblock != 0 || pLmIsConstantComp(h));
  // TODO: is it allowed to skip pairs with constants? also with constants from other components?
  if (h_lastVblock == 0) return;
  assume(pmFirstVblock(h) == 1);
  /* h comes from strat->P.p, that is LObject with LM in currRing and Tail in tailRing */
  //  atR = -1;
  if ((strat->syzComp==0)
  || (pGetComp(h)<=strat->syzComp))
  {
    int i,j;
    BOOLEAN new_pair=FALSE;
 
    int degbound = currRing->N/currRing->isLPring;
    int maxShift = degbound - h_lastVblock;
 
    if (pGetComp(h)==0)
    {
      if (strat->rightGB)
      {
        if (isFromQ)
        {
          // pairs (shifts(h),s[1..k]), (h, s[1..k])
          for (i=0; i<=maxShift; i++)
          {
            poly hh = pLPCopyAndShiftLM(h, i);
            for (j=0; j<=k; j++)
            {
              if (strat->fromQ == NULL || !strat->fromQ[j])
              {
                new_pair=TRUE;
                poly s = strat->S[j];
                enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, pmLastVblock(s), i);
              }
            }
          }
        }
        else
        {
          new_pair=TRUE;
          for (j=0; j<=k; j++)
          {
            poly s = strat->S[j];
            if (strat->fromQ != NULL && strat->fromQ[j])
            {
              // pairs (shifts(s[j]),h), (s[j],h)
              enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
            }
            else
            {
              // pair (h, s[j])
              enterOnePairWithoutShifts(j, h, s, ecart, isFromQ, strat, atR, pmLastVblock(s), 0);
            }
          }
        }
      }
      /* for Q!=NULL: build pairs (f,q),(f1,f2), but not (q1,q2)*/
      else if ((isFromQ)&&(strat->fromQ!=NULL))
      {
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          if (!strat->fromQ[j])
          {
            new_pair=TRUE;
            poly s = strat->S[j];
            enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
          }
        }
        // pairs (shifts(h),s[1..k])
        if (new_pair)
        {
          for (i=1; i<=maxShift; i++)
          {
            poly hh = pLPCopyAndShiftLM(h, i);
            for (j=0; j<=k; j++)
            {
              if (!strat->fromQ[j])
              {
                poly s = strat->S[j];
                enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, pmLastVblock(s), i);
              }
            }
          }
        }
      }
      else
      {
        new_pair=TRUE;
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          poly s = strat->S[j];
          // TODO: cache lastVblock of s[1..k] for later use
          enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
        }
        // pairs (shifts(h),s[1..k]), (shifts(h), h)
        for (i=1; i<=maxShift; i++)
        {
          poly hh = pLPCopyAndShiftLM(h, i);
          BOOLEAN delete_hh=TRUE;
          for (j=0; j<=k; j++)
          {
            poly s = strat->S[j];
            if(!enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, pmLastVblock(s), i))
              delete_hh=FALSE;
          }
          if(!enterOnePairWithoutShifts(-1, hh, h, ecart, isFromQ, strat, atR, h_lastVblock, i))
            delete_hh=FALSE;
          if (delete_hh) p_LmDelete(hh,currRing);
        }
      }
    }
    else
    {
      new_pair=TRUE;
      if (strat->rightGB)
      {
        for (j=0; j<=k; j++)
        {
          if ((pGetComp(h)==pGetComp(strat->S[j]))
              || (pGetComp(strat->S[j])==0))
          {
            assume(isFromQ == 0); // this case is not handled here and should also never happen
            poly s = strat->S[j];
            if (strat->fromQ != NULL && strat->fromQ[j])
            {
              // pairs (shifts(s[j]),h), (s[j],h)
              enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
            }
            else
            {
              // pair (h, s[j])
              enterOnePairWithoutShifts(j, h, s, ecart, isFromQ, strat, atR, pmLastVblock(s), 0);
            }
          }
        }
      }
      else
      {
        // pairs (shifts(s[1..k]),h), (s[1..k],h)
        for (j=0; j<=k; j++)
        {
          if ((pGetComp(h)==pGetComp(strat->S[j]))
              || (pGetComp(strat->S[j])==0))
          {
            poly s = strat->S[j];
            enterOnePairWithShifts(j, s, h, ecart, isFromQ, strat, atR, h_lastVblock, pmLastVblock(s));
          }
        }
        // pairs (shifts(h),s[1..k]), (shifts(h), h)
        for (i=1; i<=maxShift; i++)
        {
          poly hh = pLPCopyAndShiftLM(h, i);
          for (j=0; j<=k; j++)
          {
            if ((pGetComp(h)==pGetComp(strat->S[j]))
                || (pGetComp(strat->S[j])==0))
            {
              poly s = strat->S[j];
              enterOnePairWithoutShifts(j, hh, s, ecart, isFromQ, strat, atR, pmLastVblock(s), i);
            }
          }
          enterOnePairWithoutShifts(-1, hh, h, ecart, isFromQ, strat, atR, h_lastVblock, i);
        }
      }
    }
 
    if (new_pair)
    {
      strat->chainCrit(h,ecart,strat);
    }
    kMergeBintoL(strat);
  }
}
#endif
 
/*2
*(s[0],h),...,(s[k],h) will be put to the pairset L(via initenterpairs)
*superfluous elements in S will be deleted
*/
#ifdef HAVE_SHIFTBBA
void enterpairsShift (poly h,int k,int ecart,int pos,kStrategy strat, int atR)
{
  /* h is strat->P.p, that is LObject with LM in currRing and Tail in tailRing */
  /* Q: what is exactly the strat->fromT ? A: a local case trick; don't need it yet*/
  int j=pos;
 
  /* if (!(rField_is_Domain(currRing))) enterExtendedSpoly(h, strat); */ // TODO: enterExtendedSpoly not for LP yet
  initenterpairsShift(h,k,ecart,0,strat, atR);
  if ( (!strat->fromT)
  && ((strat->syzComp==0)
    ||(pGetComp(h)<=strat->syzComp)))
  {
    unsigned long h_sev = pGetShortExpVector(h);
    loop
    {
      if (j > k) break;
      // TODO this currently doesn't clear all possible elements because of commutative division
      if (!(strat->rightGB && strat->fromQ != NULL && strat->fromQ[j]))
        clearS(h,h_sev, &j,&k,strat);
      j++;
    }
  }
}
#endif
 
/*2
* enteres all admissible shifts of p into T
* assumes that p is already in T!
*/
#ifdef HAVE_SHIFTBBA
void enterTShift(LObject p, kStrategy strat, int atT)
{
  /* determine how many elements we have to insert */
  /* x(0)y(1)z(2) : lastVblock-1=2, to add until lastVblock=uptodeg-1 */
  /* hence, a total number of elt's to add is: */
  /*  int toInsert = 1 + (uptodeg-1) - (pLastVblock(p.p, lV) -1);  */
  pAssume(p.p != NULL);
 
  int maxPossibleShift = p_mLPmaxPossibleShift(p.p, strat->tailRing);
 
  for (int i = 1; i <= maxPossibleShift; i++)
  {
    LObject qq;
    qq.p = pLPCopyAndShiftLM(p.p, i); // don't use Set() because it'll test the poly order
    qq.shift = i;
    strat->initEcart(&qq); // initEcartBBA sets length, pLength, FDeg and ecart
 
    enterT(qq, strat, atT); // enterT is modified, so it doesn't copy and delete the tail of shifted polys
  }
}
#endif
 
#ifdef HAVE_SHIFTBBA
poly redtailBbaShift (LObject* L, int pos, kStrategy strat, BOOLEAN withT, BOOLEAN normalize)
{
  /* for the shift case need to run it with withT = TRUE */
  strat->redTailChange=FALSE;
  if (strat->noTailReduction) return L->GetLmCurrRing();
  poly h, p;
  p = h = L->GetLmTailRing();
  if ((h==NULL) || (pNext(h)==NULL))
    return L->GetLmCurrRing();
 
  TObject* With;
  // placeholder in case strat->tl < 0
  TObject  With_s(strat->tailRing);
 
  LObject Ln(pNext(h), strat->tailRing);
  Ln.pLength = L->GetpLength() - 1;
 
  pNext(h) = NULL;
  if (L->p != NULL) pNext(L->p) = NULL;
  L->pLength = 1;
 
  Ln.PrepareRed(strat->use_buckets);
 
  while(!Ln.IsNull())
  {
    loop
    {
      Ln.SetShortExpVector();
      if (withT)
      {
        int j;
        j = kFindDivisibleByInT(strat, &Ln);
        if (j < 0) break;
        With = &(strat->T[j]);
      }
      else
      {
        With = kFindDivisibleByInS_T(strat, pos, &Ln, &With_s);
        if (With == NULL) break;
      }
      if (normalize && (!TEST_OPT_INTSTRATEGY) && (!nIsOne(pGetCoeff(With->p))))
      {
        With->pNorm();
        //if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
      }
      strat->redTailChange=TRUE;
      if (ksReducePolyTail(L, With, &Ln))
      {
        // reducing the tail would violate the exp bound
        //  set a flag and hope for a retry (in bba)
        strat->completeReduce_retry=TRUE;
        if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
        do
        {
          pNext(h) = Ln.LmExtractAndIter();
          pIter(h);
          L->pLength++;
        } while (!Ln.IsNull());
        goto all_done;
      }
      if (Ln.IsNull()) goto all_done;
      if (! withT) With_s.Init(currRing);
    }
    pNext(h) = Ln.LmExtractAndIter();
    pIter(h);
    L->pLength++;
  }
 
  all_done:
  Ln.Delete();
  if (L->p != NULL) pNext(L->p) = pNext(p);
 
  if (strat->redTailChange)
  {
    L->length = 0;
  }
  L->Normalize(); // HANNES: should have a test
  kTest_L(L,strat);
  return L->GetLmCurrRing();
}
#endif