source: git/Singular/kutil.cc @ e2f1c7

/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/* $Id: kutil.cc,v 1.4 1997-04-08 16:49:21 Singular Exp $ */
/*
* ABSTRACT: kernel: utils for std
*/

#include <stdlib.h>
#include <string.h>
#include "mod2.h"
#include "tok.h"
#include "febase.h"
#include "spolys.h"
#include "mmemory.h"
#include "numbers.h"
#include "polys.h"
#include "ipid.h"
#include "ideals.h"
#include "timer.h"
#include "cntrlc.h"
#include "stairc.h"
#include "subexpr.h"
#include "kstd1.h"
#include "kutil.h"
//#include "longrat.h"

static poly redMora (poly h,int maxIndex,kStrategy strat);
static poly redBba (poly h,int maxIndex,kStrategy strat);

//int     cp, c3;
//BOOLEAN interpt;
//BOOLEAN news=FALSE;
//static BOOLEAN newt=FALSE;/*used for messageSets*/
BITSET  test=(BITSET)0;
//int     ak;
//int     syzComp=0;
int     HCord;
//LObject P;
//poly    tail;
//BOOLEAN *pairtest;/*used for enterOnePair*/
//int    // LazyPass=100,
//        LazyDegree=1;
int        Kstd1_deg;
int        mu=32000;

//polyset S;
//int     sl;
//ideal   Shdl;
//intset  ecartS;
//intset  fromQ;

//TSet    T;
//int     tl;
//int     tmax;

//LSet    L;
//int     Ll;
//int     Lmax;

//LSet    B;
//int     Bl;
//int     Bmax;

//BOOLEAN kActive=FALSE;
//BOOLEAN fromT = FALSE;
//BOOLEAN honey, sugarCrit;/*option 5*/
//BOOLEAN Gebauer;
//BOOLEAN * NotUsedAxis;
//BOOLEAN homog;
//BOOLEAN noTailReduction = FALSE;

/*0 implementation*/
/*
*static void deleteHCn(poly* p)
*{
*  poly p1;
*  if (pHEdgeFound && (*p))
*  {
*    if (pComp0(*p,pNoether) == -1)
*    {
*      pDelete(p);
*      return;
*    }
*    p1 = *p;
*    while (pNext(p1))
*    {
*      if (pComp0(pNext(p1), pNoether) == -1) pDelete(&pNext(p1));
*      else                                  pIter(p1);
*    }
*  }
*}
*/

/*2
*deletes higher monomial of p, re-compute ecart and length
*works only for orderings with ecart =pFDeg(end)-pFDeg(start)
*/
void deleteHC(poly* p, int* e, int* l,kStrategy strat)
{
  poly p1;

  if (strat->kHEdgeFound)
  {
    if (pComp(*p,strat->kNoether) == -1)
    {
      pDelete(p);
      *l = 0;
      *e = -1;
      return;
    }
    p1 = *p;
    while (pNext(p1))
    {
      if (pComp0(pNext(p1), strat->kNoether) == -1)
        pDelete(&pNext(p1));
      else
        pIter(p1);
      *e = pLDeg(*p,l)-pFDeg(*p);
    }
  }
}

/*2
*tests if p.p=monomial*unit and cancels the unit
*/
void cancelunit (LObject* p)
{
  int  i;
  poly h;

  if(!pIsVector((*p).p) && ((*p).ecart != 0))
  {
    h = pNext(((*p).p));
    loop
    {
      if (!h)
      {
        pDelete(&(pNext((*p).p)));
        (*p).ecart = 0;
        (*p).length = 1;
        return;
      }
      i = 0;
      loop
      {
        i++;
        if (pGetExp((*p).p,i) > pGetExp(h,i)) return ;
        if (i == pVariables) break;
      }
      pIter(h);
    }
  }
}

/*2
*pp is the new element in s
*returns TRUE (in strat->kHEdgeFound) 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->kHEdgeFound==FALSE !
*/
void HEckeTest (poly pp,kStrategy strat)
{
  int   j,k,p;

  strat->kHEdgeFound=FALSE;
  if (pLexOrder)
  {
    return;
  }
  if (strat->ak > 1)           /*we are in the module case*/
  {
    return; // until ....
    //if (!pVectorOut)     /*pVectorOut <=> order = c,* */
    //  return FALSE;
    //if (pGetComp(pp) < strat->ak) /* ak is the number of the last component */
    //  return FALSE;
  }
  k = 0;
  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=pVariables;j>0; j--)
  {
    if (strat->NotUsedAxis[j])
    {
      return;
    }
  }
  strat->kHEdgeFound=TRUE;
}

/*2
*utilities for TSet, LSet
*/
inline intset initec (int maxnr)
{
  return (intset)Alloc(maxnr*sizeof(int));
}

void enlargeT (TSet* T,int* length,int incr)
{
  TSet h;

  h = (TSet)Alloc(((*length)+incr)* sizeof(TObject));
  /*for (i=0; i<=(*length)-1; i++) h[i] = (*T)[i];*/
  memcpy(h, *T, (*length) * sizeof(TObject));
  Free((ADDRESS)*T,((*length)*sizeof(TObject)));
  *T = h;
  (*length) += incr;
}

void cleanT (kStrategy strat)
{
  int i,j;
  poly  p;

  for (j=0; j<=strat->tl; j++)
  {
    p = strat->T[j].p;
//    pTest(p);
    strat->T[j].p=NULL;
    i = -1;
    loop
    {
      i++;
      if (i>strat->sl)
      {
        pDelete(&p);
        break;
      }
      if (p == strat->S[i])
      {
        break;
      }
    }
  }
  strat->tl=-1;
}

LSet initL ()
{
  return (LSet)Alloc(setmax*sizeof(LObject));
}

void enlargeL (LSet* L,int* length,int incr)
{
  LSet h;

  h = (LSet)Alloc(((*length)+incr)*sizeof(LObject));
  /*for (i=0; i<(*length); i++) h[i] = (*L)[i];*/
  memcpy(h, *L, (*length) * sizeof(LObject));
  Free((ADDRESS)*L,((*length)*sizeof(LObject)));
  *L = h;
  (*length) += incr;
}

void initPairtest(kStrategy strat)
{
  strat->pairtest = (BOOLEAN *)Alloc0((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--;
  }
}

/*2
*in B all pairs have the same element p on the right
*it tests whether (q,p) is in B and returns TRUE if yes
*and the position k
*/
BOOLEAN isInPairsetB(poly q,int*  k,kStrategy strat)
{
  LObject *p=&(strat->B[strat->Bl]);

  *k = strat->Bl;
  loop
  {
    if ((*k) < 0) return FALSE;
    if (q == (*p).p1)
      return TRUE;
    (*k)--;
    p--;
  }
}

#ifdef KDEBUG
void K_Test (char *f, int l,kStrategy strat)
{
/*2
*tests, if there is some wrong (deleted) in the set s or in pairs from L
*/
  int i;
  /*- test pair P -*/
  pDBTest(strat->P.p1,f,l);
  pDBTest(strat->P.p2,f,l);
  // pDBTest(strat->P.lcm,f,l);
  /*- test set s -*/
  if ((strat->S!=NULL) && (strat->sl>=0))
  {
    for (i=0; i<=strat->sl; i++)
    {
      pDBTest(strat->S[i],f,l);
//      if(currQuotient==NULL)
//      {
//        if ((strat->ak!=0)
//        && (pGetComp(strat->S[i])==0))
//        {
//          Print("wrong comp. S (0) in %s:%d\n",f,l);
//        }
//        else
//        {
//          if (pGetComp(strat->S[i])!=0)
//            Print("wrong comp. S (%d) in %s:%d\n",pGetComp(strat->S[i]),f,l);
//        }
//      }
    }  
  }
  /*- test set L -*/
  if ((strat->L!=NULL) && (strat->Ll>=0))
  {
    for (i=0; i<=strat->Ll; i++)
    {
      pDBTest(strat->L[i].p1,f,l);
      pDBTest(strat->L[i].p2,f,l);
      int j,f=0;
      for(j=0;j<=strat->tl;j++)
      {

        if((strat->L[i].p1==NULL)
        ||(strat->L[i].p1==strat->T[j].p))
        {
          f=1;
          break;
        }
      }
      if((f==0)&&(strat->L[i].p1!=NULL))
        Print("L[%d].p1(%x) not in T ?\n",i,strat->L[i].p1);
      f=0;
      for(j=0;j<=strat->tl;j++)
      {
        if((strat->L[i].p2==NULL)
        ||(strat->L[i].p2==strat->T[j].p))
        {
          f=1;
          break;
        }
      }
      if((f==0)&&(strat->L[i].p2!=NULL))
        Print("L[%d].p2(%x) not in T ?\n",i,strat->L[i].p2);
      //pDBTest(strat->L[i].lcm,f,l);
    }
  }
/*
*  #*- test set B -*#
*  for (i=0; i<=strat->Bl; i++)
*  {
*    if (strat->B[i].p1 == (*p)) return ;
*    if (strat->B[i].p2 == (*p)) return ;
*  }
*/
  /*- test set T -*/
  if ((strat->T!=NULL) && (strat->tl>=0))
  {
    for (i=0; i<=strat->tl; i++)
    {
      pDBTest(strat->T[i].p,f,l);
//      if(currQuotient==NULL)
//      {
//        if ((strat->ak!=0)
//        && (pGetComp(strat->T[i].p)==0))
//        {
//          Print("wrong comp. T (0) in %s:%d\n",f,l);
//        }
//        else
//        {
//          if (pGetComp(strat->T[i].p)!=0)
//            Print("wrong comp. T (%d) in %s:%d\n",pGetComp(strat->T[i].p),f,l);
//        }
//      }
    }
  }
#ifdef PDEBUG
  idDBTest(strat->Shdl,f,l);
  if (strat->D!=NULL) idDBTest(strat->D,f,l);
#endif
}
#endif

/*2
*cancels the i-th polynomial in the standardbase s
*/
void deleteInS (int i,kStrategy strat)
{
  int j;

  for (j=i; j<strat->sl; j++)
  {
    strat->S[j] = strat->S[j+1];
    strat->ecartS[j] = strat->ecartS[j+1];
  }
  if (strat->fromQ!=NULL)
  {
    for (j=i; j<strat->sl; j++)
    {
      strat->fromQ[j] = strat->fromQ[j+1];
    }
  }
  strat->S[strat->sl] = NULL;
  strat->sl--;
}

/*2
*cancels the i-th polynomial in the set
*/
void deleteInL (LSet set, int *length, int j,kStrategy strat)
{
  int i;

  if (set[j].lcm!=NULL)
    pFree1(set[j].lcm);
  if (set[j].p!=NULL)
  {
    if (pNext(set[j].p) == strat->tail)
    {
      pFree1(set[j].p);
      /*- tail belongs to several int spolys -*/
    }
    else pDelete(&(set[j].p));
  }
  if ((*length)>0)
  {
    for (i=j; i < (*length); i++)
      set[i] = set[i+1];
  }
#ifdef KDEBUG
  memset(&(set[*length]),0,sizeof(LObject));
#endif
  (*length)--;
}

/*2
*is used after updating the pairset,if the leading term of p
*devides the leading term of some S[i] it will be canceled
*/
void clearS (poly p, int* at, int* k,kStrategy strat)
{
  if (!pDivisibleBy(p,strat->S[*at])) return;
  deleteInS((*at),strat);
  (*at)--;
  (*k)--;
}

/*2
*enters p at position at in L
*/
void enterL (LSet *set,int *length, int *LSetmax, LObject p,int at)
{
  int i;

  if ((*length)>=0)
  {
    if ((*length) == (*LSetmax)-1) enlargeL(set,LSetmax,setmax);
    for (i=(*length)+1; i>=at+1; i--) (*set)[i] = (*set)[i-1];
  }
  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 (LObject* h)
{
  h->ecart = pLDeg(h->p,&(h->length))-pFDeg(h->p);
}

void initEcartBBA (LObject* h)
{
  (*h).ecart = 0;
//#ifdef KDEBUG
  (*h).length = 0;
//#endif
}

void initEcartPairBba (LObject* Lp,poly f,poly g,int ecartF,int ecartG)
{
//#ifdef KDEBUG
  (*Lp).ecart = 0;
  (*Lp).length = 0;
//#endif
}

void initEcartPairMora (LObject* Lp,poly f,poly g,int ecartF,int ecartG)
{
  (*Lp).ecart = max(ecartF,ecartG);
  (*Lp).ecart = (*Lp).ecart-(pFDeg((*Lp).p)-pFDeg((*Lp).lcm));
//#ifdef KDEBUG
  (*Lp).length = 0;
//#endif
}

/*2
*if ecart1<=ecart2 it returns TRUE
*/
BOOLEAN sugarDivisibleBy(int ecart1, int ecart2)
{
  return (ecart1 <= ecart2);
}

/*2
* put the pair (s[i],p)  into the set B, ecart=ecart(p)
*/
void enterOnePair (int i,poly p,int ecart, int isFromQ,kStrategy strat)
{
  int      l,j,compare;
  LObject  Lp;

#ifdef KDEBUG
  Lp.ecart=0; Lp.length=0;
#endif
  /*- computes the lcm(s[i],p) -*/
  Lp.lcm = pInit();
  pLcm(p,strat->S[i],Lp.lcm);
  pSetm(Lp.lcm);
#ifdef DRING
//  if ((pDRING) && (pdDFlag(Lp.lcm)==0))
//  {
//    for(j=1;j<=pdN;j++)
//    {
//      if((Lp.lcm->exp[pdX(j)]>0)
//      &&(Lp.lcm->exp[pdIX(j)]>0))
//      {
//        pFree1(Lp.lcm);
//        Lp.lcm=NULL;
//        return;
//      }
//    }
//    /*delete pairs with lcm contains x_j^a*x_j^(-b)*/
//  }
#endif
  if (strat->sugarCrit)
  {
    if(
#ifdef SDRING
    (!pSDRING) &&
#endif
    (!((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 devides lcm(s,r)
    *(==> the leading term of p devides the leading term of r)
    *but the leading term of s does not devide 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++;
      pFree1(Lp.lcm);
      Lp.lcm=NULL;
      return;
    }
    else
      Lp.ecart = max(ecart,strat->ecartS[i]);
    if (strat->fromT && (strat->ecartS[i]>ecart))
    {
      pFree1(Lp.lcm);
      Lp.lcm=NULL;
      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 devides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r devides lcm(s,p) then (s,p) will not enter B
    */
#ifdef SDRING
    if (!pSDRING)
#endif
    {
      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))
          {
            pFree1(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])*/
#ifdef SDRING
    (!pSDRING) &&
#endif
    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 devides lcm(s,r)
    *(==> the leading term of p devides the leading term of r)
    *but the leading term of s does not devide 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++;
      pFree1(Lp.lcm);
      Lp.lcm=NULL;
      return;
    }
    if (strat->fromT && (strat->ecartS[i]>ecart))
    {
      pFree1(Lp.lcm);
      Lp.lcm=NULL;
      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 devides lcm(r,p) then (r,p) will be canceled
    *if the leading term of r devides lcm(s,p) then (s,p) will not enter B
    */
#ifdef SDRING
    if (!pSDRING)
#endif
    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))
        {
          pFree1(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 SDRING
  // spSpolyShortBba will not work for SDRING
  if (pSDRING)
  {
    Lp.p=spSpolyCreate(strat->S[i],p,strat->kNoether);
    if (Lp.p!=NULL)
      pDelete(&pNext(Lp.p));
  }
  else
#endif
  {
#ifdef KDEBUG
    pTest(strat->S[i]);
    pTest(p);
#endif
    Lp.p = spSpolyShortBba(strat->S[i],p);
  }
  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
    *devide lcm(r,p)). In the last case (s,r) can be canceled if the leading
    *term of p devides 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 handeled in chainCrit
    */
    if (Lp.lcm!=NULL) pFree1(Lp.lcm);
  }
  else
  {
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
    pNext(Lp.p) = strat->tail;
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
    if (TEST_OPT_INTSTRATEGY)
    {
      nDelete(&(Lp.p->coef));
    }
    l = strat->posInL(strat->B,strat->Bl,Lp,strat);
    enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
  }
#ifdef DRING
  if ((pDRING) && (pdDFlag(strat->S[i])==0) && (pdDFlag(p)==0))
  {
    Lp.lcm=pOne();
    pdLcm(strat->S[i],p,Lp.lcm);
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
#ifdef KDEBUG
    pTest(p);
    pTest(strat->S[i]);
#endif
    Lp.p = pdSpolyCreate(strat->S[i],p);
    if (Lp.p!=NULL)
    {
#ifdef KDEBUG
      pTest(p);
      pTest(strat->S[i]);
#endif
      /*spoly of p and S[i] bzgl Lp.lcm*/
      strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
      l = strat->posInL(strat->B,strat->Bl,Lp,strat);
      enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
    }
  }
#endif
}

/*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      l,j,compare;
  LObject  Lp;

  Lp.lcm = pInit();
  pLcm(p,strat->S[i],Lp.lcm);
  pSetm(Lp.lcm);
  if(
#ifdef SDRING
  (!pSDRING) &&
#endif
  (pHasNotCF(p,strat->S[i])))
  {
    strat->cp++;
    pFree1(Lp.lcm);
    Lp.lcm=NULL;
    return;
  }
  for(j = strat->Ll;j>=0;j--)
  {
    compare=pDivComp(strat->L[j].lcm,Lp.lcm);
    if ((compare==1) || (pEqual(strat->L[j].lcm,Lp.lcm)))
    {
      strat->c3++;
      pFree1(Lp.lcm);
      return;
    }
    else if (compare ==-1)
    {
      deleteInL(strat->L,&strat->Ll,j,strat);
      strat->c3++;
    }
  }
  /*-  compute the short s-polynomial -*/

#ifdef SDRING
  // spSpolyShortBba will not work for SDRING
  if (pSDRING)
  {
    Lp.p=spSpolyCreate(strat->S[i],p,strat->kNoether);
    if (Lp.p!=NULL)
      pDelete(&pNext(Lp.p));
  }
  else
#endif
  {
    Lp.p = spSpolyShortBba(strat->S[i],p);
  }
  if (Lp.p == NULL)
  {
     pFree1(Lp.lcm);
  }
  else
  {
    /*- the pair (S[i],p) enters B -*/
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
    pNext(Lp.p) = strat->tail;
    strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
    if (TEST_OPT_INTSTRATEGY)
    {
      nDelete(&(Lp.p->coef));
    }
    l = strat->posInL(strat->L,strat->Ll,Lp,strat);
    enterL(&strat->L,&strat->Ll,&strat->Lmax,Lp,l);
  }
#ifdef DRING
  if ((pDRING) && (pdDFlag(strat->S[i])==0) && (pdDFlag(p)==0))
  {
    Lp.lcm=pOne();
    pdLcm(strat->S[i],p,Lp.lcm);
    Lp.p1 = strat->S[i];
    Lp.p2 = p;
#ifdef KDEBUG
    pTest(p);
    pTest(strat->S[i]);
#endif
    Lp.p = pdSpolyCreate(strat->S[i],p);
    if (Lp.p!=NULL)
    {
#ifdef KDEBUG
      pTest(p);
      pTest(strat->S[i]);
#endif
      /*spoly of p and S[i] bzgl Lp.lcm*/
      strat->initEcartPair(&Lp,strat->S[i],p,strat->ecartS[i],ecart);
      l = strat->posInL(strat->B,strat->Bl,Lp,strat);
      enterL(&strat->B,&strat->Bl,&strat->Bmax,Lp,l);
    }
  }
#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 chainCrit (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 SDRING
    if (!pSDRING)
#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++;
            }
          }
        }
      }
    }
    Free((ADDRESS)strat->pairtest,(strat->sl+2)*sizeof(BOOLEAN));
    strat->pairtest=NULL;
  }
  if ((strat->Gebauer || strat->fromT)
#ifdef SDRING
  && (!pSDRING)
#endif
  )
  {
    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) || (pOrdSgn==1))
        && 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 (pEqual(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)||(pOrdSgn==1))
          {
            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 (pEqual(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/their order with respect to B is kept
    *j = posInL(L,j,B[i]) would permutate the order
    *if once B is ordered different from L
    *then one should use j = posInL(L,Ll,B[i])
    */
    j = strat->Ll+1;
    for (i=strat->Bl; i>=0; i--)
    {
      j = strat->posInL(strat->L,j-1,strat->B[i],strat);
      enterL(&strat->L,&strat->Ll,&strat->Lmax,strat->B[i],j);
    }
    strat->Bl = -1;
  }
  else
  {
#ifdef SDRING
    if (!pSDRING)
#endif
    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)||(pOrdSgn==1))
        {
          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
    */
    j = strat->Ll;
    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;
    j = strat->Ll;
#ifdef SDRING
    if (!pSDRING)
#endif
    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) && pEqual(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)
            && (!pEqual(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 initenterpairs (poly h,int k,int ecart,int isFromQ,kStrategy strat)
{

  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;
            enterOnePair(j,h,ecart,isFromQ,strat);
          //Print("j:%d, Ll:%d\n",j,strat->Ll);
          }
        }
      }
      else
      {
        new_pair=TRUE;
        for (j=0; j<=k; j++)
        {
          enterOnePair(j,h,ecart,isFromQ,strat);
          //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;
          enterOnePair(j,h,ecart,isFromQ,strat);
        //Print("j:%d, Ll:%d\n",j,strat->Ll);
        }
      }
    }
    if (new_pair) chainCrit(h,ecart,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 j=pos;

  initenterpairs(h,k,ecart,0,strat);
  if ((!strat->fromT)
  && ((strat->syzComp==0)
    ||(pGetComp(h)<=strat->syzComp)))
  {
    //Print("start clearS k=%d, pos=%d, sl=%d\n",k,pos,strat->sl);
    loop
    {
      if (j > k) break;
      clearS(h,&j,&k,strat);
      j++;
    }
    //Print("end clearS sl=%d\n",strat->sl);
  }
 // PrintS("end enterpairs\n");
}

/*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 j;

  for (j=0; j<=k; j++)
  {
    if ((pGetComp(h)==pGetComp(strat->S[j]))
    || (0==pGetComp(strat->S[j])))
    {
      enterOnePairSpecial(j,h,ecart,strat);
    }
  }
  j=pos;
  loop
  {
    if (j > k) break;
    clearS(h,&j,&k,strat);
    j++;
  }
}

/*2
*constructs the pairset at the beginning
*of the buchberger/mora algorithm
*/
void pairs (kStrategy strat)
{
  int j,i;
//  Print("pairs:sl=%d\n",strat->sl);
//  for (i=0; i<=strat->sl; i++)
//  {
//    Print("s%d:",i);pWrite(strat->S[i]);
//  }
  if (strat->fromQ!=NULL)
  {
    for (i=1; i<=strat->sl; i++)
    {
      initenterpairs(strat->S[i],i-1,strat->ecartS[i],strat->fromQ[i],strat);
    }
  }
  else
  {
    for (i=1; i<=strat->sl; i++)
    {
      initenterpairs(strat->S[i],i-1,strat->ecartS[i],0,strat);
    }
  }
  /*deletes superfluous elements in S*/
  i = -1;
  loop
  {
    i++;
    if (i >= strat->sl) break;
    if ((strat->syzComp==0) || (pGetComp(strat->S[i])<=strat->syzComp))
    {
      j=i;
      loop
      {
        j++;
        if (j > strat->sl) break;
        if (pDivisibleBy(strat->S[i],strat->S[j]))
        {
        //  Print("delete %d=",j);
        //  wrp(strat->S[j]);
        //  Print(" wegen %d=",i);
        //  wrp(strat->S[i]);
        //  Print("( fromQ=%d)\n", (strat->fromQ) ? strat->fromQ[j]:0);
          if ((strat->fromQ==NULL) || (strat->fromQ[j]==0))
          {
            deleteInS(j,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;
  int fq=0;
  poly  p;

  *suc = -1;
  for (i=1; i<=strat->sl; i++)
  {
    at = posInS(strat->S,i-1,strat->S[i]);
    if (at != i)
    {
      if ((*suc > at) || (*suc == -1)) *suc = at;
      p = strat->S[i];
      ecart = strat->ecartS[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->S[at] = p;
      strat->ecartS[at] = ecart;
      if (strat->fromQ!=NULL)
      {
        for (j=i; j>=at+1; j--)
        {
          strat->fromQ[j] = strat->fromQ[j-1];
        }
        strat->fromQ[at]=fq;
      }
    }
  }
}


/*2
*looks up the position of p in set
*set[0] is the smallest with respect to the ordering-procedure
*pComp
*/
int posInS (polyset set,int length,poly p)
{
  if(length==-1) return 0;
  int i;
  int an = 0;
  int en= length;
//  pTest(set[length]);
//  pTest(p);
  if (pMixedOrder)
  {
    int o=pWTotaldegree(p);
    int oo=pWTotaldegree(set[length]);

    if ((oo<o)
    || ((o==oo) && (pComp0(set[length],p)!= pOrdSgn)))
    {
      return length+1;
    }

    loop
    {
      if (an >= en-1)
      {
        if ((pWTotaldegree(set[an])>=o) && (pComp0(set[an],p) == pOrdSgn))
        {
          return an;
        }
        return en;
      }
      i=(an+en) / 2;
      if ((pWTotaldegree(set[an])>=o)
      && (pComp0(set[i],p) == pOrdSgn)) en=i;
      else                              an=i;
    }
  }
  else
  {
    if (pComp0(set[length],p)!= pOrdSgn) return length+1;

    loop
    {
      if (an >= en-1)
      {
        if (pComp0(set[an],p) == pOrdSgn) return an;
        return en;
      }
      i=(an+en) / 2;
      if (pComp0(set[i],p) == pOrdSgn) en=i;
      else                             an=i;
    }
  }
}


/*2
* looks up the position of p in set
* the position is the last one
*/
int posInT0 (TSet set,int length,LObject p)
{
  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 (TSet set,int length,LObject p)
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;

  if (pComp0(set[length].p,p.p)!= pOrdSgn) return length+1;

  loop
  {
    if (an >= en-1)
    {
      if (pComp0(set[an].p,p.p) == pOrdSgn) return an;
      return en;
    }
    i=(an+en) / 2;
    if (pComp0(set[i].p,p.p) == pOrdSgn) 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 (TSet set,int length,LObject p)
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;

  if (set[length].length<p.length) return length+1;

  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 (TSet set,int length,LObject p)
/*{
 * int j=0;
 * int o;
 *
 * o = pFDeg(p.p);
 * loop
 * {
 *   if ((pFDeg(set[j].p) > o)
 *   || ((pFDeg(set[j].p) == o) && (pComp0(set[j].p,p.p) == pOrdSgn)))
 *   {
 *     return j;
 *   }
 *   j++;
 *   if (j > length) return j;
 * }
 *}
 */
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if ((pFDeg(set[length].p) < o)
  || ((pFDeg(set[length].p) == o) && (pComp0(set[length].p,p.p) != pOrdSgn)))
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) > o)
      || ((pFDeg(set[an].p) == o) && (pComp0(set[an].p,p.p) == pOrdSgn)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) > o)
    || ((pFDeg(set[i].p) == o) && (pComp0(set[i].p,p.p) == pOrdSgn)))
      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 (TSet set,int length,LObject p)
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if ((pFDeg(set[length].p) < o)
  || ((pFDeg(set[length].p) == o) && (set[length].length<p.length))
  || ((pFDeg(set[length].p) == o) && (set[length].length == p.length)
     && (pComp0(set[length].p,p.p) != pOrdSgn)))
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) > o)
      || ((pFDeg(set[an].p) == o) && (set[an].length > p.length))
      || ((pFDeg(set[an].p) == o) && (set[an].length == p.length)
         && (pComp0(set[an].p,p.p) == pOrdSgn)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) > o)
    || ((pFDeg(set[i].p) == o) && (set[i].length > p.length))
    || ((pFDeg(set[i].p) == o) && (set[i].length == p.length)
       && (pComp0(set[i].p,p.p) == pOrdSgn)))
      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 (TSet set,int length,LObject p)
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if (pFDeg(set[length].p) <= o)
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if (pFDeg(set[an].p) > o)
        return an;
      return en;
    }
    i=(an+en) / 2;
    if (pFDeg(set[i].p) > o)
      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 (TSet set,int length,LObject p)
/*{
 *int j=0;
 * int o;
 *
 * o = pFDeg(p.p)+p.ecart;
 * loop
 * {
 *   if ((pFDeg(set[j].p)+set[j].ecart > o)
 *   || ((pFDeg(set[j].p)+set[j].ecart == o)
 *     && (pComp0(set[j].p,p.p) == pOrdSgn)))
 *   {
 *     return j;
 *   }
 *   j++;
 *   if (j > length) return j;
 * }
 *}
 */
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p) + p.ecart;

  if ((pFDeg(set[length].p)+set[length].ecart < o)
  || ((pFDeg(set[length].p)+set[length].ecart == o)
     && (pComp0(set[length].p,p.p) != pOrdSgn)))
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p)+set[an].ecart > o)
      || ((pFDeg(set[an].p)+set[an].ecart  == o)
         && (pComp0(set[an].p,p.p) == pOrdSgn)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) +set[i].ecart > o)
    || ((pFDeg(set[i].p) +set[i].ecart == o)
       && (pComp0(set[i].p,p.p) == pOrdSgn)))
      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 (TSet set,int length,LObject p)
/*
*{
* int j=0;
* int  o;
*
*  o = pFDeg(p.p)+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)
*      && (pComp0(set[j].p,p.p)==pOrdSgn)))
*      return j;
*    j++;
*    if (j > length) return j;
*  }
* }
*/
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p) + p.ecart;

  if ((pFDeg(set[length].p)+set[length].ecart < o)
  || ((pFDeg(set[length].p)+set[length].ecart == o)
     && (set[length].ecart > p.ecart))
  || ((pFDeg(set[length].p)+set[length].ecart == o)
     && (set[length].ecart==p.ecart)
     && (pComp0(set[length].p,p.p) != pOrdSgn)))
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p)+set[an].ecart > o)
      || ((pFDeg(set[an].p)+set[an].ecart == o) && (set[an].ecart < p.ecart))
      || ((pFDeg(set[an].p)+set[an].ecart  == o)
         && (set[an].ecart==p.ecart)
         && (pComp0(set[an].p,p.p) == pOrdSgn)))
        return an;
      return en;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) +set[i].ecart > o)
    || ((pFDeg(set[i].p)+set[i].ecart == o)
       && (set[i].ecart < p.ecart))
    || ((pFDeg(set[i].p) +set[i].ecart == o)
       && (set[i].ecart == p.ecart)
       && (pComp0(set[i].p,p.p) == pOrdSgn)))
      en=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 (TSet set,int length,LObject p)
{
  if (length==-1) return 0;

  int i;
  int an = 0;
  int en= length;
  int o = p.ecart;

  if ((set[length].ecart < o)
  || (((set[length].ecart == o)
     && (pFDeg(set[length].p) < pFDeg(p.p)))
  || ((set[length].ecart == o)
     && (pFDeg(set[length].p) == pFDeg(p.p))
     && (set[length].length < p.length))))
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if ((set[an].ecart > o)
      || (((set[an].ecart == o)
         && (pFDeg(set[an].p) > pFDeg(p.p)))
      || ((set[an].ecart  == o)
         && (pFDeg(set[an].p) == pFDeg(p.p))
         && (set[an].length > p.length))))
        return an;
      return en;
    }
    i=(an+en) / 2;
    if ((set[i].ecart > o)
    || (((set[i].ecart == o)
       && (pFDeg(set[i].p) > pFDeg(p.p)))
    || ((set[i].ecart == o)
       && (pFDeg(set[i].p) == pFDeg(p.p))
       && (set[i].length > p.length))))
      en=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 (LSet set, int length, LObject p,kStrategy strat)
{
  int i;
  int an = 0;
  int en= length;
  int d=pFDeg(p.p);

  if (length<0) return 0;
  if ((pFDeg(set[length].p)>d)
     || ((pFDeg(set[length].p)==d) && (p.p1!=NULL)&&(set[length].p1==NULL))
     || (pComp0(set[length].p,p.p)== pOrdSgn))
     return length+1;
  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p)>d)
         || ((pFDeg(set[an].p)==d) && (p.p1!=NULL)&&(set[an].p1==NULL))
         || (pComp0(set[an].p,p.p)== pOrdSgn))
         return en;
      return an;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p)>d)
       || ((pFDeg(set[i].p)==d) && (p.p1!=NULL)&&(set[i].p1==NULL))
       || (pComp0(set[i].p,p.p)== pOrdSgn))
       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 (LSet set, int length, LObject p,kStrategy strat)
{
  int i;
  int an = 0;
  int en= length;

  if (length<0) return 0;
  if (pComp0(set[length].p,p.p)== pOrdSgn) return length+1;
  loop
  {
    if (an >= en-1)
    {
      if (pComp0(set[an].p,p.p) == pOrdSgn) return en;
      return an;
    }
    i=(an+en) / 2;
    if (pComp0(set[i].p,p.p) == pOrdSgn) 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 ordering-procedure totaldegree,pComp
*/
int posInL11 (LSet set, int length, LObject p,kStrategy strat)
/*{
 * int j=0;
 * int o;
 *
 * o = pFDeg(p.p);
 * loop
 * {
 *   if (j > length)            return j;
 *   if ((pFDeg(set[j].p) < o)) return j;
 *   if ((pFDeg(set[j].p) == o) && (pComp0(set[j].p,p.p) == -pOrdSgn))
 *   {
 *     return j;
 *   }
 *   j++;
 * }
 *}
 */
{
  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if (length<0) return 0;
  if ((pFDeg(set[length].p) > o)
  || ((pFDeg(set[length].p) == o) && (pComp0(set[length].p,p.p) != -pOrdSgn)))
    return length+1;
  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) > o)
      || ((pFDeg(set[an].p) == o) && (pComp0(set[an].p,p.p) != -pOrdSgn)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) > o)
    || ((pFDeg(set[i].p) == o) && (pComp0(set[i].p,p.p) != -pOrdSgn)))
      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 totaldegree,pLength0
*/
int posInL110 (LSet set, int length, LObject p,kStrategy strat)
{
  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if (length<0) return 0;
  if ((pFDeg(set[length].p) > o)
  || ((pFDeg(set[length].p) == o) && (set[length].length >2*p.length))
  || ((pFDeg(set[length].p) == o) && (set[length].length <= 2*p.length)
     && (pComp0(set[length].p,p.p) != -pOrdSgn)))
    return length+1;
  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) > o)
      || ((pFDeg(set[an].p) == o) && (set[an].length >2*p.length))
      || ((pFDeg(set[an].p) == o) && (set[an].length <=2*p.length)
         && (pComp0(set[an].p,p.p) != -pOrdSgn)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) > o)
    || ((pFDeg(set[i].p) == o) && (set[i].length > 2*p.length))
    || ((pFDeg(set[i].p) == o) && (set[i].length <= 2*p.length)
       && (pComp0(set[i].p,p.p) != -pOrdSgn)))
      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 (LSet set, int length, LObject p,kStrategy strat)
{
  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p);

  if (pFDeg(set[length].p) > o)
    return length+1;

  loop
  {
    if (an >= en-1)
    {
      if (pFDeg(set[an].p) >= o)
        return en;
      return an;
    }
    i=(an+en) / 2;
    if (pFDeg(set[i].p) >= 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 (LSet set, int length, LObject p,kStrategy strat)
/*{
 * int j=0;
 * int o;
 *
 * o = p.ecart+pFDeg(p.p);
 * loop
 * {
 *   if (j > length)                       return j;
 *   if (pFDeg(set[j].p)+set[j].ecart < o) return j;
 *   if ((pFDeg(set[j].p)+set[j].ecart == o)
 *   && (pComp0(set[j].p,p.p) == -pOrdSgn))
 *   {
 *     return j;
 *   }
 *   j++;
 * }
 *}
 */
{
  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p) + p.ecart;

  if (length<0) return 0;
  if ((pFDeg(set[length].p) + set[length].ecart > o)
  || ((pFDeg(set[length].p) + set[length].ecart == o)
     && (pComp0(set[length].p,p.p) != -pOrdSgn)))
    return length+1;
  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) + set[an].ecart > o)
      || ((pFDeg(set[an].p) + set[an].ecart == o)
         && (pComp0(set[an].p,p.p) != -pOrdSgn)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) + set[i].ecart > o)
    || ((pFDeg(set[i].p) +set[i].ecart == o)
       && (pComp0(set[i].p,p.p) != -pOrdSgn)))
      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 (LSet set, int length, LObject p,kStrategy strat)
/*
*{
*  int j=0;
* int o;
*
*  o = pFDeg(p.p)+p.ecart;
*  loop
*  {
*    if (j > length)
*     return j;
*    if (pFDeg(set[j].p)+set[j].ecart < o)
*      return j;
*    if ((pFDeg(set[j].p)+set[j].ecart == o)
*    && (set[j].ecart < p.ecart))
*      return j;
*    if ((pFDeg(set[j].p)+set[j].ecart == o)
*    && (set[j].ecart == p.ecart)
*    && (pComp0(set[j].p,p.p)==(-pOrdSgn)))
*      return j;
*    j++;
*  }
* }
*/
{
  int i;
  int an = 0;
  int en= length;
  int o = pFDeg(p.p) + p.ecart;

  if (length<0) return 0;
  if ((pFDeg(set[length].p) + set[length].ecart > o)
  || ((pFDeg(set[length].p) + set[length].ecart == o)
     && (set[length].ecart > p.ecart))
  || ((pFDeg(set[length].p) + set[length].ecart == o)
     && (set[length].ecart == p.ecart)
     && (pComp0(set[length].p,p.p) != -pOrdSgn)))
    return length+1;
  loop
  {
    if (an >= en-1)
    {
      if ((pFDeg(set[an].p) + set[an].ecart > o)
      || ((pFDeg(set[an].p) + set[an].ecart == o)
         && (set[an].ecart > p.ecart))
      || ((pFDeg(set[an].p) + set[an].ecart == o)
         && (set[an].ecart == p.ecart)
         && (pComp0(set[an].p,p.p) != -pOrdSgn)))
        return en;
      return an;
    }
    i=(an+en) / 2;
    if ((pFDeg(set[i].p) + set[i].ecart > o)
    || ((pFDeg(set[i].p) + set[i].ecart == o)
       && (set[i].ecart > p.ecart))
    || ((pFDeg(set[i].p) +set[i].ecart == o)
       && (set[i].ecart == p.ecart)
       && (pComp0(set[i].p,p.p) != -pOrdSgn)))
      an=i;
    else
      en=i;
  }
}
/*2
* reduces h using the set S
* procedure used in redtail
*/
/*
*void redtailS (poly* h,int maxIndex,kStrategy strat)
*{
*  int j = 0;
*
*  while (j <= maxIndex)
*  {
*    if (pDivisibleBy((strat->S)[j],*h))
*    {
*      *h = spSpolyRed(strat->S[j],*h,strat->kNoether);
*      if (*h == NULL) return;
*      j = 0;
*    }
*    else j++;
*  }
*}
*/

/*2
*compute the normalform of the tail p->next of p
*with respect to S
*/
poly redtail (poly p, int pos, kStrategy strat)
{
  poly h, hn;
  int j, e, l;

  if (strat->noTailReduction)
  {
    return p;
  }
  h = p;
  hn = pNext(h);
  while(hn != NULL)
  {
    e = pLDeg(hn,&l)-pFDeg(hn);
    j = 0;
    while (j <= pos)
    {
      if (pDivisibleBy(strat->S[j], hn)
      && ((e >= strat->ecartS[j])
        || strat->kHEdgeFound
        || ((Kstd1_deg>0)&&(pFDeg(hn)<=Kstd1_deg)))
      )
      {
        spSpolyTail(strat->S[j], p, h, strat->kNoether);
        hn = pNext(h);
        if (hn == NULL)
        {
          return p;
        }
        e = pLDeg(hn,&l)-pFDeg(hn);
        j = 0;
      }
      else
      {
        j++;
      }
    }
    h = hn;
    hn = pNext(h);
  }
  return p;
}

/*2
*compute the normalform of the tail p->next of p
*with respect to S
*/
poly redtailBba (poly p, int pos, kStrategy strat)
{
  poly h, hn;
  int j;

  if (strat->noTailReduction)
  {
    return p;
  }
  h = p;
  hn = pNext(h);
  while(hn != NULL)
  {
    j = 0;
    while (j <= pos)
    {
      if (pDivisibleBy(strat->S[j], hn))
      {
        spSpolyTail(strat->S[j], p, h, strat->kNoether);
        hn = pNext(h);
        if (hn == NULL)
        {
          return p;
        }
        j = 0;
      }
      else
      {
        j++;
      }
    }
    h = hn;
    hn = pNext(h);
  }
  return p;
}

/*2
*compute the "normalform" of the tail p->next of p
*with respect to S for syzygies
*/
poly redtailSyz (poly p, int pos, kStrategy strat)
{
  poly h, hn;
  int j;

  if (strat->noTailReduction)
  {
    return p;
  }
  h = p;
  hn = pNext(h);
  while(hn != NULL)
  {
    j = 0;
    while (j <= pos)
    {
      if (pDivisibleBy(strat->S[j], hn) && (!pEqual(strat->S[j],h)))
      {
        spSpolyTail(strat->S[j], p, h, strat->kNoether);
        hn = pNext(h);
        if (hn == NULL)
        {
          return p;
        }
        j = 0;
      }
      else
      {
        j++;
      }
    }
    h = hn;
    hn = pNext(h);
  }
  return p;
}

/*2
*checks the change degree and write progress report
*/
void message (int i,int* reduc,int* olddeg,kStrategy strat)
{
  if (i != *olddeg)
  {
    Print("%d",i);
    *olddeg = i;
  }
  if (strat->Ll != *reduc)
  {
    if (strat->Ll != *reduc-1)
      Print("(%d)",strat->Ll+1);
    else
      PrintS("-");
    *reduc = strat->Ll;
  }
  else
    PrintS(".");
  mflush();
}

/*2
*statistics
*/
void messageStat (int srmax,int lrmax,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("\nproduct criterion:%d chain criterion:%d\n",strat->cp,strat->c3);
  if (hilbcount!=0) Print("hilbert series criterion:%d\n",hilbcount);
  /*mflush();*/
}

/*2
*debugging output: all internal sets, if changed
*for testing purpuse 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);
      wrp(strat->S[i]);
    }
    strat->news = FALSE;
  }
  if (strat->newt)
  {
    PrintS("\nset T");
    for (i=0; i<=strat->tl; i++)
    {
      Print("\n  %d:",i);
      wrp(strat->T[i].p);
      Print(" o:%d e:%d l:%d",
        /*pFDeg(strat->T[i].p)*/pGetOrder(strat->T[i].p),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);
    wrp(strat->L[i].p1);
    PrintS("  ");
    wrp(strat->L[i].p2);
    PrintS(" lcm: ");wrp(strat->L[i].lcm);
    PrintS("\n  p : ");
    wrp(strat->L[i].p);
    Print("  o:%d e:%d l:%d",
     pGetOrder(strat->L[i].p),strat->L[i].ecart,strat->L[i].length);
  }
  PrintLn();
}

/*2
*construct the set s from F
*/
void initS (ideal F, ideal Q,kStrategy strat)
{
  LObject h;
  int   i,pos;
#ifdef SDRING
  polyset aug=(polyset)Alloc(setmax*sizeof(poly));
  int augmax=setmax, augl=-1;
#endif

  h.ecart=0; h.length=0;
  if (Q!=NULL) i=IDELEMS(Q);
  else i=0;
  i=((i+IDELEMS(F)+15)/16)*16;
  strat->ecartS=initec(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)
      {
        h.p = pCopy(Q->m[i]);
        //if (TEST_OPT_INTSTRATEGY)
        //{
        //  //pContent(h.p);
        //  pCleardenom(h.p); // also does a pContent
        //}
        //else
        //{
        //  pNorm(h.p);
        //}
        strat->initEcart(&h);
        if (pOrdSgn==-1)
        {
          deleteHC(&h.p, &h.ecart, &h.length,strat);
        }
        if (h.p!=NULL)
        {
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat->S,strat->sl,h.p);
          }
          strat->enterS(h,pos,strat);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      h.p = pCopy(F->m[i]);
#ifdef SDRING
      aug[0]=h.p;
      augl=0;
#ifdef SRING
      if (pSRING)
        psAug(pCopy(h.p),pOne(),&aug,&augl,&augmax);
#endif
#ifdef DRING
      if (pDRING)
        pdAug(pCopy(h.p),&aug,&augl,&augmax);
#endif
      for (augl++;augl != 0;)
      {
        h.p=aug[--augl];
#ifdef KDEBUG
        pTest(h.p);
#endif
        if (TEST_OPT_DEBUG && pSDRING)
        {
          PrintS("new (aug) s:");
          wrp(h.p);
          PrintLn();
        }
#endif
        if (TEST_OPT_INTSTRATEGY)
        {
          //pContent(h.p);
          pCleardenom(h.p); // also does a pContent
        }
        else
        {
          pNorm(h.p);
        }
        strat->initEcart(&h);
        if (pOrdSgn==-1)
        {
          cancelunit(&h);  /*- tries to cancel a unit -*/
          deleteHC(&h.p, &h.ecart, &h.length,strat);
        }
        if (TEST_OPT_DEGBOUND
        && (((strat->honey) && (h.ecart+pFDeg(h.p)>Kstd1_deg))
          || ((!(strat->honey)) && (pFDeg(h.p)>Kstd1_deg))))
          pDelete(&h.p);
        else
        if (h.p!=NULL)
        {
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat->S,strat->sl,h.p);
          }
          strat->enterS(h,pos,strat);
        }
#ifdef SDRING
      }
#endif
    }
  }
  /*- test, if a unit is in F -*/
  if ((strat->sl>=0) && pIsConstant(strat->S[0]))
  {
    while (strat->sl>0) deleteInS(strat->sl,strat);
  }
#ifdef SDRING
  Free((ADDRESS)aug,augmax*sizeof(poly));
#endif
//  for(augl=0;augl<=strat->sl;augl++)
//    pTest(strat->S[augl]);
}

void initSL (ideal F, ideal Q,kStrategy strat)
{
  LObject h;
  int   i,pos;
#ifdef SDRING
  polyset aug=(polyset)Alloc(setmax*sizeof(poly));
  int augmax=setmax, augl=-1;
#endif

  h.ecart=0; h.length=0;
  if (Q!=NULL) i=IDELEMS(Q);
  else i=0;
  i=((i+16)/16)*16;
  strat->ecartS=initec(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)
      {
        h.p = pCopy(Q->m[i]);
        if (TEST_OPT_INTSTRATEGY)
        {
          //pContent(h.p);
          pCleardenom(h.p); // also does a pContent
        }
        else
        {
          pNorm(h.p);
        }
        strat->initEcart(&h);
        if (pOrdSgn==-1)
        {
          deleteHC(&h.p, &h.ecart, &h.length,strat);
        }
        if (h.p!=NULL)
        {
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat->S,strat->sl,h.p);
          }
          strat->enterS(h,pos,strat);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      h.p = pCopy(F->m[i]);
      h.p1=NULL;
      h.p2=NULL;
      h.lcm=NULL;
#ifdef SDRING
      aug[0]=h.p;
      augl=0;
#ifdef SRING
      if (pSRING)
        psAug(pCopy(h.p),pOne(),&aug,&augl,&augmax);
#endif
#ifdef DRING
      if (pDRING)
        pdAug(pCopy(h.p),&aug,&augl,&augmax);
#endif
      for (augl++;augl != 0;)
      {
        h.p=aug[--augl];
#ifdef KDEBUG
        pTest(h.p);
#endif
        if (TEST_OPT_DEBUG && pSDRING)
        {
          PrintS("new (aug) s:");
          wrp(h.p);
          PrintLn();
        }
#endif
        if (TEST_OPT_INTSTRATEGY)
        {
          //pContent(h.p);
          pCleardenom(h.p); // also does a pContent
        }
        else
        {
          pNorm(h.p);
        }
        strat->initEcart(&h);
        if (pOrdSgn==-1)
        {
          cancelunit(&h);  /*- tries to cancel a unit -*/
          deleteHC(&h.p, &h.ecart, &h.length,strat);
        }
        if (TEST_OPT_DEGBOUND
        && (((strat->honey) && (h.ecart+pFDeg(h.p)>Kstd1_deg))
          || ((!(strat->honey)) && (pFDeg(h.p)>Kstd1_deg))))
          pDelete(&h.p);
        else
        if (h.p!=NULL)
        {
          if (strat->Ll==-1)
            pos =0;
          else
          {
            pos = strat->posInL(strat->L,strat->Ll,h,strat);
          }
          enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos);
        }
#ifdef SDRING
      }
#endif
    }
  }
  /*- test, if a unit is in F -*/
  if ((strat->Ll>=0) && pIsConstant(strat->L[strat->Ll].p))
  {
    while (strat->Ll>0) deleteInL(strat->L,&strat->Ll,strat->Ll-1,strat);
  }
#ifdef SDRING
  Free((ADDRESS)aug,augmax*sizeof(poly));
#endif
//  for(augl=0;augl<=strat->sl;augl++)
//    pTest(strat->S[augl]);
}


/*2
*construct the set s from F u {P}
*/
void initSSpecial (ideal F, ideal Q, ideal P,kStrategy strat)
{
  LObject h;
  int   i,pos;
#ifdef SDRING
  polyset aug=(polyset)Alloc(setmax*sizeof(poly));
  int augmax=setmax, augl=-1;
#endif

  h.ecart=0; h.length=0;
  if (Q!=NULL) i=IDELEMS(Q);
  else i=0;
  i=((i+IDELEMS(F)+15)/16)*16;
  strat->ecartS=initec(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)
      {
        h.p = pCopy(Q->m[i]);
        //if (TEST_OPT_INTSTRATEGY)
        //{
        //  //pContent(h.p);
        //  pCleardenom(h.p); // also does a pContent
        //}
        //else
        //{
        //  pNorm(h.p);
        //}
        strat->initEcart(&h);
        if (pOrdSgn==-1)
        {
          deleteHC(&h.p, &h.ecart, &h.length,strat);
        }
        if (h.p!=NULL)
        {
          if (strat->sl==-1)
            pos =0;
          else
          {
            pos = posInS(strat->S,strat->sl,h.p);
          }
          strat->enterS(h,pos,strat);
          strat->fromQ[pos]=1;
        }
      }
    }
  }
  /*- put polys into S -*/
  for (i=0; i<IDELEMS(F); i++)
  {
    if (F->m[i]!=NULL)
    {
      h.p = pCopy(F->m[i]);
      if (pOrdSgn==1)
      {
        h.p=redtailBba(h.p,strat->sl,strat);
      }
      strat->initEcart(&h);
      if (pOrdSgn==-1)
      {
          deleteHC(&h.p, &h.ecart, &h.length,strat);
      }
      if (TEST_OPT_DEGBOUND
      && (((strat->honey) && (h.ecart+pFDeg(h.p)>Kstd1_deg))
        || ((!(strat->honey)) && (pFDeg(h.p)>Kstd1_deg))))
        pDelete(&h.p);
      else
      if (h.p!=NULL)
      {
        if (strat->sl==-1)
          pos =0;
        else
        {
          pos = posInS(strat->S,strat->sl,h.p);
        }
        strat->enterS(h,pos,strat);
        h.length = pLength(h.p);
        enterT(h,strat);
      }
    }
  }
  for (i=0; i<IDELEMS(P); i++)
  {
    if (P->m[i]!=NULL)
    {
      h.p=pCopy(P->m[i]);
      strat->initEcart(&h);
      h.length = pLength(h.p);
      if (TEST_OPT_INTSTRATEGY)
      {
        pCleardenom(h.p);
      }
      else
      {
        pNorm(h.p);
      }
      if(strat->sl>=0)
      {
        if (pOrdSgn==1)
        {
          h.p=redBba(h.p,strat->sl,strat);
          h.p=redtailBba(h.p,strat->sl,strat);
        }
        else
        {
          h.p=redMora(h.p,strat->sl,strat);
          strat->initEcart(&h);
        }
        if(h.p!=NULL)
        {
          if (TEST_OPT_INTSTRATEGY)
          {
            pCleardenom(h.p);
          }
          else
          {
            pNorm(h.p);
          }
          pos = posInS(strat->S,strat->sl,h.p);
          enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat);
          strat->enterS(h,pos,strat);
          enterT(h,strat);
        }
      }
      else
      {
        strat->enterS(h,0,strat);
        enterT(h,strat);
      }
    }
  }
#ifdef SDRING
  Free((ADDRESS)aug,augmax*sizeof(poly));
#endif
}
/*2
* reduces h using the set S
* procedure used in cancelunit1
*/
static poly redBba1 (poly h,int maxIndex,kStrategy strat)
{
  int j = 0;

  while (j <= maxIndex)
  {
    if (pDivisibleBy(strat->S[j],h))
       return spSpolyRedNew(strat->S[j],h,strat->kNoether);
    else j++;
  }
  return h;
}

/*2
*tests if p.p=monomial*unit and cancels the unit
*/
void cancelunit1 (LObject* p,int index,kStrategy strat )
{
  int k;
  poly r,h,h1,q;

  if (!pIsVector((*p).p) && ((*p).ecart != 0))
  {
    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;
        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;
      }
    }
  }
}

/*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;

  while ((j <= strat->sl) && (pGetComp(strat->S[j])!=0)) j++;
  start=j;
  while (j<=strat->sl)
  {
    if (pDivisibleBy(strat->S[j],h))
    {
      h = spSpolyRed(strat->S[j],h,strat->kNoether);
      if (h==NULL) return NULL;
      j = start;
    }
    else j++;
  }
  return h;
}

/*2
* reduces h using the set S
* procedure used in updateS
*/
static poly redBba (poly h,int maxIndex,kStrategy strat)
{
  int j = 0;

  while (j <= maxIndex)
  {
    if (pDivisibleBy(strat->S[j],h))
    {
      pTest(strat->S[j]);
      pTest(h);
      h = spSpolyRed(strat->S[j],h,strat->kNoether);
      if (h==NULL) return NULL;
      j = 0;
    }
    else j++;
  }
#ifdef KDEBUG
  pTest(h);
#endif
  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;
  poly h1;

  if (maxIndex >= 0)
  {
    e = pLDeg(h,&l)-pFDeg(h);
    do
    {
      if (pDivisibleBy(strat->S[j],h)
      && ((e >= strat->ecartS[j]) || strat->kHEdgeFound))
      {
        h1 = spSpolyRedNew(strat->S[j],h,strat->kNoether);
        pDelete(&h);
        if (h1 == NULL) return NULL;
        h = h1;
        e = pLDeg(h,&l)-pFDeg(h);
        j = 0;
      }
      else j++;
    }
    while (j <= maxIndex);
  }
#ifdef KDEBUG
  pTest(h);
#endif
  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;
#ifdef SDRING
  polyset aug=(polyset)Alloc(setmax*sizeof(poly));
  int augmax=setmax;
  int augl;
  int pos;
  BOOLEAN recursiv=FALSE;
#endif

//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]);
//  }
  memset(&h,0,sizeof(h));
  if (pOrdSgn==1)
  {
    while (suc != -1)
    {
      i=suc+1;
      while (i<=strat->sl)
      {
        pTest(strat->S[i]);
        if (((strat->syzComp==0) || (pGetComp(strat->S[i])<=strat->syzComp))
        && ((strat->fromQ==NULL) || (strat->fromQ[i]==0)))
        {
          if (TEST_OPT_DEBUG)
          {
            PrintS("reduce:");
            wrp(strat->S[i]);
          }
          pDelete(&redSi);
          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 (TEST_OPT_PROT && (pComp(redSi,strat->S[i])!=0))
          {
            if (strat->S[i]==NULL)
              PrintS("V");
            else
              PrintS("v");
            mflush();
          }
          if (strat->S[i]==NULL)
          {
            pDelete(&redSi);
            if (TEST_OPT_DEBUG) PrintS(" to 0");
            deleteInS(i,strat);
            i--;
          }
#ifdef SDRING
          else if ((pSDRING) && (pComp(redSi,strat->S[i])!=0))
          {
            pDelete(&redSi);
            redSi=strat->S[i];
            strat->S[i]=NULL;
            pTest(redSi);
            deleteInS(i,strat);
            suc=0;
            i=0;
            aug[0]=redSi;
            augl=0;
#ifdef SRING
            if (pSRING) psAug(pCopy(redSi),pOne(),&aug,&augl,&augmax);
#endif
#ifdef DRING
            if (pDRING) pdAug(pCopy(redSi),&aug,&augl,&augmax);
#endif
            redSi=NULL;
            if (augl>0) recursiv=TRUE;
            while (augl >= 0)
            {
              h.p=aug[augl];
              pTest(h.p);
              if (h.p!=NULL)
              {
                if (TEST_OPT_DEBUG)
                {
                  Print("new (aug %d) s:",augl);
                  wrp(h.p);
                  PrintLn();
                }
                if (TEST_OPT_INTSTRATEGY)
                {
                  //pContent(h.p);
                  pCleardenom(h.p);// also does a pContent
                }
                else
                {
                  pNorm(h.p);
                }
                strat->initEcart(&h);
                pos = posInS(strat->S,strat->sl,h.p);
                strat->enterS(h,pos,strat);
              }
              augl--;
            }
          }
#endif
          else
          {
            pDelete(&redSi);
            if (TEST_OPT_INTSTRATEGY)
            {
              //pContent(strat->S[i]);
              pCleardenom(strat->S[i]);// also does a pContent
            }
            else
            {
              pNorm(strat->S[i]);
            }
            if (TEST_OPT_DEBUG)
            {
              PrintS(" to ");
              wrp(strat->S[i]);
            }
          }
          if (TEST_OPT_DEBUG) PrintLn();
        }
        i++;
      }
      reorderS(&suc,strat);
    }
    if (toT)
    {
      for (i=0; i<=strat->sl; i++)
      {
        if (((strat->fromQ==NULL) || (strat->fromQ[i]==0))
#ifdef SDRING
        && (!pSDRING)
#endif
        )
          h.p = redtailBba(strat->S[i],i-1,strat);
        else
        {
          h.p = strat->S[i];
        }
        if (strat->honey)
        {
          strat->initEcart(&h);
          strat->ecartS[i] = h.ecart;
        }
        /*puts the elements of S also to T*/
        enterT(h,strat);
      }
    }
  }
  else
  {
    while (suc != -1)
    {
      i=suc+1;
      while (i<=strat->sl)
      {
        if (((strat->syzComp==0) || (pGetComp(strat->S[i])<=strat->syzComp))
        && ((strat->fromQ==NULL) || (strat->fromQ[i]==0)))
        {
          pDelete(&redSi);
          redSi=pHead((strat->S)[i]);
          (strat->S)[i] = redMora((strat->S)[i],i-1,strat);
          kTest(strat);
          if ((strat->S)[i]==NULL)
          {
            deleteInS(i,strat);
            i--;
          }
#ifdef SDRING
          else if ((pSDRING) && (pComp(redSi,(strat->S)[i])!=0))
          {
            pDelete(&redSi);
            redSi=(strat->S)[i];
            (strat->S)[i]=NULL;
            deleteInS(i,strat);
            i--;
            aug[0]=redSi;
            augl=0;
#ifdef SRING
            if (pSRING) psAug(pCopy(redSi),pOne(),&aug,&augl,&augmax);
#endif
#ifdef DRING
            if (pDRING) pdAug(pCopy(redSi),&aug,&augl,&augmax);
#endif
            redSi=NULL;
            if (augl>0) recursiv=TRUE;
            for (augl++;augl != 0;)
            {
              h.p=aug[--augl];
              if (TEST_OPT_DEBUG)
              {
                PrintS("new (aug) s:");
                wrp(h.p);
                PrintLn();
              }
              if (!TEST_OPT_INTSTRATEGY)
                pNorm(h.p);
              else
              {
                //pContent(h.p);
                pCleardenom(h.p);// also does a pContent
              }
              strat->initEcart(&h);
              pos = posInS(strat->S,strat->sl,h.p);
              strat->enterS(h,pos,strat);
            }
          }
#endif
          else if (TEST_OPT_INTSTRATEGY)
          {
            pDelete(&redSi);
            //pContent(strat->S[i]);
            pCleardenom(strat->S[i]);// also does a pContent
            h.p = strat->S[i];
            strat->initEcart(&h);
            strat->ecartS[i] = h.ecart;
          }
          else
          {
            pDelete(&redSi);
            pNorm(strat->S[i]);
            h.p = strat->S[i];
            strat->initEcart(&h);
            strat->ecartS[i] = h.ecart;
          }
        }
        i++;
      }
#ifdef KDEBUG
      kTest(strat);
#endif
      reorderS(&suc,strat);
      if (h.p!=NULL)
      {
        if (!strat->kHEdgeFound)
        {
          /*strat->kHEdgeFound =*/ HEckeTest(h.p,strat);
        }
        if (strat->kHEdgeFound)
          newHEdge(strat->S,strat->ak,strat);
      }
    }
    for (i=0; i<=strat->sl; i++)
    {
      if (((strat->fromQ==NULL) || (strat->fromQ[i]==0))
#ifdef SDRING
      && (!pSDRING)
#endif
      )
      {
        strat->S[i] = h.p = redtail(strat->S[i],strat->sl,strat);
        strat->initEcart(&h);
        strat->ecartS[i] = h.ecart;
      }
      else
      {
        h.p = strat->S[i];
        h.ecart=strat->ecartS[i];
      }
      if ((strat->fromQ==NULL) || (strat->fromQ[i]==0))
        cancelunit1(&h,strat->sl,strat);
      h.length = pLength(h.p);
      /*puts the elements of S also to T*/
      enterT(h,strat);
    }
  }
  if (redSi!=NULL) pDelete1(&redSi);
#ifdef SDRING
  Free((ADDRESS)aug,augmax*sizeof(poly));
  if (recursiv) updateS(FALSE,strat);
#endif
//  for(augl=0;augl<=strat->sl;augl++)
//    pTest(strat->S[augl]);
//Print("nach  updateS start mit sl=%d\n",strat->sl);
//  for (i=0; i<=strat->sl; i++)
//  {
//    Print("s%d:",i);
//    if (strat->fromQ) Print("(Q:%d) ",strat->fromQ[i]);
//    pWrite(strat->S[i]);
//  }
#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 i;

#ifdef SDRING
  if (pSDRING
  && (atS<=strat->sl)
  && pComparePolys(p.p,strat->S[atS]))
  {
    if (TEST_OPT_PROT)
      PrintS("m");
    p.p=NULL;
    return;
  }
  if (pSDRING
  && (atS<strat->sl)
  && pComparePolys(p.p,strat->S[atS+1]))
  {
    if (TEST_OPT_PROT)
      PrintS("m");
    p.p=NULL;
    return;
  }
  if (pSDRING
  && (atS>0)
  && pComparePolys(p.p,strat->S[atS-1]))
  {
    if (TEST_OPT_PROT)
      PrintS("m");
    p.p=NULL;
    return;
  }
#endif
  strat->news = TRUE;
  /*- puts p to the standardbasis s at position at -*/
  if (strat->sl == IDELEMS(strat->Shdl)-1)
  {
    strat->ecartS = (intset)ReAlloc(strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int),
                                    (IDELEMS(strat->Shdl)+setmax)*sizeof(int));
    if (strat->fromQ!=NULL)
    {
      strat->fromQ = (intset)ReAlloc(strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int),
                                    (IDELEMS(strat->Shdl)+setmax)*sizeof(int));
    }
    pEnlargeSet(&strat->S,IDELEMS(strat->Shdl),setmax);
    IDELEMS(strat->Shdl)+=setmax;
    strat->Shdl->m=strat->S;
  }
  for (i=strat->sl+1; i>=atS+1; i--)
  {
    strat->S[i] = strat->S[i-1];
    if (strat->honey) strat->ecartS[i] = strat->ecartS[i-1];
  }
  if (strat->fromQ!=NULL)
  {
    for (i=strat->sl+1; i>=atS+1; i--)
    {
      strat->fromQ[i] = strat->fromQ[i-1];
    }
    strat->fromQ[atS]=0;
  }
  /*- save result -*/
  strat->S[atS] = p.p;
  if (strat->honey) strat->ecartS[atS] = p.ecart;
  strat->sl++;
}

/*2
* puts p to the set T at position atT
*/
void enterT (LObject p,kStrategy strat)
{
  int i,atT;

#ifdef KDEBUG
  pTest(p.p);
  for (i=0; i<=strat->tl ;i++)
  {
    pTest(strat->T[i].p);
  }
#endif
  strat->newt = TRUE;
  if (strat->tl >= 0)
  {
    /*- puts p to the standardbasis s at position atT -*/
    atT = strat->posInT(strat->T,strat->tl,p);
//    if ((atT<=strat->tl)
//    && (p.p==strat->T[atT].p))
//    {
//      PrintS("?");
//      return;
//    }
//    if ((atT<strat->tl)
//    && (p.p==strat->T[atT+1].p))
//    {
//      PrintS("?");
//      return;
//    }
//    if ((atT>0)
//    && (p.p==strat->T[atT-1].p))
//    {
//      PrintS("?");
//      return;
//    }
    if (strat->tl == strat->tmax-1) enlargeT(&strat->T,&strat->tmax,setmax);
    for (i=strat->tl+1; i>=atT+1; i--)
      strat->T[i] = strat->T[i-1];
  }
  else atT = 0;
  strat->T[atT].p = p.p;
  strat->T[atT].ecart = p.ecart;
  strat->T[atT].length = p.length;
  strat->tl++;
}

/*2
* puts p to the set T at position atT
*/
void enterTBba (LObject p, int atT,kStrategy strat)
{
  int i;

  strat->newt = TRUE;
  if (strat->tl == strat->tmax-1) enlargeT(&strat->T,&strat->tmax,setmax);
  for (i=strat->tl+1; i>=atT+1; i--)
    strat->T[i] = strat->T[i-1];
  strat->T[atT].p = p.p;
  if (strat->honey)
    strat->T[atT].ecart = p.ecart;
  if (TEST_OPT_INTSTRATEGY)
    strat->T[atT].length = p.length;
  strat->tl++;
//    for (i=0; i<=strat->tl ;i++)
//    {
//      pTest(strat->T[i].p);
//    }
}

void initHilbCrit(ideal F, ideal Q, intvec **hilb,kStrategy strat)
{
  if (strat->homog!=isHomog)
  {
    *hilb=NULL;
  }
}

void initBuchMoraCrit(kStrategy strat)
{
  strat->sugarCrit =        TEST_OPT_SUGARCRIT;
  strat->Gebauer =          BTEST1(2) || strat->homog || strat->sugarCrit;
  strat->honey =            !strat->homog || strat->sugarCrit || TEST_OPT_WEIGHTM;
  if (TEST_OPT_NOT_SUGAR) strat->honey = FALSE;
  strat->pairtest = NULL;
  /* alway use tailreduction, except:
  * - in local rings, - in lex order case, -in ring over extensions */
  strat->noTailReduction = !TEST_OPT_REDTAIL;
  if (TEST_OPT_DEBUG)
  {
    if (strat->homog) PrintS("ideal/module is homogeneous\n");
    else              PrintS("ideal/module is not homogeneous\n");
  }
}

void initBuchMoraPos (kStrategy strat)
{
  if (pOrdSgn==1)
  {
    if (strat->honey)
    {
      strat->posInL = posInL15;
      strat->posInT = posInT15;
    }
    else if (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 (TEST_OPT_NOTREGULARITY) strat->posInL =posInLSpecial;
  }
  else
  {
    if (strat->homog)
    {
      strat->posInL = posInL11;
      strat->posInT = posInT11;
    }
    else
    {
      strat->posInL = posInL17;
      strat->posInT = posInT17;
    }
  }
  // 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;
}

void initBuchMora (ideal F,ideal Q,kStrategy strat)
{
  strat->interpt = BTEST1(OPT_INTERRUPT);
  strat->ak = idRankFreeModule(F);
  strat->kHEdge=NULL;
  if (pOrdSgn==1) strat->kHEdgeFound=FALSE;
  /*- creating temp data structures------------------- -*/
  strat->cp = 0;
  strat->c3 = 0;
  strat->tail = pInit();
  /*- set s -*/
  strat->sl = -1;
  /*- set L -*/
  strat->Lmax = setmax;
  strat->Ll = -1;
  strat->L = initL();
  /*- set B -*/
  strat->Bmax = setmax;
  strat->Bl = -1;
  strat->B = initL();
  /*- set T -*/
  strat->tl = -1;
  strat->tmax = setmax;
  strat->T = initT();
  /*- init local data struct.---------------------------------------- -*/
  strat->P.ecart=0;
  strat->P.length=0;
  if (pOrdSgn==-1)
  {
    if (strat->kHEdge!=NULL) pGetComp(strat->kHEdge)=strat->ak;
    if (strat->kNoether!=NULL) pGetComp(strat->kNoether)=strat->ak;
  }
  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->kIdeal = NULL;
  strat->fromT = FALSE;
  strat->noTailReduction = !TEST_OPT_REDTAIL;
  if(!TEST_OPT_SB_1)
  {
    updateS(TRUE,strat);
    pairs(strat);
  }
  if (strat->fromQ!=NULL) Free((ADDRESS)strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int));
  strat->fromQ=NULL;
}

void exitBuchMora (kStrategy strat)
{
  /*- release temp data -*/
  cleanT(strat);
  Free((ADDRESS)strat->T,(strat->tmax)*sizeof(TObject));
  Free((ADDRESS)strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int));
  /*- set L: should be empty -*/
  Free((ADDRESS)strat->L,(strat->Lmax)*sizeof(LObject));
  /*- set B: should be empty -*/
  Free((ADDRESS)strat->B,(strat->Bmax)*sizeof(LObject));
  pDelete1(&strat->tail);
  strat->syzComp=0;
  if (strat->kIdeal!=NULL)
  {
    Free((ADDRESS)strat->kIdeal,sizeof(sleftv));
    strat->kIdeal=NULL;
  }
}

/*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
      }
    }
  }
  else
  {
    int q;
    poly p;
    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)
          &&(pEqual(r->m[l],Q->m[q])))
          {
            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;
          }
        }
      }
    }
  }
  idSkipZeroes(r);
}

void completeReduce (kStrategy strat)
{
  int i;

  strat->noTailReduction = FALSE;
  if (TEST_OPT_PROT)
  {
    PrintLn();
    if (timerv) writeTime("standard base computed:");
  }
  if (TEST_OPT_PROT)
  {
    Print("(S:%d)",strat->sl);mflush();
  }
  if(pOrdSgn==1)
  {
    for (i=strat->sl; i>0; i--)
    {
      if (strat->interpt) test_int_std(strat->kIdeal);
      strat->S[i] = redtailBba(strat->S[i],i-1,strat);
      if (TEST_OPT_INTSTRATEGY)
      {
        pCleardenom(strat->S[i]);
      }
      if (TEST_OPT_PROT)
      {
        PrintS("-");mflush();
      }
    }
  }
  else
  {
    for (i=strat->sl; i>=0; i--)
    {
      if (strat->interpt) test_int_std(strat->kIdeal);
      strat->S[i] = redtail(strat->S[i],strat->sl,strat);
      if (TEST_OPT_INTSTRATEGY)
      {
        pCleardenom(strat->S[i]);
      }
      if (TEST_OPT_PROT)
      {
        PrintS("-");mflush();
      }
    }
  }
}

/*2
* computes the new strat->kHEdge and the new pNoether,
* returns TRUE, if pNoether has changed
*/
BOOLEAN newHEdge(polyset S, int ak,kStrategy strat)
{
  int i,j;
  poly newNoether;

  scComputeHC(strat->Shdl,ak,strat->kHEdge);
  /* compare old and new noether*/
  newNoether = pHead0(strat->kHEdge);
  j = pFDeg(newNoether);
  {
    short * e = (short *)Alloc((pVariables+1)*sizeof(short));
    pGetExpV(newNoether,e);
    for (i=1; i<=pVariables; i++)
    {
      if (e[i] > 0) (e[i])--;
    }
    pSetExpV(newNoether,e);
    Free((ADDRESS)e,(pVariables+1)*sizeof(short));
  }
  if (j < strat->HCord) /*- statistics -*/
  {
    if (TEST_OPT_PROT)
    {
      Print("H(%d)",j);
      mflush();
    }
    strat->HCord=j;
    if (TEST_OPT_DEBUG)
    {
      Print("H(%d):",pFDeg(strat->kHEdge));
      wrp(strat->kHEdge);
      PrintLn();
    }
  }
  if (pComp(strat->kNoether,newNoether)!=1)
  {
    pDelete(&strat->kNoether);
    strat->kNoether=newNoether;
    return TRUE;
  }
  pFree1(newNoether);
  return FALSE;
}