Function Mfwalk

Singular/walk.cc:8032–8202

* The implementation of the fractal walk algorithm * * * * The main procedure Mfwalk calls the recursive Subroutine * * rec_fractal_call to compute the wanted Groebner basis. * * At the main procedur we compute the reduced Groebner basis w.r.t. a "fast"

 * of a matrix. This matrix defines the given monomial order, e.g. "lp"        *
 *******************************************************************************/
ideal Mfwalk(ideal G, intvec* ivstart, intvec* ivtarget,
             int reduction, int printout)
{
  BITSET save1 = si_opt_1; // save current options
  if(reduction == 0)
  {
    si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis
    //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions
  }
  Set_Error(FALSE);
  Overflow_Error = FALSE;
  //Print("// pSetm_Error = (%d)", ErrorCheck());
  //Print("\n// ring ro = %s;", rString(currRing));

  nnflow = 0;
  Xngleich = 0;
  Xcall = 0;
#ifdef TIME_TEST
  xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0;
  xftinput = clock();
#endif
  ring  oldRing = currRing;
  int i, nV = currRing->N;
  XivNull = new intvec(nV);
  Xivinput = ivtarget;
  ngleich = 0;
#ifdef TIME_TEST
  to=clock();
#endif
  ideal I = MstdCC(G);
  G = NULL;
#ifdef TIME_TEST
  xftostd=clock()-to;
#endif
  Xsigma = ivstart;

  Xnlev=nV;

#ifdef FIRST_STEP_FRACTAL
  ideal Gw = MwalkInitialForm(I, ivstart);
  for(i=IDELEMS(Gw)-1; i>=0; i--)
  {
    if((Gw->m[i]!=NULL) // len >=0
    && (Gw->m[i]->next!=NULL) // len >=1
    && (Gw->m[i]->next->next!=NULL)) // len >=2
    {
      intvec* iv_dp = MivUnit(nV); // define (1,1,...,1)
      intvec* Mdp;
      if(ivstart->length() == nV)
      {
        if(MivSame(ivstart, iv_dp) != 1)
          Mdp = MivWeightOrderdp(ivstart);
        else
          Mdp = MivMatrixOrderdp(nV);
      }
      else
      {
        Mdp = ivstart;