Function id_Sat_principal

kernel/ideals.cc:3376–3454

}

ideal id_Sat_principal(ideal I, ideal J, const ring origR)
{
  rRingOrder_t    *ord;
  int    *block0,*block1;
  int    **wv;

  // construction extension ring
  ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
  block0=(int*)omAlloc0(4*sizeof(int));
  block1=(int*)omAlloc0(4*sizeof(int));
  wv=(int**) omAlloc0(4*sizeof(int**));
  wv[0]=(int*)omAlloc0((rVar(origR) + 2)*sizeof(int));
  block0[0] = block0[1] = 1;
  block1[0] = block1[1] = rVar(origR)+1;
  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
  // ignore it
  ord[0] = ringorder_aa;
  wv[0][rVar(origR)]=1;
  BOOLEAN wp=FALSE;
  for (int j=0;j<rVar(origR);j++)
    if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
  if (wp)
  {
    wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
    for (int j=0;j<rVar(origR);j++)
      wv[1][j]=p_Weight(j+1,origR);
    ord[1] = ringorder_wp;
  }
  else
    ord[1] = ringorder_dp;
  ord[2] = ringorder_C;
  ord[3] = (rRingOrder_t)0;
  char **names=(char**)omAlloc0((origR->N+1) * sizeof(char *));
  for (int j=0;j<rVar(origR);j++)
    names[j]=origR->names[j];
  names[rVar(origR)]=(char*)"@";
  ring tmpR=rDefault(nCopyCoeff(origR->cf),rVar(origR)+1,names,4,ord,block0,block1,wv);
  omFree(names);
  rComplete(tmpR, 1);
  rChangeCurrRing(tmpR);
  // map I
  ideal II=idrCopyR(I,origR,tmpR);
  // map J
  ideal JJ=idrCopyR(J,origR,tmpR);
  // J[1]*t-1
  poly t=pOne();
  p_SetExp(t,rVar(tmpR),1,tmpR);
  p_Setm(t,tmpR);
  poly p=JJ->m[0];
  p_Norm(p,currRing);
  p=p_Mult_q(p,t,tmpR);
  p=p_Sub(p,pOne(),tmpR);
  JJ->m[0]=p;
  ideal T=id_SimpleAdd(II,JJ,tmpR);
  idTest(T);
  id_Delete(&II,tmpR);
  id_Delete(&JJ,tmpR);
  // elimination