Function idMinEmbedding1

kernel/ideals.cc:2778–2799

2 * returns the presentation of an isomorphic, minimally * embedded module (arg represents the quotient!) */

* embedded  module (arg represents the quotient!)
*/
static ideal idMinEmbedding1(ideal arg,BOOLEAN inPlace, intvec **w,
  int* red_comp, int &del)
{
  if (idIs0(arg)) return idInit(1,arg->rank);
  int i,next_gen,next_comp;
  ideal res=arg;
  if (!inPlace) res = idCopy(arg);
  res->rank=si_max(res->rank,id_RankFreeModule(res,currRing));
  for (i=res->rank;i>=0;i--) red_comp[i]=i;

  loop
  {
    next_gen = id_ReadOutPivot(res, &next_comp, currRing);
    if (next_gen<0) break;
    del++;
    syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res));
    for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
    if ((w !=NULL)&&(*w!=NULL))
    {
      for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
    }
  }

  idSkipZeroes(res);