Function idLift

kernel/ideals.cc:1105–1330

2 *computes a representation of the generators of submod with respect to those * of mod */ represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result) goodShape: maximal non-zero index in generators of SM <= that of M isSB: generators of M form a Groebner basis divide: allow SM not to be a submodule of M U is an diagonal matrix of un

/// U is an diagonal matrix of units (non-constant only in local rings)
/// rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide
ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape,
             BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
{
  int lsmod =id_RankFreeModule(submod,currRing), j, k;
  int comps_to_add=0;
  int idelems_mod=IDELEMS(mod);
  int idelems_submod=IDELEMS(submod);
  poly p;

  if (idIs0(submod))
  {
    if (rest!=NULL)
    {
      *rest=idInit(1,mod->rank);
    }
    idLift_setUnit(idelems_submod,unit);
    return idInit(1,idelems_mod);
  }
  if (idIs0(mod)) /* and not idIs0(submod) */
  {
    if (rest!=NULL)
    {
      *rest=idCopy(submod);
      idLift_setUnit(idelems_submod,unit);
      return idInit(1,idelems_mod);
    }
    else
    {
      WerrorS("2nd module does not lie in the first");
      return NULL;
    }
  }
  if (unit!=NULL)
  {
    comps_to_add = idelems_submod;
    while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
      comps_to_add--;
  }
  k=si_max(id_RankFreeModule(mod,currRing),id_RankFreeModule(submod,currRing));
  if  ((k!=0) && (lsmod==0)) lsmod=1;
  k=si_max(k,(int)mod->rank);
  if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }

  ring orig_ring=currRing;
  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
  rSetSyzComp(k,syz_ring);
  rChangeCurrRing(syz_ring);

  ideal s_mod, s_temp;
  if (orig_ring != syz_ring)
  {
    s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring);
    s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring);
  }
  else
  {
    s_mod = mod;
    s_temp = idCopy(submod);