reduce()

void GBKernelComputation::reduce ( gbvector *& g, gbvector *& gsyz )

private

Definition at line 381 of file Eschreyer.cpp.

{
  exponents_t REDUCE_exp = ALLOCATE_EXPONENTS(exp_size);
  monomial REDUCE_mon = ALLOCATE_MONOMIAL(monom_size);
 
  const Ring *gbringK = GR->get_flattened_coefficients();
  ring_elem one = gbringK->from_long(1);
  gbvector *lastterm = fsyz;  // fsyz has only ONE term.
  const gbvector *r;
  int q;
 
  int nhits = 0;
  int nremoved = 0;
  int max_len = GR->gbvector_n_terms(f);
 
  int count = 0;
  if (M2_gbTrace >= 4) emit_wrapped(",");
 
  while (f != nullptr)
    {
      if (SF)
        {
          SF->schreyer_down(f->monom, f->comp - 1, REDUCE_mon);
          M->to_expvector(REDUCE_mon, REDUCE_exp);
        }
      else
        M->to_expvector(f->monom, REDUCE_exp);
      if (find_ring_divisor(REDUCE_exp, r))
        {
          ring_elem u, v;
          // Subtract off f, leave fsyz alone
          M->divide(f->monom, r->monom, REDUCE_mon);
          gbringK->syzygy(f->coeff, r->coeff, u, v);
          gbvector *h = GR->mult_by_term(F, r, v, REDUCE_mon, f->comp);
          GR->gbvector_add_to(F, f, h);
          if (!gbringK->is_equal(u, one))
            {
              GR->gbvector_mult_by_coeff_to(fsyz, u);
              GR->gbvector_mult_by_coeff_to(f, u);
              gbringK->remove(u);
              gbringK->remove(v);
            }
          total_reduce_count++;
          count++;
        }
      else if (find_divisor(mi[f->comp - 1], REDUCE_exp, q))
        {
          ring_elem u, v;
          gbringK->syzygy(f->coeff, gb[q]->coeff, u, v);
          M->divide(f->monom, gb[q]->monom, REDUCE_mon);
          gbvector *h = GR->mult_by_term(F, gb[q], v, REDUCE_mon, 0);
          if (!gbringK->is_equal(u, one))
            {
              GR->gbvector_mult_by_coeff_to(fsyz, u);
              GR->gbvector_mult_by_coeff_to(f, u);
            }
          int n1 = GR->gbvector_n_terms(h);
          wipe_unneeded_terms(h);
          int n2 = GR->gbvector_n_terms(h);
          nremoved += (n1 - n2);
          lastterm->next = make_syz_term(v, f->monom, q + 1);  // grabs v.
          lastterm = lastterm->next;
          gbringK->remove(u);
          gbringK->remove(v);
          int n3 = GR->gbvector_n_terms(f);
          GR->gbvector_add_to(F, f, h);
          int n4 = GR->gbvector_n_terms(f);
          if (n4 > max_len) max_len = n4;
          nhits +=
              (n2 + n3 - n4 -
               2);  // the -2 is to avoid counting the lead term cancellations.
          total_reduce_count++;
          count++;
        }
      else
        {
          // To get here is an ERROR!
          f = f->next;  // Just to not have an infinite loop
          emit_line(
              "error in Schreyer reduction: element does not reduce to zero!");
        }
    }
 
  if (M2_gbTrace >= 4)
    {
      buffer o;
      o << count;
      o << "[" << max_len << " " << nhits << " " << nremoved << "]";
      emit_wrapped(o.str());
    }
}

References ALLOCATE_EXPONENTS, ALLOCATE_MONOMIAL, gbvector::coeff, gbvector::comp, emit_line(), emit_wrapped(), exp_size, F, find_divisor(), find_ring_divisor(), Ring::from_long(), gb, GR, Ring::is_equal(), M, M2_gbTrace, make_syz_term(), mi, gbvector::monom, monom_size, monomial, gbvector::next, Ring::remove(), SF, buffer::str(), Ring::syzygy(), total_reduce_count, and wipe_unneeded_terms().

Referenced by calc().