make_new_pairs()

void binomialGB::make_new_pairs	(	binomial_s_pair_set *	Pairs,
		binomial_gb_elem *	f ) const

Definition at line 796 of file gb-toric.cpp.

{
  // Compute (a minimal generating set of)
  // the ideal quotient in(Gmin) : in(f).
  // Remove any that satisfy certain criteria:
  // 1. gcd(lead terms) is 1: remove.
  // 2. if homog_prime, gcd(tail terms) is not 1: remove.
  // Any that pass these tests, insert into Pairs.
 
  monomial m = f->f.lead;
  monomial_list *I = ideal_quotient(m);
 
  for (monomial_list *q = I; q != nullptr; q = q->next)
    {
      gbmin_elem *ge = q->tag;  // a list of possibles
 
      binomial_gb_elem *g = ge->elem;
 
      // Criterion 1: gcd of lead terms must be not 1.
      if (R->gcd_is_one(R->lead_monomial(f->f), R->lead_monomial(g->f)))
        {
          // remove each of the elements in 'g'.
          continue;
        }
 
      // Criterion 2: if a homogeneous prime,
      // gcd of tails must be 1.
      if (is_homogeneous_prime)
        {
          if (!R->gcd_is_one(f->f.tail, g->f.tail)) continue;
        }
 
      // Finally do the insert
      monomial lcm = R->mult(m, q->m);
      Pairs->insert(binomial_s_pair(f, g, lcm));
    }
  remove_monomial_list(I);
}

References binomialGB::gbmin_elem::elem, binomial_gb_elem::f, ideal_quotient(), is_homogeneous_prime, binomial::lead, monomial, binomialGB::monomial_list::next, R, remove_monomial_list(), and binomial::tail.