division_algorithm() [1/2]

Nterm * PolyRing::division_algorithm ( Nterm * f, Nterm * g ) const

protected

Definition at line 1517 of file poly.cpp.

{
  // This does standard division by one polynomial, returning the remainder.
  // However, it does work for Weyl algebra, skew commutative algebra,
  // as long as the coefficient ring is a field.
  ring_elem a = copy(f);
  Nterm *t = a;
  Nterm *b = g;
  Nterm remhead;
  Nterm *remt = &remhead;
  ring_elem c;
  monomial m = M_->make_one();
  while (t != nullptr)
    if (M_->divides_partial_order(b->monom, t->monom))
      {
        a = t;
        bool cancelled = imp_attempt_to_cancel_lead_term(a, g, c, m);
        t = a;
        if (!cancelled)
          {
            remt->next = t;
            remt = remt->next;
            t = t->next;
          }
      }
    else
      {
        remt->next = t;
        remt = remt->next;
        t = t->next;
      }
 
  remt->next = nullptr;
  return remhead.next;
}

References copy(), imp_attempt_to_cancel_lead_term(), PolynomialRing::M_, Nterm::monom, monomial, and Nterm::next.