normal_form()

void QRingInfo_field_basic::normal_form ( ring_elem & f ) const

virtual

Reimplemented from QRingInfo.

Definition at line 119 of file qring.cpp.

{
  exponents_t EXP1 = ALLOCATE_EXPONENTS(exp_size);
 
  const Monoid *M = R->getMonoid();
  Nterm head;
  Nterm *result = &head;
  Nterm *t = f;
  while (t != nullptr)
    {
      M->to_expvector(t->monom, EXP1);
      Bag *b;
      if (Rideal->search_expvector(EXP1, b))
        {
          Nterm *s = quotient_element(b->basis_elem());
          // Now we must replace t with
          // t + c*m*s, where in(t) = in(c*m*s), and c is 1 or -1.
          reduce_lead_term_basic_field(t, s);
        }
      else
        {
          result->next = t;
          t = t->next;
          result = result->next;
        }
    }
  result->next = nullptr;
  f = head.next;
}

References ALLOCATE_EXPONENTS, int_bag::basis_elem(), QRingInfo::exp_size, Nterm::monom, Nterm::next, QRingInfo::quotient_element(), QRingInfo::R, reduce_lead_term_basic_field(), result(), QRingInfo_field::Rideal, s, and Monoid::to_expvector().