reduce()

void HermiteComputation::reduce ( hm_elem *& p, hm_elem * q )

private

Definition at line 210 of file hermite.cpp.

{
  // compute (u,v) s.t. u lead(p) + v lead(q) = gcd
  // set p <- u*p + v*q;
  // set q <- lead(q)/gcd * p - lead(p)/gcd * q
  // DOn't forget to also reset the 'lead' fields!
  ring_elem u, v;
  ring_elem g = globalZZ->gcd_extended(p->f->coeff, q->f->coeff, u, v);
  ring_elem a = globalZZ->divide(q->f->coeff, g);  // exact
  ring_elem b = globalZZ->divide(p->f->coeff, g);  // exact
  globalZZ->negate_to(b);
 
  vec p1 = globalZZ->mult_vec(u, p->f);
  vec p2 = globalZZ->mult_vec(v, q->f);
  globalZZ->add_vec_to(p1, p2);
 
  vec syz1 = globalZZ->mult_vec(u, p->fsyz);
  vec syz2 = globalZZ->mult_vec(v, q->fsyz);
  globalZZ->add_vec_to(syz1, syz2);
 
  vec q1 = globalZZ->mult_vec(a, p->f);
  vec q2 = globalZZ->mult_vec(b, q->f);
  globalZZ->add_vec_to(q1, q2);
 
  vec qsyz1 = globalZZ->mult_vec(a, p->fsyz);
  vec qsyz2 = globalZZ->mult_vec(b, q->fsyz);
  globalZZ->add_vec_to(qsyz1, qsyz2);
 
  globalZZ->remove_vec(p->f);
  globalZZ->remove_vec(q->f);
  globalZZ->remove_vec(p->fsyz);
  globalZZ->remove_vec(q->fsyz);
  globalZZ->remove(a);
  globalZZ->remove(b);
  globalZZ->remove(g);
  globalZZ->remove(u);
  globalZZ->remove(v);
 
  // Now that the arithmetic has been done, put back into 'p', 'q':
  p->f = p1;
  p->fsyz = syz1;
  mpz_set(p->lead, p->f->coeff.get_mpz());
 
  q->f = q1;
  q->fsyz = qsyz1;
  if (q->f != nullptr) mpz_abs(q->lead, q->f->coeff.get_mpz());
 
  insert(q);
}

References hm_elem::f, hm_elem::fsyz, globalZZ, insert(), hm_elem::lead, p, and p1.

Referenced by start_computation().