syzygy()

void RingZZ::syzygy ( const ring_elem a, const ring_elem b, ring_elem & x, ring_elem & y ) const

virtual

Implements Ring.

Definition at line 386 of file ZZ.cpp.

{
  assert(!is_zero(b));
  // First check the special cases a = 0, b = 1, -1.  Other cases: use gcd.
  if (RingZZ::is_zero(a))
    {
      x = RingZZ::from_long(1);
      y = RingZZ::from_long(0);
      return;
    }
  mpz_srcptr bb = b.get_mpz();
  if (mpz_cmp_ui(bb, 1) == 0)
    {
      x = RingZZ::from_long(1);
      y = RingZZ::negate(a);
      return;
    }
  if (mask_mpz_cmp_si(bb, -1) == 0)
    {
      x = RingZZ::from_long(1);
      y = RingZZ::copy(a);
      return;
    }
  ring_elem g = RingZZ::gcd(a, b);
  y = RingZZ::divide(a, g);
  x = RingZZ::divide(b, g);
  RingZZ::remove(g);
  if (mpz_sgn(x.get_mpz()) > 0)
    y = RingZZ::negate(y);
  else
    x = RingZZ::negate(x);
}

References copy(), divide(), from_long(), gcd(), ring_elem::get_mpz(), is_zero(), mask_mpz_cmp_si(), negate(), remove(), and x.