syzygy()

void M2::ARingZZGMP::syzygy	(	const ElementType &	a,
		const ElementType &	b,
		ElementType &	x,
		ElementType &	y ) const

Definition at line 47 of file aring-zz-gmp.cpp.

{
  assert(!is_zero(b));
  // First check the special cases a = 0, b = 1, -1.  Other cases: use gcd.
  if (is_zero(a))
    {
      set_from_long(x, 1);
      set_zero(y);
      return;
    }
  if (mpz_cmp_ui(&b, 1) == 0)
    {
      set_from_long(x, 1);
      negate(y, a);
      return;
    }
  if (mpz_cmp_si(&b, -1) == 0)
    {
      set_from_long(x, 1);
      set(y, a);
      return;
    }
  elem g;
  init(g);
  mpz_gcd(&g, &a, &b);
  divide(y, a, g);
  divide(x, b, g);
  if (mpz_sgn(&x) > 0)
    negate(y, y);
  else
    negate(x, x);
  clear(g);
}

References clear(), divide(), init(), is_zero(), negate(), set(), set_from_long(), set_zero(), and x.