def _gcdex(a, b):
r"""
This supports the functions that compute Hermite Normal Form.
Explanation
===========
Let x, y be the coefficients returned by the extended Euclidean
Algorithm, so that x*a + y*b = g. In the algorithms for computing HNF,
it is critical that x, y not only satisfy the condition of being small
in magnitude -- namely that |x| <= |b|/g, |y| <- |a|/g -- but also that
y == 0 when a | b.
"""
x, y, g = ZZ.gcdex(a, b)
if a != 0 and b % a == 0:
y = 0
x = -1 if a < 0 else 1
return x, y, g
