def test_holzer():
# if the input is good, don't let it diverge in holzer()
# (but see test_fail_holzer below)
assert holzer(2, 7, 13, 4, 79, 23) == (2, 7, 13)
# None in uv condition met; solution is not Holzer reduced
# so this will hopefully change but is here for coverage
assert holzer(2, 6, 2, 1, 1, 10) == (2, 6, 2)
raises(ValueError, lambda: holzer(2, 7, 14, 4, 79, 23))
def test_fail_holzer():
eq = lambda x, y, z: a * x ** 2 + b * y ** 2 - c * z ** 2
a, b, c = 4, 79, 23
x, y, z = xyz = 26, 1, 11
X, Y, Z = ans = 2, 7, 13
assert eq(*xyz) == 0
assert eq(*ans) == 0
assert max(a * x ** 2, b * y ** 2, c * z ** 2) <= a * b * c
assert max(a * X ** 2, b * Y ** 2, c * Z ** 2) <= a * b * c
h = holzer(x, y, z, a, b, c)
assert h == ans # it would be nice to get the smaller soln