def monomial_div(a, b):
    """Division of tuples representing monomials.

       Lets divide x**3*y**4*z by x*y**2:

       >>> monomial_div((3, 4, 1), (1, 2, 0))
       (2, 2, 1)

       which gives x**2*y**2*z. However

       >>> monomial_div((3, 4, 1), (1, 2, 2))
       None

       x*y**2*z**2 does not divide x**3*y**4*z.

    """
    result = [ x - y for x, y in zip(a, b) ]

    if all(e >= 0 for e in result):
        return tuple(result)
    else:
        return None