def e_f_of_valuation(v):
    """ Return the ramification index of this valuation.

    INPUT:

    - ``v`` -- a function field valuation on an extension of a rational function field

    OUTPUT: the ramification index of `v` over the base field

    """
    from sage.rings.polynomial.polynomial_ring import PolynomialRing_field
    while not isinstance(v.domain(), PolynomialRing_field):
        v = v._base_valuation
    if hasattr(v, '_approximation'):
        v = v._approximation
    return v.E(), v.F()
