human
Complete the below
def doppler_relativistic(rest):

    ''''Return the equivalency pairs for the relativistic convention for velocity.
    The full relativistic convention for the relation between velocity and frequency is:
    :math:`V = c \frac{f_0^2 - f^2}{f_0^2 + f^2}.
 f(V) = f_0 \frac{\left(1 - (V/c)^2\right)^{1/2}}{(1+V/c)}`
    Parameters
    rest : `~astropy.units.Quantity`
    Any quantity supported by the standard spectral equivalencies
    (wavelength, energy, frequency, wave number).
    References
    `NRAO site defining the conventions <http://www.gb.nrao.edu/~fghigo/gbtdoc/doppler.html>`_
    Examples
    >>> import astropy.units as u
    >>> CO_restfreq = 115.27120*u.GHz  # rest frequency of 12 CO 1-0 in GHz
    >>> relativistic_CO_equiv = u.doppler_relativistic(CO_restfreq)
    >>> measured_freq = 115.2832*u.GHz
    >>> relativistic_velocity = measured_freq.to(u.km/u.s, equivalencies=relativistic_CO_equiv)
    >>> relativistic_velocity  # doctest: +FLOAT_CMP
    <Quantity -31.207467619351537 km / s>
    >>> measured_velocity = 1250 * u.km/u.s
    >>> relativistic_frequency = measured_velocity.to(u.GHz, equivalencies=relativistic_CO_equiv)
    >>> relativistic_frequency  # doctest: +FLOAT_CMP
    <Quantity 114.79156866993588 GHz>
    >>> relativistic_wavelength = measured_velocity.to(u.mm, equivalencies=relativistic_CO_equiv)
    >>> relativistic_wavelength  # doctest: +FLOAT_CMP
    <Quantity 2.6116243681798923 mm>'
    '''

Can you provide a the Python code you requested?
assistant
#Here is the Python code you requested.
    assert_is_spectral_unit(rest)
    ckms = _si.c.to_value(u'km/s')
    def to_vel_freq(x):
        restfreq = rest.to_value(si.Hz, equivalencies=spectral())
        return ((((restfreq ** 2) - (x ** 2)) / ((restfreq ** 2) + (x ** 2))) * ckms)
    def from_vel_freq(x):
        restfreq = rest.to_value(si.Hz, equivalencies=spectral())
        voverc = (x / ckms)
        return (restfreq * (((1 - voverc) / (1 + voverc)) ** 0.5))
    def to_vel_wav(x):
        restwav = rest.to_value(si.AA, spectral())
        return ((((x ** 2) - (restwav ** 2)) / ((restwav ** 2) + (x ** 2))) * ckms)
    def from_vel_wav(x):
        restwav = rest.to_value(si.AA, spectral())
        voverc = (x / ckms)
        return (restwav * (((1 + voverc) / (1 - voverc)) ** 0.5))
    def to_vel_en(x):
        resten = rest.to_value(si.eV, spectral())
        return ((((resten ** 2) - (x ** 2)) / ((resten ** 2) + (x ** 2))) * ckms)
    def from_vel_en(x):
        resten = rest.to_value(si.eV, spectral())
        voverc = (x / ckms)
        return (resten * (((1 - voverc) / (1 + voverc)) ** 0.5))
    return [(si.Hz, (si.km / si.s), to_vel_freq, from_vel_freq), (si.AA, (si.km / si.s), to_vel_wav, from_vel_wav), (si.eV, (si.km / si.s), to_vel_en, from_vel_en)]