def fan_isomorphic_necessary_conditions(fan1, fan2):
    """
    Check necessary (but not sufficient) conditions for the fans to be isomorphic.

    INPUT:

    - ``fan1``, ``fan2`` -- two fans.

    OUTPUT:

    Boolean. ``False`` if the two fans cannot be isomorphic. ``True``
    if the two fans may be isomorphic.

    EXAMPLES::

        sage: fan1 = toric_varieties.P2().fan()
        sage: fan2 = toric_varieties.dP8().fan()
        sage: from sage.geometry.fan_isomorphism import fan_isomorphic_necessary_conditions
        sage: fan_isomorphic_necessary_conditions(fan1, fan2)
        False
    """
    if fan1.lattice_dim() != fan2.lattice_dim():
        return False
    if fan1.dim() != fan2.dim():
        return False
    if fan1.nrays() != fan2.nrays():
        return False
    if fan1.ngenerating_cones() != fan2.ngenerating_cones():
        return False
    if fan1.is_complete() != fan2.is_complete():
        return False
    return True