def METHOD_NAME():
    R, x, _ = ring('x y', ZZ)
    f, g, h = R.fateman_poly_F_2()
    D = (1 + sum(R.gens))**2
    assert f == D*(-2 + x - sum(R.gens[1:]))**2
    assert g == D*(2 + sum(R.gens))**2
    assert h == D
    R, x, *_ = ring('x y z t', ZZ)
    f, g, h = R.fateman_poly_F_2()
    D = (1 + sum(R.gens))**2
    assert f == D*(-2 + x - sum(R.gens[1:]))**2
    assert g == D*(2 + sum(R.gens))**2
    assert h == D