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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def correct_rytov_sc_input(radius_sc, sphere_index_sc, medium_index, radius_sampling):
 """Inverse correction of refractive index and radius for Rytov This method returns the inverse of :func:`correct_rytov_output`. Parameters radius_sc: float Systematically corrected radius of the sphere [m] sphere_index_sc: float Systematically corrected refractive index of the sphere medium_index: float Refractive index of the surrounding medium radius_sampling: int Number of pixels used to sample the sphere radius when computing the Rytov field. Returns ------- radius: float Fitted radius of the sphere [m] sphere_index: float Fitted refractive index of the sphere See Also -------- correct_rytov_output: the inverse of this method """

    params = get_params(radius_sampling)

    # sage script:
    # var('sphere_index, sphere_index_sc, na, nb, medium_index')
    # x = sphere_index / medium_index - 1
    # eq = sphere_index_sc == sphere_index + ( na*x^2 + nb*x) * medium_index
    # solve([eq], [sphere_index])
    # (take the positive sign solution)
    na = params["na"]
    nb = params["nb"]

    prefac = medium_index / (2 * na)
    sm = 2 * na - nb - 1
    rt = nb**2 - 4 * na + 2 * nb + 1 + 4 / medium_index * na * sphere_index_sc
    sphere_index = prefac * (sm + np.sqrt(rt))

    x = sphere_index / medium_index - 1

    radius = radius_sc / (params["ra"] * x**2
                          + params["rb"] * x
                          + params["rc"])

    return radius, sphere_index