def _RIT_symm_express(eta, delta_m, S, Delta, coeffs):
    """
    Internal function to return the basic even-in-interchange-of-particles expression used in the RIT fits for the final mass, final spin, and peak luminosity

    The coefficients in the expression are passed as a vector as [0 1 2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d 4e 4f 4g 4h 4i] (giving the subscripts).
    """
    S2 = S * S
    dm2 = delta_m * delta_m
    Deltadm = Delta * delta_m
    Delta2 = Delta * Delta
    return 16.0 * eta * eta * (coeffs[0] + coeffs[1] * S + coeffs[2] *
        Deltadm + coeffs[3] * S2 + coeffs[4] * Delta2 + coeffs[5] * dm2 + 
        coeffs[6] * Deltadm * S + coeffs[7] * S * Delta2 + coeffs[8] * S2 *
        S + coeffs[9] * S * dm2 + coeffs[10] * Deltadm * S2 + coeffs[11] *
        Delta2 * Deltadm + coeffs[12] * Delta2 * Delta2 + coeffs[13] * S2 *
        S2 + coeffs[14] * Delta2 * S2 + coeffs[15] * dm2 * dm2 + coeffs[16] *
        Deltadm * dm2 + coeffs[17] * Delta2 * dm2 + coeffs[18] * S2 * dm2)
