  A new computational strategy is proposed to approximate, with a simple but
accurate expression, the Maier- Saupe free energy for nematic order. Instead of
the traditional approach of expanding the free energy with a truncated Taylor
series, we employ a least-squares fitting to obtain the coefficients of a
polynomial expression. Both methods are compared, and the fitting with at most
five polynomial terms is shown to provide a satisfactory fitting, and to give
much more accurate results than the traditional Taylor expansion. We perform
the analysis in terms of the tensor order parameter, so the results are valid
in uniaxial and biaxial states.
