  Within the Quartet Condensation Model (QCM), the isovector pairing
correlations for $N = Z$ nuclei are described with a very high accuracy by a
condensate of $\alpha$-like quartets. The usual approach involves cumbersome
recurrence relations in order to compute numerically the relevant quantities of
the model: the norm of the quartet states and the mean value of the isovector
pairing Hamiltonian as functions of the pair mixing amplitudes. We present the
final analytical expressions for the above mentioned quantities, for all cases
up to four quartets in the valence shell. The analytical QCM expressions were
obtained by a straightforward implementation of the SO(5) algebra in the
symbolic computer algebra system Cadabra2. The norm of the quartet states and
the mean value of the Hamiltonian are polynomial functions of the mixing
amplitudes. The numerical implementation of the QCM model is thus made trivial
as matter of copying and pasting the presented formulas. We introduce in this
work the method of computer aided analytical calculus for a many body setting.
In particular, we provide precise and easy to use tools for the description of
isovector pairing correlations.
