  One of the most debated issues related to high-$T_c$ superconductivity is the
symmetry of the Cooper pair or the gap function. In this report, we present
numerical results regarding the gap function in strongly correlated electron
systems using $t-J$ and Hubbard models in one and two dimensions. To this end,
we use exact diagonalization to study the ground states of 8- and 16-site
clusters consisting of single or coupled layers. We calculate a reduced
two-particle density matrix in momentum space which is a measure of the gap
function. We then analyze the eigenvectors of this density matrix, which
display the possible Cooper pair symmetries. The eigenvector corresponding to
the largest eigenvalue indicates a vanishing gap on the Fermi surface (which is
in favour of odd-gap pairing) although $d_{x^2-y^2}$ symmetry is seen to be a
very close contestant in many of the cases.
