  The influence of repulsion and attraction in high-Tc superconductors to the
gap functions is studied. A systematic method is proposed to compute the gap
functions using the irreducible representations of the point group. It is found
that a pure s-wave superconductivity exists only at very low temperatures, and
attractive potentials on the near shells significantly expand the gap functions
and increase significantly the critical temperature of superconductivity. A
strong on-site repulsion drives the $A_{1g}$ gap into a $B_{1g}$ gap. It is
expected that superconductivity with the $A_{1g}$ symmetry reaches a high
critical temperature due to the cooperation of the on-site and the next-nearest
neighbor attractions.
