  Given a hypersurface, $X$, prime $p$, the zeta function is a generating
function for the number of $\mathbb{F}_{p}$ rational points of $X$. Until now,
there is no algorithm for computing hypersurfaces with ADE singularities. Scott
Stetson and Vladimir Baranovsky provided an algorithm with Mathematica for the
ordinary double point case. In this paper, I go over a Sage algorithm for
computing the zeta function of a hypersurface with ADE singularities over
3-dimensional projective space. To make the algorithm more efficient, I
established an equivalence between a polynomial belonging to the Jacobian ideal
with a polynomial satisfying a set of differential operators.
