  The Gross-Keating invariant of a half-integral matrix over a $p$-adic integer
ring is a fundamental concept in the study of quadratic forms, and has
important applications to Siegel modular forms and arithmetic geometry. We
introduce the Mathematica package computeGK, a computer program for calculating
the Gross-Keating invariant and the Siegel series of a half-integral matrix
over $\mathbb{Z}_p$, as well as other related quantities. As a by-product, we
obtain a table of the arithmetic intersection numbers related to the classical
modular polynomials using the explicit formula of Gross and Keating.
