An explicit formula for the extended Gross-Keating datum of a quadratic form

In this paper, we give a formula for the extended Gross-Keating datum of a half-integral symmetric matrix over a finite extension of Q p \mathbb {Q}_p (for p > 2 p>2 ) or a finite unramified extension of Q 2 \mathbb {Q}_2 . As an application, we describe an explicit formula for the Siegel series for Q p \mathbb {Q}_p . We also present the details of algorithms implemented in a Mathematica package to compute the extended Gross-Keating datum and the Siegel series.