  Let k be an algebraically closed field of characteristic 0. Musson and
vandenBergh classified primitive ideals for rings of torus invariant
differential operators. This classification applies in particular to
subquotients of localized extended Weyl algebras where it can be made explicit
in terms of convex geometry. We recall these result and then turn to the
corresponding primitive quotients and study their Goldie ranks. We prove that
the primitive quotients fall into finitely many families whose Goldie ranks are
given by a common quasi-polynomial and then realize these quasi-polynomials as
Ehrhart quasi-polynomials arising from convex geometry.
