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Let k be an algebraically closed field of characteristic 0. Musson andvandenBergh classified primitive ideals for rings of torus invariantdifferential operators. This classification applies in particular tosubquotients of localized extended Weyl algebras where it can be made explicitin terms of convex geometry. We recall these result and then turn to thecorresponding primitive quotients and study their Goldie ranks. We prove thatthe primitive quotients fall into finitely many families whose Goldie ranks aregiven by a common quasi-polynomial and then realize these quasi-polynomials asEhrhart quasi-polynomials arising from convex geometry.

Goldie rank of primitive quotients via lattice point enumeration