Constructing arithmetic subgroups of unipotent groups

Let G be a unipotent algebraic subgroup of some GLm(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z)=G∩GLm(Z). This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.