  In this paper we generalise and unify the results and methods used by Benson,
Liardet, Evetts, and Evetts & Levine, to show that rational sets in a virtually
abelian group G have rational (relative) growth series with respect to any
generating set for G. We prove equivalences between the structures used in the
literature, and establish the rationality of important classes of sets in G:
definable sets, algebraic sets, conjugacy representatives and coset
representatives (of any fixed subgroup), among others. Furthermore, we show
that any rational set, when written as words over the generating set of G, has
several EDT0L representations.
