It is often the case that a particular expression in the original generators is important in some homomorphic image of the group in the sense that it will very often form a common subexpression of subsequent expression. For this reason, Magma provides facilities to build related SLP-groups in which particular words acquire generator status themselves.
An SLP-group H on n + q generators (where G has n generators and Q has q elements). Furthermore, the identification of G.i with H.i (i≤n) and of Q[i] with H.(n + i) is maintained, allowing coercion between G and H and also simple definition of homomorphisms.