The structure of Reed-Muller and generalised Reed-Muller transform matrices is discussed and in particular their description in terms of the Kronecker matrix product of basic forms is explained. The use of map-entered variables to enable function maps to be folded into smaller-dimension structures, thereby easing the transform process, is investigated. Methods for term-by-term transformation which are particularly suited to sparse functions are presented and it is shown that these can be incorporated into the procedures for handling incompletely specified operational-domain descriptions. The more general problem of deducing the optimum-polarity expansion of such functions is also considered.