A Practical Algorithm for Finding Matrix Representations for Polycyclic Groups

In this paper we describe a new algorithm for constructing a representation by integer matrices for a polycyclic group given by a finite presentation. This is a first step toward finding a practical algorithm for this problem. We used our algorithm to construct representations for various polycyclic groups. The examples which we studied included a collection of free nilpotent groups, and our results here led us to a new theoretical result concerning such groups.