Constructing Faithful Representations of Finitely-generated Torsion-free Nilpotent Groups

We formulate an algorithm for calculating a representation by unipotent matrices over the integers of a finitely-generated torsion-free nilpotent group given by a polycyclic presentation. The algorithm works along a polycyclic series of the group, each step extending a representation of an element of that series to the next element.