Computing polycyclic presentations for polycyclic rational matrix groups

We describe practical algorithms for computing a polycyclic presentation and for facilitating a membership test for a polycyclic subgroup of GL(d,Q). A variation of this method can be used to check whether a finitely generated subgroup of GL(d,Q) is solvable or solvable-by-finite. We report on our implementations of the algorithms for determining a polycyclic presentation and checking solvability.