The Polenta package provides functions for computation with matrix groups. Let G be a subgroup of GL(d,R) where the ring R is either equal to \Q,\Z or a finite field \F_q. Then: - We can test whether G is solvable. - We can test whether G is polycyclic. - If G is polycyclic, then we can determine a polycyclic presentation for G.

A group G which is given by a polycyclic presentation can be investigated by algorithms implemented in the GAP package Polycyclic. For example we can determine if G is torsion-free and calculate the torsion subgroup. Further we can compute the derived series and the Hirschlength of the group G. Also various methods for computations with subgroups, factorsgroups and extensions are available.

As a by-product, the Polenta package provides some functionality to compute certain module series for modules of solvable groups. For example, if G is a rational polycyclic matrix group, then we can compute the radical series of the natural \Q[G]-module \Q^d.