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.