The GAP 4 package Polenta

This 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 presentations can be largely 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 $\Q^d$.

Installing this package

The Polenta package is part of the standard distribution of GAP and so normally there should be no need to install it separately.

If by any chance it is not part of your GAP distribution, then this package is available at https://gap-packages.github.io/polenta/ in form of a gzipped tar-archive. The standard method is to unpack the package into the pkg directory of your GAP distribution. This will create a polenta subdirectory. For other non-standard options please refer to the GAP Reference Manual.

Note that the GAP-Packages Alnuth and Polycyclic are needed for this package. Normally they should be contained in your distribution. If not they can be obtained at https://www.gap-system.org/Packages/packages.html.

Loading the Polenta package

If the Package is not already loaded then you have to request it explicitly. This can be done by LoadPackage("polenta"). The LoadPackage command is described in the GAP Reference Manual.

Running the test suite

Once the package is installed, it is possible to check the correct installation by running the test suite of the package.

gap> ReadPackage( "Polenta", "tst/testall.g" );

For more details on Test Files see Section 7.9 of the GAP Reference Manual.

If the test suite runs into an error, even though the packages Polycyclic and Alnuth and their depdendencies have been correctly installed, then please send a message to [email protected] including the error message.

Author / Maintainer

The Polenta package was originally written by Bjoern Assmann, who remains his principal author.

It is currently being maintained by Max Horn [email protected].

To submit bug reports, feature requests and suggestions, please go to https://github.com/gap-packages/polenta/issues.