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 www.gap-system.org/Packages/packages.html in form of a gzipped tar-archive and as an uncompressed 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 see Chapter 74.1 in 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 http://www.gap-system.org/Packages/packages.html Getting and installing KASH =========================== Note that the GAP package Alnuth whose functionality is used by the Polenta package requires the installation of KANT respectively KASH, the shell of the computational algebraic number theory system KANT. KASH itself is not part of the Alnuth package. It has to be obtained and installed independently. KASH is available at www.math.tu-berlin.de/~kant/download.html Note that you have to download two files for a complete installation of KASH. To install version 2.4 of KASH on a Linux system you should do the following: 1. Download the files kash_2.4.common.tar.gz and kash_2.4.1.linux.tar.gz into the same directory on your system. 2. Unpack the files using tar. This will create a directory KASH_2.4 containing, amongst other files, the KASH executable called kash. The place where KASH is put is independent of the place where the Alnuth or Polenta package is installed. 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 Section 72.2.1 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 the computational algebraic number theory system KANT have been correctly installed, then please send a message to `BjoernAssmann@gmx.net' including the error message. Author ====== The Polenta package was written by: Bjoern Assmann, Mathematical Institute University of St. Andrews North Haugh St. Andrews Fife KY16 9SS Scotland, UK e-mail: BjoernAssmann@gmx.net