Applications of Lie methods for computations with infinite polycyclic groups

Version 0.96.2
Released 2018-11-15

This project is maintained by The GAP Team

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The GAP 4 package Guarana

In this package we demonstrate the algorithmic usefulness of the so-called Mal’cev correspondence for computations with infinite polycyclic groups; it is a correspondence that associates to every $\Q$-powered nilpotent group $H$ a unique rational nilpotent Lie algebra $L_H$ and vice-versa. The Mal’cev correspondence was discovered by Anatoly Mal’cev in 1951.

Installing this package

The Guarana 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

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 guarana’ subdirectory. For other non-standard options please see Chapter 74.1 in the GAP Reference Manual.

Note that the GAP-Packages Polycyclic and Polenta are needed for this package. Normally they should be contained in your distribution. If not, they can be obtained at             

Loading the Guarana package

If the Package is not already loaded then you have to request it explicitly. This can be done by LoadPackage("guarana"). 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> Read(Filename(DirectoriesPackageLibrary("guarana","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, then please submit a report to our issue tracker at

Copyright (C) 2007 Björn Assmann

Distributed under the terms of the GNU General Public License (GPL) v2

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.


You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.