<!-- HAPPRIME - algo.xml Algorithms documentation section Paul Smith Copyright (C) 2007 Paul Smith National University of Ireland Galway This file is part of HAPprime. HAPprime 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. HAPprime 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, see <http://www.gnu.org/licenses/>. $Id: algo.xml 216 2008-02-29 12:42:55Z pas $ --> <!-- ********************************************************** --> <Chapter> <Heading>Algorithms</Heading> The algorithms in &HAPprime; are designed for computations over <M>\mathbb{F}G</M>-modules and <M>\mathbb{F}G</M>-module homomorphisms. These are both represented using lists of generating vectors and permutation group actions. Matrix methods are used for much of the computation, and although the groups are small, the vector spaces involved become large. Memory use is therefore the main concern in these algorithms, and here we describe how the block structure of the vectors used in our representation enables some memory savings to be made. </Chapter>