ReLie: a Reduce program for Lie group analysis of differential equations

Abstract: Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many computer algebra packages have been developed along the years to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, which since 2008 is an open source program (http://www.reduce-algebra.com) and is available for all platforms. \relie is able to perform almost automatically the needed computations for Lie symmetry analysis of differential equations. Its source code is freely available at the url http://mat521.unime.it/oliveri. The use of the program is illustrated by means of some simple examples; nevertheless, it is to be underlined that it provides effective also for more complex computations where one has to deal with very large expressions.