Int. J. Open Problems Comput. Math. , Vol. 5, No. 1, March, 2012 ISSN 2074-2827; Copyright c ICSRS Publication, 2012 www.i-csrs.org Application of Statistical Techniques for Comparing Lie Algebra Algorithms D. Fern´ andez-Ternero 1 , J. N´ u˜ nez 1 , and A. F. Tenorio 2 1 Dpto. Geometr´ ıa y Topolog´ ıa. Universidad de Sevilla e-mail: {desamfer, jnvaldes}@us.es 2 Dpto. Econom´ ıa, M´ etodos Cuantitativos e H. a Econ´omica. Universidad Pablo de Olavide e-mail: aftenorio@upo.es Abstract This paper is devoted to study and compare two algebraic algorithms related to the computation of Lie algebras by us- ing statistical techniques. These techniques allow us to decide which of them is more suitable and less costly depending on several variables, like the dimension of the considered algebra. Keywords: Statistical techniques, algorithm, Lie algebras, computing time, complexity. 2000 Mathematics Subject Classification: 17B30, 68W40, 68Q25. 1 Introduction In this paper, several statistical techniques are used to decide on the feasibil- ity of two algebraic algorithms. More concretely, the main goal is to carry out a statistical study starting from the computational data obtained when implementing and running these two algorithms in MAPLE to compute the laws of two families of solvable Lie algebras. Indeed, these data are structured according to the following two items: the computing time and the complexity of these algorithms. So we are interested in knowing whether there exists some type of depen- dence between computing time and used memory. In the affirmative case, we would like to determine the order of this dependence (linear, quadratic, cubic, etc.) with respect to a third set of data: the dimensions of the algebras, for instance.