# Symbolic Lie algebras manipulations using COMMON LISP

## Description

Abstract We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LI... Title of program: VSPLAD Catalogue Id: ABFW_v1_0 Nature of problem Symbolic computations on the elements of a given Lie Algebra and its Enveloping Algebra: elements ordering, commutators, evaluation up to a given order of Similarity Transformations, general Baker-Campbell- Hausdorff formula. Versions of this program held in the CPC repository in Mendeley Data ABFW_v1_0; VSPLAD; 10.1016/0010-4655(89)90010-6 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)