Symbolic superalgebra manipulations using common lisp

Abstract We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie superalgebra. Using the results of our previous paper, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula in the general framework of the Z_2graded algebras. The parameters are defined as Grassmann or even and treated symbolically. It is possible to perform calculations on finite super Pois... Title of program: GRAAL Catalogue Id: ABRY_v1_0 Nature of problem Symbolic computations on the elements of a given Poisson or Lie Superalgebra and its Enveloping Algebra: elements ordering, commutators, evaluation up to a given order of Similarity Tranformations, general Baker-Campbell-Hausdorff formula. Versions of this program held in the CPC repository in Mendeley Data ABRY_v1_0; GRAAL; 10.1016/0010-4655(90)90013-Q This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)