An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebrasz

The purpose of this paper is to describe a C program FPLSA for investigating finitely presented Lie algebras and superalgebras. The program takes as input data a finite set of generators and relations for these elements. The relations have the form of Lie polynomials with coefficients being either integers or polynomials over integers in a given finite set of parameters. The program is based on an algorithm of constructing complete set of relations called also standard basis or Gröbner basis of ideal of free Lie (super)algebra generated by the input set of relations. The output data of the program are the Gröbner basis, the explicit form of basis elements for the quotient algebra of the free (super)algebra with respect to given ideal and also the table of their commutators.