Test for Leibniz n-algebra structure

For a given basis of a vector space L over a field K and a multiplication table which is defined by a multilinear map [−,…,−]:L×n→L, we present an algorithm and develop a computer program on Mathematica in order to test if the given multiplication table corresponds to a Lie n-algebra or a non-Lie Leibniz n-algebra or neither.The algorithm is based on the computation of a Gröbner basis of the ideal which is used in the construction of the universal enveloping algebra of the Leibniz algebra provided by the Daletskii-Takhtajan functor, by means of the NCAlgebra package which permits the construction of Gröbner bases in noncommutative associative algebras.