We propose an algorithm using Gröbner bases that decides in terms of the existence of a non-singular matrix P if two Leibniz algebra structures over a finite dimensional C-vector space are representative of the same isomorphism class. We apply this algorithm in order to obtain a reviewed classification of the 3-dimensional Leibniz algebras given by Ayupov and Omirov. The algorithm has been implemented in a Mathematica notebook.
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