  Recently, Paiva and Teixeira (arXiv:1108.4396) showed that the structure
constants of a Lie algebra are the solution of a system of linear equations
provided a certain subset of the structure constants are given a-priori. Here
it is noted that Lie algebras generated in this way are solvable and their
derived subalgebras are Abelian if the system of linear equations considered by
Paiva and Teixeira is not degenerate. An efficient numerical algorithm for the
calculation of their structure constants is described.
