Calculating the structure of a semisimple Lie algebra

First we briefly describe two previously published algorithms: one that constructs a Cartan subalgebra and one that decomposes a semisimple Lie algebra L as a direct sum of simple ideals. Then, by reducing L modulo a prime we derive an algorithm to obtain the type of L (thereby solving the isomorphism problem for semisimple Lie algebras over Q¯ having structure constants in Q).