The computation of structure constants according to Jacques Tits

Suppose g to be a complex semi-simple Lie algebra. In 1955, Chevalley showed that one can assign to it an essentially unique Z-structure, with structure constants of a simple form, themselves unique up to some choices of sign. An algorithm to compute these is also due implicitly to Chevalley, explained explicitly in [Carter:1972] and more recently in [Cohen-Murray-Taylor:2004]. It is reasonably efficient, and has been implemented in the computer algebra programMAGMA. The principle behind the algorithm is simple—it is based on a straightforward transcription of the Jacobi identity. [Cohen-Murray-Taylor:2004] goes on to explain in detail how to compute in semi-simple algebraic groups associated to the Lie algebra in terms of the Bruhat decomposition.