Algorithmic construction of Chevalley bases

We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When applied to a simple Chevalley Lie algebra in characteristic p≥5, our algorithm has complexity involving the seventh power of the Lie rank, which is likely to be close to best possible.