  Let L be the Lie algebra of a simple algebraic group defined over a field F
and let H be a split Cartan subalgebra of L. Then L has a Chevalley basis with
respect to H. If the characteristic of F is not 2 or 3, it is known how to find
it. In this paper, we treat the remaining two characteristics. To this end, we
present a few new methods, implemented in Magma, which vary from the
computation of centralisers of one root space in another to the computation of
a specific part of the Lie algebra of derivations of $L$.
