Mike Falk writes:

Does anyone on this list know of a facility for computation in a
finite-dimensional Lie algebra, i.e. a subalgebra of gl(n,C)? Does gap
have such capabilities? (To start with, how about finding (a basis for)
the solvable radical of L?

I don't think GAP does any Lie algebra directly. However, I have written
GAP code which can do a little bit of Lie algebra. The code does a very narrow
range of things, and works only on free Lie algebras (of finite rank) over
either a finite prime field, or the ring of integers. The only parts of the code
that might be relevant to Mike are the function that constructs the Hall basis
vectors of a given weight, and the collector (which is of limited capability).
If you want to know more and/or see the code, write to me direct.

Mark Short