A Lie algebra g is solvable if the k-th element D^k(g) in the derived series for g is 0 for some k >= 0.

Every nilpotent Lie algebra is solvable.

Query(Alg, "Solvable") returns true if Alg is a solvable Lie algebra and false otherwise.  If the algebra is unspecified, then Query is applied to the current algebra.

Query(S, "Solvable") returns true if the subalgebra S is a solvable Lie algebra and false otherwise.

The command Query is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form Query(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-Query(...).