A collection of subspaces f0, f1, ... fN of a Lie algebra g defines a decreasing filtration of g if fi in fj for i >= j, [fi, fj] in f(i + j) for i + j <=N and [fi, fj] in fN for i + j > N.

Query([f0, f1, ... fN], "Filtration") returns true if the subspaces f0, f1, ..., fN define a decreasing filtration of the Lie algebra g 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(...).

bracket of subspace 0 and 0 is [2*e1, e2, e2+e3]

bracket of subspace 0 and 1 is [-e1, -e2]

bracket of subspace 0 and 2 is [-e1, -e2]