Example 1.

First we initialize a 5 dimensional Lie algebra.

We can use the command Query/"Solvable" to check that this is a solvable Lie algebra.

Now we calculate a basis with the ascending ideals property.

The following two commands check, for example, that B[1..3] is an ideal in B[1..4].

The command  Query/"AscendingIdealsBasis" will verify that the basis B has the ascending ideals property.

The ascending ideals property becomes apparent if we re-initialize the Lie algebra using the basis B (using the command LieAlgebraData).

DifferentialGeometry, LieAlgebras, BracketOfSubspaces, GetComponents, MultiplicationTable, Query