Hi. I have a commutation table, that I've got as output of Greg Reid algorithm.

Can I use to define Lie algebra for components DifferentialGeometry & Lie Algebras?

Worksheet is attached...

FCT.mw

Let say I want to perform symmetry analysis of ODE, taking into account parameters.
In order to do it I must generate system of determining equations and them to split it for different cases.
But if I use PDETools, actually it gives me only 1 case (worksheet PDETools.mw is attached).
In that case, surely it is very easy to do it by hand and to determine that A=0 and A<>0 are two different cases.

But automatic procedure of PDETools seems to me that somewhere allows to divide by parameter...

For example, I have a commutation table of finite Lie algebra. I'd like to extract some information from it (mainly, I'm interested in maximal dimension of abelian Lie subalgebra).

I want to work (cross products, differentiating and simplificating) of three dimensional vector functions.

But I'd like to work with them as vector, not as components. Is it available in Maple?

I have an expression of derrivative, lets say (D[2, 2](G))(x, y).

How to get this numbers - [2,2] programmicaly from it?