Possibility/ease of doing some vector ops in Maxima

Hi.

I'm currently investigating the possibility of using Maxima to automate
the generation of the basis functions I want to use as part of a FEM
code. 

At the moment I don't have much experience with Maxima, and no previous
computer algebra experience, so newbie advice would also be appreciated
:)

To automate the basis function generation, I need to be able to evaluate
functions like this one:

grad(L_1*L_2*(L_1-L_2)^(p-1)), where p is the order of the basis being
generated, and L_1 and L_2 (and also L_3) represent the 2D area
coordinates.

Then I would like to simplify the expression, so that it is still in
terms of L_1,L_2,L_3 (ie, no need to take into account the linear
dependence of the area coordinates), and grad(L_1), grad(L_2),
grad(L_3).

Basically, I want the answer as coefficients of grad(L_i), i=1..3.

Could this be done simply, or would I need to write some code? In either
case, some pointers as to which part of the, rather formidable, Maxima
reference I should look at would also be nice.

Thanks in advance
Neilen



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