Software to calculate simple commutator relation ?

[aspidistra]

software to calculate simple commutator relation ??

Dear All:
I have hundred terms of commutators needs to be calculate. Each one looks like
<br /> [{\epsilon_{i m}}^n\eta^m\frac{\partial}{\partial\eta^n},C\eta_j\eta^l\frac{\partial}{\partial\theta^l}]<br /> ,where C is function of \theta^i and \eta^i.
The result of this commutator is
<br /> {\epsilon_{im}}^n\eta_j\eta^m\frac{\partial C}{\partial\eta^n}\eta^l\frac{\partial}{\partial\theta^l}-C\epsilon_{ijm}\eta^m\eta^l\frac{\partial}{\partial\theta^l}+<br /> C{\epsilon_{im}}^n\eta_j\eta^m\frac{\partial}{\partial\theta^n}<br />
Is there any software can deal with this calculation and preserve the Einstein summation convention?
I have try to use a mathematica note book from http://www.commeare.net/2008/05/03/commutator-relations-in-mathematica/
to calculate the component of the commutator ie. take i=1 j=2 for example, but mathematica 's simplification rule make the result hardly to read.
Any help will be appreciated. Thanks.

 

[strangerep]

Dear All:
I have hundred terms of commutators needs to be calculate.
Is there any software can deal with this calculation and preserve the Einstein summation convention?

Cadabra might be of some help...

http://www.aei.mpg.de/~peekas/cadabra

One of the "sample notebooks" on the website shows how to
simplify some commutators using the example of the
Poincare algebra. But you'll probably need to study the
reference manual and other examples (and maybe get a bit
of help from Cadabra's author) if you've got hundreds of
commutators to deal with.