# Software to calculate simple commutator relation ?

1. Jun 11, 2009

### aspidistra

software to calculate simple commutator relation ??

Dear All:
I have hundred terms of commutators needs to be calculate. Each one looks like
$[{\epsilon_{i m}}^n\eta^m\frac{\partial}{\partial\eta^n},C\eta_j\eta^l\frac{\partial}{\partial\theta^l}]$ ,where C is function of $\theta^i$ and $\eta^i$.
The result of this commutator is
${\epsilon_{im}}^n\eta_j\eta^m\frac{\partial C}{\partial\eta^n}\eta^l\frac{\partial}{\partial\theta^l}-C\epsilon_{ijm}\eta^m\eta^l\frac{\partial}{\partial\theta^l}+ C{\epsilon_{im}}^n\eta_j\eta^m\frac{\partial}{\partial\theta^n}$
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/ [Broken]
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.

Last edited by a moderator: May 4, 2017
2. Jun 11, 2009

### strangerep

Re: software to calculate simple commutator relation ??

Cadabra might be of some help...