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
$[{\epsilon_{i m}}^n\eta^m\frac{\partial}{\partial\eta^n},C\eta_j\eta^l\frac{\partial}{\partial\theta^l}]$ ,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/
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.

 

[Entropia]

Thank you for your inquiry about software for calculating simple commutator relations. There are several options available that can handle this type of calculation and preserve the Einstein summation convention. Mathematica, which you have already tried, is a popular choice for symbolic mathematical computations and has built-in functions for handling commutators. However, as you mentioned, its simplification rules may make the results difficult to read. Another option is Maple, which also has built-in functions for commutators and allows for customization of simplification rules. Additionally, there are specialized software packages such as the Quantum Mechanics Package for Mathematica or the QuTiP library for Python that are specifically designed for quantum mechanical calculations and can handle commutators. These packages may offer more advanced features and visualization tools for your calculations.
I hope this information is helpful and wish you success in your research.

Best regards,