Dear all,
I am looking for a Mathematica package which could handle basic tensorial calculations using the Einstein summation rules. Namely, I would like such a package to be able to take care of Kronecker Delta rules, and Levi-Civita permutation tensors.
More precisely, I wish to define some n-order tensor, with (anti-)symmetry properties for its indices, and that the Mathematica simplifies terms like this :
\deltakk = 3
\deltaik * \deltakj = \deltaij
I have found EinS (http://rcswww.urz.tu-dresden.de/~klioner/DATA/EinS27.pdf) but it seems to not take care of such simple things. At least not intuitively, but maybe I am not using it properly.
If you have any recommendation for existing packages, or advice for using EinS, thanks in advance,
Regards,
Antoine
Dear Antoine, do you already know Ricci, a free Mathematica package for tensor calculations? See link and a text file as example. Gianluca
http://library.wolfram.com/infocenter/Demos/448/
Dear Gianluca Argentini,
thanks for your quick reply.
I read a bit about it, but it seemed to me much more complex than what I need. Do you know if it can perform simple simplification with the Kronecker Delta symbols as I mentioned ?
Thanks,
Antoine
I think yes, see attached Manual, e.g. function AbsorbMetric, TensorSymplify e Dot. Also, see Mathematica standard built-in function TensorProduct. Gianluca
Dear Gianluca Argentini,
After a few weeks I finally managed to successfully use both Ricci and EinS : Ricci seems indeed more powerful because it can handle many features. Nevertheless, for simple algebra involving implicit Einstein summation, EinS turned out to be enough (with some simple extra-coding in Mathematica).
Thanks again for your help,
Antoine
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