Kasper Peeters wrote:
You may be interested to know that the current 'state of the art' for
handling tensor symmetries (i.e. simplifying expressions which are
identical because of tensor symmetries) is based on the
'double coset algorithm', which you can find in
R Portugal, "Algorithmic simplification of tensor expressions",
J. Phys. A32 (1999)
(there are several other papers by Portugal on this, as well as
a Maple implementation). This algorithm is used in the Mathematica
package "xAct" by Martin-Garcia,
http://metric.iem.csic.es/Martin-Garcia/xAct/index.html
and in my own tensor cas "Cadabra",
http://cadabra.phi-sci.com/
(I am actually just using the C engine of xPerm of xAct).
This is a highly non-trivial problem, so I would advise you to not
re-invent the wheel if you can avoid that. However, just in case
you do want to go that route, another useful reference is
Gregory Butler, "Fundamental Algorithms for Permutation Groups.",
Lecture Notes in Computer Science, vol. 559, Springer Verlag 1991.
Cheers,
Kasper
Thank you very much for your information.
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