- To: mathgroup at smc.vnet.net
- Subject: [mg58114] Nested Commutators
- From: "Shug Boabby" <Shug.Boabby at gmail.com>
- Date: Sat, 18 Jun 2005 06:08:51 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
i have searched the archive for theads on nested commutators in
mathematica, but i found no answer to my problem and i was wondering if
anyone had any helpful advise for me.
i wish to be able to define a commutator[A, B]
between 2 operators.
for example i would like to be able to define an algebra by presenting
the commutators, such as
[A, B] = B
[A, C] = C
[B, C] = D
(also explicitly defining the rest to be zero) and then be able to ask
mathematica to return the solution when i nest the operators like so
[A, [A, [A, B]]]
which should return B
[A, [B, C]]
should return 0.
it would also be nice if the Jacobi identities are used in
simplification routines, so that terms such as
[X, [Y, [X, Y]]]
-[Y, [X, [Y, X]]]
[[X, [Y, X]], Y]
are identified as being the same as
[Y, [X, [X, Y]]]
right ordering the output when the commutators cannot be calculated
apologies if you have seen this question recently... i stupidly asked
it at the end of my last posting where it is surely to be missed. this
question really warrants its own thread.
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