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Re: Nested Commutators

  • To: mathgroup at
  • Subject: [mg58124] Re: [mg58114] Nested Commutators
  • From: Pratik Desai <pdesai1 at>
  • Date: Sun, 19 Jun 2005 03:43:28 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

Shug Boabby wrote:

>hi there,
>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.
I found this package a some time back on Mathematica Information Center, 
maybe this is what you are looking for.

Best regards

Pratik Desai
Graduate Student
Department of Mechanical Engineering
Phone: 410 455 8134

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