Re: Nested Commutators

*To*: mathgroup at smc.vnet.net*Subject*: [mg58124] Re: [mg58114] Nested Commutators*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Sun, 19 Jun 2005 03:43:28 -0400 (EDT)*References*: <200506181008.GAA08906@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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] > http://mathworld.wolfram.com/Commutator.html >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 >explicitly. > >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. > > > Hi I found this package a some time back on Mathematica Information Center, maybe this is what you are looking for. http://library.wolfram.com/infocenter/MathSource/4271/ Best regards -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134

**References**:**Nested Commutators***From:*"Shug Boabby" <Shug.Boabby@gmail.com>