MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Nested Commutators

  • To: mathgroup at
  • Subject: [mg58114] Nested Commutators
  • From: "Shug Boabby" <Shug.Boabby at>
  • Date: Sat, 18 Jun 2005 06:08:51 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

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.

  • Prev by Date: Re: Mathematica 5.0 eps generation
  • Next by Date: Re: usage messages in packages
  • Previous by thread: Re: Did something change?
  • Next by thread: Re: Nested Commutators