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  • $\begingroup$ Related: Differential geometry add-ons for Mathematica. $\endgroup$ Commented Apr 6, 2013 at 17:13
  • $\begingroup$ I would probably define a separate function like commutatorExpand and/or commutatorReduce that does the transformations in the direction you want. $\endgroup$ Commented Apr 6, 2013 at 17:15
  • $\begingroup$ Possibly relevant: this and this and this $\endgroup$ Commented Apr 6, 2013 at 17:16