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Is there a software tool (perhaps Mathematica extension?) designed to help with doing algebraic manipulations of non-commutative objects? Specifically, what I'm after is an interface along the lines of

set [A,B] = C
set [A,D] = A
set [A,C] = 0
move_right(ABCD, A)
==> BCDA + BCA + C^2 D

I've implemented something like this in Python, but before sinking any more time into it I wanted to check I wasn't reinventing the wheel.

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  • $\begingroup$ Writing something like this in Mathematica isn't that hard to do, once you know it will enough. It's a matter of writing replacement rules that you can apply recursively (using //. or ReplaceRepeated) to expand out the commutators and move a particular operator to the right. There are also third-part packages written like NCAlgebra, although I don't know if that has this specific operation. $\endgroup$
    – march
    Commented Feb 25, 2022 at 18:32
  • $\begingroup$ Might Mathematics or Mathematica (if not Software Recommendations) be better suited for this math question? $\endgroup$
    – Kyle Kanos
    Commented Feb 26, 2022 at 3:37

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