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I have an expression where there are terms like

a ** (b*Tr[a ** b])

and I want to simplify it to something like

Tr[a ** b]a ** b

How can it be done? I have tried with NCExpand and haven't worked.

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    $\begingroup$ Strictly speaking, it is "cyclic". $\endgroup$
    – Αλέξανδρος Ζεγγ
    Nov 27, 2020 at 0:35
  • $\begingroup$ I mean, it is cyclic in the argument but the result is an scalar and it then commutes, isn't it? $\endgroup$
    – F3RN4ND0
    Nov 27, 2020 at 9:49

3 Answers 3

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See my edits for my earlier submission.

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    $\begingroup$ Can you edit your posted answer with this? That is the better way to do this. If not, I suggest you do this or post this as a comment. It might be helpful if you included a successful test input/output, also. $\endgroup$
    – CA Trevillian
    Nov 28, 2020 at 5:00
  • $\begingroup$ Ok, it worked even though I had to unprotect the symbol Tr with Unprotect[Tr], which could be risky isn't it? Thanks! $\endgroup$
    – F3RN4ND0
    Nov 28, 2020 at 12:27
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Edited: The command SetCommutative[Tr] forces all of the expressions whose head is Tr to be considered commutative.

If necessary, you can use UnProtect[Tr];SetCommutative[Tr];Protect[Tr];.

Another solution is Tr/:CommutativeQ[Tr[x_]] := True;

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  • $\begingroup$ Shouldm't it be the other way around? SetCommutative[Tr] . Either way it doesn't work for me. With SetNonCommutative[Tr] I get WARNING: Symbol Tr is protected. You should seriously consider not setting it as noncommutative and with SetCommutative[Tr] I get UpSet::write: Tag Tr in CommutativeQ[Tr] is Protected. $\endgroup$
    – F3RN4ND0
    Nov 27, 2020 at 9:46
  • $\begingroup$ Got the answer backward. See the other solution which I posted. $\endgroup$
    – Mark S.
    Dec 2, 2020 at 16:02
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In NCAlgebra, expressions are considered commutative only if the Head and all arguments are commutative. That is why using SetCommutative[Tr] will fail in this case. If Tr is commutative, Tr[x] will still be noncomutative if x is noncommutative. However, I would not recommend that you add rules to CommutativeQ. That can become messy. Instead use the brand new command SetCommutativeFunction which is available with the version 5.0.6 of NCAlgebra. I would also discourage you from using the built in protected symbol Tr. For example,

SetCommutativeFunction[trace];
a ** (b*trace[a ** b])

would evaluate to

trace[a ** b] * a ** b

as you want. By the way, I also implemented an operator tr that has the properties of the standard matrix trace. You might want to give it a try.

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