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so this question is most likely very simple and I have seen similar questions on here but none which quite seem to work for me. I am quite the amateur with Mathematica as I never really have much cause to use it so please do not assume much technical knowledge on my part. My problem is fairly simple, I am trying to simplify six expressions which involve two generators x, y that most certainly do not commute. In fact, yx=x^2y. What I would like to get is something of the form (x+...)(y+...)(...) or the like, but whenever I use Mathematica (I have been using the NCAlgebra package) I can't seem to make it work. Any help would be very much appreciated.

John D Evans
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  • Can you show what you've been attempting so far? It makes it a lot easier to help you. – SuperBiasedMan May 21 '15 at 13:27
  • Well I haven't exactly gotten very far. I have never had any use for Mathematica before, and so I am learning the ropes as I go. So far I have just been trying to factorise or simplify something like x^3+x**y**x using the NCSimplify[] and Factor[] commands. – John D Evans May 21 '15 at 13:36

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In the newest version of NCAlgebra you can use NCStrongCollect and NCCollect to produce something like:

<< NC`
<< NCAlgebra`
expr = x^3 + x ** y ** x
NCStrongCollect[expr, {x, y}]

which results in

x ** (x + y) ** x

or

NCCollect[expr, {x, y}, ByTotalDegree -> True]

which in this case produces the same result.

There are other "simplification" tools as well, such as NCSimplifyRational. Check out the documentation for details.

Mauricio de Oliveira
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