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If I clear the commutativity of *:

ClearAttributes[Times, Orderless]

I get that ab and ba are different now. Why is it that when I order Mathematica to compute:

(a + b) c // Expand

It yields ca + cb instead of ac + bc? How can I make it work so that it yields the latter? It seems to me that this happens because the way Expand works.

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    $\begingroup$ I think it is just the final display is based on letters chronological ordering which Front end uses for display. If you do ClearAttributes[Times, Orderless]; (a + b) c // Expand // TraditionalForm then you get same result as before which is ac + bc but no time to investigate more. $\endgroup$
    – Nasser
    Commented May 23 at 1:24
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    $\begingroup$ As stated in the documentation, "Orderless is an attribute that can be assigned to a symbol f to indicate that the elements Subscript[e, i] in expressions of the form f[Subscript[e, 1], Subscript[e, 2], [Ellipsis]] should automatically be sorted into canonical order." Consequently, if you remove the Orderless attribute, the sorting does not occur. $\endgroup$
    – Bob Hanlon
    Commented May 23 at 1:31
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    $\begingroup$ Expand might be using internal code that bypasses Times, hence fails to respect the changed attribute. $\endgroup$
    – Daniel Lichtblau
    Commented May 23 at 10:58
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    $\begingroup$ (a + b) c // Distribute? $\endgroup$
    – Goofy
    Commented May 23 at 14:46
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    $\begingroup$ Actually, I sometimes get a c + b c: i.sstatic.net/4aJN4RfL.png - Is it a bug? $\endgroup$
    – Goofy
    Commented May 23 at 14:55

1 Answer 1

Reset to default
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I recommend using ** (NonCommutativeMultiply), instead of modifying the attribute of Times.

(a + b) ** c

(* (a + b) ** c *)

Distribute[%]

(* a ** c + b ** c *)

c ** (a + b) 

(* c ** (a + b) *)

Distribute[%]

(* c ** a + c ** b *)
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