1
$\begingroup$

I define:

Unprotect[NonCommutativeMultiply];
NonCommutativeMultiply[left___, HoldPattern[Times[u[x_], p : (a[k_] | SuperDagger[a][k_])]], 
right___] := u[x] NonCommutativeMultiply[left, p, right]
Protect[NonCommutativeMultiply];

since I want the function u[x_] to commute with a[k_], SuperDagger[a][k_]

Now if i try

In:= a[k] ** u[k]*a[q]
Out= a[q] a[k] ** u[k]    (*  which is not the desired output*)

if i try

In:= a[k] ** (u[k] a[q])
Out= a[k] ** a[q] u[k]

which is better but still it's not u[k] a[k] ** a[q]

I can't figure out why my definition isn't working. What am I missing?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ The problem is that ** distributes over *. That means: a[k] ** u[k]*a[q] is interpreted as: (a[k] ** u[k]) * ( a[k] **a[q]). If you write: a[k] ** (u[k]*a[q]) you get: a[k] ** a[q] u[k] $\endgroup$ – Daniel Huber Dec 20 '20 at 12:27
  • $\begingroup$ @DanielHuber I thought my rule would take care of that? Even with a[k] ** (u[k] a[q]) the output places u[k] after a[k] ** a[q] not before. How should I change it to have the desired output? $\endgroup$ – geom Dec 20 '20 at 12:32
  • $\begingroup$ "Times" has the attribute "Orderless". Therefore MMA will rearrange the expression according to its own rules (I think, lexicographically, but I am not sure) $\endgroup$ – Daniel Huber Dec 20 '20 at 12:47
  • $\begingroup$ @DanielHuber Geez, you are right. Even if I add orderless to NonCommutativeMultiply nothing changes.The order is decided by Sort which orders symbols by their names, and in the event of a tie, by their contexts. Please post your comments as an answer. They are helpful. $\endgroup$ – geom Dec 20 '20 at 13:08
2
$\begingroup$

The problem is that NonCommutativeMultiply (**) distributes over Times.

That means: a[k] ** u[k]*a[q] is interpreted as: (a[k] ** u[k]) * (a[k] ** a[q]). If you write: a[k] ** (u[k]*a[q]) you get: a[k] ** a[q] u[k]

Furthermore, Times has the attribute Orderless. Therefore MMA will rearrange the expression according to its own rules (I think lexicographically, but I am not sure).

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.