Format operator output

Question

I have been working with non-commuting algebra, which is indicated in Mathematica by **. However, I want to suppress the ** from the output. Consider:

n = 4;    
Sum[Binomial[n, r] b^r ** a^(n - r), {r, 0, n}]

which gives

1 ** a^4 + 4 b ** a^3 + 6 b^2 ** a^2 + 4 b^3 ** a + b^4 ** 1

Note that all b's appear to the left of any a's. This is since they do not commute. Instead of the output above, I want to drop the ** to instead have:

a^4 + 4 b a^3 + 6 b^2 a^2 + 4 b^3 a + b^4

since it is better suited when n becomes large.

Answer 1

Perhaps the following code is close to what you want:

With[{n = 4}, Sum[Binomial[n, r] b^r ** a^(n - r), {r, 0, n}]]
  /. {NonCommutativeMultiply -> Dot} // InputForm

with resulting output

1 . a^4 + 4*b . a^3 + 6*b^2 . a^2 + 4*b^3 . a + b^4 . 1

You could use TradtionalForm instead which results in a more compact outuput.