I would like to be able to simplify a polynomial in two non commuting variables, the desired result being that in every term one variable occurs to the left of the other variable. An example would be the normal ordering of operators from the Weyl algebra.

In addition, I would like to be able to specify the commutation relation as well. Say, if the variables are $a$ and $b$, I would like to specify an equation involving $a$ and $b$ which is equal to zero. For example $ab-ba-1=0$ in the case of the Weyl algebra.

I've tried the non commutative multiplication $**$. It appears that this function is simply formal multiplication. I tried inputting $a**b**b$ but it's not even giving me $ab^2$. (2)