Consider the following:

with(Physics);

Setup(noncommutativeprefix = z);

(z1*z2)*z1;

gives z1 z2 z1 as it should but

z1*z2*z1*z1;

gives z1^3 z2. Thus noncommutativity has not been respected?

What can I do?

I want to be able to create expressions in the two noncommutative variables a and b such that an expression

(b+a)*a +ba symplifies to a*a. Thus the first expression expands to ba+aa, which when added to ba

yields ba+aa+ba=aa.

How to arrange for this will be greatly appreciated.