[Axiom-developer] Commutative symbols was: Re: Limits in Axiom

[Ralf Hemmecke]

> > However, I must say that your expression approach is limited in the
> > sense that it can only deal with commuting objects. Simplifying b*a+a*b
> > to 2*a*b is not correct if b is the differentiation operator D on x and
> > a=X is the "multiplication by x"-operator. Then you would have D*X=X*D+1.
>
> Of course. Try in SymPy:
>
> In [2]: x*y+y*x
> Out[2]: 2*y*x
>
> In [10]: a = Symbol("a", is_commutative=False)
>
> In [11]: b = Symbol("b", is_commutative=False)

Hmmm, I would have thought that commutativity is a property of the 
multiplication of the domain you are working in and not a property of a 
symbol.

Ralf