> True, there are non-commutative maths, but the ones that I can think of
> offhand that are generalizations of the ones implemented in Squeak, such
> as quaternions and Cayley numbers, are built out of components which are
> manipulated by commutative operators.  So it seems reasonable to build
> the general number system such that the standard operators (addition and
> multiplication in particular) are commutative, and then design the
> non-commutative systems with the appropriate constraints, rather than
> constraining the base number systems to favor the more complex and
> less-used non-commutative systems.

If you are attempting to do some kind of generic functions, you will
have to deal with non-commutative math anyway, I.E. for subtraction
and division.  It only takes a little bit of care to preserve argument
order for the traditionally-commutative operations of addition and 
multiplication as well, so it is better to preserve it when you can.

I feel it IS worth the care for numerics.

I.e.   (s is a scaler,  X is multiplication)


| a b |
| c d |  X  s

     =

| as bs |
| cs ds |


and


s  X   | a b |
       | c d |
       
       =

| sa sb |
| sc sd |



Symbolic math can be a bit tougher:

(x + y)(x + y) = x^2 + xy + yx + y^2

hence, you may want to be able to specify that the
algebra is commutative to the reduction engine.

-- Mike Klein