Re: [Axiom-developer] SAGE, Axiom, and usage

[Ralf Hemmecke]

> I agree with Steven Watt (I hope I am not overstating his views.)

I heard about Symbolic Computation vs. Computer Algebra first at the 
Dagstuhl seminar http://www.dagstuhl.de/06271/ .

I must say for me I was first a bit puzzled by this distinction, but no 
matter how you name the two distinct ends there is a difference. And we 
all know that.

We are more on the structured side (computer algebra) and most other 
systems just deal with expressions (symbolic computation).

Interestingly, there was a question after his talk which started by...

  I am not sure that I understand your distinction between Symbolic
  Computation and Computer Algebra ...

It seems that people are spoiled by all the typeless systems and usually 
SC and CA are understood to be the same or CA is a subtopic of SC. I 
haven't heard before somebody putting emphasis on a distiction wrt 
structure.

I believe there is need for both ends.

And no matter how strongly typed Axiom will be, it must provide a nice 
way to deal with arbitrary expressions. But it should allow to add more 
and more structure to these expressions as the user understands the 
mathematics behind it.

Ralf