[Axiom-developer] RE: DistributedExpression (was: How can I get every term of an expression ?)

[Page, Bill]

On Wednesday, September 21, 2005 8:52 AM Martin Rubey wrote:
>... 
> Well, output is easily changed.

Yes, you are right. As usual, I just wish we had more
documentation: both user documentation (how-to) and
conceptual documentation (why).

Axiom's approach to output as a coercion to the type OutputForm
is radically different than any other computer algebra system
that I know. There is an attempt also in Axiom to do the same
with input (InputForm and SExpressions etc.) This is a powerful
idea that depends centrally on the strong typing system.

Understanding how to use types and domains in Axiom is both
"90% of the problem" and "90% of the reasons why one might
want to use Axiom in the first place". We need to write more
about this ...

> You did notice that the *real* power of different
> representations is speed.

I wrote a short note about the concept of representation
in Aldor (which also applies to Axiom and SPAD)

http://wiki.axiom-developer.org/RepAndPer

I think that you are right that one of the main points
about different representations is the relative
computational efficiency of different implementations
for different purposes. But I think there is much more
to this concept and that the current Aldor and SPAD
syntax does not sufficiently highlight the important
place that it holds. The current syntax, i.e. 'rep'
and 'per' as macros and 'Rep' as a distinquished name
for a local domain, seems to treat representation on
a par with other programming constructs.

> Thus, my domain is rather cosmetics, however useful it
> may be. We do agree that cosmetics is useful, I guess.
> 

I just spent a couple of hours trying to add a new operation
called 'terms' to the DistributedExpression domain. The
idea was that it should return a List of Expressions in
analogy with the 'monomials' operator of POLY, but I kept
getting hung up on vague SPAD compiler messages and picky
details for explicitly specifying domains... After all this
time I still do not feel fluent in SPAD/Aldor but for some
reason I continue to admire it greatly when I see something
that works! :)

Yes, I do agree that "cosmetics" is useful. In fact I have
been know to claim that "notation is (almost) everything"
in mathematics and I think that applies equally to computer
algebra systems.

Regards,
Bill Page.