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

[Martin Rubey]

Page, Bill writes:
 > 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. 

Yes.

 > There is an attempt also in Axiom to do the same with input (InputForm and
 > SExpressions etc.) 

I think that this attempt is doomed to fail. Still it may be useful, at least
for debugging.


 > 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 ...

No. There is enough written about it (in the Aldor User Guide). A short
introductory text is in the Axiom book.

 > 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.

And this is a good thing, it seems to me.

 > 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! :)

If you send me your code and the error message you got (the latter for
cross-checking), I'll try to help.

 > Yes, I do agree that "cosmetics" is useful. In fact I have been know to
 > claim that "notation is (almost) everything" in mathematics 
 > ...

NO, NO, NO. Good notation is important, and I'd agree if you'd say that
mathematics builds on good notation. But it's not nearly "almost everything".

What (good) notation provides is a means to make your ideas and proofs clear
and enable others to follow them. The idea comes before the notation. Often
even the proof comes before the notation.

Martin