Re: [Axiom-developer] literate programming and Claerbout's Insight

[C Y]

--- Gabriel Dos Reis <address@hidden> wrote:

> address@hidden writes:
> 
> [...]
> 
> | Axiom has the opportunity to be the base of computational
> mathematics.
> 
> When it manages to meet the needs of the working computational
> mathematicians.  It cannot do that by building self-made ghetto
> with an autistic attitute of the workers.

Nor can it do so without being able to supply concrete, verifiable
reasons of why it is technically able to serve as such a foundation. 
This is why I regard the consideration of proof system integration as
fundamental to the future of the project - I don't see how we can be
credible otherwise.  Why should anyone trust us?

> I have spoken to many people at SNC/PASCO '07.  It is incredible how
> the two factors:
> 
>   (1) Axiom's history
>   (2) lack of seamless integration to working computational
>       mathematicians's development environment and insistance on
>       relic technology
> 
> generate strong negative reactions.

Um.  I can understand the lack of seamless integration, but why would
Axiom's history cause a negative reaction?

As for relic technology, do you mean Axiom's current Algebra algorithms
or use of Lisp?  Or maybe the 1980s look of Hyperdoc and graphics?

> We can write diatribes and pamphlets against commmercial systems and
> library approches all we want, but Axiom has a hard convincing task
> before it, and proving passe techniques is not going to convince
> anyone when nobody is interested in or using passe techniques.

The idea is (eventually) to be able to develop the proof as the
technique is being developed.

Also, APPLIED CAS usage (e.g. Physics) won't always be inventing new
mathematics to do what they need to do.  They need known techniques
they can trust, to give them answers they can trust.

There is more than one target audience here.

> Take a look at recent research papers and have a closer look at what
> people are using, are developing, what they think is the future trend
> of the field. 

I think it is premature to characterize the Axiom project's output - we
are in the early stages of a monumental task and how things look now
are very likely to change dramatically.  Certainly Axiom in its current
form looks dated, but changing that is a non-trivial task in ANY
toolkit.  I don't personally think Axiom is ready for heavy end user
activity.

> I have heard the following (friendly) characterization of Axiom in
> the last couple of days:
> 
>   * If you're doing computer algebra for leaving, then:
>       (i) Axiom lacks supports in many key areas;
>      (ii) most of the Axiom algorithms are a couple of generations
>           behind;

There is only one way to fix that, and it will take a lot of time.

>   * If you're a casual user, then using Axiom is like flying a
>     helicoptere to buy milk at the store next door.

Very true.  Fortunately, Maxima exists for those cases.
 
> With the inclusion of standard disclaimer about analogy, think about
> the above.

Casual use is not (as I understand it) the target of the Axiom system
as yet.  My guess (and it is only that) is end user friendly systems
will eventually come from defining assumptions in the "default" user
interaction environment.  Most systems make these assumptions unstated
- we should make them explicit.  That again means taking the long road.

FriCAS will fill the need for those who need something Axiom-like
working now.  My interest is the long term goals.

Cheers,
CY


       
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