[Axiom-developer] RE: CATS (Computer Algebra Test Suite)

[Bill Page]

On April 1, 2007 4:00 PM Tim Daly wrote:
> 
> At an even higher level of design goal it would be useful
> to construct a Computer Algebra Test Suite, a project I've
> referred to as CATS.
> 
> There are several converging ideas driving CATS.
> ...

I agree the ideas convince me that the idea is a good one.
But I have some doubts that we have any sufficiently mature
technology that could implement this on a large scale.

> ... 
> Third, there needs to be some way to organize the documentation
> within Axiom so that it follows some kind of logical outline.
> One possibility is to follow book outlines for particular
> domains but Axiom covers a large range which isn't found in
> any one book.

I think it is definitely too large for "one book". In fact
printed books are probably not a very good model for this.
It would be much better to think in terms of something like
Wikipedia as a model. Access and navigation has to be online
and collaborative. But that requires a large and willing group
of users and as far as Axiom goes, therein lies the problem.

> 
> Fourth, we've tried to organize the algebra graph within
> Axiom without success. I think there is a lot to learn about
> both Axiom's algebra graph and computational mathematics
> from a good organization.

Probably but I think this requires considerable research.
Lately I am becoming a fan of a much less structured way of
organizing information called "tagging". Perhaps you are
familiar with the web site:

http://del.icio.us

This a large collaborative system for tagging and sharing of
web browser bookmarks. There are several papers written about
this approach as an alternative to traditional classification
schemes. The idea basically is that if this system attracks
a sufficiently large number of users, then the classification
of everything on the web becomes self-organizing and it is
claimed that it will quickly approach the accuracy of manual
classification systems. I think that this is still quite
experimental but already there are some signs that it may
eventually rival Google in terms of the relevance of search
results (which I suppose it not saying much is it? :-)

Anyway, I think a "tagging" approach might be useful when
thinking about classifying the mathematics in Axiom.

> ... 
> This might end up being in a Abramowitz and Stegun style, like
> their Handbook of Mathematical Functions, crossed with books
> like Geddes. (It's unfortunate that copyright will keep these
> prior works from being directly useful.)

Think wikipedia.

> 
> The job is large but the 30 year horizon benefits are enormous.
> 

Most people and especially organization have trouble seeing
that far ahead.

> 
> Within the Axiom project we could start almost anywhere by
> just dragging topics together at random and then classifying
> categories, domains, algorithms, and example files against this
> arbitrary set. Eventually I expect that the topics will self-
> organize (not likely as a hierarchy but more as a graph).

Yes, I think that is more or less the idea of "tagging" that
I mentioned above. But successful tagging probably requires
quite a large group of users.

> 
> This project overlays all of the computational mathematics
> field so no one vendor will take it on as a project. It
> properly belongs in NIST, INRIA, or some other country-wide
> funding organization but I'm not optimistic about that
> happening.

Me niether, but it doesn't hurt to talk about it where and
when people might listen.

> ...

Regards,
Bill Page.