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

[daly]

Bill,

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.

First, there are very few people in the field and it would be good to
leverage expertise across more than one CAS. This is probably of more
interest to the SAGE people but Axiom can be a driving force.

Second, there is a NIST classification system for numeric algorithms.
Such a standard does not exist for algebraic algorithms. But it would
be useful to have a classification so we could show which parts of the
standard Axiom currently computes and which parts need work.

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.

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.

So the CATS effort is an attempt to drag these observations into one
pile and create a first draft of a "standard" computational mathematics
layout. This would allow us to place algorithms in context, place 
carefully audited, universally accepted results in context, standardize
the abilities expected in CA systems, document algorithms and results
in some standardized format, organize research tracks, etc.

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.)

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




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).

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.

Anyway, that's enough hasty-generalization...back to regression testing.

Tim