[Axiom-developer] Re: AMS Notices: Open Source Mathematical Software

[William Stein]

On Nov 18, 2007 3:49 PM, root <address@hidden> wrote:
> One possible other source for funding is NIST (although the year that
> I thought to apply they only had funding for prior project, no new
> money available).
>
> An outstanding problem is that we have many different computer algebra
> and symbolic computation systems that compute different answers to the
> same problem. Sometimes these answers are equivalent but it takes a
> great deal of work to show that.
>
> I've advocated, and done some work on, CATS (computer algebra test
> suite). The idea is to categorize (similar to the NIST numeric math
> classification) and standardize a set of symbolic problems and their
> mathematical solutions. These problems would be chosen to highlight
> behavior (e.g. branch cuts, simplifications, boundary conditions) in a
> class of problems. Each system could then provide solutions to this
> standard set. Thus there would be the beginnings of the idea that you
> could expect the same results (within simplification) on any of the
> available systems. In the ideal case such tests would also document
> the algorithm(s) that solves the problem.
>
> NIST seems to me to be the ideal funding source for such a suite.
>
> Note that the test suite is applicable to both open source and
> commercial efforts.
>
> In particular, since SAGE has many daughter systems it seems that
> you are in the ideal position to build a catalog of such tests.
> The test problems would all provide hand-solved answers as well
> as the results from each daughter subsystem.
>
> Further, since each area of classification would require an expert
> to propose and document the problems it seems to be the ideal
> project for widespread grant-based funding.
>
> The end result would be an Abramowitz & Stegun style document that
> was machine readable and freely available. Each project (e.g. MMA,
> Maple, Axiom, etc) would post their results.

Actually NIST already has been working on an " Abramowitz & Stegun
style document "
for the last decade.  I had a long talk on Friday in my office with the
guy who started that effort a decade ago...  It's actually very exciting,
and I do think there is some possibility for something like you're describing
above, maybe more in the context of the CDI initiative at NSF.

William