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

[root]

William,

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. 

Axiom has groups of such tests in its regression test suite already.

Tim