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

From: root
Subject: [Axiom-developer] Re: AMS Notices: Open Source Mathematical Software
Date: Sun, 18 Nov 2007 19:24:57 -0500


>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.

I'm familiar with the A&S document but it is not properly focused to
work as a reasonable computer algebra test suite (CATS). It does not
categorize problems based on their computational math aspects and it
does not focus on providing branch-cut, boundary cases, etc. that 
would be needed to highlight the behavior of computational math systems. 
Also missing is the textual analysis of the problem and solution.

For example, it would be useful to see a discussion of sine or square
root with regard to branch cuts, simplifications, extended fields,
etc. I've seen discussions of the numeric aspects of computing the
sine in the last decimal place or choice of polynomials but I've not
seen the equivalent discussions with respect to the symbolic aspects
such as simplifications.

In addition, A&S introduces problems that I have no idea how to
solve symbolically. It would be useful to have citations to papers
that provide the underlying algorithms.

A&S might be too ambitious. Perhaps we should think in terms of
Spiegel's (Schaum's Outlines) Mathematical Handbook. Indeed, I've
spent some time with this book in developing the latest Axiom tests
and found mistakes in some of the problem answers from the book.
The analysis is really important.

The fundamental goal would be to ensure that the mathematical
results from various systems (and later releases) at least conform
to some independently verified acceptable standard of results.

Seems like a NIST (or possibly a CDI/NSF) proposal to me.

While I am at Carnegie-Mellon University, I'm not associated with
any group that does computational mathematics so I couldn't justify
such a proposal.


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