William, >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. Tim _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
