I am working on 2 new test suites.
One involves the Rubi test suite using patterns for integration.
This is a very large test suite, well over 9000 integrals.
I have created test cases for Axiom but not yet written the
rule-based integration patterns. I'll move them into the CATS
area in the near future. This establishes a baseline against
which the new rule-based integration patterns can test. I have
to add special functions like polylogs which Axiom does not yet
recognize before I can go further and then write the pattern rules.
Piezas's work is also pattern matching. The difficulty for
computational mathematics is that some of the patterns might
not hold true across all domains. They are identities so this
should not be a problem but I'd have to look at them in more
detail to be convinced. I've done no more than glance at the pages.
The second test suite involves graphing. I am using the
CRC Standard Curves and Surfaces (David von Seggern) book
which covers a huge range of graphs, from random (fractal,
gaussian, non-guassian) to determinate (algebraic, integral,
transcendental, piecewise continuous). This is moving, but
slowly, and will probably not see the light of day until 2011.
I tried to write a test suite based on Yudell Luke's
The Special Functions and Their Approximations that involved
expansions of MeijerG function but I don't know that I've got
the chops to do it. Maybe in my next life :-)
Tim (somebody, I can't find his name) was going to try the
CATS integration test suite in Sage. It should be rather easy
as Sage uses Maxima and the syntax is very close. I don't
know what became of that effort.
If you do a test suite on graphs I'd be happy to try to
make it work in Axiom. This would likely involve writing new
algebra code so it would be helpful if you included citations
of algorithms (if you know them) as you develop it. It looks
like Gross and Yellin includes high level algorithms so that
would be exceptionally helpful. I strongly favor basing test
suites on books containing algorithms.
A test suite for sequences and series is on my wish list but
I have not found a good reference for it.
I think it would be useful to collect good reference books for
any of the mathematics we want to test. This would give other
people a good starting point for developing test suites.
For the CATS test suite each file contains the problem, the
expected answer, and Axiom's answer. The format of the files
makes it possible to run them automatically which I do with
every system build. Does Sage have such a file format?
Tim Daly
Minh Nguyen wrote:
This is a split off from the thread "Random banter about Sage
standards" at
http://groups.google.com/group/sage-devel/browse_thread/thread/c80b87648c213c5
Hi Tim,
On Fri, Aug 27, 2010 at 9:59 PM, Tim Daly <d...@axiom-developer.org> wrote:
For *standard test suites*, I believe we should have these in many
different areas. We should collect a set of reference books that are
fairly comprehensive and jointly develop tests that run on all systems.
Rubi is doing this with rule based integration.
http://www.apmaths.uwo.ca/~arich/
Axiom is doing this with the Computer Algebra Test Suite
http://axiom-developer.org/axiom-website/CATS/index.html
This is a point I at least agree on. I think it would be a moderately
difficult project to write a Sage counterpart to the Axiom CATS. It
would be an interesting project to see how one could develop a similar
test suite based on T. Piezas III's book "A Collection of Algebraic
Identities" available at
https://sites.google.com/site/tpiezas/Home
I've have been thinking about writing a test suite for Sage's graph
theory functionalities. The following comprehensive book provides a
good starting point on what to include:
* Jonathan L. Gross and Jay Yellen (eds). Handbook of Graph Theory.
CRC Press, 2004.
All of these items are on my todo list [1], but I haven't made any
headway on any of them in the last few months.
[1] http://sage.math.washington.edu/home/mvngu/todo.html
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