> Test cases.
> While this does not *prove* the correctness of the code in a
> mathematical sense, it does in a monte-carlo sense. I note that both
> maxima and axiom have test suites.
> I do not think new mathematical code or subsystems should be accepted
> unless they are accompanied by a thorough test suite.
I've been collecting test cases from different computer algebra systems.
The effort is called CATS (Computer Algebra Test Suite).
One of the problems with current systems, like Axiom, is that people
write some algebra then write some test cases. The test cases are not
comprehensive, don't test corner cases, and don't test failure modes.
And, most egregious is, they are not documented. The tests given
an answer but is it the right answer? So current test cases are only
really useful as regression tests looking for what's broken.
So the idea is to collect the various test suites, document the
underlying math and set up pamphlet files which contain code for
each of the various systems. You can get the Axiom code pile with
the CATS work using the tla from Gnu-arch.
The idea is to develop a test suite that would be similar to the
NIST (National Institute of Standards and Technology) classification
scheme for numerical software but this time for symbolic software.
Currently there is no classification scheme and no agreed-upon
There are few enough computational mathematicians. We shouldn't waste
their time duplicating tests in areas that others have already done.
Besides, tests are best when written by others :-)
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