On Mar 4, 2010, at 2:07 AM, Dr. David Kirkby wrote:
Robert Bradshaw wrote:
As I've mentioned before, internal consistency checks can be better
than comparing against commercial programs, so that way anyone can
run and verify them, and they often illustrate interesting math
(e.g. verification of deep, abstract theorems for specific examples).
Although it is true that not everyone can run tests against
commercial software, I would have thought a significant proportion
of Sage users could. There is already an interface to Mathematica.
Many Sage users and developers work in universities, which often
have Mathematica licenses.
Standards laboratories all have internal consistency checks, but
they do compare standards against each other.
IMHO, it is better if the person writing the test is not the same
person who wrote the code being tested. Sometimes one makes an
assumption about how a function should work, where the developer(s)
make a different assumption. Neither are wrong, but it highlights
areas where perhaps documentation should be clarified.
My experience in R+D has often showed me that comparing two totally
different methods is useful.
I am promoting using two totally different methods--for example
numerically vs. symbolically computing an integral and verifying they
match (to some tolerance). When I say internal, I am including (though
not restricting to) comparing the diverse codebases shipped with Sage
against each other.
I guess my main point is that I would not be happy if we were in the
situation where I was unable to do significant testing for lack of a
Mathematica (Maple, ...) license. I am not opposed to having such
functionality available (and it could be interesting).
- Robert
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