On Dec 2, 10:20 am, Robert Bradshaw <rober...@math.washington.edu> wrote: > On the topic of verifying tests, I think internal consistency checks > are much better, both pedagogically and for verifiability, than > external checks against other (perhaps inaccessible) systems. For > example, the statement above that checks a power series against its > definition and properties, or (since you brought up the idea of > factorial) factorial(10) == prod([1..10]), or taking the derivative to > verify an integral. Especially in more advanced math there are so many > wonderful connections, both theorems and conjectures, that can be > verified with a good test. For example, computing all the BSD > invariants of an elliptic curve and verifying that the BSD formula > holds is a strong indicator that the invariants were computed > correctly via their various algorithms.
A huge +1 to this. Couldn't have said it better. I sometimes become a devious doctest writer (close cousin to the devious reviewer) and try to write a doctest that links seemingly disparate parts of Sage in complicated ways expressed by a theorem. For example, automorphism groups of graphs sometimes have connections with eigenvalues of the adjacency matrices of the graph. If something breaks in either part of Sage, then such a test may expose it. And sometimes these tests are very succinct since they can be constructed so the output is simply "True." And properly written, they make for interesting reading. Rob -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
