> 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. > > - Robert
Also a huge +1 from me. This is something I have been thinking a lot about how to utilise most elegantly, and I think one could take it a step further than doctests. I often myself write "parameterised tests": tests for properties of the output of functions based on "random" input. For example, say I have a library of polynomials over fields. Then a useful property to test is for any polynomials a,b to satisfy a*b == b*a I could write a test to randomly generate 100 different pairs of polynomials a,b to check with, over "random" fields. I know that some people sometimes write such tests, and it is also suggested in the Developer's Guide somewhere. I love the Haskell test-suite QuickCheck, which allows one to write such tests extremely declaratively and succinctly. Haskell is way cool when it comes to types, so it provides an elegant way of specifying how to randomly generate your input. Transfering this directly Python or Sage can't be as elegant, but I have been working on a small python- script -- basically an extension to unittest -- which could make it at least easier to write these kinds of tests. It's not done yet and can be improved in many ways, but I use it all the time on my code; it's quite reassuring to have written a set of involved functions over bivariate polynomials over fields and then check their internal consistency with 100-degree polynomials over +1000 cardinality fields :-D My thought is that doctests are nice for educational purposes and basic testing, but I myself like to test my code better while writing it. I don't want to introduce more bureaucracy, so I don't suggest that we should _require_ such tests, but it would be nice to have a usual/standard way of writing such tests, if an author or reviewer felt like it. More importantly, if it could be done in a systematic way, all such tests could share the random generating functions: for example, all functions working over any field would need a "generate a random field"-function, and if there was a central place for these in Sage, the most common structures would quickly be available, making parameterised test writing even easier. - Johan -- 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
