On Friday, July 5, 2013 11:55:54 PM UTC-10, clicl...@freenet.de wrote:
> Your results for Mathematica 9.01 (column 4) appear to be incompatible > with Nasser's results for problems 1 to 10 at > > <http://www.12000.org/my_notes/ten_hard_integrals/index.htm> > > According to Nasser, Mathematica fails entirely on problem 5, and > succeeds on problems 6,7,8,9 only in terms of non-elementary functions > (elliptic integrals). According to your table, Mathematica succeeds > suboptimally on problems 5,7,9 and fails on problems 6,8. > > Similarly, Nasser reports Maple 17 to fail on problems 9,10, whereas you > report (column 6) a failure for problem 9 and a full success for problem > 10.
After having redone the problems in question, I stand by all the grades shown in the Charlwood Fifty test-results table.
On problems 5,7,9 Mathematica returns a mathematically correct antiderivative expressed in terms of elliptic integrals, so they receive the nonoptimal grade of 1. On problems 6,8, Mathematica times-out after 30 seconds on my computer, so they receive a grade of 0, as per the rules given. However if you wait long enough, Mathematica does return a huge, multipage result involving elliptic integrals and the imaginary unit for problems 6,8.
Nasser and I agree that Maple failed to integrate problem 9. On problem 10, I entered the integrand as
whereas he probably entered it as
Because of some bazaar quirk in Maple, it succeeds in integrating the former and not the latter! Perhaps some Maple aficionado can justify, or at least explain, this phenomena...