
Re: Charlwood Fifty test results
Posted:
Jul 6, 2013 8:41 PM


Albert Rich schrieb: > > On Friday, July 5, 2013 11:55:54 PM UTC10, 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 nonelementary > > 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 testresults 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 > timesout 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 > > x^3*exp(1)^arcsin(x)/sqrt(1x^2) > > whereas he probably entered it as > > x^3*exp(arcsin(x))/sqrt(1x^2) > > 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... >
So, while there is no real discrepancy between the Mathematica results for problems 7 and 9, your 30second timeouts explain the (apparent) failures on problems 6 and 8. What remains to be explained are the incompatible Mathematica results for problem 5 where Nasser obtained an unevaluated integral:
<http://www.12000.org/my_notes/ten_hard_integrals/inse5.htm#x650005>
The Maple quirk uncovered by problem 10 looks like a case of missing normalization again :).
Martin.

