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Topic: Charlwood Fifty test results
Replies: 16   Last Post: Sep 19, 2013 10:09 PM

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 Albert D. Rich Posts: 311 From: Hawaii Island Registered: 5/30/09
Re: Charlwood Fifty test results
Posted: Jul 6, 2013 4:32 PM

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

x^3*exp(1)^arcsin(x)/sqrt(1-x^2)

whereas he probably entered it as

x^3*exp(arcsin(x))/sqrt(1-x^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...

Albert