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

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: Charlwood Fifty test results
Posted: Jul 6, 2013 8:41 PM

Albert Rich schrieb:
>
> 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
> 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...
>

So, while there is no real discrepancy between the Mathematica results
for problems 7 and 9, your 30-second 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#x6-50005>

The Maple quirk uncovered by problem 10 looks like a case of missing
normalization again :).

Martin.