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Topic: The integration test suites for Sage.
Replies: 14   Last Post: Sep 14, 2013 1:53 PM

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 Albert D. Rich Posts: 311 From: Hawaii Island Registered: 5/30/09
Re: The integration test suites for Sage.
Posted: Sep 8, 2013 4:42 AM

On Friday, September 6, 2013 6:52:03 AM UTC-10, clicl...@freenet.de wrote:

> > Charlwood_problem(21)
> > integrand : x^3*arcsin(x)/sqrt(-x^4 + 1)
> > antideriv : 1/4*sqrt(x^2 + 1)*x - 1/2*sqrt(-x^4 + 1)*arcsin(x) + 1/4*arcsinh(x)
> > maxima : 1/4*sqrt(x^2 + 1)*x - 1/2*sqrt(-x^4 + 1)*arcsin(x) + 1/4*arcsinh(x)
> > That's easy to judge.

>
> Yes, they are identical. Perhaps Albert made a mistake here?
>

> > Charlwood_problem(23)
> > integrand : x*log(x + sqrt(x^2 + 1))*arctan(x)/sqrt(x^2 + 1)
> > antideriv : sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1))*arctan(x) - x*arctan(x) - 1/2*log(x + sqrt(x^2 + 1))^2 + 1/2*log(x^2 + 1)
> > maxima : (sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1)) - x)*arctan(x) + 1/2*log(x + sqrt(x^2 + 1))^2 - log(x + sqrt(x^2 + 1))*arcsinh(x) + 1/2*log(x^2 + 1)
> >
> > What did I overlook?

>
> Apparently nothing. [...] So number 23 must be counted as a full success.
> Perhaps Albert made a mistake here too?

I just tried Maxima 5.28 on Charlwood problems #21 and #23. It was unable to integrate #21 in closed-form, and it generated a "Lisp error" when attempting to integrate #23. Hence Maxima 5.28 was given a grade of 0 on these two problems in the table of Charlwood Fifty test results I posted.

Note that these test results are for Maxima 5.28, not some mystery version of Maxima being used by Sage. Maxima 5.28 is available for free from SourceForge at

http://sourceforge.net/projects/maxima/?source=directory

Albert