Date: Nov 15, 2013 6:11 PM
Author: Albert D. Rich
Subject: Re: The A. F. Timofeev symbolic integration test suite

On Friday, November 15, 2013 3:43:59 AM UTC-10, clicl...@freenet.de wrote:

>> Ok, for integrands of the form (c+d x)^n/(a+b x) when n is symbolic,
>> the next version of Rubi will return
>>
>> (c+d*x)^n/(b*n*(b*(c+d*x)/(d*(a+b*x)))^n)*
>> 2F1(-n,-n,1-n,-(b*c-a*d)/(d*(a+b*x)))
>>
> > The simpler equivalent rule derived using Euler's transformation is
>> not used since it is harder to simplify its derivative back to the
>> original integrand.


> But this is just an arbitrary property of the differentiator, right?
> Another differentiator may give the result you would now obtain by
> applying Euler's transformation first (and undoing it on non-elementary
> hypergeometrics that remain in the derivative).
>
> So your reason is no good reason; you are just bending to the dictate of
> WRI. I suggest that Rubi redefines 2F1 differentiation instead. The
> optimality of Rubi's antiderivatives determines the rules to which WRI
> must bend!
>
> I have spoken.
>
> Martin.


Ok, the Messiah has spoken. I modified the optimal antiderivatives for Timofeev Chapter 8 examples 6a.n, 6b.n and 14 in the test-suite to reflect use of Euler's transformation and posted the revised pdf file at

http://www.apmaths.uwo.ca/~arich/TimofeevChapter8TestResults.pdf

However, full credit is still given to those integrators that return valid, but suboptimal, antiderivatives for these problems.

Note that the revised pdf file also includes Chapter 8 test-suite results for various integrators, including the forthcoming version 4.3 of Rubi...

Albert