Date: Nov 15, 2013 11:12 AM
Author: clicliclic@freenet.de
Subject: Re: The A. F. Timofeev symbolic integration test suite


Albert Rich schrieb:
>
> On Wednesday, November 13, 2013 1:56:55 AM UTC-10, clicl...@freenet.de wrote:
>

> > I also notice now that the evaluations proposed for Examples 36a,b,c,d
> > involve TAN(x/2) and friends, whereas your evaluations for Examples 38,
> > 40, 41, 43 involve SIN(x)/(1+COS(x)) and friends instead. I propose to
> > normalize in accordance with your policy for the entire Timofeev suite.
> > (In fact, I like the latter choice more; in Example 36 I simply followed
> > Timofeev, p. 355.)

>
> The antiderivatives for examples 36i in the current Timofeev Chapter 8
> pdf file at
>
> http://www.apmaths.uwo.ca/~arich/TimofeevChapter8TestResults.pdf
>
> are free of tan(x/2) and friends. Do you approve, and if so are there
> antiderivatives for examples 38, 40, 41, and 43 free of
> sin(x)/(1+cos(x)) and friends?
>


The simplified antiderivatives for Examples 36a to 36d look nice and
seem to be correct (I have checked only one). My answer to your question
is: I don't think so. The same transformation could be used to get rid
of the 2*#i*#e^x terms in Examples 38, 40, 41, 43, but TAN(x/2) =
SIN(x)/(1+COS(x)) and friends would not vanish here (their sign would
be inverted), and the gain in simplicity would be marginal.

The perfomance table has increased your pdf file-size from 350 to 1600
kByte, that's plain crazy. I am a bit curious what Mathematica and Maple
return for integral 69 from Timofeev's Chapter 8.

Martin.