Date: Jul 1, 2013 8:34 PM
Author: Waldek Hebisch
Subject: Re: An independent integration test suite

clicliclic@freenet.de wrote:
>
> The following table summarizes the performance data made available for
> the example integrals in Timofeev's 1948 book:
>
> <http://www.math-life.com/jdownloads/view.download/27/279.html>
>
> To simplify the accounting, the numbers of examples represent the actual
> numbers of distinct integrands; for chapters where this has not yet been
> determined, the total of Timofeev's numbered examples is given instead:
>
> ch. ex's Der. Fri. Mpl MMA etc. etc.
> 6.10 1.20 17 9.xx
> -----------------------------------------------
> 1 86 83 85 85 86
> 2 90 - - - -
> 3 12 12 ? ? ?
> 4 132 - - - -
> 5 120 - - - -
> 6 26 - - - -
> 7 11 9 ? 11 ?
> 8 109 - - - -
> 9 59 - - - -
> -----------------------------------------------
> 100% 95.4% ? % ? % ? %
>
> Recent results from the threads "integration test suite / Chap 3" and
> "integration test suite / Chap 7" have been added here:
>
> <http://mathforum.org/kb/thread.jspa?threadID=2449908>
> <http://mathforum.org/kb/thread.jspa?threadID=2449867>
>
> However, a Winner cannot be determined at present because of the uneven
> distribution of results reflected in the "?" entries.
>


FriCAS can do all 12 examples from chapter 3 and 9 elementary
examples from chapter 7. The two nonelementary ones (numner 8
and 9) can be done using 'complexIntegrate' or if you
complicate them a bit (for example add 'exp(x)' to the
integral), but return unevaliated as-is.

BTW1: FriCAS is now at 1.2.1

BTW2: FriCAS answers are at:

http://axiom-wiki.newsynthesis.org/SandboxFriCASTimofeev37

RTW2: If you want "winner", then examples are not challenging enough
(in particular 12 rational examples).

--
Waldek Hebisch
hebisch@math.uni.wroc.pl