Albert Rich schrieb: > > On Friday, March 21, 2014 8:42:15 AM UTC-10, clicl...@freenet.de wrote: > > > [...] > > > > Just cosmetic defects are left to report in the Chapter 5 evaluations: > > in Example 100, different versions of the radicand are employed in > > parallel. And COS(2*x) could be used to advantage in the evaluations of > > Examples 93-94, 96 and 117. A systematic check against the evaluations > > in Timofeev's book, however, remains to be made. > > I revised the optimal antiderivatives for examples 93, 94, 96, 100 and > 117 of Chapter 5 of the Timofeev integration test suite as you > suggested, and posted the results on the Rubi website at > > http://www.apmaths.uwo.ca/~arich/ > > Please explain what is required for "A systematic check against the > evaluations in Timofeev's book". >
For the Chapters transcribed by myself (i.e. 1 and 4), all evaluations were compared against those in Timofeev's book, some even more or less adopted from the book, although I usually started with Derive's results. For the Chapters transcribed by others but checked thoroughly by me (i.e. 3, 7, 9), all evaluations were compared visually against those in the book, with the aim to match individual terms; this has uncovered problems with Examples 45-46 in Chapter 9, for example.
For the Chapters merely checked cursorily by me (i.e. 5 and 8), the evaluations were glanced over, and only where I became suspicious simplifying operations were tried, or the integral rerun in Derive or the Wolfram Integrator, or Timofeev's evaluation adopted fully or in part. The book was always consulted for such optimization candidates, leaving the impression that no systematic check against Timofeev's evaluations had been made.
I expect further problems to surface if the detailed term-by-term visual check is extended to the remaining Chapters (i.e. 2, 5, 6, 8). Misprints in Timofeev's integrands are likely to show up in this way, and unexpected possibilities of simpler evaluations might too.