Albert Rich schrieb: > > On Saturday, October 5, 2013 1:36:36 AM UTC-10, clicl...@freenet.de wrote: > > > > [...] > > > > This being a matter of principle, the choice of model antiderivatives is > > often just a matter of taste. In examples #16 and #56 you list the > > simpler but discontinuous ATAN evaluations. Are you retracting your > > statement of June 18 that "continuity of antiderivatives trumps > > compactness"? > > No. > > > In the evaluation of example #59, -4 + 4*SIN(x)^2 may be simplified to > > -4*COS(x)^2, and the evaluation of example #70 can (accidentally?) be > > written more compactly as 1/48*SIN(2*x)^3 - 1/64*SIN(4*x) + x/16. > > A revised version of the Timofeev Chapter 1 test examples and results > is now available at > > http://www.apmaths.uwo.ca/~arich/TimofeevChapter1TestResults.pdf > > It incorporates all your suggested changes except for example #70. > Generally I prefer antiderivatives that involve the same kernels as > the integrand, even though superficially more complicated. In example > #70, sin(2x) and sin(4x) do not occur in the integrand, but sin(x) and > cos(x) do. However of course, systems that return antiderivatives in > multiangle form should be given full credit for their answers. Like > you say, it's just a matter of taste.
I had my doubts about this one too.
> > I did make the optimal results for examples #16 and #56 continuous as > you suggested. However, all the systems tested, except Derive, return > the more compact, but discontinuous antiderivative. Note that even > Derive returns the discontinuous form when single-stepping through the > integration. Currently, I am being lenient (and perhaps unfair to > Derive) and giving full credit to all the systems for these two > examples. Do you concur with this grade? >
I always suspected that Derive wants to keep some of its secrets from the competition! And I am not glad to hear that Rubi no longer returns continuous antiderivatives for this type of integrand - but I suppose that's easily put back in. Otherwise I concur absolutely.