If it makes sense to use integration by parts or not deppends heavily on the actual expression. I suspect that, if you try to make a sane criterion te decide when to apply it, you could end up with something very complicated as well. Ther is reason why there are so many rules in RUBI (although I heard that the author is considering reorganizing them in a decission tree, which might simplify things to some extent).
Anyways, even if being able to run several steps of simplification->partial integration->further simplification-> further partial integration... would possibly increase the number of cases that we can integrate, the first step would be to have some support for simplification rules. El martes, 28 de febrero de 2017, 18:01:58 (UTC+1), parisse escribió: > > > > Le mardi 28 février 2017 15:57:53 UTC+1, mmarco a écrit : >> >> Many RUBI rules actually consist on applying that kind of algorithms. The >> trick with those algorithms is that sometimes they help, and sometimes they >> hurt (in the sense that you get something that is actually harder to >> integrate). >> >> One of the important things about RUBI that many people forget about is >> that it not only is able to integrate more expressions than >> Mathematica/Maple/Maxima... (and usually does it faster), but that it also >> often produces "better" output (in the sense of more compact >> expressions and/or fewer discontinuity problems). In general, each rule >> of RUBI turns the expression into something simpler, so even if you don't >> have the full set of rules, you can use the ones you have as a >> preprocessing step for other kinds of algorithms. >> >> > But what about using them in the middle of other algorithms? Because that > is what you would want to do. For example if you have a generic expression > with an inverse trig function, then it makes sense to do integration by > part, and after that you might apply some nice and compact expression > obtained by a rule on sqrt. Or maybe you should do a partial fraction > decomposition somewhere. My main concern with what I looked at is that some > rules should be grouped in one algorithm. There are too many rules in > rubi... > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
