On Sat, Jan 2, 2021 at 4:28 PM Waldek Hebisch <[email protected]> wrote: > > On Fri, Jan 01, 2021 at 08:15:42AM -0800, [email protected] wrote: > > Has there been any progress on integrals expressible in elliptic functions? > > > > I need them now, and it seems that no open source integrators can compute > > things like > > integrate(sqrt(x*(x-1)*(x-2)),x=0..1) in terms of elliptic functions. > > Nothing ready. I have a lot of distractions and on my side things > go very slowly.
Isn't integration of hypergeometric functions the right direction here? Integration is easy, identification of hypergeometrics doable, what's probably hardest is making the results canonical - I am not sure how well the relations between hypergeometric functions are understood - on the other hand for 2F1 everything is known, and this is the case of elliptic integrals, right? > > > On Tuesday, October 23, 2018 at 8:01:25 PM UTC+1 Waldek Hebisch wrote: > > > > > I looked a bit at FriCAS failures in Rubi testsutite. More than > > > 8000 positions in testsutite contains elliptic integrals in > > > answer. FriCAS currently can not generate ellipic integrals > > > in answers, so unless the integral really is elementary > > > (it happens sometimes, but is quite rare) FriCAS can not > > > do it. This is more than 10% of the testsuite and single > > > biggest reason for failures. > > > > > > More about this: it seems that most elliptic cases is > > > very simple, easily reducing to defining formulas > > > by few substitutions. It seem relatively easy to add > > > ad-hoc handling for such cases. Main problem is that > > > we do not want to loose completeness for elementary cases, > > > so we can generate elliptics only after we decided that > > > integral is nonelementary. > > > > > > Probably next biggest problem is polylogaritms (of order 5000 > > > positions). We can handle one case, when argument of > > > polylogarithm is an exponential. But Rubi testsuite seem > > > to contain mostly different case. > > > > > > There are also integrals expressed in terms of hypergeometric > > > functions (few thousends). They are used to integrate > > > algebraic functions and some mixed cases involving > > > algebraics and exponentials. I need to look closer, > > > but at least some of them we should be able to handle > > > like existing code for incomplete gamma. > > > > > > Together the cases above seem to cover vast majority of > > > failures on Rubi testsuite. There are also failures > > > which current FriCAS methods in principle should handle, > > > but are not handled due to incomplete or buggy implementation. > > > > > > ATM better handling of the above is still in planning stage. > > > I have made nice theoretical progress, both for elliptic > > > functions and for polylogarithms. But in both cases > > > theory is still too weak to give complete algorithm. > > > So we probably should try adding ad-hoc extentions. > > > There is reasonable chance that such extentions will > > > be part of complete implementation in the future. > > > > > > -- > > > Waldek Hebisch > > > > > > > -- > > You received this message because you are subscribed to the Google Groups > > "FriCAS - computer algebra system" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to [email protected]. > > To view this discussion on the web visit > > https://groups.google.com/d/msgid/fricas-devel/24a7f415-bec6-49ec-b98f-94eb188a88ecn%40googlegroups.com. > > > -- > Waldek Hebisch > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/fricas-devel/20210102162849.GA20948%40math.uni.wroc.pl. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/CAAWYfq37fbAxd45CUL5ojCGNYX7KY7NasaTb6_m88YKw8NMo0g%40mail.gmail.com.
