I also added this to the Maxima bug report El lunes, 31 de octubre de 2022 a las 10:44:12 UTC+1, Frédéric Chapoton escribió:
> amusingly, one can see that some power of 2 is lurking around : > > (%i36) expand(diff(integrate(x*log(x)**13/(1+x**2),x),x)); > 13 > 4096 x log (x) > (%o36) --------------- > 2 > 13 x + 13 > > Le dimanche 30 octobre 2022 à 23:49:31 UTC+1, pvit...@gmail.com a écrit : > >> Ok, thanks a lot. I already reported the bug. >> >> El domingo, 30 de octubre de 2022 a las 10:27:23 UTC+1, Frédéric Chapoton >> escribió: >> >>> The factor-2 problem is also present for the integral with no bounds. >>> Please report in maxima's bug reporting site. >>> >>> (%i20) integrate(x*log(x)^4/(x^2 + 1),x); >>> 4 2 >>> 2 log (x) log(x + 1) 2 2 >>> (%o20) - (3 ((- ---------------------) + li (- x ) - 2 log(x) li (- x ) >>> 3 5 4 >>> 3 >>> 2 >>> 4 log (x) li (- >>> x ) >>> 2 2 2 >>> + 2 log (x) li (- x ) - >>> -------------------))/2 >>> 3 3 >>> (%i21) diff(%,x); >>> 4 >>> 2 x log (x) >>> (%o21) ----------- >>> 2 >>> x + 1 >>> >>> Le mardi 25 octobre 2022 à 00:17:07 UTC+2, pvit...@gmail.com a écrit : >>> >>>> Thank you very much for the analysis. If I understand correctly, the >>>> bug is in this part of the integral: x*log(x)^4/(x^2 + 1) >>>> >>>> I will try to report the bug to maxima. But, as far I can see >>>> https://sourceforge.net/p/maxima/bugs/ is very quiet, with few answers >>>> to the reports. >>>> >>>> El lunes, 24 de octubre de 2022 a las 21:33:41 UTC+2, Frédéric Chapoton >>>> escribió: >>>> >>>>> where we can see that there is a factor 2 between the wrong symbolic >>>>> value and the correct numeric value >>>>> >>>>> This should be filed as a bug in maxima. >>>>> >>>>> Le lundi 24 octobre 2022 à 21:24:30 UTC+2, Frédéric Chapoton a écrit : >>>>> >>>>>> and one more step : >>>>>> >>>>>> sage: integrate(x*log(x)^4/(x^2 + 1), x,0,1).n() >>>>>> 1.45817965567036 >>>>>> sage: (x*log(x)^4/(x^2 + 1)).nintegral(x,0,1) >>>>>> (0.7290898278351722, 2.48288156701193e-09, 357, 0) >>>>>> sage: integrate(-log(x)^4/(x^2 + 1), x,0,1).n() >>>>>> -23.9077878738501 >>>>>> sage: (-log(x)^4/(x^2 + 1)).nintegral(x,0,1) >>>>>> (-23.90778787384685, 1.267767046897461e-08, 483, 0) >>>>>> >>>>>> >>>>>> Le lundi 24 octobre 2022 à 21:19:46 UTC+2, Frédéric Chapoton a écrit : >>>>>> >>>>>>> more study of the bug (coming from maxima) >>>>>>> >>>>>>> sage: C=x^2*(log(x))^4/((x+1)*(1+x^2)) >>>>>>> sage: aa,bb=C.partial_fraction_decomposition() >>>>>>> sage: integral(aa,x,0,1) >>>>>>> -5/128*pi^5 + 45/64*zeta(5) >>>>>>> sage: integral(bb,x,0,1) >>>>>>> 45/4*zeta(5) >>>>>>> sage: _+__ >>>>>>> -5/128*pi^5 + 765/64*zeta(5) >>>>>>> sage: _.n() >>>>>>> 0.440633136273039 >>>>>>> sage: aa.nintegral(x,0,1) >>>>>>> (-11.58934902297507, 5.068708119893017e-08, 525, 0) >>>>>>> sage: bb.nintegral(x,0,1) >>>>>>> (11.66543724536065, 4.943314557692702e-08, 525, 0) >>>>>>> sage: integral(aa,x,0,1).n() >>>>>>> -11.2248041090899 >>>>>>> sage: integral(bb,x,0,1).n() >>>>>>> 11.6654372453629 >>>>>>> >>>>>>> >>>>>>> >>>>>>> Le lundi 24 octobre 2022 à 00:14:09 UTC+2, pvit...@gmail.com a >>>>>>> écrit : >>>>>>> >>>>>>>> I am using Sage 9.7 running in Arch linux over WSL2 >>>>>>>> >>>>>>>> I get different results for an integral using numerical integration >>>>>>>> (which seems to agree with Mathematica) and symbolic integration: >>>>>>>> >>>>>>>> numerical_integral(x^2*(log(x))^4/((x+1)*(1+x^2)),0,1) >>>>>>>> (0.07608822217400527, 1.981757967172001e-07) >>>>>>>> >>>>>>>> integral(x^2*(log(x))^4/((x+1)*(1+x^2)),x,0,1) >>>>>>>> 6*I*polylog(5, I) - 6*I*polylog(5, -I) + 765/64*zeta(5) >>>>>>>> integral(x^2*(log(x))^4/((x+1)*(1+x^2)),x,0,1).n() >>>>>>>> 0.440633136273036 >>>>>>>> >>>>>>> -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/7b5ec2c6-a68e-4976-be05-cf0dc2ddd309n%40googlegroups.com.
