Essentially correct, bit it’s a tad less simpler :
sage: f(x) = x^2*(log(x))^4/((x+1)*(1+x^2)) sage: list(map(lambda u:u.integrate(x, 0, 1), f(x).partial_fraction_decomposition())) [-5/128*pi^5 + 45/64*zeta(5), 45/4*zeta(5)] sage: list(map(lambda u:mathematica.Integrate(u, (x, 0, 1)).sage(), f(x).partial_fraction_decomposition())) [-5/128*pi^5 + 45/128*zeta(5), 45/4*zeta(5)] HTH Le lundi 24 octobre 2022 à 21:33:41 UTC+2, Frédéric Chapoton a écrit : > 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/618495ee-6f14-407f-8187-d3cb45cf957bn%40googlegroups.com.
