Forgot : I have graphically checked the numerical quasi-equality of the symbolical integral given by Mathematica and the numerical integral given by Sage.
Le mardi 25 octobre 2022 à 15:46:13 UTC+2, Emmanuel Charpentier a écrit : > 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/ef60dab8-dd47-4c82-a274-50b3222bd41an%40googlegroups.com.
