Sage has long had problems with spherical harmonics, e.g., this thread from June 2019: https://groups.google.com/g/sage-support/c/I_d_meMxRbM/m/Esxo5UO2BAAJ
As of 9.5.beta8, spherical harmonics are (still) broken for some arguments, with the test case noted in that earlier thread still giving the same (wrong) result: sage: theta,phi = var('theta,phi') sage: spherical_harmonic(1,1,theta,phi) 1/4*sqrt(3)*sqrt(2)*sqrt(sin(theta)^2)*e^(I*phi)/sqrt(pi) The correct result would be -1/4*sqrt(6)*e^(I*phi)*sin(theta)/sqrt(pi) (see, e.g., https://en.wikipedia.org/wiki/Table_of_spherical_harmonics). In that earlier thread, Eric Gourgoulhon noted that the problem was related to https://trac.sagemath.org/ticket/25034 Unfortunately, even though that ticket is now marked "closed defect (fixed)", spherical harmonics are still broken. Eric suggested a workaround, using the spin-weighted spherical harmonics from the /kerrgeodesics_gw/ package, which for spin 0 should reduce to the standard spherical harmonics. This works if ell and emm are specific integers, but it can't handle the case where they are generic variables. E.g., this works with Sage's native spherical harmonics sage: ell,emm = var('ell,emm') sage: theta,phi = var('theta,phi') sage: diff(spherical_harmonic(ell,emm, theta,phi), theta) but the analogous sage: from kerrgeodesic_gw import spin_weighted_spherical_harmonic sage: diff(spin_weighted_spherical_harmonic(0, ell,emm, theta,phi), theta) fails. -- -- "Jonathan Thornburg [remove color- to reply]" <jthorn4...@pink-gmail.com> on the west coast of Canada, eh? "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" -- 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/YdTZEHWuPGRnsh9c%40gold.bkis-orchard.net.