I changed priority to "critical". This feature is obviously highly demanded 
among the community (cf. https://trac.sagemath.org/ticket/25034#comment:6).

Best,
Michael
Jonathan Thornburg schrieb am Donnerstag, 8. April 2021 um 20:12:19 UTC+2:

> There have been longstanding issues with spherical harmonics in SageMath,
> notably as described in
> https://groups.google.com/g/sage-support/c/I_d_meMxRbM/m/Esxo5UO2BAAJ
> In that the latter thread, Eric Gourgoulhon's message of 2019-06-15 gives
> a simple test case: 
> from sage.functions.special import SphericalHarmonic
> theta,phi = var('theta phi')
> spherical_harmonic(1,1, theta,phi)
> producing the (wrong) result
> -1/4*sqrt(3)*sqrt(2)*sqrt(-sin(theta)^2)*e^(I*phi)/sqrt(pi)
> whereas the correct result would be
> -1/4*sqrt(6)*e^(I*phi)*sin(theta)/sqrt(pi)
>
> Eric also noted that this problem was apparently a consequence of
> https://trac.sagemath.org/ticket/25034
> and suggested a workaround, using the spin-weighted spherical harmonics
> from the SageMath /kerrgeodesics_gw/ package.
>
>
> An update:
> * As of 9.3.rc2, SageMath's builting spherical harmonics are still broken
> (same result as above for Eric's test case).
> * As of 9.3.rc2, the /kerrgeodesics_gw/ package fails to load (it worked
> fine for me in 9.2.). I'll report that error to the bhptoolkit.org
> issue tracker.
>
> And a question:
> Given that the underlying problem
> https://trac.sagemath.org/ticket/25034
> is unlikely to be fixed for 9.3, should we perhaps put a note in the
> documentation for 9.3 that spherical harmonics are unreliable at present?
>
> -- 
> -- "Jonathan Thornburg [remove -animal to reply]" <[email protected]>
> Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
> currently on the west coast of Canada
> "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"
>

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