Legendre transform drops imaginary part for m=0

[Keaton Burns]

First off, thanks for making this great code available! I’m using the associated Legendre transform routines (fixed m) and have noticed that the m=0 transforms seems to drop the imaginary component of the input. This makes sense if the underlying SHT is real, because then the m=0 Fourier component is purely real. But if the underlying SHT is complex, then there should be an imaginary component too for m=0. I can work around this by running two m=0 transforms for the real and imaginary parts separately, but it would be nice not to have to special case this. Short example attached.

[Nathanaël Schaeffer]

Yes, this is indeed the intended behaviour, and it only makes sense for real physical data.
I agree the correct behaviour should be to keep the imaginary part. I will think of how to implement this without making too many changes to the actual behaviour.
As you mention, for now, you need to run two m=0 transforms, one for real, one for imaginary part.