gen_lengendre_p bug

asked 2020-02-12 18:40:28 +0200

bso
156 ●1 ●4 ●15

Hi, wonder if someone here familiar with associated Legendre function can verify:

sage: gen_legendre_P(2, 2, x)
3*x^2 - 3

I think it should be

3 - 3*x^2

In Sage 8.9

Thanks

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answered 2020-02-12 21:19:00 +0200

eric_g
8209 ●10 ●61 ●162 https://luth.obspm.fr/...

updated 2021-05-17 23:30:13 +0200

You are unfortunately facing a known issue, which is not solved yet:

https://trac.sagemath.org/ticket/25034

Associated Legendre functions and spherical harmonics in Sage require someone to work of them. Would you volunteer to do it?

EDIT (17 May 2021): the bug has been fixed in SageMath 9.3 (released a week ago):

sage:  gen_legendre_P(2, 2, x)                                                                      
-3*x^2 + 3

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answered 2020-02-13 02:38:42 +0200

bso
156 ●1 ●4 ●15

Thanks, Eric_G. I am interested to help out. Is there a page with Sage volunteering process? I will sign up. I have computer science degrees but new to math (but seriously interested to learn).

Correct definition:

def legendre_function(l, m, f):
    return ((-1)^m * (1 - x^2)^(m/2) * diff(legendre_P(l, x), x, m)).subs(x = f)

sage: legendre_function(2, 2, x)
-3*x^2 + 3

sage: legendre_function(2, 2, cos(x))
-3*cos(x)^2 + 3

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