Fix crash and remove pexpect-Maxima usage in Y(m,n)

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sage: spherical_harmonic(3, 2, 1, 2*pi/3)
...
TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

The eval function of SphericalHarmonic uses pexpect-Maxima. Since this needs only a formula the call to Maxima could be replaced by a few lines of Python.

http://dlmf.nist.gov/14.30.E1

Replacing pexpect-Maxima is part of #17753.

Depends on #21614
Depends on #21963

Upstream: Fixed upstream, in a later stable release.

Component: symbolics

Author: Ralf Stephan

Branch/Commit: bb4630f

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/20939

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Dependencies: 16813

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comment:1

This depends on the associated Legendre polynomials being implemented, e,g, #16813.

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Changed dependencies from 16813 to #16813

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comment:3

It won't be dependent on P(l,m,x) if the P special value formula is directly used in _eval_. The Y floating point evaluation is done via mpmath anyway.

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Description changed:

--- 
+++ 
@@ -1,12 +1,11 @@
-The eval function of `SphericalHarmonic` uses pexpect-Maxima:
 
 ```
-        if n in ZZ and m in ZZ and n > -1:
-            if abs(m) > n:
-                return ZZ(0)
-            return maxima("spherical_harmonic({},{},{},{})".format(
-                ZZ(n), ZZ(m), maxima(theta), maxima(phi))).sage()
+sage: spherical_harmonic(3, 2, 1, 2*pi/3)
+...
+TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.
 ```
-This should be replaced by `maxima_lib` or something different without Maxima.
+The eval function of `SphericalHarmonic` uses pexpect-Maxima. Since this needs only a formula the call to Maxima could be replaced by a few lines of Python.
 
-Part of #17753.
+http://dlmf.nist.gov/14.30.E1
+
+Replacing pexpect-Maxima is part of #17753.

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Changed dependencies from #16813 to none

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Branch: u/rws/remove_pexpect_maxima_usage_in_y_m_n_

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Commit: f233afa