
    sg
                         d dl mZ d dlmZmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZ d dlmZmZmZ d dlmZmZmZ d	 Zd
 Zd Zy)    )diff)Ipi)Symbol)	conjugate)exp)sqrt)coscotsin)YnmZnmYnm_cc            	      h
   t        dd      t        dd      }} ddlm}m} t	        dd| |      j                  d      dd	t        t              z  z  k(  sJ t	        dd
| |      t        dt        z  |z         t	        dd| |      z  k(  sJ t	        dd
| |      j                  d      t        d      t        |       z  t        t         |z        z  dt        t              z  z  k(  sJ t	        dd| |      j                  d      t        d      t        |       z  d	t        t              z  z  k(  sJ t	        dd| |      j                  d      t        d       t        |       z  t        t        |z        z  dt        t              z  z  k(  sJ t	        d	d| |      j                  d      dt        d      z  t        |       d	z  z  dt        t              z  z  t        d      dt        t              z  z  z
  k(  sJ t	        d	d| |      j                  d      t        d       t        |       z  t        t        |z        z  t        |       z  dt        t              z  z  k(  sJ t	        d	d| |      j                  d      t        d       t        dt        z  |z        z  t        |       d	z  z  dt        t              z  z  t        d      t        dt        z  |z        z  dt        t              z  z  z   k(  sJ t	        d	d	| |      j                  d      t        d       t        d	t        z  |z        z  t        |       d	z  z  dt        t              z  z  t        d      t        d	t        z  |z        z  dt        t              z  z  z   k(  sJ t        t	        ||| |      |       |t        |       z  t	        ||| |      z  t        | |z   ||z   dz   z        t        t         |z        z  t	        ||dz   | |      z  z   k(  sJ t        t	        ||| |      |      t        |z  t	        ||| |      z  k(  sJ t        t	        ||| |            d
d	|z  z  t        dt        z  |z  |z        z  t	        ||| |      z  k(  sJ t	        |||  |      t	        ||| |      k(  sJ t	        ||| |       t        dt        z  |z  |z        t	        ||| |      z  k(  sJ t	        || | |      d
|z  t        dt        z  |z  |z        z  t	        ||| |      z  k(  sJ y )NthetaTrealphir   nmfunc                        )r   	sympy.abcr   r   r   expandr	   r   r   r   r   r
   r   r   r   thphr   r   s       i/var/www/html/venv/lib/python3.12/site-packages/sympy/functions/special/tests/test_spherical_harmonics.pytest_Ynmr*      s   G$'D)ABq!R###.!QtBxZ.@@@q"b"#bd2g,s1aR/@!@@@@q"b"$$$$/473r7?3r"u:3MqQUVXQYz3ZZZZq!R###.$q'#b'/1T"X:2NNNNq!R###.47(3r72B3qt92LaPTUWPXj2YYYYq!R###.!DG)CGQJ2F$r(
2SVZ[\V]_`aefhai_iVj2jjjjq!R###.48)CG2CC"I2McRTg2UWXY]^`YaWa2bbbbq"b"$$$$/T"XIc"Q$r'l4J3r7TU:4UWXY]^`YaWa4b6:2hs2a47|6KQtTVxZ6X5Y Z Z Zq!R###.DH9S1R[3HRRS3SUVW[\^W_U_3`59"Xc!A#b&k5I1TRTX:5V4W X X X Aq"b!2&1SW9SAr25F+F-1A26AEAI2F-GQBrE
-RSVWXZ[^_Z_acegSh-h,i j j jAq"b!2&!A#c!QB.?*????SAr2&'B!A#;s2a46"9~+Ec!QPRTVFW+WWWWq!bS"Q2r!2222q!R"RT!VBYAq"b0A!AAAAq1"b""qRT!VBY!7Aq"b8I!IIII    c                      t        dd      t        dd      }} ddlm}m} t	        ||| |      dd|z  z  t        d	t        z  |z  |z        z  t        ||| |      z  k(  sJ y )
Nr   Tr   r   r   r   r   r   r   )r   r$   r   r   r   r   r   r   r&   s       r)   
test_Ynm_cr-   '   sb    G$'D)ABAr221+c"Q$q&)n"<SAr2=N"NNNNr+   c            
      v	   t        dd      t        dd      }} t        dd| |      t        dd| |      k(  sJ t        dd| |      t        d       t        z  t        dd| |      t        d	t        z  |z        t        dd| |      z  z
  z  dz  k(  sJ t        dd| |      t        dd| |      k(  sJ t        dd| |      t        d      t        dd| |      t        d	t        z  |z        t        dd| |      z  z   z  dz  k(  sJ t        dd| |      j                  d
      ddt        t              z  z  k(  sJ t        dd| |      j                  d
      t        d      t        z  t        |       z  t        t        |z        z  dt        t              z  z  t        d      t        z  t        |       z  t        t         |z        z  dt        t              z  z  z
  k(  sJ t        dd| |      j                  d
      t        d      t        |       z  dt        t              z  z  k(  sJ t        dd| |      j                  d
      t        d       t        |       z  t        t        |z        z  dt        t              z  z  t        d      t        |       z  t        t         |z        z  dt        t              z  z  z
  k(  sJ t        dd| |      j                  d
      t        d      t        z  t        |       z  t        t        |z        z  t        |       z  dt        t              z  z  t        d      t        z  t        |       z  t        t         |z        z  t        |       z  dt        t              z  z  z
  k(  sJ t        dd| |      j                  d
      dt        d      z  t        |       dz  z  dt        t              z  z  t        d      dt        t              z  z  z
  k(  sJ t        dd| |      j                  d
      t        d       t        |       z  t        t        |z        z  t        |       z  dt        t              z  z  t        d      t        |       z  t        t         |z        z  t        |       z  dt        t              z  z  z
  k(  sJ y )Nr   Tr   r   r   r   r   r   r   r   r    r      r!   )
r   r   r   r	   r   r   r%   r   r   r
   )r'   r(   s     r)   test_Znmr0   .   s   G$'D)ABq!RAq"b 1111q"b"47(1*c!QB.?$'1RLQ2r1B$B/C #DDE#F G G Gq!RAq"b 1111q!Ra#aB*;#&r!tBw<Aq"b0A#A+B "CCD"E F F Fq!R###.!QtBxZ.@@@q"b"$$$$/DGAIc"g4Ec!B$i4OQRSWXZS[Q[4\6:1gaiB6GQBrE
6RTUVZ[]V^T^6_5` a a aq!R###.$q'#b'/1T"X:2NNNNq!R###.DG8CG3CC"I3MqQUVXQYz3Z59!WSW_S!BZ5OQRSWXZS[Q[5\4] ^ ^ ^q"b"$$$$/DHQJs2w4Fs1R4y4PQTUWQX4XZ[\`ac\dZd4e6:2hqjR6HaRPRU6STWXZT[6[]^_cdf_g]g6h5i j j jq!R###.!DG)CGQJ2F$r(
2SVZ[\V]_`aefhai_iVj2jjjjq!R###.DH9SW3DS2Y3NsSUw3VXYZ^_aZbXb3c59"Xc"g5Ec1"R%j5PQTUWQX5XZ[\`ac\dZd5e4f g g gr+   N)sympy.core.functionr   sympy.core.numbersr   r   sympy.core.symbolr   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr	   (sympy.functions.elementary.trigonometricr
   r   r   +sympy.functions.special.spherical_harmonicsr   r   r   r*   r-   r0    r+   r)   <module>r:      s5    $ & $ : 6 9 D D G GJ8Ogr+   