o
    GZŽh
  ã                   @   s   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	d
„ Zdd„ Zdd„ ZdS )é    )Údiff)ÚIÚpi)ÚSymbol)Ú	conjugate)Úexp)Úsqrt)ÚcosÚcotÚsin)ÚYnmÚZnmÚYnm_cc                  C   sJ  t dddt ddd} }ddlm}m} tdd| |ƒjdddd	ttƒ  ks*J ‚tdd
| |ƒtdt	 | ƒ tdd| |ƒ ksCJ ‚tdd
| |ƒjddtdƒt
| ƒ tt	 | ƒ dttƒ  kseJ ‚tdd| |ƒjddtdƒt| ƒ d	ttƒ  ks€J ‚tdd| |ƒjddtdƒ t
| ƒ tt	| ƒ dttƒ  ks¢J ‚td	d| |ƒjdddtdƒ t| ƒd	  dttƒ  tdƒdttƒ   ksËJ ‚td	d| |ƒjddtdƒ t
| ƒ tt	| ƒ t| ƒ dttƒ  ksñJ ‚td	d| |ƒjddtdƒ tdt	 | ƒ t| ƒd	  dttƒ  tdƒtdt	 | ƒ dttƒ   ks*J ‚td	d	| |ƒjddtdƒ td	t	 | ƒ t| ƒd	  dttƒ  tdƒtd	t	 | ƒ dttƒ   kscJ ‚tt||| |ƒ| ƒ|t| ƒ t||| |ƒ t| | || d  ƒtt	 | ƒ t||d | |ƒ  ksšJ ‚tt||| |ƒ|ƒt	| t||| |ƒ ks²J ‚tt||| |ƒƒd
d	|  tdt	 | | ƒ t||| |ƒ ksÕJ ‚t|||  |ƒt||| |ƒksçJ ‚t||| | ƒtdt	 | | ƒt||| |ƒ ksJ ‚t|| | |ƒd
| tdt	 | | ƒ t||| |ƒ ks#J ‚d S )NÚthetaT©ÚrealÚphir   ©ÚnÚm©Úfuncé   é   éÿÿÿÿéþÿÿÿé   é   é   é   é   é   )r   Ú	sympy.abcr   r   r   Úexpandr   r   r   r   r   r	   r   r
   r   ©ÚthÚphr   r   © r'   úe/var/www/auris/lib/python3.10/site-packages/sympy/functions/special/tests/test_spherical_harmonics.pyÚtest_Ynm   s.   *2D6DRLD"ÿD"ÿ*8ÿ0F$8Dr)   c                  C   sn   t dddt ddd} }ddlm}m} t||| |ƒdd|  td	t | | ƒ t||| |ƒ ks5J ‚d S )
Nr   Tr   r   r   r   r   r   r   )r   r"   r   r   r   r   r   r   r$   r'   r'   r(   Ú
test_Ynm_c'   s   Dr*   c               	   C   s–  t dddt ddd} }tdd| |ƒtdd| |ƒksJ ‚tdd| |ƒtdƒ t tdd| |ƒtd	t | ƒtdd| |ƒ   d ksEJ ‚tdd| |ƒtdd| |ƒksUJ ‚tdd| |ƒtdƒtdd| |ƒtd	t | ƒtdd| |ƒ   d kszJ ‚tdd| |ƒjdd
ddttƒ  ksJ ‚tdd| |ƒjdd
tdƒt t| ƒ tt| ƒ dttƒ  tdƒt t| ƒ tt | ƒ dttƒ   ksÉJ ‚tdd| |ƒjdd
tdƒt	| ƒ dttƒ  ksäJ ‚tdd| |ƒjdd
tdƒ t| ƒ tt| ƒ dttƒ  tdƒt| ƒ tt | ƒ dttƒ   ksJ ‚tdd| |ƒjdd
tdƒt t| ƒ tt| ƒ t	| ƒ dttƒ  tdƒt t| ƒ tt | ƒ t	| ƒ dttƒ   ks_J ‚tdd| |ƒjdd
dtdƒ t	| ƒd  dttƒ  tdƒdttƒ   ks‰J ‚tdd| |ƒjdd
tdƒ t| ƒ tt| ƒ t	| ƒ dttƒ  tdƒt| ƒ tt | ƒ t	| ƒ dttƒ   ksÉJ ‚d S )Nr   Tr   r   r   r   r   r   r   r   r   r   é   r   )
r   r   r   r   r   r   r#   r   r   r	   )r%   r&   r'   r'   r(   Útest_Znm.   s8    $ÿ
ÿ ÿ
ÿ*>,
ÿ6<(ÿF4ÿTD0ÿr,   N)Zsympy.core.functionr   Zsympy.core.numbersr   r   Zsympy.core.symbolr   Z$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr	   r
   r   Z+sympy.functions.special.spherical_harmonicsr   r   r   r)   r*   r,   r'   r'   r'   r(   Ú<module>   s    