
    gj                        d dl mZ d dlmZmZmZ d dlmZ d dlm	Z	 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mZmZ d d
lmZ d dlmZmZ d dlmZmZmZm Z m!Z! d Z"d Z#d Z$d Z%d Z&ed             Z'd Z(d Z)d Z*d Z+d Z,d Z-d Z.dS )    )Function)IRationalpi)S)Symbol)	factorial)explog)tanh)sqrt)cotsintan)residue)XFAILraises)xzaskc                  &   t          dt          z  t          d          dk    sJ t          dt          z  t          d          dk    sJ t          dt          z  t          d          dk    sJ t          dt          dz  z  t          d          dk    sJ t          dt          d          dk    sJ t          dt          d          dk    sJ t          t          t          d          dk    sJ t          t          dz  t          d          dk    sJ d S )N   r   Q         r   r        \/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_residues.pytest_basic1r#      s   1Q31""""2a4A"$$$$2a4A"$$$$1QT61a  A%%%%1aq    1aq    1aq    1a4A!######r!   c                  &   t          dt          z  t          d          dk    sJ t          dt          z  t          d          dk    sJ t          dt          z  t          d          dk    sJ t          dt          dz  z  t          d          dk    sJ t          dt          d          dk    sJ t          dt          d          dk    sJ t          t          t          d          dk    sJ t          t          dz  t          d          dk    sJ d S )Nr   r   r   r   r   r   r   r    r!   r"   test_basic2r&      s   1Q31""""2a4A!####2a4B1$$$$1QT61a  A%%%%1aq    1aq    1aq    1a4A!######r!   c                     t          d          } t           | t                    t          dz  z  t          d           | t                                        t          d                              t          d          dz  k    sJ d S )Nfr   r         )r   r   r   diffsubsr(   s    r"   test_fr.   %   si    A11Q4419a##qqttyyA';';Aq'A'A"'DDDDDDDr!   c                     t          dt          t                    z  t          d          dk    sJ t          dt          t                    z  t          d          dk    sJ t          dt          t                    dz  z  t          d          dk    sJ t          dt          t                    dz  z  t          d          t          dd          k    sJ d S )Nr   r   r   r         )r   r   r   r   r    r!   r"   test_functionsr2   *   s    1SVV8Q""a''''1SVV8Q""a''''1SVVQY;1%%****1SVVQY;1%%!Q777777r!   c                     t          dt          dz   z  t          d          dk    sJ t          dt          dz   z  t          d          dk    sJ t          dt          dz  dz   z  t          d          dk    sJ t          dt          dz  dz   z  t          t                    t           dz  k    sJ t          dt          dz  dz   z  t          t                     t          dz  k    sJ t          dt          dz  dz   z  t          d          dk    sJ t          dt          dz  dz   z  t          t          t          t          z  dz                                          t          dd          t          dz  z    t          d          z            sJ t          dt          dz  t          dz  z   dz  z  t          t          t          z            t           dz  t          dz  z  k    sJ d S )Nr   r   r%   r   r)   r0   )	r   r   r   r
   r   equalsr   r   r   r    r!   r"   test_expressionsr5   1   s   1a!e9a##q((((1a!e9a$$))))1adQh<B''1,,,,1adQh<A&&1"Q$....1adQh<QB''1Q3....1adQh<A&&!++++1adQh<C"QKK0077(1a..1Q3:N8OPTUVPWPW8WXXXXX1adQTkA%%q!A#..1"Q$q!t);;;;;;r!   c                  l   t          ddd          } t          t          t                    t          t          t
          z  dz  t          z  z
  | z  z  t          t
          t          z  t          z            t          t
          t          z  t          z  dz            t          | dz
            z  k    sJ d S )NnT)integerpositiver)   r   )r   r   r
   r   r   r   r   r	   )r7   s    r"   test_expressions_failingr:   <   s    sD4000A3q661r!tAvax<!++Q"Q77AbDF1HiA&&&' ' ' ' ' 'r!   c                  2    t          t          d            d S )Nc                  X    t          t          dt          z            t          d          S Nr   r   r   r
   r   r    r!   r"   <lambda>z%test_NotImplemented.<locals>.<lambda>D   s    AaC!Q(?(? r!   )r   NotImplementedErrorr    r!   r"   test_NotImplementedrA   C   s    
 ? ?@@@@@r!   c                  &   t          dt          z  t          t          z   z  dt          z
  t          z
  z  t          dz  z  t          d          dt          t          d          z  z   t          dz  t          d          z  z
  dt          z  z
  k    sJ d S )Nr   r   r   )r   r   r   r   r    r!   r"   test_bugrC   G   s~    1q61q5>1q519-ad2Aq99	Ac!ffHq!tCFF{"QqS() ) ) ) ) )r!   c                  $   t          dt          dz  t          dz  z   dz  z  t          t          t          z            t           dt          dz  z  z  k    sJ t          dt          z  dz  t
          t          t                    z
  z  t          d          dt
          dz
  z  k    sJ t          dt          z   t          z  dz  t
          t          t                    z
  z  t          d          t          t
          dz
  z  dt
          dz
  z  z   k    sJ d S )Nr   r   r)   r0   r   )r   r   r   r   r   r   r
   r   r    r!   r"   test_issue_5654rE   L   s    1adQTkA%%q!A#..1"a1f+====1Q3q5!c!ff*%q!,,1q5	9999AE19Q;CFF
+Q22aQi!QU)6KKKKKKKr!   c                  n    t          dt          t                    dz
  z  t          d          dk    sJ d S r=   r>   r    r!   r"   test_issue_6499rG   R   s3    1c!ffqj>1a((A------r!   c                  ~    t          t          t          dz            t          dz  z  t          d          dk    sJ d S )N2   3   r   r   )r   r   r   r    r!   r"   test_issue_14037rK   V   s8    3q"u::ae#Q**a//////r!   c                     t           dz  t          t          t           z            z  t           dz  dz   z  } t          | t           t	          d           dz  t	          d          t
          z  dz  z
                                                                d          t	          d          dt
          z
  z  dt          t	          d          t          z  dt
          z   z  dz            z  z  k    sJ d S )Nr   r)   r   T)deepr1   )	r   r   r   r   r   r   canceltogetherr   r-   s    r"   test_issue_21176rP   Z   s    	1SAYY1q!A1a$q''!d1ggaik12299;;DD$DOO77AE?Ac$q''"*a!e"4Q"677789 9 9 9 9 9r!   c                     t          d           t          t          d          t          z  dz            z  dz  } t          t	          t          t
          z            t
          dz
  t
          dz
  z  dz   z  t
          t          d          dz  t          d          t          z  dz  z
            }t          t	          t          t
          z            t
          dz  dt
          z  z
  dz   z  t
          t          d          dz  t          d          t          z  dz  z
            }|| k    sJ ||z
                                  dk    sJ d S )Nr0   r   r   r   )	r   r   r   r   r   r   r   r   rN   )rr   bs      r"   test_issue_21177rT   `   s    	ad1ggbjl###A%ABqD		AEAE?Q./AaDDFT!WWQYq[4HIIABqD		1a4!A#:>*AqttAvQ	!/CDDA6666E>>q      r!   N)/sympy.core.functionr   sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr	   &sympy.functions.elementary.exponentialr
   r   %sympy.functions.elementary.hyperbolicr   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   sympy.series.residuesr   sympy.testing.pytestr   r   	sympy.abcr   r   r   r   r   r#   r&   r.   r2   r5   r:   rA   rC   rE   rG   rK   rP   rT   r    r!   r"   <module>ra      s   ( ( ( ( ( ( 0 0 0 0 0 0 0 0 0 0 " " " " " " $ $ $ $ $ $ > > > > > > = = = = = = = = 6 6 6 6 6 6 9 9 9 9 9 9 D D D D D D D D D D ) ) ) ) ) ) . . . . . . . . # # # # # # # # # # # # # #$ $ $$ $ $E E E
8 8 8< < < ' ' 'A A A) ) )
L L L. . .0 0 09 9 9! ! ! ! !r!   