
    \h                     j    S SK Jr  S SKJr  S SKJrJrJrJr  S SK	J
r
  S SKJr  S SKJr  S rS rS	 rg
)    )Rational)symbols)FallingFactorialRisingFactorialbinomial	factorial)gamma)combsimp)xc                     [        SSS9u  pn[        [        U5      5      [        U5      :X  d   e[        [        X 5      5      [        X 5      :X  d   e[        [        U5      [        US-
  5      -  5      USU-   -  SU-   -  :X  d   e[        [        US-   U S-   5      [        X 5      -  5      SU-   SU -   -  :X  d   e[        [        SU-  S-   US-   5      [        SU-  S-   U5      -  5      [	        SS	5      SU-  S	-   SU-  S-   -  US-   S	U-  S-   -  -  -  :X  d   e[        [        U5      S	-  [        US-
  5      -  5      [        U5      U-  SU-   -  SU-   -  :X  d   e[        [        U5      [        US-   U S-   5      -  [        X 5      -  5      [        US-   5      SU -   -  :X  d   e[        [        US-   5      5      [        US	-   5      :X  d   e[        [        [        5      5      [        [        S-   5      :X  d   e[        US-   [        U5      -  5      [        US-   5      :X  d   e[        [        U5      U-  5      [        US-
  5      :X  d   e[        [        X"U -
  5      5      [        X 5      :X  d   e[        [        U5      [        U 5      [        X -
  5      -  -  5      [        X 5      :X  d   e[        [        U 5      [        X -
  5      -  [        U5      -  5      S[        X 5      -  :X  d   e[        [        S	U-  5      [        U5      S	-  -  5      [        S	U-  U5      :X  d   e[        [        S	U-  5      [        U 5      -  [        X -
  5      -  [        U5      S-  -  5      [        S	U-  U5      [        X 5      -  :X  d   e[        [        USU-   -  US	-  -
  U-
  5      5      S:X  d   e[        S
[        SU5      -  [        U5      -  5      SU-  US-   -  US	-   -  US-   -  :X  d   e[        S
[        SUS-
  5      -  [        US-
  5      -  5      SUS-
  -  U-  US-   -  US	-   -  :X  d   e[        S
[        SUS-
  5      -  [        US-
  5      -  5      SUS-
  -  U-  US-
  -  US	-
  -  :X  d   e[        S
[        SU* S-
  5      -  [        U* S-
  5      -  5      SU* S-
  -  * U-  US-
  -  US	-
  -  :X  d   e[        S
[        SU5      -  [        U5      -  5      US-   US	-   -  US-   -  :X  d   e[        S
[        SUS-
  5      -  [        US-
  5      -  5      X"S-   -  US	-   -  :X  d   e[        S
[        SUS-
  5      -  [        US-
  5      -  5      X"S-
  -  US	-
  -  :X  d   e[        S
[        SU* S-
  5      -  [        U* S-
  5      -  5      U* US-
  -  US	-
  -  :X  d   eg )Nzk m nTinteger               )	r   r
   r   r   r   r	   r   r   r   )kmns      Z/var/www/auris/envauris/lib/python3.13/site-packages/sympy/simplify/tests/test_combsimp.pytest_combsimpr   	   s1   g.GA!IaL!Yq\111HQN#x~555IaL1q5!112aaj"q&6IIIIHQUAE*8A>9:q1uq1uoMMMHQqS1Wa!e,XacAgq-AABA1q1Q37+a!eacAg->?@A A A IaL!OIa!e$445!QQa() ) )IaL!a%Q!77FG!a%!a% ! ! ! E!a%L!Yq1u%5555IaL!U1q5\111 QUIaL()Yq1u-====IaLN#y1~555 HQA&'8A>999 IaL)A,y/?"?@A  IaL15!11)A,>?	(1.  IacN9Q<?23x!Q7GGGGIacN9Q</	!%0@@!a $QqS!,Xa^;< < < IaQi!Q$.234999A&r1--il:;	aQQQ'( ( (A&r1q511)AE2BBC	q1uaQQ'( ( (A&r1q511)AE2BBC	q1uaQQ'( ( (A&rA26229aR!V3DDE
Q1q5!1q5)* * * Aoa++IaL89	
QQQ     AoaQ//	!a%0@@A	q5	1q5  AoaQ//	!a%0@@A	q5	1q5  Aoa!a00A261BBC	
AE
AE      c                  x    [        SSS9n [        [        SU 5      5      SSU -  -  [        SU -
  5      -  :X  d   eg )Nr   Tr   ii _7 r   
   )r   r
   r   r   )r   s    r   test_issue_6878r   C   s>    T"AOC+,a	"q&@Q0QQQQr   c                      [        SSSS9n [        [        SU 5      5      S[        U 5      [        SU -
  5      -  -  :X  d   e[        [        SU -
  5      5      [        SU -
  5      :X  d   eg )NpT)r   positiver   r   )r   r
   r   r   )r!   s    r   test_issue_14528r#   H   sb    TD1AHQqM"a1i!n)D&EEEEIacN#y1~555r   N)sympy.core.numbersr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   r   r   r   'sympy.functions.special.gamma_functionsr	   sympy.simplify.combsimpr
   	sympy.abcr   r   r   r#    r   r   <module>r+      s+    ' % m m 9 , 7tR
6r   