
    sg                     j    d dl mZ d dlmZ d dlmZmZmZmZ d dl	m
Z
 d dlmZ d dlmZ d Zd Zd	 Zy
)    )Rational)symbols)FallingFactorialRisingFactorialbinomial	factorial)gamma)combsimp)xc                  t   t        dd      \  } }}t        t        |            t        |      k(  sJ t        t        ||             t        ||       k(  sJ t        t        |      t        |dz
        z        |d|z   z  d|z   z  k(  sJ t        t        |dz   | dz         t        ||       z        d|z   d| z   z  k(  sJ t        t        d|z  dz   |dz         t        d|z  dz   |      z        t	        dd	      d|z  d	z   d|z  dz   z  |dz   d	|z  dz   z  z  z  k(  sJ t        t        |      d	z  t        |dz
        z        t        |      |z  d|z   z  d|z   z  k(  sJ t        t        |      t        |dz   | dz         z  t        ||       z        t        |dz         d| z   z  k(  sJ t        t        |dz               t        |d	z         k(  sJ t        t        t                    t        t        dz         k(  sJ t        |dz   t        |      z        t        |dz         k(  sJ t        t        |      |z        t        |dz
        k(  sJ t        t        ||| z
              t        ||       k(  sJ t        t        |      t        |       t        || z
        z  z        t        ||       k(  sJ t        t        |       t        || z
        z  t        |      z        dt        ||       z  k(  sJ t        t        d	|z        t        |      d	z  z        t        d	|z  |      k(  sJ t        t        d	|z        t        |       z  t        || z
        z  t        |      dz  z        t        d	|z  |      t        ||       z  k(  sJ t        t        |d|z   z  |d	z  z
  |z
              dk(  sJ t        d
t        d|      z  t        |      z        d|z  |dz   z  |d	z   z  |dz   z  k(  sJ t        d
t        d|dz
        z  t        |dz
        z        d|dz
  z  |z  |dz   z  |d	z   z  k(  sJ t        d
t        d|dz
        z  t        |dz
        z        d|dz
  z  |z  |dz
  z  |d	z
  z  k(  sJ t        d
t        d| dz
        z  t        | dz
        z        d| dz
  z   |z  |dz
  z  |d	z
  z  k(  sJ t        d
t        d|      z  t        |      z        |dz   |d	z   z  |dz   z  k(  sJ t        d
t        d|dz
        z  t        |dz
        z        ||dz   z  |d	z   z  k(  sJ t        d
t        d|dz
        z  t        |dz
        z        ||dz
  z  |d	z
  z  k(  sJ t        d
t        d| dz
        z  t        | dz
        z        | |dz
  z  |d	z
  z  k(  sJ y )Nzk m nTinteger               )	r   r
   r   r   r   r	   r   r   r   )kmns      U/var/www/html/venv/lib/python3.12/site-packages/sympy/simplify/tests/test_combsimp.pytest_combsimpr   	   sO   g.GAq!IaL!Yq\111HQN#x1~555IaL1q5!112aaj"q&6IIIIHQUAE*8Aq>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A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 HQA&'8Aq>999 IaL)A,yQ/?"?@AA  IaL1q5!11)A,>?	(1a.  IacN9Q<?23x!Q7GGGGIacN9Q</	!a%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	1q5	1q5  AoaQ//	!a%0@@A	1q5	1q5  Aoa!a00A261BBC	
AE
AE      c                  |    t        dd      } t        t        d|             dd| z  z  t        d| z
        z  k(  sJ y )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                      t        ddd      } t        t        d|             dt        |       t        d| z
        z  z  k(  sJ t        t        d| z
              t        d| z
        k(  sJ y )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   