
    g                     l    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d
S )    )Rational)symbols)FallingFactorialRisingFactorialbinomial	factorial)gamma)combsimp)xc                  l   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 d S )Nzk m nTinteger               )	r   r
   r   r   r   r	   r   r   r   )kmns      ^/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/simplify/tests/test_combsimp.pytest_combsimpr   	   s   g...GAq!IaLL!!Yq\\1111HQNN##x1~~5555IaLL1q5!1!1122aaj"q&6IIIIIHQUAE**8Aq>>9::q1uq1uoMMMMHQqS1Wa!e,,XacAgq-A-AABBA1q1Q37+a!eacAg->?@A A A A IaLL!OIa!e$4$4455!QQa() ) ) )IaLL!a%Q!7!77AFGG!a%!a% ! ! ! ! E!a%LL!!Yq1u%5%55555IaLL!!U1q5\\1111 QUIaLL())Yq1u-=-=====IaLLN##y1~~5555 HQA&&''8Aq>>9999 IaLL)A,,yQ/?/?"?@AAA   IaLL1q5!1!11)A,,>??	(1a..   IacNN9Q<<?233x!Q7G7GGGGGIacNN9Q<</	!a%0@0@@!a  $QqS!,,Xa^^;< < < < IaQi!Q$.233449999A&r1---ill:;;	aQQQ'( ( ( (A&r1q5111)AE2B2BBCC	q1uaQQ'( ( ( (A&r1q5111)AE2B2BBCC	q1uaQQ'( ( ( (A&rA262229aR!V3D3DDEE
Q1q5!1q5)* * * * Aoa+++IaLL899	
QQQ       AoaQ///	!a%0@0@@AA	1q5	1q5   AoaQ///	!a%0@0@@AA	1q5	1q5   Aoa!a000A261B1BBCC	
AE
AE         c                      t          dd          } t          t          d|                     dd| z  z  t          d| z
            z  k    sJ d S )Nr   Tr   ii _7 r   
   )r   r
   r   r   )r   s    r   test_issue_6878r   C   sV    T"""AOC++,,a	"q&@Q@Q0QQQQ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 d S )NpT)r   positiver   r   )r   r
   r   r   )r!   s    r   test_issue_14528r#   H   s    TD111AHQqMM""a1i!nn)D&EEEEEIacNN##y1~~555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 m m m m m m m m m m 9 9 9 9 9 9 , , , , , ,      7 7 7tR R R
6 6 6 6 6r   