
    g(	                     8    d dl mZmZmZ d dl mZ d Zd Zd ZdS )    )binomial_coefficientsbinomial_coefficients_listmultinomial_coefficients)!multinomial_coefficients_iteratorc                  F   t          d          dgk    sJ t          d          ddgk    sJ t          d          g dk    sJ t          d          g dk    sJ t          d          g dk    sJ t          d	          g d
k    sJ t          d          g dk    sJ d S )Nr         )r   r	   r      )r   r
   r
   r      )r   r      r   r      )r   r   
   r   r   r   r   )r   r         r   r   r   )r        `/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/ntheory/tests/test_multinomial.pytest_binomial_coefficients_listr      s    %a((QC////%a((QF2222%a((III5555%a((LLL8888%a((OOO;;;;%a((,@,@,@@@@@%a((,D,D,DDDDDDDr   c                      t          d          D ]A} t          |           fdt                    D             }|t          |           k    sJ Bd S )Nr   c                      g | ]
}|         S r   r   ).0kcs     r   
<listcomp>z.test_binomial_coefficients.<locals>.<listcomp>   s    %%%aQqT%%%r   )ranger   sortedr   )nlr   s     @r   test_binomial_coefficientsr      sk    2YY 2 2!!$$%%%%6!99%%%.q11111112 2r   c                     t          dd          ddik    sJ t          dd          ddik    sJ t          dd          ddik    sJ t          dd          ddik    sJ t          dd          ddd	k    sJ t          dd          dddd
k    sJ t          dd          dddddk    sJ t          dd          ddddk    sJ t          dd          dddddddk    sJ t          dd          } | ddddddddddd
k    sJ t          t          dd                    ddik    sJ t          t          dd                    ddd	k    sJ t          t          dd                    dddd
k    sJ t          t          dd                    | k    sJ t          dd          fdt          d          D             g dk    sJ d S )Nr   )r   r	   )r	   r
   )r
   r   )r   r   ))r   r   )r   r   ))r	   r   )r   r	   )r   r   ))r
   r   )r   r	   )r   r
   )r	   r   ))r   r   r   )r   r   r   )r   r   r   ))r   r   r   )r   r   r	   )r   r   r   )r   r	   r   )r   r   r   )r	   r   r   r   )
)r	   r   r   )r   r
   r   )r   r   r	   )r   r	   r   )r   r   r	   )r
   r   r   )r	   r   r   )r   r	   r   )r   r   r   )r   r   r
      c                 .    g | ]}t                    S r   )next)r   iits     r   r   z1test_multinomial_coefficients.<locals>.<listcomp>.   s    '''DHH'''r   r   )))r	   r   r   r   r   r   r   r   ))r   r   r   r   r   r   r   r	   ))r   r	   r   r   r   r   r   r   ))r   r   r   r   r   r   r   r	   )r   dictr   r   )mcr%   s    @r   test_multinomial_coefficientsr(      s   #Aq))dAY6666#Aq))dAY6666#Aq))dAY6666#Aq))fa[8888#Aq))a-C-CCCCC#Aq))aA-N-NNNNN#Aq))aA. .    #Aq))q. .    #Aq))qQ1.D .D D D D D	!!Q	'	'BQ1Q1Q1D D D D D D 1!Q7788VQKGGGG)!Q//1 1=>4J4JK K K K1!Q7788Aq))* * * *1!Q7788B>>>>	*1a	0	0B''''eAhh'''	> 	> 	>> > > > > >r   N)sympy.ntheory.multinomialr   r   r   r   r   r   r(   r   r   r   <module>r*      so    s s s s s s s s s s G G G G G GE E E2 2 2> > > > >r   