
    sg(	                     6    d dl mZmZmZ d dl mZ d Zd Zd Zy)    )binomial_coefficientsbinomial_coefficients_listmultinomial_coefficients)!multinomial_coefficients_iteratorc                      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 y )Nr         )r   r	   r      )r   r
   r
   r      )r   r      r   r      )r   r   
   r   r   r   r   )r   r         r   r   r   )r        W/var/www/html/venv/lib/python3.12/site-packages/sympy/ntheory/tests/test_multinomial.pytest_binomial_coefficients_listr      s    %a(QC///%a(QF222%a(I555%a(L888%a(O;;;%a(,@@@@%a(,DDDDr   c                      t        d      D ]8  } t        |       }t        |      D cg c]  }||   	 }}|t        |       k(  r8J  y c c}w )Nr   )ranger   sortedr   )nckls       r   test_binomial_coefficientsr      sQ    2Y 2!!$!!9%aQqT%%.q11112%s   Ac                     t        dd      ddik(  sJ t        dd      ddik(  sJ t        dd      ddik(  sJ t        dd      ddik(  sJ t        dd      ddd	k(  sJ t        dd      dddd
k(  sJ t        dd      dddddk(  sJ t        dd      ddddk(  sJ t        dd      dddddddk(  sJ t        dd      } | ddddddddddd
k(  sJ t        t        dd            ddik(  sJ t        t        dd            ddd	k(  sJ t        t        dd            dddd
k(  sJ t        t        dd            | k(  sJ t        dd      }t        d      D cg c]  }t	        |       c}g dk(  sJ y c c}w )Nr   )r   r	   )r	   r
   )r
   r   )r   r   ))r   r   )r   r   ))r	   r   )r   r	   )r   r   ))r
   r   )r   r	   )r   r
   )r	   r   ))r   r   r   )r   r   r   )r   r   r   ))r   r   r   )r   r   r	   )r   r   r   )r   r	   r   )r   r   r   )r	   r   r   r   )
)r	   r   r   )r   r
   r   )r   r   r	   )r   r	   r   )r   r   r	   )r
   r   r   )r	   r   r   )r   r	   r   )r   r   r   )r   r   r
      r   )))r	   r   r   r   r   r   r   r   ))r   r   r   r   r   r   r   r	   ))r   r	   r   r   r   r   r   r   ))r   r   r   r   r   r   r   r	   )r   dictr   r   next)mcitis      r   test_multinomial_coefficientsr$      s   #Aq)dAY666#Aq)dAY666#Aq)dAY666#Aq)fa[888#Aq)a-CCCC#Aq)aA-NNNN#Aq)aA.   #Aq)q.   #Aq)qQ1.D D D D	!!Q	'BQ1Q1Q1D D D D 1!Q78VQKGGG)!Q/1=>4JK K K1!Q78Aq)* * *1!Q78B>>>	*1a	0B#Ah'DH'	>> > >'s   !E>N)sympy.ntheory.multinomialr   r   r   r   r   r   r$   r   r   r   <module>r&      s    s s GE2>r   