
    g                         d dl mZ d dl mZ d dlmZ d dlmZmZ d dl	m
Z
  e ej        dd                    d	             Z e ej        dd                    d
             ZdS )    )given)
strategies)divisors)divisor_sigmatotient)	is_square   l    d(	 )nc                     t                     }t          |          }t                     |dz  dk    k    sJ d |D             } fd|D             }d t          ||          D             } |z  t	          |          k    sJ d S )N   r	   c                 ,    g | ]}t          |          S  )r   .0is     _/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/ntheory/tests/test_hypothesis.py
<listcomp>z'test_tau_hypothesis.<locals>.<listcomp>   s     ,,,1mA,,,    c                 4    g | ]}t          |z            S r   r   )r   r   r
   s     r   r   z'test_tau_hypothesis.<locals>.<listcomp>   s#    ---AQ---r   c                     g | ]
\  }}||z  S r   r   )r   abs      r   r   z'test_tau_hypothesis.<locals>.<listcomp>   s     
3
3
3TQ1q5
3
3
3r   )r   lenr   zipsum)r
   divtau_nsigmastotientsmuls   `     r   test_tau_hypothesisr"      s    
1++CHHEQ<<EAIN++++,,,,,F-------H
3
3S22
3
3
3Cu9C      r   c                     t          |           | k    sJ t          |           }d |D             }| t          |          k    sJ d S )Nc                 ,    g | ]}t          |          S r   r   r   s     r   r   z+test_totient_hypothesis.<locals>.<listcomp>   s    (((q

(((r   )r   r   r   )r
   r   r    s      r   test_totient_hypothesisr%      sP    1::????
1++C((C(((HHr   N)
hypothesisr   r   stsympyr   %sympy.functions.combinatorial.numbersr   r   sympy.ntheory.primetestr   integersr"   r%   r   r   r   <module>r,      s          ' ' ' ' ' '       H H H H H H H H - - - - - - Q		   ! ! ! ! Q		     !   r   