
    Qi
                     D    d dl mZ d dlmZmZmZ d dlmZ d Zd Z	d Z
dS )    )Permutation)SymmetricGroupAlternatingGroupDihedralGroup)Matrixc                     t          d          t          d          t          d                              d          t          d                              d          t          d                              d          t          d          g} t          d                              d          }|                                d         }|                     |           t          d	                              d          }|                     |           t          d
                              d          }|                                d         }|                     |           | D ]}|                                }|j        }|j        }|j        }|j	        }i }t          |j        |          D ]
\  }	}
|
||	<   |                                D ]\  }}|j        }|dk    r|j        }t                      }|D ] }|d         }	|d         }|||	         |z  z  }!|dk    r
|j        sJ Zt                      }|D ] }|d         }	|d         }|||	         |z  z  }!||k    sJ d S )N      	         
   }         y       r      )r   sylow_subgroupr   derived_seriesappendpolycyclic_group	collectorpc_presentationpcgs
free_groupzipsymbolsitems
array_formr   is_identity)GroupsSGPcGroupr   r   r   r   free_to_permsgkvk_arrayv_arraylhsgenerhss                      /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/combinatorics/tests/test_pc_groups.pytest_pc_presentationr3      s   Q!2!2N14E4E4T4TUV4W4W				)	)!	,	,nQ.?.?.N.Nq.Q.QS`acSdSdfF 	s**1--A	1A
MM!r))!,,A
MM!u,,R00A	1A
MM!    $$&&%	#3|)

*D11 	  	 DAqLOO#))++ 	 	DAqlGBww,--C - -FF,q/1,,Bww&&&--C - -FF,q/1,,#:::::+	       c                  :   t          d          t          d          t          d                              d          t          d                              d          t          d                              d          g} | D ]}|                                }|j        }|j        }|j        D ]j}|                    |          }t                      }t          t          |                    D ] }||         r|||         ||         z  z  n|}!||k    sJ kd S )Nr	   r
   r   r   r   )
r   r   r   r   r   
generatorsexponent_vectorr   rangelen)	r#   r%   r&   r   r   r/   expr)   is	            r2   test_exponent_vectorr<   7   s(   Q!2!2N14E4E4T4TUV4W4W				)	)!	,	,nQ.?.?.N.Nq.Q.QSF   $$&&%	| < 	 	C++C00CA3s88__ 7 7),Q6Ad1gs1vo%%Q88888	 r4   c            
      R   t          d                              d          t          d                              d          t          d          t          d          t          d          t          d          t          d          t          d          g} | D ]}|                                }|j        }t          |j                  }|                    |          }g }|D ]*}|	                    |
                    |                     +t          |          j        sJ d S )Nr   r	      r   r
   r   )r   r   r   r   r   r   listr6   induced_pcgsr   r7   r   is_upper)r%   r)   r&   r   gensipcgsmr;   s           r2   test_induced_pcgsrE   K   s!   				)	)!	,	,nR.@.@.O.OPQ.R.RTdefTgTg!mB''q)9)9>!;L;Ln]^N_N_	aA  " "$$&&%	AL!!&&t,, 	3 	3AHHY..q112222ayy!!!!!" "r4   N) sympy.combinatorics.permutationsr    sympy.combinatorics.named_groupsr   r   r   sympy.matricesr   r3   r<   rE   r   r4   r2   <module>rI      s    8 8 8 8 8 8 \ \ \ \ \ \ \ \ \ \ ! ! ! ! ! !/ / /d  (" " " " "r4   