
    \h
                         S r SSKJrJrJrJr  SSKJr  SSKJ	r	J
r
Jr  S rS rSr0 r\(       a  \" \" \5      6 rS rS	 rg
)z*Test groups defined by the galois module.     )S4TransitiveSubgroupsS5TransitiveSubgroupsS6TransitiveSubgroupsfind_transitive_subgroups_of_S6)is_isomorphic)SymmetricGroupAlternatingGroupCyclicGroupc                  *   [         R                  R                  5       n [        S5      nU R	                  U5      (       d   eU R
                  S:X  d   eU R                  5       (       d   eU R                  5       S:X  d   eU R                  (       a   eg )N   )	r   Vget_perm_groupr	   is_subgroupdegreeis_transitiveorder	is_cyclic)GA4s     ]/var/www/auris/envauris/lib/python3.13/site-packages/sympy/combinatorics/tests/test_galois.pytest_four_groupr      sx    ..0A	!	B==88q==??779>>{{?{    c                  J   [         R                  R                  5       n [        S5      n[	        S5      nU R                  U5      (       d   eU R                  U5      (       a   eU R                  S:X  d   eU R                  5       (       d   eU R                  5       S:X  d   eg )N      )	r   M20r   r   r	   r   r   r   r   )r   S5A5s      r   test_M20r      s    !!002A		B	!	B==}}R    88q==??779??r   Fc                 n    U R                  5       /n[        (       a  UR                  [        U    5        U$ )N)r   INCLUDE_SEARCH_REPSappendS6_randomized)nameverss     r   get_versions_of_S6_subgroupr&   +   s/    !"DM$'(Kr   c                     [         n [        S5      nU R                  SS[        S5      S4U R                  SS[        S5      S4U R                  SSSS4U R                  SSSS4U R                  SSSS4U R                  SSS[        S	5      4U R                  SS[        S	5      S4U R                  SSSS4U R                  SS
SS4U R                  SS
SS4U R                  SSSS4U R                  SSSS4U R                   SSSS4U R"                  SSSS4U R$                  SSSS4U R&                  SSSS44 H  u  p#pEn[)        U5       H  nUR+                  5       (       d   eUR,                  S:X  d   eUR/                  U5      UL d   eUR1                  5       U:X  d   eU(       a  [3        Xu5      (       d   eU(       d  Mz  [3        Xv5      (       d  M   e   M     g)zI
Test enough characteristics to distinguish all 16 transitive subgroups.
   FN      T      r   $   0   <   H   x   ih  i  )r   r	   C6r
   S3r   D6r   G18A4xC2S4mS4pG36mG36pS4xC2PSL2F5G72PGL2F5A6S6r&   r   r   r   r   r   )tsr?   r$   altr   is_isomnot_isomr   s           r   test_S6_transitive_subgroupsrE   2   s    
B	!	B	EaQ6	Ea!2D9	ERt,	DRt,	ERt,	ER~a'89	ER!2D9	DRt,	ERt,	DRt,	ERt,	DRt,	ERt,	ECt,	DCt,	ECt,!0+58$ -T2A??$$$$88q= ===$+++779%%%$Q0000x(5555 3%0r   N)__doc__sympy.combinatorics.galoisr   r   r   r   !sympy.combinatorics.homomorphismsr    sympy.combinatorics.named_groupsr   r	   r
   r   r   r!   r#   listr&   rE    r   r   <module>rL      sU    0  < 
  3T:O5PQM 6r   