+
    i
                         R t ^ RIHtHtHtHt ^ RIHt ^ RIH	t	H
t
Ht R tR tRt/ t]'       d   ]! ]! ]4      !  tR tR tR	# )
z*Test groups defined by the galois module. )S4TransitiveSubgroupsS5TransitiveSubgroupsS6TransitiveSubgroupsfind_transitive_subgroups_of_S6)is_isomorphic)SymmetricGroupAlternatingGroupCyclicGroupc                  6   \         P                  P                  4       p \        ^4      pV P	                  V4      '       g   Q hV P
                  ^8X  g   Q hV P                  4       '       g   Q hV P                  4       ^8X  g   Q hV P                  '       d   Q hR# )   N)	r   Vget_perm_groupr   is_subgroupdegreeis_transitiveorder	is_cyclic)GA4s     c/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/combinatorics/tests/test_galois.pytest_four_groupr      sz    ..0A	!	B==88q==??779>>{{{?{    c                  V   \         P                  P                  4       p \        ^4      p\	        ^4      pV P                  V4      '       g   Q hV P                  V4      '       d   Q hV P                  ^8X  g   Q hV P                  4       '       g   Q hV P                  4       ^8X  g   Q hR# )   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                 x    V P                  4       .p\        '       d   VP                  \        V ,          4       V# )N)r   INCLUDE_SEARCH_REPSappendS6_randomized)nameverss   & r   get_versions_of_S6_subgroupr$   +   s/    !"DM$'(Kr   c                    \         p \        ^4      pV P                  R^\        ^4      R3V P                  R^\        ^4      R3V P                  R^RR3V P                  R^RR3V P                  R^RR3V P                  R^R\        ^4      3V P                  R^\        ^4      R3V P                  R^RR3V P                  R^$RR3V P                  R^$RR3V P                  R^0RR3V P                  R^<RR3V P                   R^HRR3V P"                  R^xRR3V P$                  RRRR3V P&                  RRRR33 F  w  r#rEp\)        V4       F  pVP+                  4       '       g   Q hVP,                  ^8X  g   Q hVP/                  V4      VJ g   Q hVP1                  4       V8X  g   Q hV'       d   \3        Wu4      '       g   Q hV'       g   K  \3        Wv4      '       g   K  Q h	  K  	  R# )zI
Test enough characteristics to distinguish all 16 transitive subgroups.
FNTih  i  )r   r   C6r	   S3r   D6r   G18A4xC2S4mS4pG36mG36pS4xC2PSL2F5G72PGL2F5A6S6r$   r   r   r   r   r   )tsr3   r"   altr   is_isomnot_isomr   s           r   test_S6_transitive_subgroupsr9   2   s    
B	!	B	EaQ6	Ea!2D9	ERt,	DRt,	ERt,	ER~a'89	ER!2D9	DRt,	ERt,	DRt,	ERt,	DRt,	ERt,	ECt,	DCt,	ECt,!0+58$ -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$   r9    r   r   <module>r@      sU    0  < 
  3T:O5PQM 6r   