+
    i                        R t ^ RIHtHt ^ RIHt ^ RIHt ^ RIH	t	 R t
R tR t]! ^
]4      t]
! ^
]]4      t]! ^]4      t]
! ^]]4      tR tR	 tR
 tR t]! ^]4      t]! ^
]]4      t]! ^]4      t]! ^]]4      tR tR tR tR tR# )z/Benchmarks for polynomials over Galois fields. )gf_from_dictgf_factor_sqf)ZZ)pi)	nextprimec                 `    \        WP                  ^VP                  ^ VP                  /W4      #    )r   one)npKs   &&&f/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/polys/benchmarks/bench_galoispolys.pygathen_polyr   
   s&    EE1aeeQ6==    c                     VP                   .V ^,           ,          p\        ^V ^,           4       F3  pW4^,
          ,          ^,          VP                   ,           V,          W4&   K5  	  V# r   )r
   range)r   r   r   fis   &&&  r   
shoup_polyr      sN    	
1q5A1a!e_a%!aee#q( Hr   c                 v    V! \        \        ^V ,          \        ,          P                  4       4      4      4      # )   )r   intr   evalf)r   r   s   &&r   genprimer      s(    YsAqD2I,,./011r   c                  <    \        \        \        \        R R7       R# 
zassenhausmethodNr   f_10p_10r    r   r   !timeit_gathen_poly_f10_zassenhausr$          $b6r   c                  <    \        \        \        \        R R7       R# shoupr   Nr    r#   r   r   timeit_gathen_poly_f10_shoupr)   #       $b1r   c                  <    \        \        \        \        R R7       R# r   r   f_20p_20r   r#   r   r   !timeit_gathen_poly_f20_zassenhausr/   '   r%   r   c                  <    \        \        \        \        R R7       R# r'   r,   r#   r   r   timeit_gathen_poly_f20_shoupr1   +   r*   r   c                  <    \        \        \        \        R R7       R# r   r   F_10P_08r   r#   r   r    timeit_shoup_poly_F10_zassenhausr6   5   r%   r   c                  <    \        \        \        \        R R7       R# r'   r3   r#   r   r   timeit_shoup_poly_F10_shoupr8   9   r*   r   c                  <    \        \        \        \        R R7       R# r   r   F_20P_18r   r#   r   r    timeit_shoup_poly_F20_zassenhausr=   =   r%   r   c                  <    \        \        \        \        R R7       R# r'   r:   r#   r   r   timeit_shoup_poly_F20_shoupr?   A   r*   r   N)__doc__sympy.polys.galoistoolsr   r   sympy.polys.domainsr   sympy.core.numbersr   sympy.ntheory.generater   r   r   r   r"   r!   r.   r-   r$   r)   r/   r1   r5   r4   r<   r;   r6   r8   r=   r?   r#   r   r   <module>rE      s    5 @ " ! ,>2 B2tR B2tR 7272 2"dBB"dB7272r   