+
    if                         ^ RI HtHt ^ RIHtHt ^ RIHt ^ RIH	t	 ^ RI
Ht ^ RIHt ^ RIHt ^ RIHt ^ R	IHtHt ^ R
IHtHtHt ^ RIHt R tR tR tR# )    )Qask)IRational)S)Abs)exp)sqrt)simplify)symbols)DFTIDFT)detMatrixIdentity)raisesc                  z  a  \        ^4      '       g   Q h\        ^ 4      '       g   Q h\        \        R 4       \        \        R 4       \        \        R 4       \        R4      o \        S 4      '       g   Q h\        RRR7      o \        \        V 3R l4       \        RRR	7      o \        \        V 3R
 l4       R# )   c                      \        R4      # )   r        k/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/matrices/expressions/tests/test_fourier.py<lambda>#test_dft_creation.<locals>.<lambda>   s    s2wr   c                      \        R 4      # )g       @r   r   r   r   r   r      s    s3xr   c                      \        R4      # )r   y       @      ?r   r   r   r   r   r      s    s6{r   nF)integerc                     < \        S 4      # Nr   r    s   r   r   r      	    s1vr   T)negativec                     < \        S 4      # r#   r   r$   s   r   r   r      r%   r   N)r   r   
ValueErrorr   r$   s   @r   test_dft_creationr)      s    q66M6q66M6
:'
:'(
:*+Aq66M6U#A
:~&d#A
:~&r   c                  J   \        R 4      w  rp\        ^4      P                  R8X  g   Q h\        \        P
                  ! \        ^4      4      4      '       g   Q h\        \        \        \        \        ^4      4      4      4      4      ^8X  g   Q h\        V 4      \        V 4      ,          \        V 4      8X  g   Q h\        V 4      W3,          \        R\        P                  ,          \        ,          V ,          4      W,          ,          \!        V 4      ,          8X  g   Q hR# )zn i jN)   r+   )r   r   shaper   r   unitaryr   r   r   r   r   r   r	   r   Pir   r
   )r    ijs      r   test_dftr2      s    gGA!q6<<6!!!qyyQ !!!!xF3q6N+,-222q6$q'>Xa[(((q6!$<3r!$$wqy{+ac2T!W<<<<r   c                     \        ^4      P                  4       \        ^..4      8X  g   Q h\        ^4      P                  4       ^\        ^4      ,          \        ^^.^R..4      ,          8X  g   Q h\        ^4      P                  4       \        \        P
                  \        P
                  \        P
                  \        P
                  .\        P
                  \        ) ^,          \        R^4      \        ^,          .\        P
                  \        R^4      \        P
                  \        R^4      .\        P
                  \        ^,          \        R^4      \        ) ^,          ..4      8X  g   Q hR# )r   Nr   )r   as_explicitr   r
   r   Halfr   r   r   r   r   	test_dft2r6   &   s   q66A3%=000q61T!W9VaUAb6N-C#CCCCq66AFFQVVaffaff+M,-FFQBqD(2a.1Q3+O,-FFHRNQVVXVXYZ^+\,-FFQqS(2a.1"Q$+O+Q $R R R Rr   N)sympy.assumptions.askr   r   sympy.core.numbersr   r   sympy.core.singletonr   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr	   (sympy.functions.elementary.miscellaneousr
   sympy.simplify.simplifyr   sympy.core.symbolr   "sympy.matrices.expressions.fourierr   r   sympy.matricesr   r   r   sympy.testing.pytestr   r)   r2   r6   r   r   r   <module>rB      s9    * , " 4 6 9 , % 8 0 0 ''=Rr   