+
    i                         ^ RI Ht ^ RIHt ^ RIHtHt ^ RIHtH	t	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Ht ]! R4      w  ttR tR tR tR tR tR t R t!R t"R t#R t$R t%R t&R t'R t(R# )    )Product)Sum)
DerivativeFunction)IntegerRationalFloatoo)Rel)symbols)sin)Integral)Order)
precedence
PRECEDENCEzx,yc                      \        \        \        ,           4      \        R ,          8X  g   Q h\        \        \        ,          ^,           4      \        R ,          8X  g   Q hR# )AddNr   xyr        b/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/printing/tests/test_precedence.pytest_Addr      s>    a!e
5 1111acAg*U"3333r   c                  Z    \        \        \        4      4      \        R ,          8X  g   Q hR# )FuncN)r   r   r   r   r   r   r   test_Functionr      s    c!fF!3333r   c                  d    \        \        \        \        4      4      \        R ,          8X  g   Q hR# AtomN)r   r   r   r   r   r   r   r   test_Derivativer!      s!    jA&':f+====r   c                  d    \        \        \        \        4      4      \        R ,          8X  g   Q hR# r   )r   r   r   r   r   r   r   r   test_Integralr#      s     hq!n%F);;;;r   c                      \        \        \        ,          4      \        R ,          8X  g   Q h\        \        ) \        ,          4      \        R,          8X  g   Q hR# )Mulr   Nr   r   r   r   test_Mulr&      s;    ac?j////qbdz%0000r   c                     \        \        ^ 4      4      \        R,          8X  g   Q h\        \        ^4      4      \        R,          8X  g   Q h\        \        R4      4      \        R,          8X  g   Q h\        \        ^
4      4      \        R,          8X  g   Q h\        \        ^^4      4      \        R,          8X  g   Q h\        \        R^4      4      \        R,          8X  g   Q h\        \	        ^4      4      \        R,          8X  g   Q h\        \	        R4      4      \        R,          8X  g   Q h\        \
        4      \        R,          8X  g   Q h\        \
        ) 4      \        R,          8X  g   Q hR# )r   r    r   r%   N)r   r   r   r   r	   r
   r   r   r   test_Numberr*   $   s   gaj!Z%7777gaj!Z%7777gbk"j&7777gbk"j&8888hq!n%E)::::hr1o&*U*;;;;eAh:f#5555eBi Ju$5555b>Z////rc?j////r   c                  Z    \        \        \        4      4      \        R ,          8X  g   Q hR# r   )r   r   r   r   r   r   r   
test_Orderr,   1   s    eAh:f#5555r   c                     \        \        \        ,          4      \        R ,          8X  g   Q h\        \        \        ,          ) 4      \        R,          8X  g   Q h\        \        \        ) ,          4      \        R ,          8X  g   Q hR# )Powr   Nr   r   r   r   test_Powr/   5   sZ    adz%0000q!te
5 1111a!e
5 1111r   c            	          \        \        \        \        \        \        ^,           34      4      \        R,          8X  g   Q hR#    r    N)r   r   r   r   r   r   r   r   test_Productr3   ;   s+    ga!QA/0Jv4FFFFr   c                  |    \        \        \        \        ,           \        R 4      4      \        R,          8X  g   Q hR# )<
RelationalN)r   r   r   r   r   r   r   r   test_Relationalr7   ?   s'    c!a%C()Z-EEEEr   c            	          \        \        \        \        \        \        ^,           34      4      \        R,          8X  g   Q hR# r1   )r   r   r   r   r   r   r   r   test_Sumr9   C   s+    c!aAE]+,
60BBBBr   c                  H    \        \        4      \        R ,          8X  g   Q hR# r   )r   r   r   r   r   r   test_Symbolr;   G   s    a=Jv....r   c                  N   \        \        \        ,          4      \        \        \        ,          4      8  g   Q h\        \        ( 4      \        \        \        ,          4      8  g   Q h\        \        \        ,           4      \        \        \        ,          4      8  g   Q h\        \        \        ,           4      \        \        \        ,          4      8  g   Q h\        \        \        ,          4      \        \        \        ,          4      8  g   Q h\        \        \        ,          4      \        \        \        ,          4      8  g   Q h\        \        ( 4      \        \        \        ,          4      8  g   Q h\        \        ( 4      \        \        \        ,
          4      8  g   Q h\        \        \        ,          4      \        R ,          8X  g   Q h\        \        \        ,          4      \        R,          8X  g   Q h\        \        ( 4      \        R,          8X  g   Q hR# )AndOrNotNr   r   r   r   test_And_Orr@   K   sG   a!ez!a%0000qb>Jq1u----a!ez!a%0000a!ez!a%0000ac?ZA....ac?ZA....qb>JqsO+++qb>Jq1u----a!e
5 1111a!e
4 0000qb>Z....r   c                 z   aa  ! R R\         4      o ! R R\         4      oV3R lp V3R lpV ! 4        V! 4        R# )a?  
Test cases for custom functions with different precedence values,
specifically handling:
1. Functions with precedence < PRECEDENCE["Mul"] (50)
2. Functions with precedence = Func (70)

Key distinction:
1. Lower precedence functions (45) need parentheses: -2*(x F y)
2. Higher precedence functions (70) don't: -2*x F y
c                   F   a  ] tR t^gt o ]R,          ^,
          tR tRtV tR# )Btest_custom_function_precedence_comparison.<locals>.LowPrecedenceFr%   c                    VP                  V P                  ^ ,          4       RVP                  V P                  ^,          4       2# r   z F _printargsselfprinters   &&r   	_sympystrLtest_custom_function_precedence_comparison.<locals>.LowPrecedenceF._sympystri   8    nnTYYq\233w~~diiPQl7S6TUUr   r   N	__name__
__module____qualname____firstlineno__r   r   rL   __static_attributes____classdictcell____classdict__s   @r   LowPrecedenceFrC   g   s      &*
	V 	Vr   rX   c                   8   a  ] tR t^lt o ]R,          tR tRtV tR# )Ctest_custom_function_precedence_comparison.<locals>.HighPrecedenceFr   c                    VP                  V P                  ^ ,          4       RVP                  V P                  ^,          4       2# rE   rF   rI   s   &&r   rL   Mtest_custom_function_precedence_comparison.<locals>.HighPrecedenceF._sympystrn   rN   r   r   NrO   rV   s   @r   HighPrecedenceFrZ   l   s     '
	V 	Vr   r]   c                     < ^S! \         \        4      ,          p \        V 4      R8X  g   Q hRS! \         \        4      ,          p\        V4      R8X  g   Q hR# )   z	2*(x F y)z
-2*(x F y)Nr   r   str)expr1expr2rX   s     r   test_low_precedenceGtest_custom_function_precedence_comparison.<locals>.test_low_precedenceq   sI    N1a((5z[(((^Aq))5z\)))r   c                     < ^S! \         \        4      ,          p \        V 4      R8X  g   Q hRS! \         \        4      ,          p\        V4      R8X  g   Q hR# )r_   z2*x F yz-2*x F yNr`   ra   )rc   rd   r]   s     r   test_high_precedenceHtest_custom_function_precedence_comparison.<locals>.test_high_precedencex   sI    OAq))5zY&&&_Q**5zZ'''r   N)r   )re   rh   r]   rX   s     @@r   *test_custom_function_precedence_comparisonrj   \   s7    V V
V( V
*( r   N))sympy.concrete.productsr   sympy.concrete.summationsr   sympy.core.functionr   r   sympy.core.numbersr   r   r	   r
   sympy.core.relationalr   sympy.core.symbolr   sympy.functionsr   sympy.integrals.integralsr   sympy.series.orderr   sympy.printing.precedencer   r   r   r   r   r   r!   r#   r&   r*   r,   r/   r3   r7   r9   r;   r@   rj   r   r   r   <module>ru      s|    + ) 4 ; ; % %  . $ <u~14
4><1

062GFC//"$r   