
    Цiq                        S r SSSSSSSSS	S
SSSSS.r0 S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S   _S\S    _S!\S    _S"\S   _\S    \S    \S   \S    \S    \S    S#.ErS$ rS% rS& rS' rS( rS) rS* r	\\\\\\\	S+.r
S, r\R                  5       r\S    \S-'   \S    \S.'   \S    \S/'   \S    \S0'   \S    \S1'   \S    \S2'   \S   \S3'   \S   \S4'   \S    S-
  \S5'   \S    S-
  \S6'   \S    S-
  \S7'   \S    S-
  \S8'   \S    S-
  \S9'   \S    S-
  \S:'   \S   \S;'   \S   \S<'   \S   \S='   \S   \S>'   \S   \S?'   S@ rgA)Bz>A module providing information about the necessity of brackets   
         #   (   2   <   F   d   i  $   %   &   )LambdaXorOrAnd
RelationalAddMulPowFuncNotAtom	BitwiseOr
BitwiseXor
BitwiseAnd
Equivalentr   Impliesr   r   r   r   r   Subr   Functionr   NegativeInfinityMatAddMatPowMatrixSolver   ModTensAdd)TensMulHadamardProductHadamardPowerKroneckerProductEquality
Unequalityc                 P    U R                  5       (       a	  [        S   $ [        S   $ )Nr   r   )could_extract_minus_sign
PRECEDENCEitems    X/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/printing/precedence.pyprecedence_Mulr3   =   s'    $$&&%  e    c                 F    U R                   S:  a	  [        S   $ [        S   $ )N    r   r   pr/   r0   s    r2   precedence_Rationalr9   C   s#    vvz%  er4   c                 F    U R                   S:  a	  [        S   $ [        S   $ Nr6   r   r   r7   r0   s    r2   precedence_Integerr<   I   s#    vvz%  fr4   c                 2    U S:  a	  [         S   $ [         S   $ r;   )r/   r0   s    r2   precedence_Floatr>   O   s    ax%  fr4   c                     U R                   (       a	  [        S   $ U R                  (       a  [        U R	                  S5      5      $ U R
                  (       a	  [        S   $ [        S   $ )Nr   r   r   r   )is_generatorr/   	is_ground
precedencecoeffis_termr0   s    r2   precedence_PolyElementrE   U   sM    &!!	$**Q-((	%  %  r4   c                 ^    U R                   S:X  a  [        U R                  5      $ [        S   $ )Nr   r   )denomrE   numerr/   r0   s    r2   precedence_FracElementrI   `   s'    zzQ%djj11%  r4   c                 8    [        U R                  S   5      S-
  $ )Nr6   g      ?)rB   argsr0   s    r2   precedence_UnevaluatedExprrL   g   s    diil#c))r4   )Integerr   RationalFloatPolyElementFracElementUnevaluatedExprc                 0   [        U S5      (       a  U R                  $ [        U [        5      (       d\  [        U 5      R	                  5        H?  nUR
                  nU[        ;   a  [        U   " U 5      s  $ U[        ;   d  M6  [        U   s  $    [        S   $ )zRReturns the precedence of a given object.

This is the precedence for StrPrinter.
rB   r   )	hasattrrB   
isinstancetypemro__name__PRECEDENCE_FUNCTIONSPRECEDENCE_VALUESr/   )r1   ins      r2   rB   rB   v   s    
 t\""dD!!d!A

A((+A.t44''(++ " fr4   IntegralSumProductLimit
DerivativeTensorProduct	TransposeAdjointDotCrossGradient
DivergenceCurl	LaplacianUnionIntersection
ComplementSymmetricDifference
ProductSetc                     SSK Jn  [        X5      (       a  [        U R                  S   5      $ U R
                  R                  nU[        ;   a	  [        U   $ [        U 5      $ )zReturns the precedence of a given object according to the
traditional rules of mathematics.

This is the precedence for the LaTeX and pretty printer.
r6   )rR   )	sympy.core.exprrR   rU   precedence_traditionalrK   	__class__rX   PRECEDENCE_TRADITIONALrB   )r1   rR   r\   s      r2   rr   rr      sS     0$((%diil33A""%a((dr4   N)__doc__r/   rZ   r3   r9   r<   r>   rE   rI   rL   rY   rB   copyrt   rr    r4   r2   <module>rx      sB   D
 

**U#	:e z%  	*T
	
 
:e 
:e 
:e *\* 
:e 
:e F# 
5) j j :e$  
:e!" z% #& % !%(&"5)5!U#1 F!!*
 "#))1 " $* %/%6 z " *5 1 u $.u$5 y !",U"3 w '1%'8 | $*4U*;  '&0&7 { #$.u$5 y ! *5 1A 5 u ",U"3a"7 w %/%6%: z "'1%'81'< | $!+E!2Q!6 v &0&7!&; { #",U"3 w )3E): ~ &'1%'8 | $0:50A , -'1%'8 | $r4   