
    \h                        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$ rS% rS& rS' rS( rS) rS* r	\\\\\\\	S+.r
S, r\R                  5       r\S    \S-'   \S    \S.'   \S    \S/'   \S    \S0'   \S    \S1'   \S    \S2'   \S   \S3'   \S   \S4'   \S    S-
  \S5'   \S    S-
  \S6'   \S    S-
  \S7'   \S    S-
  \S8'   \S    S-
  \S9'   \S    S-
  \S:'   \S   \S;'   \S   \S<'   \S   \S='   \S   \S>'   \S   \S?'   \S5   \S@'   SA rgB)Cz>A module providing information about the necessity of brackets   
         #   (   2   <   F   d   i  $   %   &   )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                    ^ SSK Jm  [        U4S jU R                   5       5      (       a	  [        S   $ U R                  5       (       a	  [        S   $ [        S   $ )N    )r    c              3      >#    U  HA  n[        US 5      =(       a)    [        UT5      =(       a    UR                  [        S   :  v   MC     g7f)
precedencer   N)hasattr
isinstancer0   
PRECEDENCE).0argr    s     Q/var/www/auris/envauris/lib/python3.13/site-packages/sympy/printing/precedence.py	<genexpr>!precedence_Mul.<locals>.<genexpr>?   sI      D9B# 3% .*S(*C .>>Ju--.9Bs   A	Ar   r   )sympy.core.functionr    anyargsr3   could_extract_minus_sign)itemr    s    @r6   precedence_Mulr>   =   sX    ,
 D9=D D D%  $$&&%  e    c                 F    U R                   S:  a	  [        S   $ [        S   $ )Nr.   r   r   pr3   r=   s    r6   precedence_RationalrD   H   s#    vvz%  er?   c                 F    U R                   S:  a	  [        S   $ [        S   $ Nr.   r   r   rA   rC   s    r6   precedence_IntegerrG   N   s#    vvz%  fr?   c                 2    U S:  a	  [         S   $ [         S   $ rF   )r3   rC   s    r6   precedence_FloatrI   T   s    ax%  fr?   c                     U R                   (       a	  [        S   $ U R                  (       a  [        U R	                  S5      5      $ U R
                  (       a	  [        S   $ [        S   $ )Nr   r   r   r   )is_generatorr3   	is_groundr0   coeffis_termrC   s    r6   precedence_PolyElementrO   Z   sM    &!!	$**Q-((	%  %  r?   c                 ^    U R                   S:X  a  [        U R                  5      $ [        S   $ )Nr   r   )denomrO   numerr3   rC   s    r6   precedence_FracElementrS   e   s'    zzQ%djj11%  r?   c                 8    [        U R                  S   5      S-
  $ )Nr.   g      ?)r0   r;   rC   s    r6   precedence_UnevaluatedExprrU   l   s    diil#c))r?   )Integerr   RationalFloatPolyElementFracElementUnevaluatedExprc                 0   [        U S5      (       a  U R                  $ [        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.
r0   r   )	r1   r0   r2   typemro__name__PRECEDENCE_FUNCTIONSPRECEDENCE_VALUESr3   )r=   ins      r6   r0   r0   {   s    
 t\""dD!!d!A

A((+A.t44''(++ " fr?   IntegralSumProductLimit
DerivativeTensorProduct	TransposeAdjointDotCrossGradient
DivergenceCurl	LaplacianUnionIntersection
ComplementSymmetricDifference
ProductSet
DotProductc                     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.
r.   )r[   )	sympy.core.exprr[   r2   precedence_traditionalr;   	__class__r_   PRECEDENCE_TRADITIONALr0   )r=   r[   rc   s      r6   rz   rz      sS     0$((%diil33A""%a((dr?   N)__doc__r3   ra   r>   rD   rG   rI   rO   rS   rU   r`   r0   copyr|   rz    r?   r6   <module>r      sR   D
 

**U#	:e z%  	*T
	
 
:e 
:e 
:e *\* 
:e 
:e F# 
5) j j :e$  
: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 | $0:50A , -'1%'8 | $'=e'D | $r?   