ó
    Š*£h’  ã                   óþ  • 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$ rS% rS& rS' rS( rS) rS* r	\\\\\\\	S+.r
S, r\R                  5       r\S    \S-'   \S    \S.'   \S    \S/'   \S    \S0'   \S    \S1'   \S    \S2'   \S   \S3'   \S   \S4'   \S    S-
  \S5'   \S    S-
  \S6'   \S    S-
  \S7'   \S    S-
  \S8'   \S    S-
  \S9'   \S    S-
  \S:'   \S   \S;'   \S   \S<'   \S   \S='   \S   \S>'   \S   \S?'   \S5   \S@'   SA rgB)Cz>A module providing information about the necessity of bracketsé   é
   é   é   é#   é(   é2   é<   éF   éd   iè  é$   é%   é&   )ÚLambdaÚXorÚOrÚAndÚ
RelationalÚAddÚMulÚPowÚFuncÚNotÚAtomÚ	BitwiseOrÚ
BitwiseXorÚ
BitwiseAndÚ
Equivalentr   ÚImpliesr   r   r   r   r   ÚSubr   ÚFunctionr   ÚNegativeInfinityÚMatAddÚMatPowÚMatrixSolver   ÚModÚTensAdd)ÚTensMulÚHadamardProductÚHadamardPowerÚKroneckerProductÚEqualityÚ
Unequalityc                 ó¸   ^• SSK Jm  [        U4S jU R                   5       5      (       a	  [        S   $ U R                  5       (       a	  [        S   $ [        S   $ )Né    )r    c              3   óœ   >#   • U  HA  n[        US 5      =(       a)    [        UT5      =(       a    UR                  [        S   :  v •  MC     g7f)Ú
precedencer   N)ÚhasattrÚ
isinstancer0   Ú
PRECEDENCE)Ú.0Úargr    s     €ÚV/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/printing/precedence.pyÚ	<genexpr>Ú!precedence_Mul.<locals>.<genexpr>?   sI   øé € ð DÚ9B°#ô �3˜Ó%÷ .¬*°S¸(Ó*C÷ .Ø�>‰>œJ uÑ-Ñ-ô.Ú9Bùs   ƒA	Ar   r   )Úsympy.core.functionr    ÚanyÚargsr3   Úcould_extract_minus_sign)Úitemr    s    @r6   Úprecedence_Mulr>   =   sX   ø€ Ý,Ü
ô DØ9=¿ºóD÷ Dñ Dä˜%Ñ Ð à×$Ñ$×&Ñ&Ü˜%Ñ Ð Ü�eÑÐó    c                 óF   • U R                   S:  a	  [        S   $ [        S   $ )Nr.   r   r   ©Úpr3   ©r=   s    r6   Úprecedence_RationalrD   H   s#   € Ø‡v�v�ƒzÜ˜%Ñ Ð Ü�eÑÐr?   c                 óF   • U R                   S:  a	  [        S   $ [        S   $ ©Nr.   r   r   rA   rC   s    r6   Úprecedence_IntegerrG   N   s#   € Ø‡v�v�ƒzÜ˜%Ñ Ð Ü�fÑÐr?   c                 ó2   • U S:  a	  [         S   $ [         S   $ rF   )r3   rC   s    r6   Úprecedence_FloatrI   T   s   € ØˆaƒxÜ˜%Ñ Ð Ü�fÑÐr?   c                 óÒ   • U R                   (       a	  [        S   $ U R                  (       a  [        U R	                  S5      5      $ U R
                  (       a	  [        S   $ [        S   $ )Nr   r   r   r   )Úis_generatorr3   Ú	is_groundr0   ÚcoeffÚis_termrC   s    r6   Úprecedence_PolyElementrO   Z   sM   € Ø××Ü˜&Ñ!Ð!Ø	��Ü˜$Ÿ*™* Q›-Ó(Ð(Ø	��Ü˜%Ñ Ð ä˜%Ñ Ð r?   c                 ó^   • U R                   S:X  a  [        U R                  5      $ [        S   $ )Nr   r   )ÚdenomrO   Únumerr3   rC   s    r6   Úprecedence_FracElementrS   e   s'   € Ø‡z�z�QƒÜ% d§j¡jÓ1Ð1ä˜%Ñ Ð r?   c                 ó8   • [        U R                  S   5      S-
  $ )Nr.   g      à?)r0   r;   rC   s    r6   Úprecedence_UnevaluatedExprrU   l   s   € Ü�d—i‘i ‘lÓ# cÑ)Ð)r?   )ÚIntegerr   ÚRationalÚFloatÚPolyElementÚFracElementÚUnevaluatedExprc                 ó0  • [        U S5      (       a  U R                  $ [        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   ÚtypeÚmroÚ__name__ÚPRECEDENCE_FUNCTIONSÚPRECEDENCE_VALUESr3   )r=   ÚiÚns      r6   r0   r0   {   s€   € ô
 ˆt�\×"Ñ"Ø�‰ÐÜ�dœD×!Ñ!Ü�d“—‘Ö!ˆAØ—
‘
ˆAØÔ(Ó(Ü+¨AÒ.¨tÓ4Ò4ØÔ'Õ'Ü(¨Ñ+Ò+ñ "ô �fÑÐr?   ÚIntegralÚSumÚProductÚLimitÚ
DerivativeÚTensorProductÚ	TransposeÚAdjointÚDotÚCrossÚGradientÚ
DivergenceÚCurlÚ	LaplacianÚUnionÚIntersectionÚ
ComplementÚSymmetricDifferenceÚ
ProductSetÚ
DotProductc                 óÆ   • SSK Jn  [        X5      (       a  [        U R                  S   5      $ U R
                  R                  nU[        ;   a	  [        U   $ [        U 5      $ )z–Returns 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[   )	Úsympy.core.exprr[   r2   Úprecedence_traditionalr;   Ú	__class__r_   ÚPRECEDENCE_TRADITIONALr0   )r=   r[   rc   s      r6   rz   rz   £   sS   € õ 0ä�$×(Ñ(Ü% d§i¡i°¡lÓ3Ð3à�‰×Ñ€AØÔ"Ó"Ü% aÑ(Ð(ä�dÓÐr?   N)Ú__doc__r3   ra   r>   rD   rG   rI   rO   rS   rU   r`   r0   Úcopyr|   rz   © r?   r6   Ú<module>r€      sR  ðÙ Dð
 ØØ
ØØØØØØØØØØØñ€
ð*Ø�*˜UÑ#ðà	ˆ:�eÑðð ˆz˜%Ñ ðð 	ˆ*�TÑ
ð	ð
 
ˆ:�eÑðð 
ˆ:�eÑðð 
ˆ:�eÑðð �*˜\Ñ*ðð 
ˆ:�eÑðð 
ˆ:�eÑðð �˜FÑ#ðð ˜
 5Ñ)ðð ˆj˜Ñðð ˆj˜Ñðð �:˜eÑ$ðð  
ˆ:�eÑð!ð" ˆz˜%Ñ ð#ð& ˜%Ñ Ø! %Ñ(Ø Ñ&Ø" 5Ñ)Ø˜5Ñ!Ø˜UÑ#ò1Ð òFòòòò!ò!ò*ð
 "ØØ#ØØ)Ø)Ø1ñÐ òð" $Ÿ™Ó*Ð Ø%/°Ñ%6Ð �zÑ "Ø *¨5Ñ 1Ð �uÑ Ø$.¨uÑ$5Ð �yÑ !Ø",¨UÑ"3Ð �wÑ Ø'1°%Ñ'8Ð �|Ñ $Ø*4°UÑ*;Ð �Ñ 'Ø&0°Ñ&7Ð �{Ñ #Ø$.¨uÑ$5Ð �yÑ !Ø *¨5Ñ 1°AÑ 5Ð �uÑ Ø",¨UÑ"3°aÑ"7Ð �wÑ Ø%/°Ñ%6¸Ñ%:Ð �zÑ "Ø'1°%Ñ'8¸1Ñ'<Ð �|Ñ $Ø!+¨EÑ!2°QÑ!6Ð �vÑ Ø&0°Ñ&7¸!Ñ&;Ð �{Ñ #Ø",¨UÑ"3Ð �wÑ Ø)3°EÑ):Ð �~Ñ &Ø'1°%Ñ'8Ð �|Ñ $Ø0:¸5Ñ0AÐ Ð,Ñ -Ø'1°%Ñ'8Ð �|Ñ $Ø'=¸eÑ'DÐ �|Ñ $ór?   