ó
    Š*£h�  ã                   óð  • S SK Jr  S SKJr  S SKJrJr  S SKJrJ	r	J
r
JrJrJrJrJr  S SKJrJrJrJrJrJr  S SKJr  \" S5      r\R5                  \\5      S 5       r\R5                  \\5      S	 5       r\R5                  \\5      S
 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \\5      S 5       r\R5                  \	\	5      S 5       r\R5                  \	\5      S 5       r\R5                  \\5      S 5       rg)é    )ÚS)Úsympify)ÚMinÚMax)ÚEmptySetÚ	FiniteSetÚIntersectionÚIntervalÚ
ProductSetÚSetÚUnionÚUniversalSet)ÚComplexRegionÚNaturalsÚ	Naturals0ÚIntegersÚ	RationalsÚReals)Ú
DispatcherÚ
union_setsc                 ó   • U $ ©N© ©ÚaÚbs     ÚV/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/sets/handlers/union.pyÚ_r      ó   € à€Hó    c                 ó   • U $ r   r   r   s     r   r   r      r   r    c                 ó   • U $ r   r   r   s     r   r   r      r   r    c                 ó   • U $ r   r   r   s     r   r   r      r   r    c                 ó   • U $ r   r   r   s     r   r   r      r   r    c                 ó   • U $ r   r   r   s     r   r   r   "   r   r    c                 ó6   • [        X5      nX :X  a  U$ X!:X  a  U $ g r   )r	   )r   r   Ú	intersects      r   r   r   &   s%   € ä˜QÓ"€IØƒ~ØˆØ	‹Øˆð 
r    c                 óÄ  • UR                  [        R                  5      (       a  [        R                  " U5      nUR
                  (       a•  U R                  (       d:  UR                  (       d)  [        [        U R                  UR                  5      5      $ U R                  (       a9  UR                  (       a(  [        [        U R                  UR                  5      SS9$ g )NT)Úpolar)	Ú	is_subsetr   r   r   Ú	from_realÚis_ComplexRegionr)   r   Úsetsr   s     r   r   r   .   s�   € à‡{�{”1—7‘7×Ñä×#Ò# AÓ&ˆà××à—— !§'§'Ü ¤ q§v¡v¨q¯v©vÓ!6Ó7Ð7à�W�W˜ŸŸÜ ¤ q§v¡v¨q¯v©vÓ!6¸dÑCÐCØr    c                 ó   • U$ r   r   r   s     r   r   r   =   r   r    c                 ó   • U $ r   r   r   s     r   r   r   B   r   r    c                 óD  • UR                  U 5      (       a  U $ [        UR                  5      [        U R                  5      :w  a  g [        U R                  5      S:X  aB  U R                  u  p#UR                  u  pEX$:X  a  U[        X55      -  $ X5:X  a  [        X$5      U-  $ g )Né   )r*   Úlenr-   r   )r   r   Úa1Úa2Úb1Úb2s         r   r   r   F   s€   € à‡{�{�1‡~�~ØˆÜ
ˆ1�6‰6ƒ{”c˜!Ÿ&™&“kÓ!ØÜ
ˆ1�6‰6ƒ{�aÓØ—‘‰ˆØ—‘‰ˆØ‹8Øœ˜b›Ñ%Ð%Ø‹8Ü˜“= 2Ñ%Ð%Ør    c                 ó4   • UR                  U 5      (       a  U $ g r   )r*   r   s     r   r   r   U   s   € à‡{�{�1‡~�~ØˆØr    c                 ó   • U R                  U5      (       Ga7  [        U R                  UR                  5      n[        U R                  UR                  5      nX#:  d  X#:X  a  X ;  a  X!;  a  g [        U R                  UR                  5      n[        U R                  UR                  5      nU R                  U:g  =(       d    U R
                  =(       a"    UR                  U:g  =(       d    UR
                  nU R                  U:g  =(       d    U R                  =(       a"    UR                  U:g  =(       d    UR                  n[        X2XE5      $ g r   )Ú_is_comparabler   Úendr   ÚstartÚ	left_openÚ
right_openr
   )r   r   r:   r;   r<   r=   s         r   r   r   [   sð   € à×Ñ˜×Òä�!—%‘%˜Ÿ™ÓˆÜ�A—G‘G˜QŸW™WÓ%ˆØ‹KØ‹L˜c›l¨s«|Øä˜Ÿ™ §¡Ó)ˆEÜ�a—e‘e˜QŸU™UÓ#ˆCàŸ'™' UÑ*×9¨a¯k©k÷ ;ØŸ'™' UÑ*×9¨a¯k©kð àŸ5™5 C™<×7¨1¯<©<÷ 9ØŸ5™5 C™<×7¨1¯<©<ð ä˜E¨	Ó>Ð>ð r    c                 ó"   • [         R                  $ r   )r   r   r   s     r   r   r   n   s   € ä�>‰>Ðr    c                 ó€  • U R                   =(       aQ    [        UR                  U R                  5      5      [        R
                  L =(       a    U R                  R                  nU R                  =(       aQ    [        UR                  U R                  5      5      [        R
                  L =(       a    U R                  R                  nU(       d  U(       ah  U R                   =(       a    U R                  U;  nU R                  =(       a    U R                  U;  n[        U R                  U R                  XE5      nXa1$ g r   )
r<   r   Úcontainsr;   r   ÚtrueÚ	is_finiter=   r:   r
   )r   r   Úopen_left_in_b_and_finiteÚopen_right_in_b_and_finiteÚ	open_leftÚ
open_rightÚnew_as          r   r   r   r   sÜ   € ð
 "#§¡÷ "7Ü%,¨Q¯Z©Z¸¿¹Ó-@Ó%AÄQÇVÁVÐ%K÷"7à%&§W¡W×%6Ñ%6ð ð #$§,¡,÷ #6Ü&-¨a¯j©j¸¿¹Ó.?Ó&@ÄAÇFÁFÐ&J÷#6à&'§e¡e§o¡oð ö !Ö$>à—K‘K×4 A§G¡G°1Ñ$4ˆ	Ø—\‘\×4 a§e¡e°1¡nˆ
Ü˜Ÿ™ !§%¡%¨Ó?ˆØˆzÐØr    c                 ó@   • [        U R                  UR                  -  6 $ r   )r   Ú	_elementsr   s     r   r   r   …   s   € ä�q—{‘{ Q§[¡[Ñ0Ð2Ð2r    c                 ó¨   ^• [        U4S jU  5       5      (       a2  [        U  Vs/ s H  nTR                  U5      S:w  d  M  UPM     sn6 T1$ g s  snf )Nc              3   óL   >#   • U  H  nTR                  U5      S :H  v •  M     g7f)TN)r@   )Ú.0Úxr   s     €r   Ú	<genexpr>Ú_.<locals>.<genexpr>Œ   s   øé € Ð
,ª! Qˆ1�:‰:�a‹=˜DÖ ª!ùs   ƒ!$T)Úanyr   r@   )r   r   rM   s    ` r   r   r   ‰   sR   ø€ ô Ô
,©!Ó
,×,Ñ,ä¡1Ó>¢1˜a¨¯
©
°1«¸Ñ(=Ÿ¡1Ñ>Ð?ÀðDð 	Dàùò ?s   ¥AÁAc                 ó   • g r   r   r   s     r   r   r   ‘   s   € àr    N)Úsympy.core.singletonr   Úsympy.core.sympifyr   Ú(sympy.functions.elementary.miscellaneousr   r   Úsympy.sets.setsr   r   r	   r
   r   r   r   r   Úsympy.sets.fancysetsr   r   r   r   r   r   Úsympy.multipledispatchr   r   Úregisterr   r   r    r   Ú<module>rY      sˆ  ðÝ "Ý &ß =÷4÷ 4ó 4÷ ÷  å -ñ ˜Ó%€
ð ×Ñ�Y Ó)ñó *ðð ×Ñ�Y Ó)ñó *ðð ×Ñ�Y 	Ó*ñó +ðð ×Ñ�U˜HÓ%ñó &ðð ×Ñ�U˜IÓ&ñó 'ðð ×Ñ�U˜IÓ&ñó 'ðð ×Ñ�X˜sÓ#ñó $ðð ×Ñ�] CÓ(ñó )ðð ×Ñ�X˜sÓ#ñó $ðð ×Ñ�\ 3Ó'ñó (ðð ×Ñ�Z Ó,ñó -ðð ×Ñ�Z Ó%ñó &ðð
 ×Ñ�X˜xÓ(ñ?ó )ð?ð$ ×Ñ�X˜|Ó,ñó -ðð ×Ñ�X˜sÓ#ñó $ðð$ ×Ñ�Y 	Ó*ñ3ó +ð3ð ×Ñ�Y Ó$ñó %ðð ×Ñ�S˜#Óñó ñr    