+
    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HtHtHtHt ^ RIHtHtHtHtHtHt ^ RIHt ]! R4      t]P5                  ]]4      R 4       t]P5                  ]]4      R	 4       t]P5                  ]]4      R
 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]]4      R 4       t]P5                  ]	]	4      R 4       t]P5                  ]	]4      R 4       t]P5                  ]]4      R 4       tR# )    )S)sympify)MinMax)EmptySet	FiniteSetIntersectionInterval
ProductSetSetUnionUniversalSet)ComplexRegionNaturals	Naturals0Integers	RationalsReals)
Dispatcher
union_setsc                     V # N abs   &&W/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/sets/handlers/union.py_r          H    c                     V # r   r   r   s   &&r   r   r      r   r    c                     V # r   r   r   s   &&r   r   r      r   r    c                     V # r   r   r   s   &&r   r   r      r   r    c                     V # r   r   r   s   &&r   r   r      r   r    c                     V # r   r   r   s   &&r   r   r   "   r   r    c                 <    \        W4      pW 8X  d   V# W!8X  d   V # R # r   )r	   )r   r   	intersects   && r   r   r   &   s%    Q"I~	 
r    c                    VP                  \        P                  4      '       d   \        P                  ! V4      pVP
                  '       d   V P                  '       g<   VP                  '       g*   \        \        V P                  VP                  4      4      # V P                  '       d>   VP                  '       d,   \        \        V P                  VP                  4      R R7      # R# )T)polarN)		is_subsetr   r   r   	from_realis_ComplexRegionr)   r   setsr   s   &&r   r   r   .   s    {{177##A&!''' qvvqvv!677WWW qvvqvv!6dCCr    c                     V# r   r   r   s   &&r   r   r   =   r   r    c                     V # r   r   r   s   &&r   r   r   B   r   r    c                 b   VP                  V 4      '       d   V # \        VP                  4      \        V P                  4      8w  d   R # \        V P                  4      ^8X  dM   V P                  w  r#VP                  w  rEW$8X  d   V\        W54      ,          # W58X  d   \        W$4      V,          # R # r   )r*   lenr-   r   )r   r   a1a2b1b2s   &&    r   r   r   F   s    {{1~~
166{c!&&k!
166{a8b%%8=2%%r    c                 8    VP                  V 4      '       d   V # R # r   )r*   r   s   &&r   r   r   U   s    {{1~~r    c                    V P                  V4      '       EdC   \        V P                  VP                  4      p\        V P                  VP                  4      pW#8  g   W#8X  d   W 9  d	   W!9  d   R # \        V P                  VP                  4      p\        V P                  VP                  4      pV P                  V8g  ;'       g    V P
                  ;'       d$    VP                  V8g  ;'       g    VP
                  pV P                  V8g  ;'       g    V P                  ;'       d$    VP                  V8g  ;'       g    VP                  p\        W2WE4      # R # r   )_is_comparabler   endr   start	left_open
right_openr
   )r   r   r9   r:   r;   r<   s   &&    r   r   r   [   s   !%%AGGQWW%KLcls|)EaeeQUU#C''U*99akk ; ;''U*99akk 55C<771<< 9 955C<771<< E	>> r    c                 "    \         P                  # r   )r   r   r   s   &&r   r   r   n   s    >>r    c                    V P                   ;'       dS    \        VP                  V P                  4      4      \        P
                  J ;'       d    V P                  P                  pV P                  ;'       dS    \        VP                  V P                  4      4      \        P
                  J ;'       d    V P                  P                  pV'       g	   V'       dk   V P                   ;'       d    V P                  V9  pV P                  ;'       d    V P                  V9  p\        V P                  V P                  WE4      pWa0# R # r   )
r;   r   containsr:   r   true	is_finiter<   r9   r
   )r   r   open_left_in_b_and_finiteopen_right_in_b_and_finite	open_left
open_rightnew_as   &&     r   r   r   r   s    
 "# "7 "7%,QZZ-@%AQVV%K"7 "7%&WW%6%6  #$,, #6 #6&-ajj.?&@AFF&J#6 #6&'eeoo  !$>KK44AGG1$4	\\44aee1n
!%%?zr    c                 J    \        V P                  VP                  ,          !  # r   )r   	_elementsr   s   &&r   r   r      s    q{{Q[[022r    c                    a \         ;QJ d    V3R  lV  4       F  '       g   K   RM	  RM! V3R  lV  4       4      '       d4   \        V  Uu. uF  pSP                  V4      R8w  g   K  VNK  	  up!  S0# R# u upi )c              3   L   <"   T F  pSP                  V4      R 8H  x  K  	  R# 5i)TN)r?   ).0xr   s   & r   	<genexpr>_.<locals>.<genexpr>   s     
,!Q1::a=D !s   !$TFN)anyr   r?   )r   r   rL   s   &f r   r   r      sd     s
,!
,sss
,!
,,,1>1a

1(=1>?D 	D ?s   A7(A7c                     R # r   r   r   s   &&r   r   r      s    r    N)sympy.core.singletonr   sympy.core.sympifyr   (sympy.functions.elementary.miscellaneousr   r   sympy.sets.setsr   r   r	   r
   r   r   r   r   sympy.sets.fancysetsr   r   r   r   r   r   sympy.multipledispatchr   r   registerr   r   r    r   <module>rX      s   " & =4 4 4    - %
 Y) * Y) * Y	* + UH% & UI& ' UI& ' Xs# $ ]C( ) Xs# $ \3' ( Z, - Z% &
 Xx(? )?$ X|, - Xs# $$ Y	*3 +3 Y$ % S# r    