
    \h                        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)    )S)sympify)MinMax)EmptySet	FiniteSetIntersectionInterval
ProductSetSetUnionUniversalSet)ComplexRegionNaturals	Naturals0Integers	RationalsReals)
Dispatcher
union_setsc                     U $ N abs     Q/var/www/auris/envauris/lib/python3.13/site-packages/sympy/sets/handlers/union.py_r          H    c                     U $ r   r   r   s     r   r   r      r   r    c                     U $ r   r   r   s     r   r   r      r   r    c                     U $ r   r   r   s     r   r   r      r   r    c                     U $ r   r   r   s     r   r   r      r   r    c                     U $ r   r   r   s     r   r   r   "   r   r    c                 6    [        X5      nX :X  a  U$ X!:X  a  U $ g r   )r	   )r   r   	intersects      r   r   r   &   s%    Q"I~	 
r    c                    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)polar)		is_subsetr   r   r   	from_realis_ComplexRegionr)   r   setsr   s     r   r   r   .   s    {{177##A&!'' qvvqvv!677WW qvvqvv!6dCCr    c                     U$ r   r   r   s     r   r   r   =   r   r    c                     U $ r   r   r   s     r   r   r   B   r   r    c                 D   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 )N   )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                 4    UR                  U 5      (       a  U $ g r   )r*   r   s     r   r   r   U   s    {{1~~r    c                    U R                  U5      (       Ga7  [        U R                  UR                  5      n[        U R                  UR                  5      nX#:  d  X#:X  a  X ;  a  X!;  a  g [        U R                  UR                  5      n[        U R                  UR                  5      nU R                  U:g  =(       d    U R
                  =(       a"    UR                  U:g  =(       d    UR
                  nU R                  U:g  =(       d    U R                  =(       a"    UR                  U:g  =(       d    UR                  n[        X2XE5      $ g r   )_is_comparabler   endr   start	left_open
right_openr
   )r   r   r:   r;   r<   r=   s         r   r   r   [   s    !%%AGGQWW%KLcls|)EaeeQUU#C''U*9akk ;''U*9akk 55C<71<< 955C<71<< E	>> r    c                 "    [         R                  $ r   )r   r   r   s     r   r   r   n   s    >>r    c                    U R                   =(       aQ    [        UR                  U R                  5      5      [        R
                  L =(       a    U R                  R                  nU R                  =(       aQ    [        UR                  U R                  5      5      [        R
                  L =(       a    U R                  R                  nU(       d  U(       ah  U R                   =(       a    U R                  U;  nU R                  =(       a    U R                  U;  n[        U R                  U R                  XE5      nXa1$ g r   )
r<   r   containsr;   r   true	is_finiter=   r:   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%,QZZ-@%AQVV%K"7%&WW%6%6  #$,, #6&-ajj.?&@AFF&J#6&'eeoo  !$>KK4AGG1$4	\\4aee1n
!%%?zr    c                 @    [        U R                  UR                  -  6 $ r   )r   	_elementsr   s     r   r   r      s    q{{Q[[022r    c                    ^ [        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$ g s  snf )Nc              3   L   >#    U  H  nTR                  U5      S :H  v   M     g7f)TN)r@   ).0xr   s     r   	<genexpr>_.<locals>.<genexpr>   s     
,!Q1::a=D !s   !$T)anyr   r@   )r   r   rM   s    ` r   r   r      sR     
,!
,,,1>1a

1(=1>?D 	D ?s   AAc                     g 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>rY      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    