
    \hr                        S SK JrJr  S SKJr  S SKJrJrJrJ	r	J
r
  S SKJr  S SKJr  S SKJrJr  S SKJr  S SKJr  S S	KJrJrJrJr  S S
KJr  \" S5      u  rr\" S5      r\RA                  \\5      S 5       r!\RA                  \\5      S 5       r!\RA                  \\5      S 5       r!\RA                  \\	5      S 5       r!\RA                  \\
5      S 5       r!\RA                  \\5      S 5       r!\RA                  \\5      S 5       r!g)    )BasicExpr)Lambda)ooInfinityNegativeInfinityZeroInteger)S)symbols)MaxMin)ImageSet)set_div)SetInterval	FiniteSetUnion)
Dispatcherzx y_set_powc                     g N xys     Q/var/www/auris/envauris/lib/python3.13/site-packages/sympy/sets/handlers/power.py_r      s        c                 X    [        [        [        [        4[        [        -  5      X5      $ r   )r   r   _x_yr   s     r   r   r      s    FB8bBh0!77r   c                 
    X-  $ r   r   r   s     r   r   r      s	    4Kr   c                 4    [        [        R                  5      $ r   )r   r   One)r   zs     r   r   r      s    QUUr   c                 Z   U R                   U-  nU R                  U-  nUS:  a  X2:  OU R                  U R                   * :  S:X  a  U R                  nU R                  nUnOU R                  nU R                  nUnU R                   R                  (       a  [        [        X#5      [        X#5      XE5      $ U R                  R                  (       a  [        [        X#5      [        X#5      XE5      $ UR                  (       a  UR                  (       a  U R                   R                  (       a  [        U[        U R                  5      $ U R                  R                  (       a  [        [        * USU R                  5      $ [        [        [        * USU R                  5      [        U[        U R                  5      5      $ [        X#U R                  U R                  5      $ UR                  (       a  UR                  (       a|  U R                   R                  (       a  [        U[        U R                  5      $ U R                  R                  (       a  [        U[        U R                  5      $ [        S[        5      $ [        [        R                  U[        R                  U ;  U5      $ g)zQ
Powers in interval arithmetic
https://en.wikipedia.org/wiki/Interval_arithmetic
r   TN)startend	left_open
right_openis_positiver   r   r   is_negativeis_oddis_zeror   r   is_evenr   r	   )r   exponents1s2r*   r+   slefts          r   r   r   #   s    
(	B	
B\(8dBKK	\\
 LL	[[
wwKK0 	0 
		KK0 	0
 wwB55uu}}Rq{{;;2#r4=xBPQP\P\?]^^BAKK>>			wwB55uu}}B44Ar?"AFFE166?IFF 
r   c                    U R                   R                  (       ab  U R                  S:  a  [        [        R
                  5      $ U R                   S:  a  [        [        R                  5      $ [        S[        5      $ U R                  R                  (       ac  U R                   S:  a  [        [        R
                  5      $ U R                  S:  a  [        [        * [        5      $ [        [        * [        5      $ U R                   S:  a9  U R                  S:  a  [        [        R
                  5      $ [        S[        5      $ [        [        * [        5      $ )N   r   )
r(   is_nonnegativer)   r   r   r	   r   r   r   r-   bes     r   r   r   S   s     	ww5519QVV$$77Q;QZZ((2	
		77R<QVV$$552:bS"%%R  77R<uuqy ((Ar?"R  r   c                 R    [        [        [        R                  U 5      [        5      $ r   )r   r   r   r%   r   r9   s     r   r   r   i   s    GAEE1%r**r   N)"
sympy.corer   r   sympy.core.functionr   sympy.core.numbersr   r   r   r	   r
   sympy.core.singletonr   sympy.core.symbolr   (sympy.functions.elementary.miscellaneousr   r   sympy.sets.fancysetsr   sympy.sets.setexprr   sympy.sets.setsr   r   r   r   sympy.multipledispatchr   r!   r"   r   registerr   r   r   r   <module>rH      s/   " & L L " % ? ) & ; ; - 
B j! 
5%  ! 
38 8 
4  
8T" # 
8W%-G &-G^ 
8X&! '!* 
8-.+ /+r   