
    \hM
                     ^    S SK JrJrJrJr  S SKJr  S rS rS r	S r
S rS rS	 rS
 rS rg)    )Ordinal
OmegaPowerord0omega)raisesc            	         [        [        5      S:X  d   e[        [        [        SS5      [        SS5      5      5      S:X  d   e[        [        [        SS5      [        SS5      5      5      S:X  d   e[        [        [        SS5      [        SS5      5      5      S	:X  d   e[        [        [        [        S-   S5      [        SS5      5      5      S
:X  d   eg )Nw         zw**5*3 + w**3*2r   z
w**5*3 + 5   zw*3 + 5zw**(w + 1) + w**3*2)strr   r   r        V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/sets/tests/test_ordinals.pytest_string_ordinalsr      s    u:wz!Q'Aq)9:;?PPPPwz!Q'Aq)9:;|KKKwz!Q'Aq)9:;yHHHwz%!)Q/Aq1ABCG\\\\r   c                  l   S[        [        SS5      5      -   [        [        SS5      5      :X  d   e[        [        SS5      5      S-   [        [        SS5      [        SS5      5      :X  d   e[        [        SS5      [        SS5      5      S-   [        [        SS5      [        SS5      5      :X  d   eg )Nr   r
   r   r   )r   r   r   r   r   test_addition_with_integersr      s    wz!Q'((GJq!4D,EEEE:a#$Q&'*Q2BJqRSDT*UUUU:a#Z1%56q8
1a *Q"234 4 4r   c                  0   [        [        SS5      [        SS5      5      [        [        SS5      5      -   [        [        SS5      [        SS5      5      :X  d   e[        [        SS5      [        SS5      5      [        [        SS5      5      -   [        [        SS5      [        SS5      5      :X  d   e[        [        [        S5      [        SS5      5      [        [        SS5      5      -   [        [        [        S5      [        SS5      5      :X  d   eg )Nr
   r   r      r   r   r   r   r   r   test_addition_with_ordinalsr      s    :a#Z1%56AqAQ9RR
1a *Q"234 4 4:a#Z1%56AqAQ9RR
1a *Q"234 4 4:eQ'Aq)9:WZPQSTEU=VV
5!$jA&678 8 8r   c                     [        [        SS5      5      [        [        SS5      [        SS5      5      :  d   e[        [        SS5      [        SS5      5      [        [        SS5      5      :  d   e[        [        SS5      5      [        [        SS5      [        SS5      5      :  d   e[        [        SS5      [        SS5      5      [        [        SS5      [        SS5      5      :X  d   e[        [        SS5      [        SS5      5      [        [        SS5      5      :X  a   e[        [        [        S5      5      [        [        SS5      5      :  d   eg )Nr
   r   r   r   r   r   r   r   r   test_comparisonr      s%   :a#$wz!Q/?AqAQ'RRRR:a#Z1%56AqAQ9RRRR:a#$wz!Q/?AqAQ'RRRR:a#Z1%56
1a *Q"234 4 4z!Q'Aq)9:gjQRTUFV>WWWW:eQ'(7:a3C+DDDDr   c                  b    [         n SU -  U :X  d   eU S-  [        [        SS5      5      :X  d   eg )Nr   	   r   r   r   r   r	   s    r   !test_multiplication_with_integersr   $   s4    AQ3!8O8Q3'*Q*++++r   c                  &   [         n X S-   -  X -  U -   :X  d   eU S-   U S-   -  X -  U -   S-   :X  d   eU S-  U :X  d   eSU -  U :X  d   eU [        -  [        :X  d   e[        U -  [        :X  d   eX -  X U -  -  :X  d   eX -  U -  U -  X S-   -  :X  d   eg )Nr   r   )r   r   r   s    r   test_multiplicationr!   )   s    A!e9aEAE?qsQw{***Q3!8O8Q3!8O8T6T>>6T>>41!t8D!8A:U###r   c                      [         n U S-  X -  :X  d   eU S-  X -  U -  :X  d   eX S-   -  [        [        [         S-   S5      5      :X  d   eX -  X -  -  X S-  -  :X  d   eg )Nr   r   r   r   r   s    r   test_exponentiationr#   4   so    Aa413;;a413q5==1u:EAIq!9::::D14=A!H$$$r   c                  t   ^  [        [        S-   S5      m T S :X  a   eT S:  a   e[        [        U 4S j5        g )Nr   r
   c                     > T S:  $ )Ngp=
ף@r   r   s   r   <lambda>+test_comapre_not_instance.<locals>.<lambda>?   s	    a$hr   )r   r   r   	TypeErrorr   s   @r   test_comapre_not_instancer)   ;   s6    519a AT	?A;
9&'r   c                  T    [        [        SS5      5      n U R                  (       a   eg )Nr
   r   )r   r   is_successor_ordinalr   s    r   test_is_successortr,   A   s%    
1a !A%%%%%r   N)sympy.sets.ordinalsr   r   r   r   sympy.testing.pytestr   r   r   r   r   r   r!   r#   r)   r,   r   r   r   <module>r/      s=    @ @ ']48E,
	$%(&r   