
    sgM
                     ^    d dl mZmZmZmZ d dlmZ d Zd Zd Z	d Z
d Zd Zd	 Zd
 Zd Zy)    )Ordinal
OmegaPowerord0omega)raisesc            	         t        t              dk(  sJ t        t        t        dd      t        dd                  dk(  sJ t        t        t        dd      t        dd                  dk(  sJ t        t        t        dd      t        dd                  d	k(  sJ t        t        t        t        dz   d      t        dd                  d
k(  sJ y )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        Q/var/www/html/venv/lib/python3.12/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                  f   dt        t        dd            z   t        t        dd            k(  sJ t        t        dd            dz   t        t        dd      t        dd            k(  sJ t        t        dd      t        dd            dz   t        t        dd      t        dd            k(  sJ y )Nr   r
   r   r   )r   r   r   r   r   test_addition_with_integersr      s    wz!Q'((GJq!4D,EEEE:a#$Q&'*Q2BJqRSDT*UUUU:a#Z1%56q8
1a *Q"234 4 4r   c                  *   t        t        dd      t        dd            t        t        dd            z   t        t        dd      t        dd            k(  sJ t        t        dd      t        dd            t        t        dd            z   t        t        dd      t        dd            k(  sJ t        t        t        d      t        dd            t        t        dd            z   t        t        t        d      t        dd            k(  sJ y )Nr
   r   r      r   r   r   r   r   r   test_addition_with_ordinalsr      s    :a#Z1%56AqAQ9RR
1a *Q"234 4 4:a#Z1%56AqAQ9RR
1a *Q"234 4 4:eQ'Aq)9:WZPQSTEU=VV
5!$jA&678 8 8r   c                     t        t        dd            t        t        dd      t        dd            kD  sJ t        t        dd      t        dd            t        t        dd            k  sJ t        t        dd            t        t        dd      t        dd            k  sJ t        t        dd      t        dd            t        t        dd      t        dd            k(  sJ t        t        dd      t        dd            t        t        dd            k(  rJ t        t        t        d            t        t        dd            kD  sJ y )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#$wz!Q/?AqAQ'RRRR:a#Z1%56
1a *Q"234 4 4z!Q'Aq)9:gjQRTUFV>WWWW:eQ'(7:a3C+DDDDr   c                  ^    t         } d| z  | k(  sJ | dz  t        t        dd            k(  sJ y )Nr   	   r   r   r   r   r	   s    r   !test_multiplication_with_integersr   $   s4    AQ3!8O8Q3'*Q*++++r   c                  $   t         } | | dz   z  | | z  | z   k(  sJ | dz   | dz   z  | | z  | z   dz   k(  sJ | dz  | k(  sJ d| z  | k(  sJ | t        z  t        k(  sJ t        | z  t        k(  sJ | | z  | | | z  z  k(  sJ | | z  | z  | z  | | dz   z  k(  sJ y )Nr   r   )r   r   r   s    r   test_multiplicationr!   )   s    Aa!e9!aEAE?qsQw{***Q3!8O8Q3!8O8T6T>>6T>>a41q!t8qD!8A:QU###r   c                      t         } | dz  | | z  k(  sJ | dz  | | z  | z  k(  sJ | | dz   z  t        t        t         dz   d            k(  sJ | | z  | | z  z  | | dz  z  k(  sJ y )Nr   r   r   r   r   s    r   test_exponentiationr#   4   s{    Aa41Q3;;a41Q3q5==q1u:EAIq!9::::qD1a4=A!H$$$r   c                  n     t        t        dz   d        d k(  rJ  dk  rJ t        t         fd       y )Nr   r
   c                       dk  S )Ngp=
ף@r   r   s   r   <lambda>z+test_comapre_not_instance.<locals>.<lambda>?   s    a$h r   )r   r   r   	TypeErrorr   s   @r   test_comapre_not_instancer(   ;   s6    519a AT	?A;
9&'r   c                  J    t        t        dd            } | j                  rJ y )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   