
    gM
                     `    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dS )    )Ordinal
OmegaPowerord0omega)raisesc            	      B   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 d S )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        Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/sets/tests/test_ordinals.pytest_string_ordinalsr      s   u::wz!Q''Aq)9)9::;;?PPPPPwz!Q''Aq)9)9::;;|KKKKwz!Q''Aq)9)9::;;yHHHHwz%!)Q//Aq1A1ABBCCG\\\\\\\r   c                     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 d S )Nr   r
   r   r   )r   r   r   r   r   test_addition_with_integersr      s    wz!Q''(((GJq!4D4D,E,EEEEE:a##$$Q&'*Q2B2BJqRSDTDT*U*UUUUU:a##Z1%5%566q8
1a  *Q"2"2334 4 4 4 4 4r   c                     t          t          dd          t          dd                    t          t          dd                    z   t          t          dd          t          dd                    k    sJ t          t          dd          t          dd                    t          t          dd                    z   t          t          dd          t          dd                    k    sJ t          t          t          d          t          dd                    t          t          dd                    z   t          t          t          d          t          dd                    k    sJ d S )Nr
   r   r      r   r   r   r   r   r   test_addition_with_ordinalsr      sU   :a##Z1%5%566AqAQAQ9R9RR
1a  *Q"2"2334 4 4 4:a##Z1%5%566AqAQAQ9R9RR
1a  *Q"2"2334 4 4 4:eQ''Aq)9)9::WZPQSTEUEU=V=VV
5!$$jA&6&6778 8 8 8 8 8r   c                     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                    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                    k    sJ d S )Nr
   r   r   r   r   r   r   r   r   test_comparisonr      s   :a##$$wz!Q/?/?AqAQAQ'R'RRRRR:a##Z1%5%566AqAQAQ9R9RRRRR:a##$$wz!Q/?/?AqAQAQ'R'RRRRR:a##Z1%5%566
1a  *Q"2"2334 4 4 4z!Q''Aq)9)9::gjQRTUFVFV>W>WWWWW:eQ''((7:a3C3C+D+DDDDDDDr   c                  v    t           } d| z  | k    sJ | dz  t          t          dd                    k    sJ d S )Nr   	   r   r   r   r   r	   s    r   !test_multiplication_with_integersr   $   sE    AQ3!8888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 d S )Nr   r   )r   r   r   s    r   test_multiplicationr!   )   s    Aa!e9!aEAE?qsQw{****Q3!8888Q3!8888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 d S )Nr   r   r   r   r   s    r   test_exponentiationr#   4   s    Aa41Q3;;;;a41Q3q5====q1u:EAIq!9!9::::::qD1a4=A!H$$$$$$r   c                       t          t          dz   d            d k    rJ  dk     rJ t          t           fd           d S )Nr   r
   c                       dk     S )Ngp=
ף@r   r   s   r   <lambda>z+test_comapre_not_instance.<locals>.<lambda>?   s    a$h r   )r   r   r   	TypeErrorr   s   @r   test_comapre_not_instancer(   ;   sP    519a  AT				A
9&&&&'''''r   c                  R    t          t          dd                    } | j        rJ d S )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 4 48 8 8E E E, , ,
	$ 	$ 	$% % %( ( (& & & & &r   