Ë
    7^(hû+  ã                  óÖ   — d Z ddlmZ ddlZddlmZ ddlmZ ddlm	Z	 ddl
Z
ddlmZ e
j                  j                  Ze
j                  j                   Z G d„ d	«      Zeeee	fe_        y)
a�  
PythonMPQ: Rational number type based on Python integers.

This class is intended as a pure Python fallback for when gmpy2 is not
installed. If gmpy2 is installed then its mpq type will be used instead. The
mpq type is around 20x faster. We could just use the stdlib Fraction class
here but that is slower:

    from fractions import Fraction
    from sympy.external.pythonmpq import PythonMPQ
    nums = range(1000)
    dens = range(5, 1005)
    rats = [Fraction(n, d) for n, d in zip(nums, dens)]
    sum(rats) # <--- 24 milliseconds
    rats = [PythonMPQ(n, d) for n, d in zip(nums, dens)]
    sum(rats) # <---  7 milliseconds

Both mpq and Fraction have some awkward features like the behaviour of
division with // and %:

    >>> from fractions import Fraction
    >>> Fraction(2, 3) % Fraction(1, 4)
    1/6

For the QQ domain we do not want this behaviour because there should be no
remainder when dividing rational numbers. SymPy does not make use of this
aspect of mpq when gmpy2 is installed. Since this class is a fallback for that
case we do not bother implementing e.g. __mod__ so that we can be sure we
are not using it when gmpy2 is installed either.
é    )ÚannotationsN)Úgcd)ÚDecimal)ÚFraction)ÚTypec                  óî   ‡ — e Zd ZU dZdZd"d„Zed„ «       Zeˆ fd„«       Zd„ Z	d„ Z
d„ Zd	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!dZ"d e#d!<   ˆ xZ$S )#Ú	PythonMPQa  Rational number implementation that is intended to be compatible with
    gmpy2's mpq.

    Also slightly faster than fractions.Fraction.

    PythonMPQ should be treated as immutable although no effort is made to
    prevent mutation (since that might slow down calculations).
    ©Ú	numeratorÚdenominatorc                ó  — |�Ht        |t        «      rìt        |t        «      rÜt        ||«      }||z  }||z  }| j                  ||«      S t        |t        «      r| j	                  |d«      S t        |t
        «      r&| j	                  |j                  |j                  «      S t        |t        t        t        f«      rt        |«      }t        |t        «      r&| j	                  |j                  |j                  «      S t        d«      ‚)z3Construct PythonMPQ with gcd computation and checksé   z/PythonMPQ() requires numeric or string argument)Ú
isinstanceÚintr   Ú
_new_checkÚ_newr	   r   r   r   ÚfloatÚstrr   Ú	TypeError)Úclsr   r   Údivisors       úV/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/external/pythonmpq.pyÚ__new__zPythonMPQ.__new__9   sä   € àÐ"ô ˜)¤SÔ)¬j¸ÄcÔ.Jä˜i¨Ó5�Ø˜gÑ%�	Ø Ñ'�Ø—~‘~ i°Ó=Ð=ô ˜)¤SÔ)Ø—x‘x 	¨1Ó-Ð-Ü˜I¤yÔ1Ø—x‘x 	× 3Ñ 3°Y×5JÑ5JÓKÐKô ˜)¤g¬u´cÐ%:Ô;Ü$ YÓ/�	Ü˜)¤XÔ.Ø—x‘x 	× 3Ñ 3°Y×5JÑ5JÓKÐKô ÐIÓJÐJó    c                ób   — |st        d|› d|› �«      ‚|dk  r| }| }| j                  ||«      S )z@Construct PythonMPQ, check divide by zero and canonicalize signszZero divisor ú/r   )ÚZeroDivisionErrorr   )r   r   r   s      r   r   zPythonMPQ._new_check]   sE   € ñ Ü# m°I°;¸aÀ¸}Ð$MÓNÐNØ˜1Š_Ø"˜
ˆIØ&˜,ˆKØ�x‰x˜	 ;Ó/Ð/r   c                óB   •— t         ‰| �  | «      }||_        ||_        |S )z+Construct PythonMPQ efficiently (no checks))Úsuperr   r   r   )r   r   r   ÚobjÚ	__class__s       €r   r   zPythonMPQ._newg   s&   ø€ ô ‰g‰o˜cÓ"ˆØ!ˆŒØ%ˆŒØˆ
r   c                óT   — | j                   | j                  }}|dk  r| |z   S ||z  S )z'Convert to int (truncates towards zero)r   r
   )ÚselfÚpÚqs      r   Ú__int__zPythonMPQ.__int__o   s2   € à�~‰~˜t×/Ñ/ˆ1ˆØˆqŠ5Ø�R˜‘U�8ˆOØ�!‰tˆr   c                ó4   — | j                   | j                  z  S )z Convert to float (approximately)r
   ©r#   s    r   Ú	__float__zPythonMPQ.__float__v   s   € à�~‰~ × 0Ñ 0Ñ0Ð0r   c                ó,   — t        | j                  «      S )zTrue/False if nonzero/zero)Úboolr   r(   s    r   Ú__bool__zPythonMPQ.__bool__z   s   € ä�D—N‘NÓ#Ð#r   c                óö   — t        |t        «      r4| j                  |j                  k(  xr | j                  |j                  k(  S t        || j                  «      r| j                  t        |«      «      S t        S )z=Compare equal with PythonMPQ, int, float, Decimal or Fraction)r   r	   r   r   Ú_compatible_typesÚ__eq__ÚNotImplemented©r#   Úothers     r   r/   zPythonMPQ.__eq__~   sd   € ä�eœYÔ'Ø—N‘N e§o¡oÑ5ò :Ø×$Ñ$¨×(9Ñ(9Ñ9ð;ä˜˜t×5Ñ5Ô6Ø—;‘;œy¨Ó/Ó0Ð0ä!Ð!r   c                óò   — 	 t        | j                  dt        «      }t        t        t	        | j
                  «      «      |z  «      }| j
                  dk\  r|n| }|dk(  rdS |S # t        $ r	 t        }Y Œ.w xY w)zhash - same as mpq/Fractionéÿÿÿÿr   éþÿÿÿ)Úpowr   Ú_PyHASH_MODULUSÚhashÚabsr   Ú
ValueErrorÚ_PyHASH_INF)r#   ÚdinvÚhash_Úresults       r   Ú__hash__zPythonMPQ.__hash__ˆ   su   € ð	;Ü�t×'Ñ'¨¬_Ó=ˆDô œœc $§.¡.Ó1Ó2°TÑ9Ó:ˆEØŸ.™.¨AÒ-‘°E°6ˆØ˜r’\ˆrÐ- vÐ-øô ò 	 ÜŠEð	 ús   ‚A$ Á$A6Á5A6c                óH   — t        | «      | j                  | j                  ffS )zDeconstruct for pickling)Útyper   r   r(   s    r   Ú
__reduce__zPythonMPQ.__reduce__“   s    € ä�D‹z˜DŸN™N¨D×,<Ñ,<Ð=Ð=Ð=r   c                óp   — | j                   dk7  r| j                  › d| j                   › �S | j                  › S )úConvert to stringr   r   )r   r   r(   s    r   Ú__str__zPythonMPQ.__str__—   s:   € à×Ñ˜qÒ Ø—n‘nÐ% Q t×'7Ñ'7Ð&8Ð9Ð9à—n‘nÐ%Ð&r   c                ó<   — d| j                   › d| j                  › d�S )rD   zMPQ(ú,ú)r
   r(   s    r   Ú__repr__zPythonMPQ.__repr__ž   s#   € à�d—n‘nÐ% Q t×'7Ñ'7Ð&8¸Ð:Ð:r   c                ó°   — t        || j                  «      st        S | j                  |j                  z  }|j                  | j                  z  } |||«      S )zHelper for lt/le/gt/ge)r   r.   r0   r   r   )r#   r2   ÚopÚlhsÚrhss        r   Ú_cmpzPythonMPQ._cmp¢   sL   € ä˜% ×!7Ñ!7Ô8Ü!Ð!Ø�n‰n˜u×0Ñ0Ñ0ˆØ�o‰o × 0Ñ 0Ñ0ˆÙ�#�s‹|Ðr   c                óB   — | j                  |t        j                  «      S )zself < other)rN   ÚoperatorÚltr1   s     r   Ú__lt__zPythonMPQ.__lt__ª   ó   € à�y‰y˜¤§¡Ó,Ð,r   c                óB   — | j                  |t        j                  «      S )zself <= other)rN   rP   Úler1   s     r   Ú__le__zPythonMPQ.__le__®   rS   r   c                óB   — | j                  |t        j                  «      S )zself > other)rN   rP   Úgtr1   s     r   Ú__gt__zPythonMPQ.__gt__²   rS   r   c                óB   — | j                  |t        j                  «      S )zself >= other)rN   rP   Úger1   s     r   Ú__ge__zPythonMPQ.__ge__¶   rS   r   c                ó`   — | j                  t        | j                  «      | j                  «      S )zabs(q))r   r9   r   r   r(   s    r   Ú__abs__zPythonMPQ.__abs__º   s"   € à�y‰yœ˜TŸ^™^Ó,¨d×.>Ñ.>Ó?Ð?r   c                ó   — | S )z+q© r(   s    r   Ú__pos__zPythonMPQ.__pos__¾   s   € àˆr   c                óP   — | j                  | j                   | j                  «      S )z-q)r   r   r   r(   s    r   Ú__neg__zPythonMPQ.__neg__Â   s   € à�y‰y˜$Ÿ.™.˜¨$×*:Ñ*:Ó;Ð;r   c                óÐ  — t        |t        «      r†| j                  | j                  }}|j                  |j                  }}t	        ||«      }|dk(  r||z  ||z  z   }||z  }ns||z  ||z  }
}	||
z  ||	z  z   |	|
z  }}t	        ||«      }||z  |||z  z  }}n?t        |t
        «      r)| j                  | j                  |z  z   }| j                  }nt        S | j                  ||«      S )zq1 + q2r   ©r   r	   r   r   r   r   r0   r   ©r#   r2   ÚapÚaqÚbpÚbqÚgr$   r%   Úq1Úq2Úg2s               r   Ú__add__zPythonMPQ.__add__Æ   sî   € ä�eœYÔ'ð —^‘^ T×%5Ñ%5�ˆBØ—_‘_ e×&7Ñ&7�ˆBÜ�B˜“ˆAØ�AŠvØ�r‘E˜B˜r™E‘M�Ø�r‘E‘à˜Q™  A¡�B�Ø˜"‘u˜r "™u‘} b¨¡e�1�Ü˜˜A“Y�Ø˜R™ ! q¨B¡w¡-�1‘ä˜œsÔ#Ø—‘ ×!1Ñ!1°EÑ!9Ñ9ˆAØ× Ñ ‰Aä!Ð!à�y‰y˜˜A‹Ðr   c                ó¢   — t        |t        «      r:| j                  | j                  |z  z   }| j                  }| j	                  ||«      S t
        S )zz1 + q2)r   r   r   r   r   r0   ©r#   r2   r$   r%   s       r   Ú__radd__zPythonMPQ.__radd__ç   sF   € ä�eœSÔ!Ø—‘ ×!1Ñ!1°EÑ!9Ñ9ˆAØ× Ñ ˆAØ—9‘9˜Q “?Ð"ä!Ð!r   c                óÐ  — t        |t        «      r†| j                  | j                  }}|j                  |j                  }}t	        ||«      }|dk(  r||z  ||z  z
  }||z  }ns||z  ||z  }
}	||
z  ||	z  z
  |	|
z  }}t	        ||«      }||z  |||z  z  }}n?t        |t
        «      r)| j                  | j                  |z  z
  }| j                  }nt        S | j                  ||«      S )zq1 - q2r   re   rf   s               r   Ú__sub__zPythonMPQ.__sub__ð   sì   € ä�eœYÔ'Ø—^‘^ T×%5Ñ%5�ˆBØ—_‘_ e×&7Ñ&7�ˆBÜ�B˜“ˆAØ�AŠvØ�r‘E˜B˜r™E‘M�Ø�r‘E‘à˜Q™  A¡�B�Ø˜"‘u˜r "™u‘} b¨¡e�1�Ü˜˜A“Y�Ø˜R™ ! q¨B¡w¡-�1‘Ü˜œsÔ#Ø—‘ ×!1Ñ!1°%Ñ!7Ñ7ˆAØ× Ñ ‰Aä!Ð!à�y‰y˜˜A‹Ðr   c                ó¢   — t        |t        «      r:| j                  |z  | j                  z
  }| j                  }| j	                  ||«      S t
        S )zz1 - q2)r   r   r   r   r   r0   rq   s       r   Ú__rsub__zPythonMPQ.__rsub__  sF   € ä�eœSÔ!Ø× Ñ  5Ñ(¨4¯>©>Ñ9ˆAØ× Ñ ˆAØ—9‘9˜Q “?Ð"ä!Ð!r   c                ó   — t        |t        «      r_| j                  | j                  }}|j                  |j                  }}t	        ||«      }t	        ||«      }||z  ||z  z  ||z  ||z  z  }	}nNt        |t
        «      r8t	        || j                  «      }
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z  z  }| j                  |
z  }	nt        S | j                  ||	«      S )zq1 * q2re   ©r#   r2   rg   rh   ri   rj   Úx1Úx2r$   r%   Úxs              r   Ú__mul__zPythonMPQ.__mul__  s¿   € ä�eœYÔ'Ø—^‘^ T×%5Ñ%5�ˆBØ—_‘_ e×&7Ñ&7�ˆBÜ�R˜“ˆBÜ�R˜“ˆBØ˜‘V˜b "™fÑ%¨¨B©°°R±Ñ'8ˆq‰AÜ˜œsÔ#Ü�E˜4×+Ñ+Ó,ˆAØ—‘  q¡Ñ)ˆAØ× Ñ  !Ñ#‰Aä!Ð!à�y‰y˜˜A‹Ðr   c                óÀ   — t        |t        «      rIt        | j                  |«      }| j                  ||z  z  }| j                  |z  }| j                  ||«      S t        S )zz1 * q2)r   r   r   r   r   r   r0   ©r#   r2   r{   r$   r%   s        r   Ú__rmul__zPythonMPQ.__rmul__   sV   € ä�eœSÔ!Ü�D×$Ñ$ eÓ,ˆAØ—‘  q¡Ñ)ˆAØ× Ñ  !Ñ#ˆAØ—9‘9˜Q “?Ð"ä!Ð!r   c                óz   — | j                   | j                  }}|dk  r||| }}}| j                  ||z  ||z  «      S )zq ** zr   )r   r   r   )r#   Úexpr$   r%   s       r   Ú__pow__zPythonMPQ.__pow__*  sD   € à�~‰~˜t×/Ñ/ˆ1ˆà�Š7Ø˜1˜s˜d�#ˆqˆAà�‰˜q #™v q¨#¡vÓ.Ð.r   c                ó   — t        |t        «      r_| j                  | j                  }}|j                  |j                  }}t	        ||«      }t	        ||«      }||z  ||z  z  ||z  ||z  z  }	}nNt        |t
        «      r8t	        || j                  «      }
| j                  |
z  }| j                  ||
z  z  }	nt        S | j                  ||	«      S )zq1 / q2)r   r	   r   r   r   r   r0   r   rx   s              r   Ú__truediv__zPythonMPQ.__truediv__3  s¾   € ä�eœYÔ'Ø—^‘^ T×%5Ñ%5�ˆBØ—_‘_ e×&7Ñ&7�ˆBÜ�R˜“ˆBÜ�R˜“ˆBØ˜‘V˜b "™fÑ%¨¨B©°°R±Ñ'8ˆq‰AÜ˜œsÔ#Ü�E˜4Ÿ>™>Ó*ˆAØ—‘ Ñ!ˆAØ× Ñ  %¨¡(Ñ+‰Aä!Ð!à�‰˜q !Ó$Ð$r   c                óÀ   — t        |t        «      rIt        | j                  |«      }| j                  ||z  z  }| j                  |z  }| j                  ||«      S t        S )zz / q)r   r   r   r   r   r   r0   r~   s        r   Ú__rtruediv__zPythonMPQ.__rtruediv__D  sU   € ä�eœSÔ!Ü�D—N‘N EÓ*ˆAØ× Ñ  %¨¡(Ñ+ˆAØ—‘ Ñ!ˆAØ—?‘? 1 aÓ(Ð(ä!Ð!r   r`   ztuple[Type, ...]r.   )N)%Ú__name__Ú
__module__Ú__qualname__Ú__doc__Ú	__slots__r   Úclassmethodr   r   r&   r)   r,   r/   r?   rB   rE   rI   rN   rR   rV   rY   r\   r^   ra   rc   ro   rr   rt   rv   r|   r   r‚   r„   r†   r.   Ú__annotations__Ú__classcell__)r!   s   @r   r	   r	   .   sË   ø… ñð -€Ió"KðH ñ0ó ð0ð óó ðòò1ò$ò"ò	.ò>ò'ò;òò-ò-ò-ò-ò@òò<òòB"òò,"òò""ò/ò%ò""ð +-ÐÐ'×,r   r	   )rŠ   Ú
__future__r   rP   Úmathr   Údecimalr   Ú	fractionsr   ÚsysÚtypingr   Ú	hash_infoÚmodulusr7   Úinfr;   r	   r   r.   r`   r   r   ú<module>r˜      sa   ðñõ> #Û Ý Ý Ý Û 
Ý ð —-‘-×'Ñ'€Ø�m‰m×Ñ€÷`-ñ `-ðN	  )¨#¨w¸ÐA€	Õ r   