+
    i                     b    R t ^ RIHtHtHt ^ RIHt ^ RIHt ^ RI	H
t
 ]
 ! R R]4      4       tR# )z6Implementation of :class:`PythonRationalField` class. )PythonIntegerPythonRationalSymPyRational)RationalField)CoercionFailed)publicc                      a  ] tR t^	t o Rt]t]! ^ 4      t]! ^4      tRt	R t
R tR tR tR tR tR	 tR
 tR tR tR tRtV tR# )PythonRationalFieldzRational field based on :ref:`MPQ`.

This will be used as :ref:`QQ` if ``gmpy`` and ``gmpy2`` are not
installed. Elements are instances of :ref:`MPQ`.
	QQ_pythonc                    R # )N )selfs   &ڇ/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/polys/domains/pythonrationalfield.py__init__PythonRationalField.__init__   s        c                    ^ RI Hp V! 4       # )z'Returns ring associated with ``self``. )PythonIntegerRing)sympy.polys.domainsr   )r   r   s   & r   get_ringPythonRationalField.get_ring   s    9 ""r   c                B    \        VP                  VP                  4      # )zConvert `a` to a SymPy object. )r   	numeratordenominatorr   as   &&r   to_sympyPythonRationalField.to_sympy   s    Q[[!--88r   c                   VP                   '       d!   \        VP                  VP                  4      # VP                  '       d8   ^ RIHp VP                  V4      w  r4\        \        V4      \        V4      4      # \        RV,          4      h)z%Convert SymPy's Rational to `dtype`. )RRz"expected `Rational` object, got %s)
is_Rationalr   pqis_Floatr   r   to_rationalintr   )r   r   r   r!   r"   s   &&   r   
from_sympyPythonRationalField.from_sympy"   sb    ===!!##qss++ZZZ.>>!$DA!#a&#a&11 !E!IJJr   c                    \        V4      # )z*Convert a Python `int` object to `dtype`. )r   K1r   K0s   &&&r   from_ZZ_python"PythonRationalField.from_ZZ_python-   s    a  r   c                    V# )z/Convert a Python `Fraction` object to `dtype`. r   r)   s   &&&r   from_QQ_python"PythonRationalField.from_QQ_python1   s    r   c                *    \        \        V4      4      # )z(Convert a GMPY `mpz` object to `dtype`. )r   r   r)   s   &&&r   from_ZZ_gmpy PythonRationalField.from_ZZ_gmpy5   s    mA.//r   c                v    \        \        VP                  4       4      \        VP                  4       4      4      # )z(Convert a GMPY `mpq` object to `dtype`. )r   r   numerdenomr)   s   &&&r   from_QQ_gmpy PythonRationalField.from_QQ_gmpy9   s*    mAGGI6+AGGI68 	8r   c                d    VP                  V4      w  r4\        \        V4      \        V4      4      # )z*Convert a mpmath `mpf` object to `dtype`. )r$   r   r%   )r*   r   r+   r!   r"   s   &&&  r   from_RealField"PythonRationalField.from_RealField>   s'    ~~a c!fc!f--r   c                    VP                   # )zReturns numerator of `a`. )r   r   s   &&r   r5   PythonRationalField.numerC   s    {{r   c                    VP                   # )zReturns denominator of `a`. )r   r   s   &&r   r6   PythonRationalField.denomG   s    }}r   r   N)__name__
__module____qualname____firstlineno____doc__r   dtypezeroonealiasr   r   r   r&   r,   r/   r2   r7   r:   r5   r6   __static_attributes____classdictcell__)__classdict__s   @r   r	   r	   	   se      E8D
(CE#
9	K!08
.
 r   r	   N)rD   sympy.polys.domains.groundtypesr   r   r   !sympy.polys.domains.rationalfieldr   sympy.polys.polyerrorsr   sympy.utilitiesr   r	   r   r   r   <module>rP      s3    < Y X ; 1 "?- ? ?r   