\h^SrSSKJr SSKJrJrJr SSKJr SSK J r SSK J r SSK Jr SSKJr \"S S \ \\ 55r\"5rg ) z0Implementation of :class:`RationalField` class. MPQ) SymPyRational is_squaresqrtrem)CharacteristicZero)Field) SimpleDomain)CoercionFailed)publicc\rSrSrSrSrSrS=rrSr Sr Sr \ r \ "S5r\ "S5r\"\5rSrSrS rS rS rS rS S.SjrSrSrSrSrSrSrSrSr Sr!Sr"Sr#Sr$Sr%Sr&Sr'Sr(S r)S!r*g )" RationalFieldaAbstract base class for the domain :ref:`QQ`. The :py:class:`RationalField` class represents the field of rational numbers $\mathbb{Q}$ as a :py:class:`~.Domain` in the domain system. :py:class:`RationalField` is a superclass of :py:class:`PythonRationalField` and :py:class:`GMPYRationalField` one of which will be the implementation for :ref:`QQ` depending on whether either of ``gmpy`` or ``gmpy2`` is installed or not. See also ======== Domain QQTrcg)Nselfs Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/polys/domains/rationalfield.py__init__RationalField.__init__-s c:[U[5(ag[$)z0Returns ``True`` if two domains are equivalent. T) isinstancerNotImplemented)rothers r__eq__RationalField.__eq__0s e] + +! !rc[S5$)zReturns hash code of ``self``. r)hashrs r__hash__RationalField.__hash__7s DzrcSSKJn U$)z'Returns ring associated with ``self``. r)ZZ)sympy.polys.domainsr%)rr%s rget_ringRationalField.get_ring;s * rcf[[UR5[UR55$)z!Convert ``a`` to a SymPy object. )rint numerator denominatorras rto_sympyRationalField.to_sympy@s!S-s1==/ABBrcUR(a [URUR5$UR(a+SSKJn [[[URU556$[SU-5e)z&Convert SymPy's Integer to ``dtype``. r)RRz"expected `Rational` object, got %s) is_Rationalrpqis_Floatr&r2mapr* to_rationalr )rr.r2s r from_sympyRationalField.from_sympyDsS ==qssACC= ZZ .C!234 4 !E!IJ JrN)aliasc&SSKJn U"U/UQ7SU06$)aReturns an algebraic field, i.e. `\mathbb{Q}(\alpha, \ldots)`. Parameters ========== *extension : One or more :py:class:`~.Expr` Generators of the extension. These should be expressions that are algebraic over `\mathbb{Q}`. alias : str, :py:class:`~.Symbol`, None, optional (default=None) If provided, this will be used as the alias symbol for the primitive element of the returned :py:class:`~.AlgebraicField`. Returns ======= :py:class:`~.AlgebraicField` A :py:class:`~.Domain` representing the algebraic field extension. Examples ======== >>> from sympy import QQ, sqrt >>> QQ.algebraic_field(sqrt(2)) QQ r)AlgebraicFieldr;)r&r=)rr; extensionr=s ralgebraic_fieldRationalField.algebraic_fieldNs6 7drsM6$MME+91"w#E-|w#w#r_r