+ i^Rt^RIHt^RIHtHtHt^RIHt^RI H t ^RI H t ^RI Ht^RIHt]!RR ] ]] 44t]!4tR #) z0Implementation of :class:`RationalField` class. MPQ) SymPyRational is_squaresqrtrem)CharacteristicZero)Field) SimpleDomain)CoercionFailed)publicc a]tRt^toRtRtRtR;ttRt Rt Rt ] t ] !^4t] !^4t]!]4tRtRtRtRtRtR tR R /R ltR tRtRtRtRtRtRtRt Rt!Rt"Rt#Rt$Rt%Rt&Rt'Rt(Rt)Rt*Vt+R #) 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 QQTcR#)Nselfs&ځ/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/polys/domains/rationalfield.py__init__RationalField.__init__-s c >\V\4'dR#\#)z0Returns ``True`` if two domains are equivalent. T) isinstancer NotImplemented)rothers&&r__eq__RationalField.__eq__0s e] + +! !rc \R4#)zReturns hash code of ``self``. r)hashrs&r__hash__RationalField.__hash__7s Dzrc ^RIHpV#)z'Returns ring associated with ``self``. )ZZ)sympy.polys.domainsr")rr"s& rget_ringRationalField.get_ring;s * rc f\\VP4\VP44#)z!Convert ``a`` to a SymPy object. )rint numerator denominatorras&&rto_sympyRationalField.to_sympy@s!S-s1==/ABBrc VP'd!\VPVP4#VP'd-^RIHp\\\VPV44!#\RV,4h)z&Convert SymPy's Integer to ``dtype``. )RRz"expected `Rational` object, got %s) is_Rationalrpqis_Floatr#r/mapr' to_rationalr )rr+r/s&& r from_sympyRationalField.from_sympyDsW ===qssACC= ZZZ .C!234 4 !E!IJ JraliasNc &^RIHpV!V.VO5RV/#)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 )AlgebraicFieldr8)r#r:)rr8 extensionr:s&$* ralgebraic_fieldRationalField.algebraic_fieldNs6 7drsM6$MME+91"w#E-|w#w#r_r