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� y)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
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� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zy)r af Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, **, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
r c � � y)z, and >=.
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* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
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� � "�!r c � � t �)z$Finds the greatest Integral <= self.r r s r � __floor__zReal.__floor__� r' r c � � t �)z!Finds the least Integral >= self.r r s r �__ceil__z
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__rfloordiv__zReal.__rfloordiv__� r' r c � � t �)z self % otherr r$ s r �__mod__z Real.__mod__� r' r c � � t �)z other % selfr r$ s r �__rmod__z
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self <= otherr r$ s r �__le__z Real.__le__ r' r c �* � t t | � � S )z(complex(self) == complex(float(self), 0))�complex�floatr s r r zReal.__complex__ s � ��u�T�{�#�#r c � � | �S )z&Real numbers are their real component.r r s r r z Real.real � � � �u� r c � � y)z)Real numbers have no imaginary component.r r r s r r" z Real.imag � � � r c � � | �S )z Conjugate is a no-op for Reals.r r s r rC zReal.conjugate s � ��u� r �N)r r
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$� �� �� �� ��r r c �N � e Zd ZdZdZeed� � � Zeed� � � Zd� Z y)r z6.numerator and .denominator should be in lowest terms.r c � � t �rl r r s r � numeratorzRational.numerator) r' r c � � t �rl r r s r � denominatorzRational.denominator. r' r c �X � t | j � t | j � z S )a float(self) = self.numerator / self.denominator
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bit-string operations.
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or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
r )r r; �moduluss r r< zIntegral.__pow__Q s
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self >> otherr r$ s r �
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