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1 d)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators.� )�ABCMeta�abstractmethod)�Number�Complex�Real�Rational�Integralc s � X oO oOoOoOoOoOod)r i% z�All numbers inherit from this class.
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oXO 1 oXO 1 oXO 1 oXO 1 oXO 1 oXO 1 oXO 1 oXO 1 oXO 1 oOoQ o d)r i9 aN 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 � � d)z<Return a builtin complex instance. Called for complex(self).Nr ��self� r � __complex__ZComplex.__complex__F s � r c s � Q O6g ! )z)True if self != 0. Called for bool(self).r r r r r �__bool__ZComplex.__bool__J s � ��q�y�r c � � W b)zHRetrieve the real component of this number.
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� � "�!r c r )zMRetrieve the imaginary component of this number.
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� � "�!r c r )z other + selfr r r r �__radd__ZComplex.__radd__e r r c r )z-selfr r r r �__neg__ZComplex.__neg__j r r c r )z+selfr r r r �__pos__ZComplex.__pos__o r r c s � T' * ! )z self - otherr r r r �__sub__ZComplex.__sub__t s � ��f�}� r c s � Q ' Q* ! )z other - selfr r r r �__rsub__ZComplex.__rsub__x s � ��u�u�}� r c r )z self * otherr r r r �__mul__ZComplex.__mul__| r r c r )z other * selfr r r r �__rmul__ZComplex.__rmul__� r r c r )z5self / other: Should promote to float when necessary.r r r r � __truediv__ZComplex.__truediv__� r r c r )z other / selfr r r r � __rtruediv__ZComplex.__rtruediv__� r r c r )zDself ** exponent; should promote to float or complex when necessary.r )r �exponentr r �__pow__ZComplex.__pow__� r r c r )z base ** selfr )r Zbaser r �__rpow__ZComplex.__rpow__� r r c r )z7Returns the Real distance from 0. Called for abs(self).r r r r �__abs__ZComplex.__abs__� r r c r )z$(x+y*i).conjugate() returns (x-y*i).r r r r � conjugateZComplex.conjugate� r r c r )z
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"�!r c r )a trunc(self): Truncates self to an Integral.
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� � "�!r c r )z$Finds the greatest Integral <= self.r r r r � __floor__ZReal.__floor__� r r c r )z!Finds the least Integral >= self.r r r r �__ceil__Z
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�t�|�,�,r c s � T* T* 0! )z�divmod(other, self): The pair (other // self, other % self).
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__rfloordiv__ZReal.__rfloordiv__� r r c r )z self % otherr r r r �__mod__Z Real.__mod__� r r c r )z other % selfr r r r �__rmod__Z
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self <= otherr r r r �__le__Z Real.__le__ r r c �* � W W Q 1 1 ! )z(complex(self) == complex(float(self), 0))�complex�floatr r r r ZReal.__complex__ s � ��u�T�{�#�#r c � � Q 3! )z&Real numbers are their real component.r r r r r Z Real.real � � � �u� r c r )z)Real numbers have no imaginary component.r r r r r r Z Real.imag � � � r c rE )z Conjugate is a no-op for Reals.r r r r r. ZReal.conjugate s � ��u� r �N)r r
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