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� dS )z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
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edd� �Zdd� Zdd� Zedd� �Zedd� �Zedd � �Zed d � �Zed d � �Zed!d"� �Zed#d$� �Zed%d&� �Zed'd(� �Zd)S )*r af Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, **, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
r c C � dS )z<Return a builtin complex instance. Called for complex(self).Nr ��selfr r r � __complex__- s zComplex.__complex__c C s | dkS )z)True if self != 0. Called for bool(self).r r r r r r �__bool__1 � zComplex.__bool__c C � t �)zXRetrieve the real component of this number.
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This should subclass Real.
r r r r r �imag> r z Complex.imagc C r )z self + otherr �r �otherr r r �__add__G � zComplex.__add__c C r )z other + selfr r r r r �__radd__L r! zComplex.__radd__c C r )z-selfr r r r r �__neg__Q r! zComplex.__neg__c C r )z+selfr r r r r �__pos__V r! zComplex.__pos__c C s
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zComplex.__sub__c C s
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r c C r )zTAny Real can be converted to a native float object.
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* i>0 iff self>0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
r r r r r � __trunc__� s zReal.__trunc__c C r )z$Finds the greatest Integral <= self.r r r r r � __floor__� r! zReal.__floor__c C r )z!Finds the least Integral >= self.r r r r r �__ceil__� r! z
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returns a Real. Rounds half toward even.
r )r Zndigitsr r r � __round__� r zReal.__round__c C s | | | | fS )z�divmod(self, other): The pair (self // other, self % other).
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operations.
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__divmod__� � zReal.__divmod__c C s || || fS )z�divmod(other, self): The pair (self // other, self % other).
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r r r r r � __rdivmod__� r; zReal.__rdivmod__c C r )z)self // other: The floor() of self/other.r r r r r � __floordiv__� r! zReal.__floordiv__c C r )z)other // self: The floor() of other/self.r r r r r �
__rfloordiv__� r! zReal.__rfloordiv__c C r )z self % otherr r r r r �__mod__� r! z Real.__mod__c C r )z other % selfr r r r r �__rmod__� r! z
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< on Reals defines a total ordering, except perhaps for NaN.r r r r r �__lt__� r5 z Real.__lt__c C r )z
self <= otherr r r r r �__le__� r! z Real.__le__c C � t t| ��S )z(complex(self) == complex(float(self), 0))�complex�floatr r r r r � � zReal.__complex__c C � |
S )z&Real numbers are their real component.r r r r r r � � z Real.realc C r )z)Real numbers have no imaginary component.r r r r r r r � r! z Real.imagc C rG )z Conjugate is a no-op for Reals.r r r r r r1 s zReal.conjugate�N)r
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r z6.numerator and .denominator should be in lowest terms.r c C r rI r r r r r � numerator r! zRational.numeratorc C r rI r r r r r � denominator r! zRational.denominatorc C s t | j�t | j� S )a float(self) = self.numerator / self.denominator
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so that ratios of huge integers convert without overflowing.
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edd� �Zedd� �Zedd� �Zedd� �Zed d � �Zed d � �Zd d!� Zed"d#� �Zed$d%� �ZdS )'r z�Integral adds methods that work on integral numbers.
In short, these are conversion to int, pow with modulus, and the
bit-string operations.
r c C r )z int(self)r r r r r �__int__/ r! zIntegral.__int__c C s t | �S )z6Called whenever an index is needed, such as in slicing)rL r r r r � __index__4 r zIntegral.__index__Nc C r )a4 self ** exponent % modulus, but maybe faster.
Accept the modulus argument if you want to support the
3-argument version of pow(). Raise a TypeError if exponent < 0
or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
r )r r, �modulusr r r r- 8 s zIntegral.__pow__c C r )z
self << otherr r r r r �
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other << selfr r r r r � __rlshift__H r! zIntegral.__rlshift__c C r )z
self >> otherr r r r r �
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other >> selfr r r r r � __rrshift__R r! zIntegral.__rrshift__c C r )z self & otherr r r r r �__and__W r! zIntegral.__and__c C r )z other & selfr r r r r �__rand__\ r! zIntegral.__rand__c C r )z self ^ otherr r r r r �__xor__a r! zIntegral.__xor__c C r )z other ^ selfr r r r r �__rxor__f r! zIntegral.__rxor__c C r )z self | otherr r r r r �__or__k r! zIntegral.__or__c C r )z other | selfr r r r r �__ror__p r! zIntegral.__ror__c C r )z~selfr r r r r �
__invert__u r! zIntegral.__invert__c C rC )z float(self) == float(int(self)))rE rL r r r r r4 { rF zIntegral.__float__c C rG )z"Integers are their own numerators.r r r r r rJ rH zIntegral.numeratorc C r )z!Integers have a denominator of 1.� r r r r r rK � r! zIntegral.denominatorrI )r
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