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� dS )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 e Zd ZdZdZdZdS )r z�All numbers inherit from this class.
If you just want to check if an argument x is a number, without
caring what kind, use isinstance(x, Number).
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__module__� __qualname__�__doc__� __slots__�__hash__r r r � /usr/lib/python3.8/numbers.pyr s )� metaclassc @ s� e Zd ZdZdZedd� �Zdd� Zeedd� ��Z eed d
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edd� �Zdd� Zdd� Zedd� �Zedd� �Zedd � �Zed d � �Zed d � �Zed!d"� �Zed#d$� �Zed%d&� �Zed'd(� �Zd)S )*r ab Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
r c C s dS )z<Return a builtin complex instance. Called for complex(self).Nr ��selfr r r � __complex__- s zComplex.__complex__c C s | dkS )z)True if self != 0. Called for bool(self).r r r r r r �__bool__1 s zComplex.__bool__c C s t �dS )zXRetrieve the real component of this number.
This should subclass Real.
N��NotImplementedErrorr r r r �real5 s z Complex.realc C s t �dS )z]Retrieve the imaginary component of this number.
This should subclass Real.
Nr r r r r �imag> s z Complex.imagc C s t �dS )z self + otherNr �r �otherr r r �__add__G s zComplex.__add__c C s t �dS )z other + selfNr r r r r �__radd__L s zComplex.__radd__c C s t �dS )z-selfNr r r r r �__neg__Q s zComplex.__neg__c C s t �dS )z+selfNr r r r r �__pos__V s zComplex.__pos__c C s
| | S )z self - otherr r r r r �__sub__[ s zComplex.__sub__c C s
| | S )z other - selfr r r r r �__rsub___ s zComplex.__rsub__c C s t �dS )z self * otherNr r r r r �__mul__c s zComplex.__mul__c C s t �dS )z other * selfNr r r r r �__rmul__h s zComplex.__rmul__c C s t �dS )z5self / other: Should promote to float when necessary.Nr r r r r � __truediv__m s zComplex.__truediv__c C s t �dS )z other / selfNr r r r r � __rtruediv__r s zComplex.__rtruediv__c C s t �dS )zBself**exponent; should promote to float or complex when necessary.Nr )r �exponentr r r �__pow__w s zComplex.__pow__c C s t �dS )z base ** selfNr )r �baser r r �__rpow__| s zComplex.__rpow__c C s t �dS )z7Returns the Real distance from 0. Called for abs(self).Nr r r r r �__abs__� s zComplex.__abs__c C s t �dS )z$(x+y*i).conjugate() returns (x-y*i).Nr r r r r � conjugate� s zComplex.conjugatec C s t �dS )z
self == otherNr r r r r �__eq__� s zComplex.__eq__N)r
r r r
r r r r �propertyr r r r r r r r! r" r# r$ r% r' r) r* r+ r, r r r r r sN
c @ s� e Zd ZdZdZedd� �Zedd� �Zedd� �Zed d
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edd� �Zedd� �Zedd� �Zedd� �Zed d � �Zd d � Zed d!� �Zed"d#� �Zd$d%� Zd S )'r z�To Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
r c C s t �dS )zTAny Real can be converted to a native float object.
Called for float(self).Nr r r r r � __float__� s zReal.__float__c C s t �dS )aG trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i>0 iff self>0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
Nr r r r r � __trunc__� s zReal.__trunc__c C s t �dS )z$Finds the greatest Integral <= self.Nr r r r r � __floor__� s zReal.__floor__c C s t �dS )z!Finds the least Integral >= self.Nr r r r r �__ceil__� s z
Real.__ceil__Nc C s t �dS )z�Rounds self to ndigits decimal places, defaulting to 0.
If ndigits is omitted or None, returns an Integral, otherwise
returns a Real. Rounds half toward even.
Nr )r Zndigitsr r r � __round__� s zReal.__round__c C s | | | | fS )z�divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r r r r r �
__divmod__� s zReal.__divmod__c C s || || fS )z�divmod(other, self): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r r r r r � __rdivmod__� s zReal.__rdivmod__c C s t �dS )z)self // other: The floor() of self/other.Nr r r r r � __floordiv__� s zReal.__floordiv__c C s t �dS )z)other // self: The floor() of other/self.Nr r r r r �
__rfloordiv__� s zReal.__rfloordiv__c C s t �dS )z self % otherNr r r r r �__mod__� s z Real.__mod__c C s t �dS )z other % selfNr r r r r �__rmod__� s z
Real.__rmod__c C s t �dS )zRself < other
< on Reals defines a total ordering, except perhaps for NaN.Nr r r r r �__lt__� s z Real.__lt__c C s t �dS )z
self <= otherNr r r r r �__le__� s z Real.__le__c C s t t| ��S )z(complex(self) == complex(float(self), 0))�complex�floatr r r r r � s zReal.__complex__c C s |
S )z&Real numbers are their real component.r r r r r r � s z Real.realc C s dS )z)Real numbers have no imaginary component.r r r r r r r � s z Real.imagc C s |
S )z Conjugate is a no-op for Reals.r r r r r r+ s zReal.conjugate)N)r
r r r
r r r. r/ r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r: r r- r r r+ r r r r r � s@
c @ s< e Zd ZdZdZeedd� ��Zeedd� ��Zdd� Z d S )
r z6.numerator and .denominator should be in lowest terms.r c C s t �d S �Nr r r r r � numerator s zRational.numeratorc C s t �d S r= r r r r r � denominator s zRational.denominatorc C s | j | j S )a float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
)r> r? r r r r r. s zRational.__float__N)
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edd� �Z edd� �Z edd� �Z
edd� �Zedd� �Zedd� �Zedd� �Zed d � �Zed d � �Zd d!� Zed"d#� �Zed$d%� �ZdS )'r z@Integral adds a conversion to int and the bit-string operations.r c C s t �dS )z int(self)Nr r r r r �__int__+ s zIntegral.__int__c C s t | �S )z6Called whenever an index is needed, such as in slicing)�intr r r r � __index__0 s zIntegral.__index__Nc C s t �dS )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.
Nr )r r& �modulusr r r r' 4 s zIntegral.__pow__c C s t �dS )z
self << otherNr r r r r �
__lshift__? s zIntegral.__lshift__c C s t �dS )z
other << selfNr r r r r � __rlshift__D s zIntegral.__rlshift__c C s t �dS )z
self >> otherNr r r r r �
__rshift__I s zIntegral.__rshift__c C s t �dS )z
other >> selfNr r r r r � __rrshift__N s zIntegral.__rrshift__c C s t �dS )z self & otherNr r r r r �__and__S s zIntegral.__and__c C s t �dS )z other & selfNr r r r r �__rand__X s zIntegral.__rand__c C s t �dS )z self ^ otherNr r r r r �__xor__] s zIntegral.__xor__c C s t �dS )z other ^ selfNr r r r r �__rxor__b s zIntegral.__rxor__c C s t �dS )z self | otherNr r r r r �__or__g s zIntegral.__or__c C s t �dS )z other | selfNr r r r r �__ror__l s zIntegral.__ror__c C s t �dS )z~selfNr r r r r �
__invert__q s zIntegral.__invert__c C s t t| ��S )z float(self) == float(int(self)))r< rA r r r r r. w s zIntegral.__float__c C s |
S )z"Integers are their own numerators.r r r r r r> { s zIntegral.numeratorc C s dS )z!Integers have a denominator of 1.� r r r r r r? � s zIntegral.denominator)N)r
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