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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. )ABCMetaabstractmethodNumberComplexRealRationalIntegralc @ s e Zd ZdZdZdZdS )r zAll 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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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 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$(x+y*i).conjugate() returns (x-y*i).Nr r r r r conjugate s zComplex.conjugatec C s t dS )z
self == otherNr r r r r __eq__ s zComplex.__eq__N)r
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r r r r propertyr r r r r r r r! r" r# r$ r% r' r) r* r+ r, r r r r r sN
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edd Zedd Zedd Zedd Zed d Zd d Zed d! Zed"d# Zd$d% Zd S )'r zTo Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
r c C s t dS )zTAny Real can be converted to a native float object.
Called for float(self).Nr r r r r __float__ s zReal.__float__c C s t dS )aG trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i>0 iff self>0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
Nr r r r r __trunc__ s zReal.__trunc__c C s t dS )z$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 )zRounds 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 )zdivmod(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 )zdivmod(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))complexfloatr 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
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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
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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 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 |
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