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¬ÿ fž( c @ sÍ d Z d d l m Z m Z d d d d d g Z Gd d „ d d e ƒZ Gd
d „ d e ƒ Z e j e ƒ Gd d „ d e ƒ Z e j e
ƒ Gd d „ d e ƒ Z Gd
d „ d e ƒ Z e j e
ƒ d S( u~ Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators.i ( u ABCMetau abstractmethodu Numberu Complexu Realu Rationalu Integralc B s& | Ee Z d Z d Z f Z d Z d S( u NumberuŸ 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).
N( u __name__u
__module__u __qualname__u __doc__u __slots__u Noneu __hash__( u
__locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Number s u metaclassc B s| | Ee Z d Z d Z f Z e d d „ ƒ Z d d „ Z e e d d „ ƒ ƒ Z e e d d „ ƒ ƒ Z
e d
d „ ƒ Z e d d
„ ƒ Z e d d „ ƒ Z
e d d „ ƒ Z d d „ Z d d „ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d! „ ƒ Z e d" d# „ ƒ Z e d$ d% „ ƒ Z e d& d' „ ƒ Z d( d) „ Z d* S(+ u Complexua 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 heterogenous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
c C s d S( u< Return a builtin complex instance. Called for complex(self).N( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __complex__- s u Complex.__complex__c C s
| d k S( u) True if self != 0. Called for bool(self).i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __bool__1 s u Complex.__bool__c C s
t ‚ d S( uX Retrieve the real component of this number.
This should subclass Real.
N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu real5 s u Complex.realc C s
t ‚ d S( u] Retrieve the imaginary component of this number.
This should subclass Real.
N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu imag> s u Complex.imagc C s
t ‚ d S( u self + otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __add__G s u Complex.__add__c C s
t ‚ d S( u other + selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __radd__L s u Complex.__radd__c C s
t ‚ d S( u -selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __neg__Q s u Complex.__neg__c C s
t ‚ d S( u +selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pos__V s u Complex.__pos__c C s | | S( u self - other( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __sub__[ s u Complex.__sub__c C s | | S( u other - self( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rsub___ s u Complex.__rsub__c C s
t ‚ d S( u self * otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __mul__c s u Complex.__mul__c C s
t ‚ d S( u other * selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rmul__h s u Complex.__rmul__c C s
t ‚ d S( u5 self / other: Should promote to float when necessary.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __truediv__m s u Complex.__truediv__c C s
t ‚ d S( u other / selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rtruediv__r s u Complex.__rtruediv__c C s
t ‚ d S( uB self**exponent; should promote to float or complex when necessary.N( u NotImplementedError( u selfu exponent( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pow__w s u Complex.__pow__c C s
t ‚ d S( u base ** selfN( u NotImplementedError( u selfu base( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rpow__| s u Complex.__rpow__c C s
t ‚ d S( u7 Returns the Real distance from 0. Called for abs(self).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __abs__ s u Complex.__abs__c C s
t ‚ d S( u$ (x+y*i).conjugate() returns (x-y*i).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu conjugate† s u Complex.conjugatec C s
t ‚ d S( u
self == otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __eq__‹ s u Complex.__eq__c C s | | k S( u
self != other( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ne__ s u Complex.__ne__N( u __name__u
__module__u __qualname__u __doc__u __slots__u abstractmethodu __complex__u __bool__u propertyu realu imagu __add__u __radd__u __neg__u __pos__u __sub__u __rsub__u __mul__u __rmul__u __truediv__u __rtruediv__u __pow__u __rpow__u __abs__u conjugateu __eq__u __ne__( u
__locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Complex s0 c B s= | Ee Z d Z d Z f Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d$ d
d „ ƒ Z d d
„ Z d d „ Z
e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z d d „ Z e d d „ ƒ Z e d d! „ ƒ Z d" d# „ Z d$ S(% u RealuÜ 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.
c C s
t ‚ d S( uT Any Real can be converted to a native float object.
Called for float(self).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__£ s u Real.__float__c C s
t ‚ d S( uG 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".
N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __trunc__ª s u Real.__trunc__c C s
t ‚ d S( u$ Finds the greatest Integral <= self.N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __floor__· s u Real.__floor__c C s
t ‚ d S( u! Finds the least Integral >= self.N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ceil__¼ s u
Real.__ceil__c C s
t ‚ d S( u¸ 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.
N( u NotImplementedError( u selfu ndigits( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __round__Á s u Real.__round__c C s | | | | f S( u™ divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu
__divmod__Ê s u Real.__divmod__c C s | | | | f S( u™ divmod(other, self): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rdivmod__Ò s u Real.__rdivmod__c C s
t ‚ d S( u) self // other: The floor() of self/other.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __floordiv__Ú s u Real.__floordiv__c C s
t ‚ d S( u) other // self: The floor() of other/self.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu
__rfloordiv__ß s u Real.__rfloordiv__c C s
t ‚ d S( u self % otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __mod__ä s u Real.__mod__c C s
t ‚ d S( u other % selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rmod__é s u
Real.__rmod__c C s
t ‚ d S( uR self < other
< on Reals defines a total ordering, except perhaps for NaN.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __lt__î s u Real.__lt__c C s
t ‚ d S( u
self <= otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __le__õ s u Real.__le__c C s t t | ƒ ƒ S( u( complex(self) == complex(float(self), 0)( u complexu float( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __complex__û s u Real.__complex__c C s |
S( u& Real numbers are their real component.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu realÿ s u Real.realc C s d S( u) Real numbers have no imaginary component.i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu imag s u Real.imagc C s |
S( u Conjugate is a no-op for Reals.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu conjugate s u Real.conjugateN( u __name__u
__module__u __qualname__u __doc__u __slots__u abstractmethodu __float__u __trunc__u __floor__u __ceil__u Noneu __round__u
__divmod__u __rdivmod__u __floordiv__u
__rfloordiv__u __mod__u __rmod__u __lt__u __le__u __complex__u propertyu realu imagu conjugate( u
__locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Real˜ s(
c B s\ | Ee Z d Z d Z f Z e e d d „ ƒ ƒ Z e e d d „ ƒ ƒ Z d d „ Z d S( u Rationalu6 .numerator and .denominator should be in lowest terms.c C s
t ‚ d S( N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu numerator s u Rational.numeratorc C s
t ‚ d S( N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu denominator s u Rational.denominatorc C s | j | j S( u 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.
( u numeratoru denominator( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__ s u Rational.__float__N(
u __name__u
__module__u __qualname__u __doc__u __slots__u propertyu abstractmethodu numeratoru denominatoru __float__( u
__locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Rational s c B sI | Ee Z d Z d Z f Z e d d „ ƒ Z d d „ Z e d$ d d „ ƒ Z e d d „ ƒ Z
e d
d „ ƒ Z e d d
„ ƒ Z e d d „ ƒ Z
e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z e d d „ ƒ Z d d „ Z e d d! „ ƒ Z e d" d# „ ƒ Z d$ S(% u Integralu@ Integral adds a conversion to int and the bit-string operations.c C s
t ‚ d S( u int(self)N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __int__0 s u Integral.__int__c C s
t | ƒ S( u6 Called whenever an index is needed, such as in slicing( u int( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __index__5 s u Integral.__index__c C s
t ‚ d S( u4 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.
N( u NotImplementedError( u selfu exponentu modulus( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pow__9 s u Integral.__pow__c C s
t ‚ d S( u
self << otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu
__lshift__D s u Integral.__lshift__c C s
t ‚ d S( u
other << selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rlshift__I s u Integral.__rlshift__c C s
t ‚ d S( u
self >> otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu
__rshift__N s u Integral.__rshift__c C s
t ‚ d S( u
other >> selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rrshift__S s u Integral.__rrshift__c C s
t ‚ d S( u self & otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __and__X s u Integral.__and__c C s
t ‚ d S( u other & selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rand__] s u Integral.__rand__c C s
t ‚ d S( u self ^ otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __xor__b s u Integral.__xor__c C s
t ‚ d S( u other ^ selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rxor__g s u Integral.__rxor__c C s
t ‚ d S( u self | otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __or__l s u Integral.__or__c C s
t ‚ d S( u other | selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ror__q s u Integral.__ror__c C s
t ‚ d S( u ~selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu
__invert__v s u Integral.__invert__c C s t t | ƒ ƒ S( u float(self) == float(int(self))( u floatu int( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__| s u Integral.__float__c C s |
S( u" Integers are their own numerators.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu numerator€ s u Integral.numeratorc C s d S( u! Integers have a denominator of 1.i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu denominator… s u Integral.denominatorN( u __name__u
__module__u __qualname__u __doc__u __slots__u abstractmethodu __int__u __index__u Noneu __pow__u
__lshift__u __rlshift__u
__rshift__u __rrshift__u __and__u __rand__u __xor__u __rxor__u __or__u __ror__u
__invert__u __float__u propertyu numeratoru denominator( u
__locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Integral+ s(
N( u __doc__u abcu ABCMetau abstractmethodu __all__u Numberu Complexu registeru complexu Realu floatu Rationalu Integralu int( ( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu s u
u
_