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��YZej e�ej e�dS(s~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.

TODO: Fill out more detailed documentation on the operators.i����(tdivision(tABCMetatabstractmethodtabstractpropertytNumbertComplextRealtRationaltIntegralcB s eZdZeZdZdZRS(s�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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��Zed��Zed��Zed��Zed��Zed��Zed��Zed��Zed��Zd�ZRS(saComplex 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.
cC sdS(s<Return a builtin complex instance. Called for complex(self).N((tself((s/usr/lib64/python2.7/numbers.pyt __complex__/tcC s
|dkS(s)True if self != 0. Called for bool(self).i((R((s/usr/lib64/python2.7/numbers.pyt __nonzero__4scC s
t�dS(sXRetrieve the real component of this number.

This should subclass Real.
N(tNotImplementedError(R((s/usr/lib64/python2.7/numbers.pytreal8scC s
t�dS(s]Retrieve the imaginary component of this number.

This should subclass Real.
N(R(R((s/usr/lib64/python2.7/numbers.pytimag@scC s
t�dS(s self + otherN(R(Rtother((s/usr/lib64/python2.7/numbers.pyt__add__HscC s
t�dS(s other + selfN(R(RR((s/usr/lib64/python2.7/numbers.pyt__radd__MscC s
t�dS(s-selfN(R(R((s/usr/lib64/python2.7/numbers.pyt__neg__RscC s
t�dS(s+selfN(R(R((s/usr/lib64/python2.7/numbers.pyt__pos__WscC s || S(s self - other((RR((s/usr/lib64/python2.7/numbers.pyt__sub__\scC s | |S(s other - self((RR((s/usr/lib64/python2.7/numbers.pyt__rsub__`scC s
t�dS(s self * otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__mul__dscC s
t�dS(s other * selfN(R(RR((s/usr/lib64/python2.7/numbers.pyt__rmul__iscC s
t�dS(sPself / other without __future__ division

May promote to float.
N(R(RR((s/usr/lib64/python2.7/numbers.pyt__div__nscC s
t�dS(s(other / self without __future__ divisionN(R(RR((s/usr/lib64/python2.7/numbers.pyt__rdiv__vscC s
t�dS(s`self / other with __future__ division.

Should promote to float when necessary.
N(R(RR((s/usr/lib64/python2.7/numbers.pyt __truediv__{scC s
t�dS(s%other / self with __future__ divisionN(R(RR((s/usr/lib64/python2.7/numbers.pyt __rtruediv__�scC s
t�dS(sBself**exponent; should promote to float or complex when necessary.N(R(Rtexponent((s/usr/lib64/python2.7/numbers.pyt__pow__�scC s
t�dS(s base ** selfN(R(Rtbase((s/usr/lib64/python2.7/numbers.pyt__rpow__�scC s
t�dS(s7Returns the Real distance from 0. Called for abs(self).N(R(R((s/usr/lib64/python2.7/numbers.pyt__abs__�scC s
t�dS(s$(x+y*i).conjugate() returns (x-y*i).N(R(R((s/usr/lib64/python2.7/numbers.pyt conjugate�scC s
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self == otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__eq__�scC s ||k S(s
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RRRRRRRRRRRRRRR R!R"R#R%R'R(R)R*R+(((s/usr/lib64/python2.7/numbers.pyR"s0    cB s�eZdZdZed��Zed��Zd�Zd�Zed��Z ed��Z
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��Zd�ZRS(s�To Complex, Real adds the operations that work on real numbers.

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%, <, <=, >, and >=.

Real also provides defaults for the derived operations.
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t�dS(sTAny Real can be converted to a native float object.

Called for float(self).N(R(R((s/usr/lib64/python2.7/numbers.pyt __float__�scC s
t�dS(sGtrunc(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(R(R((s/usr/lib64/python2.7/numbers.pyt __trunc__�s cC s||||fS(s�divmod(self, other): The pair (self // other, self % other).

Sometimes this can be computed faster than the pair of
operations.
((RR((s/usr/lib64/python2.7/numbers.pyt
__divmod__�scC s||||fS(s�divmod(other, self): The pair (self // other, self % other).

Sometimes this can be computed faster than the pair of
operations.
((RR((s/usr/lib64/python2.7/numbers.pyt __rdivmod__�scC s
t�dS(s)self // other: The floor() of self/other.N(R(RR((s/usr/lib64/python2.7/numbers.pyt __floordiv__�scC s
t�dS(s)other // self: The floor() of other/self.N(R(RR((s/usr/lib64/python2.7/numbers.pyt
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t�dS(s self % otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__mod__�scC s
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t�dS(sRself < other

< on Reals defines a total ordering, except perhaps for NaN.N(R(RR((s/usr/lib64/python2.7/numbers.pyt__lt__�scC s
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self <= otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__le__�scC stt|��S(s(complex(self) == complex(float(self), 0)(tcomplextfloat(R((s/usr/lib64/python2.7/numbers.pyR�scC s|
S(s&Real numbers are their real component.((R((s/usr/lib64/python2.7/numbers.pyR�scC sdS(s)Real numbers have no imaginary component.i((R((s/usr/lib64/python2.7/numbers.pyRscC s|
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  cB s;eZdZdZed��Zed��Zd�ZRS(s6.numerator and .denominator should be in lowest terms.cC s
t�dS(N(R(R((s/usr/lib64/python2.7/numbers.pyt numeratorscC s
t�dS(N(R(R((s/usr/lib64/python2.7/numbers.pyt denominatorscC s|j|jS(s 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.

(R9R:(R((s/usr/lib64/python2.7/numbers.pyR,s((R R
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long(self)N(R(R((s/usr/lib64/python2.7/numbers.pyt__long__,scC s
t|�S(s6Called whenever an index is needed, such as in slicing(tlong(R((s/usr/lib64/python2.7/numbers.pyt __index__1scC s
t�dS(s4self ** 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(R(RR$tmodulus((s/usr/lib64/python2.7/numbers.pyR%5s cC s
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t�dS(s self & otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__and__TscC s
t�dS(s other & selfN(R(RR((s/usr/lib64/python2.7/numbers.pyt__rand__YscC s
t�dS(s self ^ otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__xor__^scC s
t�dS(s other ^ selfN(R(RR((s/usr/lib64/python2.7/numbers.pyt__rxor__cscC s
t�dS(s self | otherN(R(RR((s/usr/lib64/python2.7/numbers.pyt__or__hscC s
t�dS(s other | selfN(R(RR((s/usr/lib64/python2.7/numbers.pyt__ror__mscC s
t�dS(s~selfN(R(R((s/usr/lib64/python2.7/numbers.pyt
__invert__rscC stt|��S(s float(self) == float(long(self))(R7R<(R((s/usr/lib64/python2.7/numbers.pyR,xscC s|
S(s"Integers are their own numerators.((R((s/usr/lib64/python2.7/numbers.pyR9|scC sdS(s!Integers have a denominator of 1.i((R((s/usr/lib64/python2.7/numbers.pyR:�s(N(R R
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