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„ƒYZeieƒeieƒdS(s~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.

TODO: Fill out more detailed documentation on the operators.iÿÿÿÿ(tdivision(tABCMetatabstractmethodtabstractpropertytNumbertComplextRealtRationaltIntegralcB s eZdZeZdZdZRS(sŸAll numbers inherit from this class.

    If you just want to check if an argument x is a number, without
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    (N(t__name__t
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__metaclass__t	__slots__tNonet__hash__(((s/usr/lib64/python2.6/numbers.pyR
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„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZd„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/python2.6/numbers.pyt__complex__/scC s
|djS(s)True if self != 0. Called for bool(self).i((R((s/usr/lib64/python2.6/numbers.pyt__nonzero__4scC s
t‚dS(sXRetrieve the real component of this number.

        This should subclass Real.
        N(tNotImplementedError(R((s/usr/lib64/python2.6/numbers.pytreal8scC s
t‚dS(sXRetrieve the real component of this number.

        This should subclass Real.
        N(R(R((s/usr/lib64/python2.6/numbers.pytimag@scC s
t‚dS(sself + otherN(R(Rtother((s/usr/lib64/python2.6/numbers.pyt__add__HscC s
t‚dS(sother + selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__radd__MscC s
t‚dS(s-selfN(R(R((s/usr/lib64/python2.6/numbers.pyt__neg__RscC s
t‚dS(s+selfN(R(R((s/usr/lib64/python2.6/numbers.pyt__pos__WscC s	||S(sself - other((RR((s/usr/lib64/python2.6/numbers.pyt__sub__\scC s	||S(sother - self((RR((s/usr/lib64/python2.6/numbers.pyt__rsub__`scC s
t‚dS(sself * otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__mul__dscC s
t‚dS(sother * selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rmul__iscC s
t‚dS(sPself / other without __future__ division

        May promote to float.
        N(R(RR((s/usr/lib64/python2.6/numbers.pyt__div__nscC s
t‚dS(s(other / self without __future__ divisionN(R(RR((s/usr/lib64/python2.6/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/python2.6/numbers.pyt__truediv__{scC s
t‚dS(s%other / self with __future__ divisionN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rtruediv__ƒscC s
t‚dS(sBself**exponent; should promote to float or complex when necessary.N(R(Rtexponent((s/usr/lib64/python2.6/numbers.pyt__pow__ˆscC s
t‚dS(sbase ** selfN(R(Rtbase((s/usr/lib64/python2.6/numbers.pyt__rpow__scC s
t‚dS(s7Returns the Real distance from 0. Called for abs(self).N(R(R((s/usr/lib64/python2.6/numbers.pyt__abs__’scC s
t‚dS(s$(x+y*i).conjugate() returns (x-y*i).N(R(R((s/usr/lib64/python2.6/numbers.pyt	conjugate—scC s
t‚dS(s
self == otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__eq__œscC s||jS(s
self != other((RR((s/usr/lib64/python2.6/numbers.pyt__ne__¡s((R	R
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RRRRRRRRRRRRRRRR R!R"R$R&R'R(R)R*(((s/usr/lib64/python2.6/numbers.pyR"s0				cB sÎeZdZdZed„ƒZed„ƒZd„Zd„Zed„ƒZ	ed„ƒZ
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„ƒZd„Zed„ƒZed
„ƒZd„ZRS(sÜTo 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.
    cC s
t‚dS(sTAny Real can be converted to a native float object.

        Called for float(self).N(R(R((s/usr/lib64/python2.6/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/python2.6/numbers.pyt	__trunc__»scC 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/python2.6/numbers.pyt
__divmod__ÈscC 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/python2.6/numbers.pyt__rdivmod__ÐscC s
t‚dS(s)self // other: The floor() of self/other.N(R(RR((s/usr/lib64/python2.6/numbers.pyt__floordiv__ØscC s
t‚dS(s)other // self: The floor() of other/self.N(R(RR((s/usr/lib64/python2.6/numbers.pyt
__rfloordiv__ÝscC s
t‚dS(sself % otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__mod__âscC s
t‚dS(sother % selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rmod__çscC s
t‚dS(sRself < other

        < on Reals defines a total ordering, except perhaps for NaN.N(R(RR((s/usr/lib64/python2.6/numbers.pyt__lt__ìscC s
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self <= otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__le__óscC stt|ƒƒS(s(complex(self) == complex(float(self), 0)(tcomplextfloat(R((s/usr/lib64/python2.6/numbers.pyRùscC s|
S(s&Real numbers are their real component.((R((s/usr/lib64/python2.6/numbers.pyRýscC sdS(s)Real numbers have no imaginary component.i((R((s/usr/lib64/python2.6/numbers.pyRscC s|
S(sConjugate is a no-op for Reals.((R((s/usr/lib64/python2.6/numbers.pyR(s((R	R
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RR+R,R-R.R/R0R1R2R3R4RtpropertyRRR((((s/usr/lib64/python2.6/numbers.pyR©s 
			cB s;eZdZdZed„ƒZed„ƒZd„ZRS(s6.numerator and .denominator should be in lowest terms.cC s
t‚dS(N(R(R((s/usr/lib64/python2.6/numbers.pyt	numeratorscC s
t‚dS(N(R(R((s/usr/lib64/python2.6/numbers.pytdenominatorscC s|i|iS(sfloat(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.

        (R8R9(R((s/usr/lib64/python2.6/numbers.pyR+s((R	R
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„ƒZed„ƒZd„Zed„ƒZed„ƒZRS(sAIntegral adds a conversion to long and the bit-string operations.cC s
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long(self)N(R(R((s/usr/lib64/python2.6/numbers.pyt__long__,scC s
t|ƒS(sindex(self)(tlong(R((s/usr/lib64/python2.6/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/python2.6/numbers.pyR$5s	cC s
t‚dS(s
self << otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt
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other >> selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rrshift__OscC s
t‚dS(sself & otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__and__TscC s
t‚dS(sother & selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rand__YscC s
t‚dS(sself ^ otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__xor__^scC s
t‚dS(sother ^ selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__rxor__cscC s
t‚dS(sself | otherN(R(RR((s/usr/lib64/python2.6/numbers.pyt__or__hscC s
t‚dS(sother | selfN(R(RR((s/usr/lib64/python2.6/numbers.pyt__ror__mscC s
t‚dS(s~selfN(R(R((s/usr/lib64/python2.6/numbers.pyt
__invert__rscC stt|ƒƒS(s float(self) == float(long(self))(R6R;(R((s/usr/lib64/python2.6/numbers.pyR+xscC s|
S(s"Integers are their own numerators.((R((s/usr/lib64/python2.6/numbers.pyR8|scC sdS(s!Integers have a denominator of 1.i((R((s/usr/lib64/python2.6/numbers.pyR9s(N(R	R
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