Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
 
TODO: Fill out more detailed documentation on the operators.

Classes
		__builtin__.object Number Complex Real Rational Integral   class Complex(Number)     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.     Method resolution order: Complex Number __builtin__.object Methods defined here: __abs__(self) Returns the Real distance from 0. Called for abs(self). __add__(self, other) self + other __complex__(self) Return a builtin complex instance. Called for complex(self). __div__(self, other) self / other without __future__ division   May promote to float. __eq__(self, other) self == other __mul__(self, other) self * other __ne__(self, other) self != other __neg__(self) -self __nonzero__(self) True if self != 0. Called for bool(self). __pos__(self) +self __pow__(self, exponent) self**exponent; should promote to float or complex when necessary. __radd__(self, other) other + self __rdiv__(self, other) other / self without __future__ division __rmul__(self, other) other * self __rpow__(self, base) base ** self __rsub__(self, other) other - self __rtruediv__(self, other) other / self with __future__ division __sub__(self, other) self - other __truediv__(self, other) self / other with __future__ division.   Should promote to float when necessary. conjugate(self) (x+y*i).conjugate() returns (x-y*i). Data descriptors defined here: imag Retrieve the imaginary component of this number.   This should subclass Real. real Retrieve the real component of this number.   This should subclass Real. Data and other attributes defined here: __abstractmethods__ = frozenset(['__abs__', '__add__', '__complex__', '__div__', '__eq__', '__mul__', ...]) Data and other attributes inherited from Number: __hash__ = None __metaclass__ = <class 'abc.ABCMeta'> Metaclass for defining Abstract Base Classes (ABCs).   Use this metaclass to create an ABC.  An ABC can be subclassed directly, and then acts as a mix-in class.  You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as 'virtual subclasses' -- these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won't show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).   class Integral(Rational)     Integral adds a conversion to long and the bit-string operations.     Method resolution order: Integral Rational Real Complex Number __builtin__.object Methods defined here: __and__(self, other) self & other __float__(self) float(self) == float(long(self)) __index__(self) Called whenever an index is needed, such as in slicing __invert__(self) ~self __long__(self) long(self) __lshift__(self, other) self << other __or__(self, other) self | other __pow__(self, exponent, modulus=None) 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. __rand__(self, other) other & self __rlshift__(self, other) other << self __ror__(self, other) other | self __rrshift__(self, other) other >> self __rshift__(self, other) self >> other __rxor__(self, other) other ^ self __xor__(self, other) self ^ other Data descriptors defined here: denominator Integers have a denominator of 1. numerator Integers are their own numerators. Data and other attributes defined here: __abstractmethods__ = frozenset(['__abs__', '__add__', '__and__', '__div__', '__eq__', '__floordiv__', ...]) Methods inherited from Real: __complex__(self) complex(self) == complex(float(self), 0) __divmod__(self, other) divmod(self, other): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __floordiv__(self, other) self // other: The floor() of self/other. __le__(self, other) self <= other __lt__(self, other) self < other   < on Reals defines a total ordering, except perhaps for NaN. __mod__(self, other) self % other __rdivmod__(self, other) divmod(other, self): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __rfloordiv__(self, other) other // self: The floor() of other/self. __rmod__(self, other) other % self __trunc__(self) 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". conjugate(self) Conjugate is a no-op for Reals. Data descriptors inherited from Real: imag Real numbers have no imaginary component. real Real numbers are their real component. Methods inherited from Complex: __abs__(self) Returns the Real distance from 0. Called for abs(self). __add__(self, other) self + other __div__(self, other) self / other without __future__ division   May promote to float. __eq__(self, other) self == other __mul__(self, other) self * other __ne__(self, other) self != other __neg__(self) -self __nonzero__(self) True if self != 0. Called for bool(self). __pos__(self) +self __radd__(self, other) other + self __rdiv__(self, other) other / self without __future__ division __rmul__(self, other) other * self __rpow__(self, base) base ** self __rsub__(self, other) other - self __rtruediv__(self, other) other / self with __future__ division __sub__(self, other) self - other __truediv__(self, other) self / other with __future__ division.   Should promote to float when necessary. Data and other attributes inherited from Number: __hash__ = None __metaclass__ = <class 'abc.ABCMeta'> Metaclass for defining Abstract Base Classes (ABCs).   Use this metaclass to create an ABC.  An ABC can be subclassed directly, and then acts as a mix-in class.  You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as 'virtual subclasses' -- these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won't show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).   class Number(__builtin__.object)     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).     Data and other attributes defined here: __abstractmethods__ = frozenset([]) __hash__ = None __metaclass__ = <class 'abc.ABCMeta'> Metaclass for defining Abstract Base Classes (ABCs).   Use this metaclass to create an ABC.  An ABC can be subclassed directly, and then acts as a mix-in class.  You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as 'virtual subclasses' -- these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won't show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).   class Rational(Real)     .numerator and .denominator should be in lowest terms.     Method resolution order: Rational Real Complex Number __builtin__.object Methods defined here: __float__(self) 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. Data descriptors defined here: denominator numerator Data and other attributes defined here: __abstractmethods__ = frozenset(['__abs__', '__add__', '__div__', '__eq__', '__floordiv__', '__le__', ...]) Methods inherited from Real: __complex__(self) complex(self) == complex(float(self), 0) __divmod__(self, other) divmod(self, other): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __floordiv__(self, other) self // other: The floor() of self/other. __le__(self, other) self <= other __lt__(self, other) self < other   < on Reals defines a total ordering, except perhaps for NaN. __mod__(self, other) self % other __rdivmod__(self, other) divmod(other, self): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __rfloordiv__(self, other) other // self: The floor() of other/self. __rmod__(self, other) other % self __trunc__(self) 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". conjugate(self) Conjugate is a no-op for Reals. Data descriptors inherited from Real: imag Real numbers have no imaginary component. real Real numbers are their real component. Methods inherited from Complex: __abs__(self) Returns the Real distance from 0. Called for abs(self). __add__(self, other) self + other __div__(self, other) self / other without __future__ division   May promote to float. __eq__(self, other) self == other __mul__(self, other) self * other __ne__(self, other) self != other __neg__(self) -self __nonzero__(self) True if self != 0. Called for bool(self). __pos__(self) +self __pow__(self, exponent) self**exponent; should promote to float or complex when necessary. __radd__(self, other) other + self __rdiv__(self, other) other / self without __future__ division __rmul__(self, other) other * self __rpow__(self, base) base ** self __rsub__(self, other) other - self __rtruediv__(self, other) other / self with __future__ division __sub__(self, other) self - other __truediv__(self, other) self / other with __future__ division.   Should promote to float when necessary. Data and other attributes inherited from Number: __hash__ = None __metaclass__ = <class 'abc.ABCMeta'> Metaclass for defining Abstract Base Classes (ABCs).   Use this metaclass to create an ABC.  An ABC can be subclassed directly, and then acts as a mix-in class.  You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as 'virtual subclasses' -- these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won't show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).   class Real(Complex)     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.     Method resolution order: Real Complex Number __builtin__.object Methods defined here: __complex__(self) complex(self) == complex(float(self), 0) __divmod__(self, other) divmod(self, other): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __float__(self) Any Real can be converted to a native float object.   Called for float(self). __floordiv__(self, other) self // other: The floor() of self/other. __le__(self, other) self <= other __lt__(self, other) self < other   < on Reals defines a total ordering, except perhaps for NaN. __mod__(self, other) self % other __rdivmod__(self, other) divmod(other, self): The pair (self // other, self % other).   Sometimes this can be computed faster than the pair of operations. __rfloordiv__(self, other) other // self: The floor() of other/self. __rmod__(self, other) other % self __trunc__(self) 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". conjugate(self) Conjugate is a no-op for Reals. Data descriptors defined here: imag Real numbers have no imaginary component. real Real numbers are their real component. Data and other attributes defined here: __abstractmethods__ = frozenset(['__abs__', '__add__', '__div__', '__eq__', '__float__', '__floordiv__', ...]) Methods inherited from Complex: __abs__(self) Returns the Real distance from 0. Called for abs(self). __add__(self, other) self + other __div__(self, other) self / other without __future__ division   May promote to float. __eq__(self, other) self == other __mul__(self, other) self * other __ne__(self, other) self != other __neg__(self) -self __nonzero__(self) True if self != 0. Called for bool(self). __pos__(self) +self __pow__(self, exponent) self**exponent; should promote to float or complex when necessary. __radd__(self, other) other + self __rdiv__(self, other) other / self without __future__ division __rmul__(self, other) other * self __rpow__(self, base) base ** self __rsub__(self, other) other - self __rtruediv__(self, other) other / self with __future__ division __sub__(self, other) self - other __truediv__(self, other) self / other with __future__ division.   Should promote to float when necessary. Data and other attributes inherited from Number: __hash__ = None __metaclass__ = <class 'abc.ABCMeta'> Metaclass for defining Abstract Base Classes (ABCs).   Use this metaclass to create an ABC.  An ABC can be subclassed directly, and then acts as a mix-in class.  You can also register unrelated concrete classes (even built-in classes) and unrelated ABCs as 'virtual subclasses' -- these and their descendants will be considered subclasses of the registering ABC by the built-in issubclass() function, but the registering ABC won't show up in their MRO (Method Resolution Order) nor will method implementations defined by the registering ABC be callable (not even via super()).

Data
		__all__ = ['Number', 'Complex', 'Real', 'Rational', 'Integral']