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#ˆl–ß=¿JJj"Tâ‚ ÆÛ¸ÔÅ£Ï ƒh¹Î¿Ì1 ˆÆÏ „eïοÌ(b# Copyright 2007 Google, Inc. All Rights Reserved. # Licensed to PSF under a Contributor Agreement. """Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.""" from abc import ABCMeta, abstractmethod __all__ = ["Number", "Complex", "Real", "Rational", "Integral"] class Number(metaclass=ABCMeta): """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). """ __slots__ = () # Concrete numeric types must provide their own hash implementation __hash__ = None ## Notes on Decimal ## ---------------- ## Decimal has all of the methods specified by the Real abc, but it should ## not be registered as a Real because decimals do not interoperate with ## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But, ## abstract reals are expected to interoperate (i.e. R1 + R2 should be ## expected to work if R1 and R2 are both Reals). 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 heterogeneous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. """ __slots__ = () @abstractmethod def __complex__(self): """Return a builtin complex instance. Called for complex(self).""" def __bool__(self): """True if self != 0. Called for bool(self).""" return self != 0 @property @abstractmethod def real(self): """Retrieve the real component of this number. This should subclass Real. """ raise NotImplementedError @property @abstractmethod def imag(self): """Retrieve the imaginary component of this number. This should subclass Real. """ raise NotImplementedError @abstractmethod def __add__(self, other): """self + other""" raise NotImplementedError @abstractmethod def __radd__(self, other): """other + self""" raise NotImplementedError @abstractmethod def __neg__(self): """-self""" raise NotImplementedError @abstractmethod def __pos__(self): """+self""" raise NotImplementedError def __sub__(self, other): """self - other""" return self + -other def __rsub__(self, other): """other - self""" return -self + other @abstractmethod def __mul__(self, other): """self * other""" raise NotImplementedError @abstractmethod def __rmul__(self, other): """other * self""" raise NotImplementedError @abstractmethod def __truediv__(self, other): """self / other: Should promote to float when necessary.""" raise NotImplementedError @abstractmethod def __rtruediv__(self, other): """other / self""" raise NotImplementedError @abstractmethod def __pow__(self, exponent): """self**exponent; should promote to float or complex when necessary.""" raise NotImplementedError @abstractmethod def __rpow__(self, base): """base ** self""" raise NotImplementedError @abstractmethod def __abs__(self): """Returns the Real distance from 0. Called for abs(self).""" raise NotImplem