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Title: numbers — Numeric abstract base classes — Python 3.13.18 documentation Authors: Venue: pydoc Year: 2001 Canonical: pydoc:numbers@3.13 URL: https://docs.python.org/3.13/library/numbers.html Collector: pydoc OA: true ABSTRACT numbers — Numeric abstract base classes — Python 3.13.18 documentation Navigation index modules | next | previous | Python » 3.13.18 Documentation » The Python standard library » Numeric and Mathematical Modules » numbers — Numeric abstract base classes | Theme Auto Light Dark | numbers — Numeric abstract base classes¶ Source code: Lib/numbers.py The numbers module (PEP 3141) defines a hierarchy of numeric abstract base classes which progressively define more operations. None of the types defined in this module are intended to be instantiated. class numbers.Number¶ The root of the numeric hierarchy. If you just want to check if an argument x is a number, without caring what kind, use isinstance(x, Number). The numeric tower¶ class numbers.Complex¶ Subclasses of this type describe complex numbers and include the operations that work on the built-in complex type. These are: conversions to complex and bool, real, imag, +, -, *, /, **, abs(), conjugate(), ==, and !=. All except - and != are abstract. real¶ Abstract. Retrieves the real component of this number. imag¶ Abstract. Retrieves the imaginary component of this number. abstractmethod conjugate()¶ Abstract. Returns the complex conjugate. For example, (1+3j).conjugate() == (1-3j). class numbers.Real¶ To Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, math.trunc(), round(), math.floor(), math.ceil(), divmod(), //, %, , and =. Real also provides defaults for complex(), real, imag, and conjugate(). class numbers.Rational¶ Subtypes Real and adds numerator and denominator properties. It also provides a default for float(). The numerator and denominator values should be instances of Integral and should be in lowest terms with denominator positive. numerator¶ Abstract. The numerator of this rational number. denominator¶ Abstract. The denominator of this rational number. class numbers.Integral¶ Subtypes Rational and adds a conversion to int. Provides defaults for float(), numerator, and denominator. Adds abstract methods for pow() with modulus and bit-string operations: , &, ^, |, ~. Notes for type implementers¶ Implementers should be careful to make equal numbers equal and hash them to the same values. This may be subtle if there are two different extensions of the real numbers. See also Hashing of numeric types. Adding More Numeric ABCs¶ There are, of course, more possible ABCs for numbers, and this would be a poor hierarchy if it precluded the possibility of adding those. You can add MyFoo between Complex and Real with: class MyFoo(Complex): ... MyFoo.register(Real) Implementing the arithmetic operations¶ We want to implement the arithmetic operations so that mixed-mode operations either call an implementation whose author knew about the types of both arguments, or convert both to the nearest built in type and do the operation there. For subtypes of Integral, this means that __add__() and __radd__() should be defined as: class MyIntegral(Integral): def __add__(self, other): if isinstance(other, MyIntegral): return do_my_adding_stuff(self, other) elif isinstance(other, OtherTypeIKnowAbout): return do_my_other_adding_stuff(self, other) else: return NotImplemented def __radd__(self, other): if isinstance(other, MyIntegral): return do_my_adding_stuff(other, self) elif isinstance(other, OtherTypeIKnowAbout): return do_my_other_adding_stuff(other, self) elif isinstance(other, Integral): return int(other) + int(self) elif isinstance(other, Real): return float(other) + float(self) elif isinstance(other, Complex): return complex(other) + complex(self) else: return NotImplemented There are 5 different cases for a mixed-type operation on subclasses of Complex. I’ll refer to all of the above code that doesn’t refer to MyIntegral and OtherTypeIKnowAbout as “boilerplate”. a will be an instance of A, which is a subtype of Complex (a : A