PEP: 239
Title: Adding a Rational Type to Python
Author: Christopher A. Craig <python-pep@ccraig.org>, Moshe Zadka <moshez@zadka.site.co.il>
Status: Rejected
Type: Standards Track
Created: 11-Mar-2001
Python-Version: 2.2
Post-History: 16-Mar-2001

.. rejected::

   The needs outlined in the rationale section
   have been addressed to some extent by the acceptance of :pep:`327`
   for decimal arithmetic.  Guido also noted, "Rational arithmetic
   was the default 'exact' arithmetic in ABC and it did not work out as
   expected".  See the python-dev discussion on 17 June 2005 [1]_.

   *Postscript:* With the acceptance of :pep:`3141`, "A Type Hierarchy
   for Numbers", a 'Rational' numeric abstract base class was added
   with a concrete implementation in the 'fractions' module.



Abstract
========

Python has no numeric type with the semantics of an unboundedly
precise rational number.  This proposal explains the semantics of
such a type, and suggests builtin functions and literals to
support such a type.  This PEP suggests no literals for rational
numbers; that is left for :pep:`another PEP <240>`.


Rationale
=========

While sometimes slower and more memory intensive (in general,
unboundedly so) rational arithmetic captures more closely the
mathematical ideal of numbers, and tends to have behavior which is
less surprising to newbies.  Though many Python implementations of
rational numbers have been written, none of these exist in the
core, or are documented in any way.  This has made them much less
accessible to people who are less Python-savvy.


RationalType
============

There will be a new numeric type added called ``RationalType``.  Its
unary operators will do the obvious thing.  Binary operators will
coerce integers and long integers to rationals, and rationals to
floats and complexes.

The following attributes will be supported: ``.numerator`` and
``.denominator``.  The language definition will promise that::

    r.denominator * r == r.numerator

that the GCD of the numerator and the denominator is 1 and that
the denominator is positive.

The method ``r.trim(max_denominator)`` will return the closest
rational ``s`` to ``r`` such that ``abs(s.denominator) <= max_denominator``.


The rational() Builtin
======================

This function will have the signature ``rational(n, d=1)``.  ``n`` and ``d``
must both be integers, long integers or rationals.  A guarantee is
made that::

    rational(n, d) * d == n


Open Issues
===========

- Maybe the type should be called rat instead of rational.
  Somebody proposed that we have "abstract" pure mathematical
  types named complex, real, rational, integer, and "concrete"
  representation types with names like float, rat, long, int.

- Should a rational number with an integer value be allowed as a
  sequence index?  For example, should ``s[5/3 - 2/3]`` be equivalent
  to ``s[1]``?

- Should ``shift`` and ``mask`` operators be allowed for rational numbers?
  For rational numbers with integer values?

- Marcin 'Qrczak' Kowalczyk summarized the arguments for and
  against unifying ints with rationals nicely on c.l.py

  Arguments for unifying ints with rationals:

  - Since ``2 == 2/1`` and maybe ``str(2/1) == '2'``, it reduces surprises
    where objects seem equal but behave differently.

  - ``/`` can be freely used for integer division when I *know* that
    there is no remainder (if I am wrong and there is a remainder,
    there will probably be some exception later).

  Arguments against:

  - When I use the result of ``/`` as a sequence index, it's usually
    an error which should not be hidden by making the program
    working for some data, since it will break for other data.

  - (this assumes that after unification int and rational would be
    different types:) Types should rarely depend on values. It's
    easier to reason when the type of a variable is known: I know
    how I can use it. I can determine that something is an int and
    expect that other objects used in this place will be ints too.

  - (this assumes the same type for them:) Int is a good type in
    itself, not to be mixed with rationals.  The fact that
    something is an integer should be expressible as a statement
    about its type. Many operations require ints and don't accept
    rationals. It's natural to think about them as about different
    types.


References
==========

.. [1] Raymond Hettinger, Propose rejection of PEPs 239 and 240 -- a builtin
       rational type and rational literals
       https://mail.python.org/pipermail/python-dev/2005-June/054281.html

Copyright
=========

This document has been placed in the public domain.
