PEP: 239 Title: Adding a Rational Type to Python Version: $Revision$ Author: pep@zadka.site.co.il (Moshe Zadka) Status: Draft Type: Standards Track Created: 11-Mar-2001 Python-Version: 2.2 Post-History: 16-Mar-2001 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 another PEP[1]. 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? References [1] PEP 240, Adding a Rational Literal to Python, Zadka, http://www.python.org/peps/pep-0240.html Copyright This document has been placed in the public domain. Local Variables: mode: indented-text indent-tabs-mode: nil End: