2001-03-15 23:24:17 -05:00
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PEP: 239
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Title: Adding a Rational Type to Python
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Version: $Revision$
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Author: pep@zadka.site.co.il (Moshe Zadka)
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Status: Draft
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Type: Standards Track
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Created: 11-Mar-2001
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Python-Version: 2.2
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2001-03-16 11:02:24 -05:00
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Post-History: 16-Mar-2001
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2001-03-15 23:24:17 -05:00
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Abstract
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Python has no numeric type with the semantics of an unboundedly
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precise rational number. This proposal explains the semantics of
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such a type, and suggests builtin functions and literals to
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support such a type. This PEP suggests no literals for rational
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numbers; that is left for another PEP[1].
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Rationale
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While sometimes slower and more memory intensive (in general,
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unboundedly so) rational arithmetic captures more closely the
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mathematical ideal of numbers, and tends to have behavior which is
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less surprising to newbies. Though many Python implementations of
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rational numbers have been written, none of these exist in the
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core, or are documented in any way. This has made them much less
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accessible to people who are less Python-savvy.
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RationalType
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There will be a new numeric type added called RationalType. Its
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unary operators will do the obvious thing. Binary operators will
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coerce integers and long integers to rationals, and rationals to
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floats and complexes.
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The following attributes will be supported: .numerator and
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2001-03-19 14:36:46 -05:00
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.denominator. The language definition will promise that
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r.denominator * r == r.numerator
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2001-03-19 14:36:46 -05:00
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that the GCD of the numerator and the denominator is 1 and that
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the denominator is positive.
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The method r.trim(max_denominator) will return the closest
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rational s to r such that abs(s.denominator) <= max_denominator.
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The rational() Builtin
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This function will have the signature rational(n, d=1). n and d
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must both be integers, long integers or rationals. A guarantee is
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made that
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rational(n, d) * d == n
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2001-07-29 05:49:26 -04:00
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Open Issues
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- Maybe the type should be called rat instead of rational.
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Somebody proposed that we have "abstract" pure mathematical
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types named complex, real, rational, integer, and "concrete"
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representation types with names like float, rat, long, int.
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- Should a rational number with an integer value be allowed as a
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sequence index? For example, should s[5/3 - 2/3] be equivalent
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to s[1]?
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- Should shift and mask operators be allowed for rational numbers?
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For rational numbers with integer values?
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2001-03-15 23:24:17 -05:00
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References
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[1] PEP 240, Adding a Rational Literal to Python, Zadka,
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2001-07-05 15:20:16 -04:00
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http://www.python.org/peps/pep-0240.html
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2001-03-15 23:24:17 -05:00
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Copyright
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This document has been placed in the public domain.
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Local Variables:
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mode: indented-text
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indent-tabs-mode: nil
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End:
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