[Python-Dev] Rational approximation methods

[Jeffrey Yasskin]

In the Rational class that I've recently checked into Python 2.6
(http://bugs.python.org/issue1682), it might be nice to provide a
method that, given a particular rational number, returns a nearby
number that's nicer in some way. I know of two reasonable behaviors
for this operation. Since I don't know which is likely to be more
useful, or even if either is useful enough to include in the first
version of the module, I'm coming to you guys for advice. Both were
implemented a while ago in
http://svn.python.org/view/sandbox/trunk/rational/Rational.py?rev=40988&view=markup
and are based on the continued fraction representation of the number
(http://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approximations).

The first returns the closest rational whose denominator is less than
a given integer. For discussion, we might call it
.limit_denominator(), although I'm also looking for good names. This
seems useful for computations in which you want to sacrifice some
accuracy for speed. On the other hand, Decimal may fill the niche for
fast-ish computation that surprises people less than float.

The second returns the simplest rational within some distance. For
instance, it'll prefer 22/7 over 333/106 if both are close enough. We
might call it .simplest_within() for now. This seems useful for
converting from float and displaying results to users, where we prefer
readability over accuracy or have reason to believe that a simpler
fraction might be more correct.

What does the list think?

Jeffrey