Rationals?

[Bengt Richter]

On Wed, 17 Nov 2004 19:47:27 -0800, Josiah Carlson <jcarlson at uci.edu> wrote:

>
>Mike Meyer <mwm at mired.org> wrote:
>> 
>> With the decimals and the unification of int and long coming, it's natural
>> (for me, anyway) to wonder how much interest there is in a rational type.
>> There are two PEPs (239 and 240), and the Guido rejects them as no one
>> seems interested in doing the work, but points out that the python
>> distribution comes with examples/Demo/classes/Rat.py.
>> 
>> I propose - in the spirit of "batteries included" - that Rat.py be
>> cleaned up some (mostly to take advantage of the union of ints and
>> longs) and moved into the standard library.
>> 
>> Any good reasons not to do this?
>
>Update the PEP, do the work, and offer a good rational number object (if
>you are interested in doing such). I have personally written at least
>two different rational classes, and I am aware of at least 3 others
>(though I can't remember their names).
>
>If it is implemented in Python; stay away from the binary GCD algorithm,
>Euclid's is faster.
>
I just looked at Rat.py in the demos, and I am wondering why floating point
is at all included. IMO rationals should be exact, and unless you define
what exact value you would like to have a floating point value represent (e.g.,
all available bits, or some rounding specification) you don't have a way
to make an exact rational. With longs there is no legal floating point double
number whose value can't be represented exactly as a rational, so there's no
problem except deciding. Likewise any floating point string literal can be
converted exactly, e.g., '123.4e-5' => Rat(1234, 1000000) etc., which I think
can be handy. BTW, IIRC complex is implemented strictly with floating point pairs,
so that doesn't seem satisfactory, unless a new complex class is implemented using
rational pairs. Otherwise I'd say leave complex out.

Obviously fractional powers can produce non-rational results, so that poses
a design problem if you want to handle them at all.

Anyway, am I the only one who thinks that rational should be exact?

Regards,
Bengt Richter