About Rational Number (PEP 239/PEP 240)

[Mel]

Steven D'Aprano wrote:

> Yes, but my point (badly put, I admit) was that people find fractions far 
> easier to work with than they find floating point numbers. 

I'm not so sure.  I got caught by the comic XKCD's 
infinite-resistor-grid thing, and simplified it to a ladder network -- 
call it L -- made up of 2 1-ohm resistors in series with a 1-ohm 
resistor paralleled by L.  Simulating this -- assuming an arbitrary 
endpoint with resistance 3 -- well, it takes a little thought to 
decide that 11/15 < 3/4, and a lot more to decide the same thing for 
153/209 and thus decide whether the series is coming or going.

Then when you work out the right answer from

L = 2 + (L / (L+1))

that answer depends on sqrt(12), which Rationals handle just as badly 
as floats, and at far greater expense.

I wrote a Rational class back when I was learning to do these things 
in Python, and it was actually pretty easy: a dash of GCD, a pinch of 
partial fractions, and a lot of following the Python Reference Manual. 
    It eventually worked as advertised, but I haven't used it since. 
It could stand to be updated to use the __new__ method and produce 
genuinely immutable instances, if I could find the source.

	Mel.
And with any
> rational data type worth the name, you simply should never get anything 
> as unintuitive as this:
> 
>>>> from __future__ import division
>>>> 4/10 + 2/10 == 6/10
> False
> 
> 
>