[issue1682] Move Demo/classes/Rat.py to Lib/rational.py and fix it up.

[Mark Dickinson]

Mark Dickinson added the comment:

The latest version of rational.py looks good to me---nice work!  (I haven't looked properly at 
numbers.py or test_rational.py, yet.  I do plan to, eventually.)

I do think it's important to be able to create Rational instances from strings:  e.g., for 
easy reading from and writing to files.  But maybe I'm alone in this opinion.  You say there's 
more than one possible format---what other formats were you considering?

And since you pointed it out, I think Rational(Rational(a, b)) should work too.

There's also the not-entirely-insignificant matter of documentation :)

Other than that, I don't see why this shouldn't go in.

Other comments:

I have a weak preference for no parentheses on the str() of a Rational, but it's no big deal 
either way.

I agree that equality and comparisons are messy.  This seems almost inevitable:  one obvious 
cause is that the existing int <-> float comparisons already break the `numeric tower' model 
(push both operands to the highest common type before operating).  So I'm not sure there can 
be an easy and elegant solution here :(

I like the name Rational for this class.  Maybe change the name of numbers.Rational instead?

Postponing trim, approximate, from_decimal sounds fine to me.

Finally:  the very first line of rational.py is, I think, no longer accurate.  Please add your 
name so everyone knows who to blame/credit/assign bug reports to :)

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