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

[Mark Dickinson]

Mark Dickinson added the comment:

We still need to sort out the trim/approximate/convergents decisions.

Currently, we have:

  from_continued_fraction
  to_continued_fraction
  approximate (what we've been calling trim: limit the denominator)

At this point I'm not sure how much I care about what is or is not 
included, but here are a few thoughts:

(1) if to_continued_fraction is kept it should be a generator instead of 
returning a list.
(2) from_continued_fraction would be better replaced by convergents, 
since a user is just as (more?) likely to be interested in the whole 
sequence of convergents than just the final convergent.  If 
from_continued_fraction is kept in addition to convergents then it 
should work forwards instead of backwards, so that it doesn't need to 
use reversed (and hence works on the output of to_continued_fraction).
(3) approximate needs finishing up and possibly renaming to trim.

Can we remove {from,to}_continued_fraction and just leave trim?

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