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

[Mark Dickinson]

Mark Dickinson added the comment:

More comments, questions, and suggestions on the latest patch:

1. In _binary_float_to_ratio, the indentation needs adjusting.  Also 'top = 0L' could be replaced with 'top = 
0', unless you need this code to work with Python 2.3 and earlier, in which case top needs to be a long so 
that << behaves correctly.  Otherwise, this looks good.

2. Rational() should work, and it should be possible to initialize from a string.  I'd suggest that
Rational('  1729  '), Rational('-3/4') and ('  +7/18  \n') should be acceptable:  i.e.  leading and trailing 
whitespace, and an optional - or + sign should be permitted.  But space between the optional sign and the 
numerator, or on either side of the / sign, should be disallowed.  Not sure whether the numerator and 
denominator should be allowed to have leading zeros or not---probably yes, for consistency with int().

3. I don't think representing +/-inf and nan as Rationals (1/0, -1/0, 0/0) is a good idea---special values 
should be kept out of the Rational type, else it won't be an implementation of the Rationals any more---it'll 
be something else.

4. hash(n) doesn't agree with hash(Rational(n)) for large integers (I think you already mentioned this 
above).

5. Equality still doesn't work for complex numbers:

>>> from rational import *
>>> Rational(10**23) == complex(10**23)  # expect False here
True
>>> Rational(10**23) == float(10**23)
False
>>> float(10**23) == complex(10**23)
True

6. Why the parentheses around the str() of a Rational?

7. How about having hash of a Rational (in the case that it's not equal to an integer or a float) be
given by hash((self.numerator, self.denominator))?  That is, let the tuple hash take care of avoiding lots of 
hash collisions.

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