[discussion on the syntax to create rationals]
Are you sure that you really want a special syntax for this
rather than just a simply constructor like rat(2,3) ?
Just think of how difficult it would be to explain how the
following would work (assuming that you use @ as the magical
operator):
1 @ 2.3
1.5 @ 1.3
1j+3.4 @ 2
Note that intution isn't going to help here because you are
missing a precision indicator. mxNumber has a constructor called
FareyRational() which converts floats to rationals:
FareyRational(value, maxden)
Returns a Rational-object reflecting the given value
and using maxden as maximum denominator
Here's the algorithm:
/* Farey Function
This is a GNU MP implementation of the following function which
Scott David Daniels posted to the Python Cookbook;
http://www.activestate.com/ASPN/Python/Cookbook/Recipe/52317 :
def farey(v, lim):
'''Named after James Farey, an English surveyor.
No error checking on args -- lim = max denominator,
results are (numerator, denominator), (1,0) is infinity
'''
if v < 0:
n,d = farey(-v, lim)
return -n,d
z = lim-lim # get 0 of right type for denominator
lower, upper = (z,z+1), (z+1,z)
while 1:
mediant = (lower[0] + upper[0]), (lower[1]+upper[1])
if v * mediant[1] > mediant[0]:
if lim < mediant[1]: return upper
lower = mediant
elif v * mediant[1] == mediant[0]:
if lim >= mediant[1]: return mediant
if lower[1] < upper[1]: return lower
return upper
else:
if lim < mediant[1]: return lower
upper = mediant
A nice proof of the algorithm can be found at "Cut the Knot":
http://www.cut-the-knot.com/blue/Farey.html
*/
--
Marc-Andre Lemburg
CEO eGenix.com Software GmbH
_______________________________________________________________________
eGenix.com -- Makers of the Python mx Extensions: mxDateTime,mxODBC,...
Python Consulting: http://www.egenix.com/
Python Software: http://www.egenix.com/files/python/
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