This Python class is an object-oriented implementation of the algorithm
that I and Roland Backhouse created in 2008 to enumerate the positive 
rational numbers in two different ways. The algorithm is new and it has 
never been implemented in Python before (as far as I know). 
See [0] for the complete formal derivation, proofs, and other details.

[0] Recounting the Rationals: Twice!, Roland Backhouse and Joao F. Ferreira,
    Published in Mathematics of Program Construction, Springer-Verlag, LNCS 5133,
    pp. 79--91 (proceedings of the 9th International Conference Mathematics of
    Program Construction, MPC 2008, Marseille, France, July 15--18, 2008)
    Available from http://joaoff.com/publications/2008/rationals


Example
=======

from rationals import *

e = RationalsEnumeration()  # create a new enumeration
print e                     # show the first rational (see note below)
print e.next()              # show the second rational
print e.previous()          # show the first rational again
print e.se()                # show the current stern-eisenstein rational (as a pair)
print e.sb()                # show the current stern-brocot rational (as a pair)
print e.jump(5)             # show the fifth rational
print e.jump(-5)            # show the first rational again
print e.goto(10)            # show the tenth rational
print e.goto(0)             # show the first rational again

# Note: an object of RationalsEnumeration keeps track of the current
#       position in the enumeration and both rationals (the stern-einsenstein
#       and the stern-brocot rationals). Example:

# Current position in the enumeration: 0
# Current rational (Stern-Brocot order):     (1,1)
# Current rational (Stern-Eisenstein order): (1,1)