Alternatively, a function can be used to toggle between the two representations:
def mixed(r):
if isinstance(r, Integer):
return r
if isinstance(r, Rational):
s = sign(r)
p, q = s*r.p, r.q
w, x = divmod(p, q)
return '%s %s/%s' % (s*w, x, q) if w else r
elif isinstance(r, str):
try:
a, b = [Rational(s) for s in r.split()]
if a < 0:
return a - b
else:
return a + b
except:
pass
return r
R = Rational
>>> R(5,3)
5/3
>>> mixed(_)
'1 2/3'
>>> mixed(_)
5/3
>>> R(2,3)
2/3
>>> mixed(_)
2/3
>>> mixed(_)
2/3
>>> [mixed(i/S(3)) for i in range(10,16)]
['3 1/3', '3 2/3', 4, '4 1/3', '4 2/3', 5]
>>> [mixed(i) for i in _]
[10/3, 11/3, 4, 13/3, 14/3, 5]
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