sage: K.<a> = QuadraticField(47)
sage: c = a.continued_fraction()
sage: c
[6; (1, 5, 1, 12)*]

sage: c.convergents()
lazy list [6, 7, 41/6, ...]

sage: for k in [0..10]:
....:     ck = c.convergent(k)
....:     print "%s. convergent = %s = %s" % (k, ck, ck.n())
....:
0. convergent = 6 = 6.00000000000000
1. convergent = 7 = 7.00000000000000
2. convergent = 41/6 = 6.83333333333333
3. convergent = 48/7 = 6.85714285714286
4. convergent = 617/90 = 6.85555555555556
5. convergent = 665/97 = 6.85567010309278
6. convergent = 3942/575 = 6.85565217391304
7. convergent = 4607/672 = 6.85565476190476
8. convergent = 59226/8639 = 6.85565458965158
9. convergent = 63833/9311 = 6.85565460208356
10. convergent = 378391/55194 = 6.85565460013770