I just started using maxima and I haven't looked at the continued
fraction capabilities in any detail yet. I gather from your examples
that the cf tools can deal with quadratic surds. Has there been any
effort to incorporate aperiodic infinite continued fractions? Knuth (1)
presents an algorithm for generating successive terms of some aperiodic
continued fractions, but the only citation is to a paper by Lagrange
1767. I have an implementation in Scheme which I built blindly from
Knuth's description; I don't understand the math behind it very well.
(1) D.E.Knuth, The Art of Computer Programming, vol. 2, Seminumerical
Algorithms, 3rd ed., p. 375, problem 13.
-- Bill Wood