From: israel@math.ubc.ca (Robert Israel) Newsgroups: sci.math.symbolic,sci.math Subject: Re: Continued Fractions Date: 13 Nov 1998 22:44:18 GMT In article <72i785$rck$1@lagrange.rutgers.edu>, bumby@lagrange.rutgers.edu (Richard Bumby) writes: |> However, the book you mention may not be what the original poster was |> looking for. Indeed, while it is tempting to think of doing |> calculations directly with the continued fraction expansion, there do |> not seem to be any useful algorithms. What continued fractions do |> well is find rational approximations p/q within 1/q^2 of the number |> being approximated. Combining such good approximations by addition or |> multiplication is likely to greatly increase the denominator and fail to |> get any closer to the number. Any general-purpose procedure for |> calculating with continued fractions is likely to be "calculate first, |> then find the continued fraction". For Gosper's algorithm for doing arithmetic with continued fractions, see http://www.inwap.com/pdp10/hbaker/hakmem/cf.html Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2