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Program to calculate division of continued fractions

• To: mathgroup at smc.vnet.net
• Subject: [mg69922] Program to calculate division of continued fractions
• From: "Diana" <diana.mecum at gmail.com>
• Date: Wed, 27 Sep 2006 06:05:32 -0400 (EDT)

Folks,

If I define in Mathematica a fraction of two continued fractions, in
polynomials of t, is there a program which will calculate the quotient
of them as a continued fraction?

For example,

[0, 1, t, t^2 + 1, t^2, t^2 + 2, ...]/[0, 2, t^2, t^3, t^4, t + 1, ...]

I want the answer in the form

[0, t, t^2, t + 1, ...], as a single continued fraction, for example.
(This sample answer is just representational, and not an answer to the
posed question.)

Assume that the continued fractions do not repeat, and that 100 terms
have been entered for each.

Diana