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Algebraic computations with continued fractions. (English) Zbl 0929.11066

The authors describe several algorithms, in terms of transducers, which perform algebraic computations with continued fractions. In particular, they come up with an efficient formal algorithm which produces consecutive partial quotients of \((a\omega+ b)/c\omega+d)\), with \(a,b,c,d \in\mathbb{Z}\) and \((ad-bc)\neq 0\), by reading the consecutive partial quotients of the irrational number \(\omega\). Other nice new results are obtained as well.

MSC:

11Y65 Continued fraction calculations (number-theoretic aspects)
11A55 Continued fractions
11K50 Metric theory of continued fractions
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