Continued fractions and number-theoretic computations

Abstract

The purpose of this mainly expository paper is to describe how continued fractions over JT = Q( yD) can be used in the development of algorithms for solving computational problems in number theory. These problems include: the factoring problem, i. e., the determination of whether an ideal in X* is principal; and the class group structure of X. Some attention is also given to the extension of these methods to complex cubic fields.