Computation of the Fundamental Units of Number Rings Using a Generalized Continued Fraction

Аннотация

A global generalization of continued fraction is proposed. It is based on computer algebra and can be used to find the best Diophantine approximations. This generalization provides a basis for computing the fundamental units of algebraic rings and for finding all solutions of a class of Diophantine equations. Examples in dimensions two, three, and four are given.