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

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Abstract

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.

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ACKNOWLEDGMENTS

I am grateful to A. B. Batkhin and A. A. Sokolov for their big help in the preparation of this paper.

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00422а.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. D. Bruno

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  1. A. D. Bruno
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Correspondence to A. D. Bruno.

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Devoted to the memory of I. R. Shafarevich

Translated by A. Klimontovich

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Bruno, A.D. Computation of the Fundamental Units of Number Rings Using a Generalized Continued Fraction. Program Comput Soft 45, 37–50 (2019). https://doi.org/10.1134/S036176881902004X

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  • DOI: https://doi.org/10.1134/S036176881902004X