Email this article Computation of the Fundamental Units of Number Rings Using a Generalized Continued Fraction
- Authors: Bruno A.D.1
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Affiliations:
- Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Issue: Vol 45, No 2 (2019)
- Pages: 37-50
- Section: Article
- URL: https://journal-vniispk.ru/0361-7688/article/view/176754
- DOI: https://doi.org/10.1134/S036176881902004X
- ID: 176754
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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.
About the authors
A. D. Bruno
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Author for correspondence.
Email: abruno@keldysh.ru
Russian Federation, Moscow, 125047
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