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

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

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...

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Veröffentlicht in:Programming and computer software 2019-03, Vol.45 (2), p.37-50
1. Verfasser: Bruno, A. D.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Artificial Intelligence
Computer algebra
Computer Science
Diophantine equation
Fractions
Operating Systems
Rings (mathematics)
Software Engineering
Software Engineering/Programming and Operating Systems
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Zusammenfassung: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.
ISSN:0361-7688
1608-3261
DOI:10.1134/S036176881902004X