Geodesic continued fractions and LLL

F Beukers

doi:10.1016/j.indag.2014.04.003

Geodesic continued fractions and LLL

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Abstract

We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to dd real numbers α1,…,αdα1,…,αd. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter tt as t↓0t↓0. Suggestions in this direction have been made several times over in the literature, e.g. Chevallier (2013) [4] or Bosma and Smeets (2013) [2]. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in tt.

Original language	English
Pages (from-to)	632-645
Number of pages	14
Journal	Indagationes Mathematicae
Volume	25
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2014.04.003
Publication status	Published - 2014

Keywords

Multidimensional continued fraction
Minkowski reduction
LLL-reduction

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KW - Multidimensional continued fraction

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Geodesic continued fractions and LLL

Abstract

Keywords

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