Computation of the Euclidean minimum of algebraic number fields

DOI10.1090/S0025-5718-2013-02746-9zbMath1287.11143MaRDI QIDQ5401707

Pierre Lezowski

Publication date: 12 March 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Euclidean minimuminhomogeneous minimumEuclidean number fieldstwo-stage Euclidean rings

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Euclidean rings and generalizations (13F07)

Related Items (6)

Totally indefinite Euclidean quaternion fields ⋮ Euclidean minima of algebraic number fields ⋮ On the finiteness of $\mathfrak{P}$-adic continued fractions for number fields ⋮ The Euclidean algorithm in quintic and septic cyclic fields ⋮ Computation of Euclidean minima in totally definite quaternion fields ⋮ The Kronecker-Vahlen theorem fails in real quadratic norm-Euclidean fields

Uses Software

• PARI/GP

Cites Work

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• Upper bounds for Euclidean minima of algebraic number fields
• Euclidean real quadratic number fields
• Euclidean number fields. I. II. III
• Euclidean number fields of large degree
• The Euclidean algorithm in algebraic number fields
• The inhomogeneous minima of binary quadratic forms. II
• Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
• Euclidean minima of totally real number fields: Algorithmic determination
• The Euclidean Algorithm in Cubic Number Fields
• A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
• Depth-First Search and Linear Graph Algorithms
• LINEAR FORMS ASSOCIATED WITH AN ALGEBRAIC NUMBER-FIELD

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