Computation of an Integral Basis of Quartic Number Fields

2009/07/16 by Lhoussain El Fadil, Fadil, Lhoussain El
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0907.2786

openalex publication_date 2009/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial P(X) = X4 + aX + b ∈\z[X] in methodical and complete generality.

Citations

• Newton polygons of higher order in algebraic number theory

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