Computation of integral bases

DOI10.1016/j.jnt.2016.01.011zbMath1349.13041arXiv1507.04058OpenAlexW2963942707MaRDI QIDQ271785

Jens-Dietrich Bauch

Publication date: 20 April 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.04058

zbMATH Keywords

Dedekind domain\(\mathfrak p\)-integral basismaximal orderMontes algorithm

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Algebraic numbers; rings of algebraic integers (11R04) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (3)

Counting points on curves using a map to \(\mathbf P^1\). II. ⋮ Computation of triangular integral bases ⋮ Explicit Coleman integration for curves

Uses Software

• Magma

Cites Work

• A new computational approach to ideal theory in number fields
• Single-factor lifting and factorization of polynomials over local fields
• Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
• Higher Newton polygons and integral bases
• Construction of integral basis. I
• Construction and estimation of bases in function fields
• Implementing the Round Four maximal order algorithm
• The Magma algebra system. I: The user language
• Fast multiplication of large numbers
• Genetics of polynomials over local fields
• Complexity of OM factorizations of polynomials over local fields
• Newton polygons of higher order in algebraic number theory
• Unnamed Item

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