Computing integral bases via localization and Hensel lifting

DOI10.1016/j.jsc.2020.07.007zbMath1484.13057arXiv1505.05054OpenAlexW2249727573MaRDI QIDQ820962

Wolfram Decker, Janko Böhm, Santiago Laplagne, Gerhard Pfister

Publication date: 29 September 2021

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

Full work available at URL: https://arxiv.org/abs/1505.05054

zbMATH Keywords

normalizationPuiseux seriesintegral basisintegral closurecurve singularity

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Integral closure of commutative rings and ideals (13B22) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Algebraic number theory computations (11Y40) Computational aspects of algebraic curves (14Q05) Algebraic functions and function fields in algebraic geometry (14H05)

Uses Software

• Magma
• Maple
• SINGULAR

Cites Work

• Normalization of rings
• Implementing the Round Four maximal order algorithm
• The Magma algebra system. I: The user language
• Modular algorithms for computing Gröbner bases.
• An algorithm for computing an integral basis in an algebraic function field
• Parallel algorithms for normalization
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Algebraic Function Fields and Codes
• A Singular Introduction to Commutative Algebra
• Fundamental Group for Some Cuspidal Curves
• Local to Global Algorithms for the Gorenstein Adjoint Ideal of a Curve
• The use of bad primes in rational reconstruction
• An algorithm for computing the integral closure
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