Computing splitting fields using Galois theory and other Galois constructions

DOI10.1016/j.jsc.2022.10.001OpenAlexW4304084194MaRDI QIDQ2100056

Claus Fieker, Nicole Sutherland

Publication date: 21 November 2022

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2022.10.001

zbMATH Keywords

Galois groupssplitting fieldsradical extensionsfixed fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Galois theory (11R32) Separable extensions, Galois theory (12F10) Algebraic number theory computations (11Y40)

Related Items (1)

Computing splitting fields using Galois theory and other Galois constructions

Uses Software

• GAP
• Magma

Cites Work

• Algebraic function fields and codes
• Computing splitting fields using Galois theory and other Galois constructions
• Galois groups over rational function fields and explicit Hilbert irreducibility
• Computing Galois groups of polynomials (especially over function fields of prime characteristic)
• Constructing transitive permutation groups.
• The Transitive Permutation Groups of Degree 32
• Computing automorphisms of abelian number fields
• The Determination of Galois Groups
• Morikawa’s Unsolved Problem
• Computation of Galois groups of rational polynomials
• Algorithmic Number Theory
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