Computing splitting fields using Galois theory and other Galois constructions. (May 2023)

• Record Type: Journal Article
• Authors: Fieker, Claus; Sutherland, Nicole
• Is Part Of: Journal of symbolic computation. Volume 116(2023)
• Page Start: 243
• Page End: 262
• Publication Date: 2023-05
• Subjects: primary 11R32 11R58 11Y40 12F10 -- secondary 12F12; Galois groups -- Fixed fields -- Splitting fields -- Radical extensions; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.10.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe algorithms to compute splitting fields and towers of radical extensions in which a polynomial splits, without using polynomial factorisation in towers or constructing any field properly containing the constructed field, instead extending Galois group computations for this task. We also describe the computation of geometric Galois groups (monodromy groups) and their use in computing absolute factorizations.