Computing Galois groups of polynomials (especially over function fields of prime characteristic). (November 2015)

• Record Type: Journal Article
• Authors: Sutherland, Nicole
• Is Part Of: Journal of symbolic computation. Volume 71(2016)
• Page Start: 73
• Page End: 97
• Publication Date: 2015-11
• Subjects: 11R32; Galois groups -- Function fields; 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.2014.09.043
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe a general algorithm for the computation of Galois groups of polynomials over global fields from the point of view of using it to compute Galois groups of polynomials over function fields with prime characteristic, including characteristic 2 in which some invariants which are efficient to use in other characteristics are invariant for too large a group. We state new invariants for most of these situations when the characteristic is 2. We also describe the use of this algorithm for computing Galois groups of reducible polynomials over both number fields and function fields.