An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups. (November 2020)

• Record Type: Journal Article
• Authors: Barth, Dominik; König, Joachim; Wenz, Andreas
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 352
• Page End: 366
• Publication Date: 2020-11
• Subjects: Galois theory -- Explicit computation -- Hurwitz spaces -- Belyi maps; 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.2019.10.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We propose an approach for the computation of multi-parameter families of Galois extensions with prescribed ramification type. More precisely, we combine existing deformation and interpolation techniques with recently developed strong tools for the computation of 3-point covers. To demonstrate the applicability of our method in relatively large degrees, we compute several families of polynomials with symplectic Galois groups, in particular obtaining the first totally real polynomials with Galois group PSp 6 ( 2 ) .