Genus computation of global function fields. (January 2015)

• Record Type: Journal Article
• Authors: Bauch, Jens-Dietrich
• Is Part Of: Journal of symbolic computation. Volume 66(2015)
• Page Start: 8
• Page End: 20
• Publication Date: 2015-01
• Subjects: Riemann–Roch -- Function field -- Genus -- Montes algorithm; 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.2014.03.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper we present a randomized algorithm that computes the genus of a global function field. Let F / k be function field over a field k, and let k 0 be the full constant field of F / k . By using lattices over subrings of F, we can express the genus g of F in terms of [ k 0 : k ] and the indices of certain orders of the finite and infinite maximal orders of F . If k is a finite field, the Montes algorithm computes the latter indices as a by-product. This leads us to a fast computation of the genus of global function fields. Our algorithm does not require the computation of any basis, neither of finite nor infinite maximal order.