Genus computation of global function fields. (January 2015) - Bauch, Jens-Dietrich
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.