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TitleGenus computation of global function fields
Author(s) Jens-Dietrich Bauch
TypeArticle in Journal
AbstractAbstract 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.
KeywordsMontes algorithm
URL http://www.sciencedirect.com/science/article/pii/S0747717114000327
JournalJournal of Symbolic Computation
Pages8 - 20
Translation No
Refereed No