Genus computation of global function fields ?
In this paper we present a randomized algorithm that computes the genus of a global function field. Let F/k F / k be function field over a field k , and let k0 k 0 be the full constant field of F/k F / k . By using lattices over subrings of F, we can express the genus g of F  in terms of [k0:k] [ 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.
genus function field montes algorithm riemannroch