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/kF/k be function field over a field k  , and let k0k0 be the full constant field of F/kF/k. By using lattices over subrings of F, we can express the genus g of F   in terms of [k0:k][k0: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.