Efficient computation of maximal orders in Artin-Schreier extensions

We describe an algorithm, linear in the degree of the field, for computing pseudo bases for integral closures of holomorphy rings in Artin-Schreier extensions of global function fields and a similar algorithm, also linear in the degree of the field, for computing pseudo bases for S-maximal orders of Artin-Schreier extensions of global function fields. We give examples comparing the running time of our algorithm to that of Round 2 and Fraatz (2005). (C) 2012 Elsevier B.V. All rights reserved.