Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

A Framework for TEI-Based Scholarly Text Editions

In this paper, we describe an interdisciplinary project in which visualization techniques were developed for and applied to scholarly work from literary studies. The aim was to bring Christof Schöch's electronic edition of Bérardier de Bataut's Essai sur le récit (1776) to the web. This edition is based on the Text Encoding Initiative's XML-based encoding scheme (TEI P5, subset TEI-Lite). This now de facto standard applies to machine-readable texts used chiefly in the humanities and social sciences. The intention of this edition is to make the edited text freely available on the web, to allow for alternative text views (here original and modern/corrected text), to ensure reader-friendly annotation and navigation, to permit on-line collaboration in encoding and annotation as well as user comments, all in an open source, generically usable, lightweight package. These aims were attained by relying on a GPL-based, public domain CMS (Drupal) and combining it with XSL-Stylesheets and Java Script.