No abstract

Unambiguous representation of mathematics is crucial for communications among humans or among computer systems. OpenMath is a standard aimed at supporting a semantically rich interchange of mathematics among varied computational software tools such as computer algebra systems, theorem provers, and tools for visualizing or editing mathematical text. MathML is a W3C Recommendation for the encoding of mathematics 'on the web' which also includes mechanisms for encoding mathematical semantics. We introduce each of these two languages and describe their relationships.

We discuss the developments within the OpenMath framework regarding programs that make it possible for a software package to interact with other packages or agents, namely Phrasebooks. Recently, several implementations of Phrasebooks have come about; we shall describe some of them. Most of the software is freely available, so, by downloading it and inspecting implemented examples, builders of software packages can pick up the examples and provide the mathematical community with further computational servers that can easily be interfaced.

This paper focuses on how to use Pocklington's criterion to produce efficient formal proof-objects for showing primality of large positive numbers. First, we describe a formal development of Pocklington's criterion, done using the proof assistant Coq. Then we present an algorithm in which computer algebra software is employed as oracle to the proof assistant to generate the necessary witnesses for applying the criterion. Finally, we discuss the implementation of this approach and tackle the proof of primality for some of the largest numbers expressible in Coq.

Abstract. New technologies such as xml, xsl and both MathML and OpenMath make it possible to bring mathematics to the Internet. Indeed, OpenMath, a markup language for mathematical content, and OmDoc, its extension to mathematical documents, open a way of communicating mathematics between computers, between software applications and over the Internet without losing information. In this paper we describe the latest applications of OpenMath related technologies for Interactive Mathematical Documents. As an example we describe the way we incorporate these new technologies in a new version of Algebra Interactive, an interactive course on first and second year university algebra.