OpenMath

Abstract: This document proposes OpenMath as a standard for the communication of semantically rich mathematical objects. This draft of the OpenMath standard comprises the following: a description of OpenMath objects, the grammar of xml and of the binary encoding of objects, a description of Content Dictionaries and an xml document type definition for validating Content Dictionaries. The non-normative Chapter 1 of this document briefly overviews the history of OpenMath.

Abstract: This paper describes the "light-weight" Small Type System of OpenMath. It is based on various discussion with the OpenMath Consortium, and notably with the NAG team. Section 7 lists the open issues for debate.

Abstract: Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading time, taking reader preferences into account. We present a representational infrastructure for notations in living mathematical documents. Mathematical notations can be defined declaratively. Author and reader can extensionally define the set of available notation definitions at arbitrary document levels, and they can guide the notation selection function via intensional annotations. We give an abstract specification of notation definitions and the flexible rendering algorithms and show their coverage on paradigmatic examples. We show how to use this framework to render OpenMath and Content- MathML to Presentation- MathML , but the approach extends to arbitrary content and presentation formats. We discuss prototypical implementations of all aspects of the rendering pipeline.