Introduction to MathML

MathML is about encoding the structure of mathematical expressions so that they can be displayed, manipulated and shared over the World Wide Web. A carefully encoded MathML expression can be evaluated in a computer algebra system, rendered in a Web browser, edited in your word processor, and printed on your laser printer. Mathematical software vendors are adding MathML support at a rapid pace, and MathML is fast becoming the lingua franca of scientific publication on the Web.

Short for Mathematical Markup Language, an XML application for describing mathematical notations and capturing both its structure (including its complex two-dimensional symbolic notations) and its content and enabling that structure and content to be communicated over the Web. To communicate mathematics over the Web, it is essential to have a system that facilitates the processing, searching and indexing of data, and the reuse of that data in other mathematical applications and contexts.

The W3C MathML 2.0 Recommendation represents a major step forward in the standardization of mathematical communication over the web, both for end users and software systems and tools. In this tutorial we present an introduction to the Mathematical Markup Language (MathML) and its syntax and scope, illustrate leading software technologies and applications that provide support for MathML in current browsers, and explore how MathML interacts with other web standards to drive the development of languages, tools, and frameworks for the delivery of semantically rich web content that promises to enable a new generation of mathematical applications.

MathML is designed to allow mathematical, scientific, and other technical information to be served, received, and processed on the World Wide Web. It is an official recommendation of the World Wide Web Consortium (W3C) working group on mathematics. Users of webMathematica can benefit from MathML in a number of ways. They can use MathML for documents that contain a mixture of mathematics and text, they can generate MathML dynamically on their webMathematica site, and they can use a MathML entry mechanism to enter mathematical notation into their web browser and send this to webMathematica for computation.

MathML is an extensive system for displaying mathematics on the Web. This page is a quick guide to installing and using it. I've written this guide for members of the MIT Intelligent Book Project, but it should be generally useful as well.

MathML (Mathematical Markup Language) is an XML application from the World Wide Web Consortium (W3C) Math Working Group for describing mathematical notation and capturing both its structure and content. It provides a much needed foundation for the inclusion of mathematical expressions in web pages.

The web has gained new powers of technical communication, thanks to MathML, the recently promulgated standard for describing mathematical expressions. The MathML standard has been adopted by the World Wide Web Consortium, an international organization which defines the formats for storing and transmitting web information. And the key ideas forming the core of the MathML standard are derived directly from Wolfram Research's typesetting technology.

The XSLT MathML Library, xsltml, provides the XSLT developer with a set of XSLT templates for MathML 2.0 to LaTeX translation. These are implemented purely in XSLT, that is they do not use any extensions.

"MathML is intended to facilitate the use and re-use of mathematical and scientific content on the Web, and for other applications such as computer algebra systems, print typesetting, and voice synthesis. MathML can be used to encode both the presentation of mathematical notation for high-quality visual display, and mathematical content, for applications where the semantics plays more of a key role such as scientific software or voice synthesis. MathML is cast as an application of XML.

MathML is an XML application for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the World Wide Web, just as HTML has enabled this functionality for text.

To support MathML in webMathematica 1.0, a patch is available. This patch contains a number of useful updates and components for MathML as shown below.

The project is a component for the Apache Cocoon project(xml.apache.org). This component converts MathML documents to GIF images or SVG. So the user can easy write documents with embedding MathML fragments, and the component create in situ the GIF images. The SVG converter is used to create documents with embedding SVG fragments for e.g. the FOP to create PDF, or what else, documents.

This paper outlines the state of MathML[1] in Mathematica[5]. It details the changes that have occurred in Mathematica's handling of MathML as compared to previous versions[2]. These include changes to incorporate content and, as near as possible, lossless translations. It also details several novel aspects of the MathML and XML handling which are now possible in Mathematica. These involve the ability to perform integrated computations with MathML and to add specific conversions between Mathematica and MathML. This paper further goes on to detail some of the aspects of MathML which were problematic to implement. And finally, we conclude with our plans for the future and some of the more speculative things we are working on.

As the Web gains in importance and as the needs of mathematical formalism on the Web are beginning to be met by MathML, it is an opportune time to reflect on the design decisions made by the W3C Math Working Group that resulted in the verbose markup language for transport of math on the Web that MathML turns out to be. The TEX community need not be frightened by the advent of MathML, but may learn to work in the Web environment it provides.

To be effective, MathML must work well with a wide variety of renderers, processors, translators and editors. This chapter addresses some of the interface issues involved in generating and rendering MathML. Since MathML exists primarily to encode mathematics in Web documents, perhaps the most important interface issues are related to embedding MathML in HTML.

Mozilla is the open source browser, on which the next Netscape browser will be based. As well as being fast, cross-platform, and standards compliant, Mozilla is the first major browser to natively support MathML.

A MathML document must be a well-formed XML documents using elements in the MathML namespace as defined by this specification, however it is not required that the document refer to any specific Document Type Definition or Schema that specifies MathML. It is sometimes advantagous not to specify such a language definition as these files are large, often much larger than the MathML expression and unless they have been previously cached by the MathML application, the time taken to fetch the DTD or schema may have an appreciable effect on the processing of the MathML document.

The MathML Module Adds the ability to display the MathML language inside Mozilla.

Computer languages typically employ either prefix, infix, or postfix notation to capture the idea of applying an operator to arguments. For example, Postscript and Hewlett-Packard calculators use postfix notation. Most programing languages and computer algebra systems use the infix notation we are accustomed to seeing in print. However, the computer language LISP uses prefix notation, which also corresponds more closely to many natural language constructions like "f of x" and "subtract 5 from 8". For this and other reasons, MathML content mark-up also uses prefix notation.