Mathematical Markup Language (MathML) Version 2.0
W3C Recommendation 21 February 2001
- This version:
-
http://www.w3.org/TR/2001/REC-MathML2-20010221
Also available as: HTML zip archive, XHTML zip archive, XML zip archive, PDF (screen), PDF (paper)
- Latest version:
-
http://www.w3.org/TR/MathML2
- Previous version:
-
http://www.w3.org/TR/2001/PR-MathML2-20010108
- Editors:
-
David Carlisle
(NAG)
Patrick Ion
(Mathematical Reviews, American Mathematical Society)
Robert Miner
(Design Science, Inc.)
Nico Poppelier
(Penta Scope)
- Principal Authors:
- Ron Ausbrooks, Stephen Buswell, Stéphane Dalmas, Stan Devitt, Angel Diaz, Roger Hunter, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt
Copyright © 1998-2001 W3C® (MIT,
INRIA,
Keio), All Rights Reserved. W3C
liability,
trademark,
document
use and software
licensing rules apply.
This specification defines the Mathematical Markup Language, or MathML. 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.
This specification of the markup language MathML is intended
primarily for a readership consisting of those who will be developing
or implementing renderers or editors using it, or software that will
communicate using MathML as a protocol for input or output. It is
not a User's Guide but rather a reference document.
This document begins with background information on mathematical
notation, the problems it poses, and the philosophy underlying the
solutions MathML 2.0 proposes. MathML can be used to encode both
mathematical notation and mathematical content. About thirty of the
MathML tags describe abstract notational structures, while another
about one hundred and fifty provide a way of unambiguously specifying
the intended meaning of an expression. Additional chapters discuss how
the MathML content and presentation elements interact, and how MathML
renderers might be implemented and should interact with
browsers. Finally, this document addresses the issue of MathML
characters and their relation to fonts.
While MathML is human-readable, it is anticipated that, in all but
the simplest cases, authors will use equation editors, conversion
programs, and other specialized software tools to generate
MathML. Several early versions of such MathML tools already exist, and
a number of others, both freely available software and commercial
products, are under development.
This section describes the status of this document at the
time of its publication. Other documents may supersede this document.
The latest status of this document series is maintained at the W3C.
This document has been reviewed by W3C Members and other interested
parties and has been endorsed by the Director as a
W3C Recommendation. It is a stable document and may be used as reference
material or cited as a normative reference from another
document. W3C's role in making the Recommendation is to draw attention
to the specification and to promote its widespread deployment. This
enhances the functionality and interoperability of the Web.
This document has been produced by the
W3C Math Working Group
as part of the activity of the W3C User Interface Domain. The
goals of that W3C Math Working Group are discussed in the W3C Math WG
Charter (revised February 2000 from original of 11 June 1998).
A list of participants in the W3C Math
Working Group is available.
The MathML 2.0 specification was reviewed extensively during its
development, as provided by the W3C Process. During end of that
period the W3C Math Working Group members encouraged implementation
using the specification and comment on it; a report on Implementation and
Interoperability experiences and issues has been made public.
It is intended that this will be updated from time to time by the
continuing work of the W3C that oversees the MathML 2.0 Recommendation. The W3C
Math Working Group maintains a public Web page http://www.w3.org/Math/ which
contains further background information.
Public discussion of MathML and issues of support through the W3C
for mathematics on the Web takes place on the public mailing list of the Math Working
Group (list archives). To
subscribe send an email to [email protected]
with the word subscribe in the subject line.
Please report errors in this document to [email protected]. The list of known errors in
this document is available at
http://www.w3.org/2001/02/MathML2-errata.
The English version of this specification is the only normative
version. Information about translations of this document is available
at http://www.w3.org/2001/02/MathML2-translations.
The MathML 2.0 Recommendation is made available in different formats.
In case of a discrepancy between any of the derived forms and that found
in the W3C's archive of Recommendations the definitive version is
naturally the archived Recommendation.
A list of all current W3C Technical Reports can be found at http://www.w3.org/TR.
MathML 2.0 is a revision of the earlier corrected W3C
Recommendation MathML 1.01. It differs from it in that all
chapters have been updated and two new ones and some appendices added.
Chapters 1 and 2, which are introductory material, have been revised
to reflect the changes elsewhere in the document, and in the rapidly
evolving Web environment. Chapters 3 and 4 have been extended to
describe new functionalities added as well as smaller improvements of
material already proposed. Chapter 5 has been newly written to reflect
changes in the technology available. The major tables in Chapter 6
have been regenerated and reorganized to reflect an improved list of
characters useful for mathematics, and the text revised to reflect the
new situation in regard to Unicode. Chapter 7 has been completely
revised since Web technology has changed. A new Chapter 8 on the DOM for
MathML 2.0 has been added; the latter points to new appendices D and E for
detailed listings.
The appendices have been reorganized into normative and
non-normative groups. Appendices D, E and G are completely new.
1 Introduction
1.1 Mathematics and its Notation
1.2 Origins and Goals
1.3 The Role of MathML on the Web
2 MathML Fundamentals
2.1 MathML Overview
2.2 MathML in a Document
2.3 Some MathML Examples
2.4 MathML Syntax and Grammar
3 Presentation Markup
3.1 Introduction
3.2 Token Elements
3.3 General Layout Schemata
3.4 Script and Limit Schemata
3.5 Tables and Matrices
3.6 Enlivening Expressions
4 Content Markup
4.1 Introduction
4.2 Content Element Usage Guide
4.3 Content Element Attributes
4.4 The Content Markup Elements
5 Combining Presentation and Content Markup
5.1 Why Two Different Kinds of Markup?
5.2 Mixed Markup
5.3 Parallel Markup
5.4 Tools, Style Sheets and Macros for Combined Markup
6 Characters, Entities and Fonts
6.1 Introduction
6.2 MathML Characters
6.3 Character Symbol Listings
6.4 Differences from Characters in MathML 1
7 The MathML Interface
7.1 Embedding MathML in other Documents
7.2 Conformance
7.3 Future Extensions
8 Document Object Model for MathML
8.1 Introduction
Appendices
A Parsing MathML
A.1 DOCTYPE Declaration for MathML
A.2 MathML as a DTD Module
A.3 Namespace prefix declarations
A.4 Use of MathML without a DTD
A.5 SGML
A.6 The MathML DTD
B Content Markup Validation Grammar
C Content Element Definitions
C.1 About Content Markup Elements
C.2 Definitions of MathML Content Elements
D Document Object Model for MathML
D.1 IDL Interfaces
D.2 MathML DOM Tables
E MathML Document Object Model Bindings (Non-normative)
E.1 MathML Document Object Model IDL Binding
E.2 MathML Document Object Model Java Binding
E.3 MathML Document Object Model ECMAScript Binding
F Operator Dictionary (Non-normative)
F.1 Format of operator dictionary entries
F.2 Indexing of operator dictionary
F.3 Choice of entity names
F.4 Notes on lspace and
rspace attributes
F.5 Operator dictionary entries
G Sample CSS Style Sheet for MathML (Non-normative)
H Glossary (Non-normative)
I Working Group Membership and Acknowledgments (Non-normative)
I.1 The Math Working Group Memberships
I.2 Acknowledgments
J Changes (Non-normative)
K References (Non-normative)