The presentation of this document has been augmented to
use XHTML rather than HTML, and to include all MathML
examples as inlined MathML markup that should be rendered by
a MathML enabled browser. The MathML examples that have
been added, and which should be displayed in your browser,
are marked like this.
Mathematical Markup Language (MathML) Version 3.0
W3C Working Draft 14 December 2007
- This version:
-
http://www.w3.org/TR/2007/WD-MathML3-20071214/
- Latest MathML 3 version:
- http://www.w3.org/TR/MathML3/
- Latest MathML Recommendation:
- http://www.w3.org/TR/MathML/
- Previous version:
- http://www.w3.org/TR/2007/WD-MathML3-20071005/
- Editors:
- David Carlisle, NAG
- Patrick Ion, Mathematical Reviews, American Mathematical Society
- Robert Miner, Design Science, Inc.
- Principal Authors:
- Ron Ausbrooks, Bert Bos, Olga Caprotti, David Carlisle, Giorgi Chavchanidze, Ananth Coorg, Stéphane Dalmas, Stan Devitt, Sam Dooley, Margaret Hinchcliffe, Patrick Ion, Michael Kohlhase, Azzeddine Lazrek, Dennis Leas, Paul Libbrecht, Manolis Mavrikis, Bruce Miller, Robert Miner, Murray Sargent, Kyle Siegrist, Neil Soiffer, Stephen Watt, Mohamed Zergaoui
Please refer to the errata
for this document, which may include some normative corrections.
In addition to the HTML version, this document is also available in these non-normative formats: XHTML+MathML version.
See also translations.
Copyright © 1998-2007 W3C® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark and document use rules apply.
Abstract
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.
MathML can be used to encode both
mathematical notation and mathematical content. About thirty-five of the
MathML tags describe abstract notational structures, while another
about one hundred and seventy 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 special
characters used for mathematics, their handling in MathML,
their presence in Unicode, and their relation to fonts.
While MathML is human-readable, in all but
the simplest cases, authors use equation editors, conversion
programs, and other specialized software tools to generate
MathML. Several versions of such MathML tools exist, and
more, both freely available software and commercial
products, are under development.
Status of this Document
This section describes the status of this document at the time
of its publication. Other documents may supersede this document. A
list of current W3C publications and the latest revision of this
technical report can be found in the W3C technical reports index at
http://www.w3.org/TR/.
This document is a W3C Public Working Draft produced by the W3C Math Working Group as
part of the
W3C Math
Activity.
The goals of the W3C Math Working Group are
discussed in the W3C Math WG
Charter (revised July 2006). A list of participants in the W3C Math Working Group
is available.
Publication as a Working Draft does not imply endorsement by the W3C Membership.
This is a draft document and may be updated, replaced or made obsolete by other
documents at any time. It is inappropriate to cite this document as other
than work in progress.
This third Public Working Draft specifies a new version of the the
Mathematical Markup Language, MathML 3.0 which is at present under
active development. The Math WG hopes this draft
will permit informed feedback. There is a description of some
considerations underlying this work in the W3C Math WG's public
Roadmap [roadmap]. Feedback should be sent to the Public W3C Math mailing list .
The MathML 2.0 (Second Edition) specification has been a W3C
Recommendation since 2001. After its
recommendation, a W3C Math Interest Group collected
reports of experience
with the deployment of MathML and identified issues with MathML that
might be ameliorated. The rechartering of a Math Working Group allows
the revision to MathML 3.0 in the light of that experience, of other
comments on the markup language, and of recent changes in
specifications of the W3C and in the technological context. MathML
3.0 does not signal any change in the overall design of MathML.
The major additions in MathML 3 are support for
bidirectional layout, better linebreaking and explicit positioning,
elementary math notations, and a new strict content MathML vocabulary
with well-defined semantics generated from formal content
dictionaries. The MathML 3 Specification has also been
restructured.
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 www-math-request@w3.org
with the word subscribe in the subject line.
Please report errors in this document to www-math@w3.org.
This document was produced by a group operating under
the 5
February 2004 W3C Patent Policy. W3C maintains a
public list of any patent disclosures made in connection with
the deliverables of the group; that page also includes instructions
for disclosing a patent. An individual who has actual knowledge of
a patent which the individual believes contains
Essential Claim(s)
must disclose the information in accordance with
section 6
of the W3C Patent Policy.
The basic chapter structure of this document is based on the earlier
MathML 2.0 Recommendation [MathML2]. That MathML 2.0
itself was a revision of the earlier W3C Recommendation MathML 1.01
[MathML1]; MathML 3.0 is a revision of the W3C
Recommendation MathML 2.0. It differs from it in that
all previous
chapters have been updated,
some new elements and attributes added
and some deprecated. This Public Working
Draft differs in structure from the initial Public Working
Draft as renewed efforts to separate the formal
from the explanatory have resulted in eight chapters not seven.
Much has been moved to
separate documents containing Primer material, material on Characters
and Entities and on the MathML DOM. First Working Drafts of these
documents will be published soon. A current list of open issues, pointing into the relevant
places in the draft, follows the Table of Contents.
-
With the second Working Draft, much of the non-normative explication
that formerly was found in Chapters 1 and 2, and many examples from
elsewhere in the previous MathML specifications, were removed
from the MathML3 specification and incorporated into a MathML Primer
being prepared as a separate document. It is expected this will help
the use of this formal MathML3 specification as a reference document
in implementations, and offer the new user better help in
understanding MathML's deployment. The remaining content of Chapters 1
and 2 is being edited to reflect the changes elsewhere in the
document, and in the rapidly evolving Web environment. Some of their
text used to go back to early days of the Web and XML, and its
explanations are now commonplace.
-
Chapter 3, on presentation-oriented markup, in this
draft adds new material on linebreaking and on markup for elementary
math notations. Material introduced in the last draft revising the
mpadded and maction elements has been further
revised as a result of active discussion. It is possible it may undergo
further modification. In addition, the matter of layout for schemata like
that for long division and its associated mcolumn element have been
carefully revised. Earlier work, as recorded in the W3C Note Arabic
mathematical notation, has allowed clarification of the
relationship with bidirectional text and examples
with RTL text have been added.
-
Chapter 4, on content-oriented markup, contains
further changes and additions in this Working Draft. The
actual content remains as before in essence, but a lot of work has been
done on refining it. The text of this chapter is generated by filtered
extraction from XML Content Dictionaries written in accordance with
OpenMath. The details of the Content Dictionary format have been
further specified and the generation procedure improved. It is
expected that
the Content Dictionaries will become a separate joint publication of
the W3C and OpenMath referenced by the MathML3 specification. As yet,
the Content Dictionaries are not yet available in public draft although
much work has been done on refining them. Their format is given in Chapter 8.
-
Chapter 5 is being refined as its purpose
has been further clarified. This chapter deals with interrelations of
parts of the MathML specification, especially with presentation and content markup.
-
Chapter 6 has been rewritten and reorganized to reflect the
new situation in regard to Unicode, and
the changed W3C context with regard to named character entities. The
new W3C specification of Entity Definitions for Characters in XML,
which incorporates
those used for mathematics is becoming a public working draft [Entities].
It is expected that some new ancillary tables will be provided that reflect requests
the Math WG has received.
-
Chapter 7 has been restored with a new and clearer purpose. This chapter looks outward to
the larger world in which MathML must function.
-
Chapter 8 now specifies the format of MathML3 Content Dictionaries,
as previously handled more briefly in sections 4.5 and 4.6.
The DOM for MathML, previously in a chapter at this point,
is being prepared as a separate specification.
-
The Appendices, of which
there are eight shown, have not been fully reworked. Eventually
what amount to revisions of the present appendices A, F, G, H, I
and J are all that are expected to remain.
Appendix A now contains
the new RelaxNG schema for MathML3
as well as discussion of MathML3 DTD issues.
