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<h1>Mathematical Markup Language (MathML<sup>&#8482;</sup>) 1.01
Specification</h1>

<h2>W3C Recommendation, revision of 7 July 1999</h2>

<p>
<I>REC-MathML-19980407; revised 19990707</I>
</p>

<dl>
<dt>This version:</dt>
<dd>
<a href="http://www.w3.org/1999/07/REC-MathML-19990707">http://www.w3.org/1999/07/REC-MathML-19990707</a>
</dd>
<dt>Latest version:</dt>
<dd>
<a href="http://www.w3.org/TR/REC-MathML">http://www.w3.org/TR/REC-MathML</a>
</dd>
<dt>Previous version:</dt>
<dd>
<a href="http://www.w3.org/TR/1998/REC-MathML-19980407">http://www.w3.org/TR/1998/REC-MathML-19980407</a>
</dd>
<dt>Editors:</dt>
<dd>
Patrick Ion <a href="mailto:ion@ams.org">&lt;ion@ams.org></a><br>
(Mathematical Reviews / American Mathematical Society) <br>
</dd>
<dd>
Robert Miner <a
href="mailto:rminer@geomtech.com">&lt;rminer@geomtech.com></a><br>
(Geometry Technologies, Inc.) <br>
</dd>
<dt>Principal Writers:</dt>
<dd>
Stephen Buswell, Stan Devitt, Angel Diaz, Patrick Ion, Robert
Miner,<br>
Nico Poppelier, Bruce Smith, Neil Soiffer, Robert Sutor, Stephen Watt
</dd>
</dl>

<p class="copyright"><a
href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright"><br>
Copyright</a> &copy; 1999 <a href="http://www.w3.org/">W3C</a> (<a
href="http://www.lcs.mit.edu/">MIT</a>, <a
href="http://www.inria.fr/">INRIA</a>, <a
href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C
<a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>,
<a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>,
<a href="http://www.w3.org/Consortium/Legal/copyright-documents">document
use</a> and
<a href="http://www.w3.org/Consortium/Legal/copyright-software">software
licensing</a> rules apply.</p>
<hr title="Separator for header">

</div>

<h2><a name="abstract">Abstract</a></h2>

<p>This specification defines the Mathematical Markup
Language, or
<acronym title="Mathematical Markup Language">MathML</acronym>.
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 Web, just as
<acronym title="Hypertext Markup Language">HTML</acronym>
has enabled this functionality for text.</p>

<p>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.</p>

<p>This document begins with background information on
mathematical notation, the problems it poses, and the
philosophy underlying the solutions MathML proposes.  MathML
can be used to encode both mathematical notation and
mathematical content.  Twenty-eight of the MathML tags
describe abstract notational structures, while another
seventy-five 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 entities (extended characters)
and their relation to fonts.</p>

<p>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.</p>

<h2><a name="status">Status of this document</a></h2>

<p>This document has been reviewed by
<acronym title="World Wide Web Consortium">W3C</acronym>
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.</p>

<p>The fundamental
<a href="http://www.w3.org/pub/WWW/TR/REC-xml">eXtensible Markup
Language
(<acronym title="Extensible Markup
Language">XML</acronym>)</a>
1.0 specification upon which MathML is based has been adopted
as a W3C Recommendation.  Should future changes in the XML
specification necessitate changes in the MathML specification,
it is the intention of the W3C Math Working Group to issue a
revision of the MathML specification.  However, any changes
are very unlikely to be substantial.</p>

<p>Most of this document represents technology tested by multiple
implementations.  A summary of MathML rendering and authoring software
is described on the <a href="http://www.w3.org/Math">W3C Math Working
Group</a> home page.</p>

<p>The <a href="http://lists.w3.org/Archives/Public/www-math">www-math</a>
mailing list is a public forum for questions and comments about MathML
and issues related to putting math on the Web.</p>

<P>The W3C Math Working Group intends further development of
recommendations for mathematics on the Web, as set out
<a href="chapter1.html#goals">below</a>.</p>

<p>A list of current W3C Recommendations and other technical reports
can be found at <a href="http://www.w3.org/TR">http://www.w3.org/TR</a>.</P>

<p><em>This document is a revised version of the document first released
on 7 April 1998. <a href="appendixG.html">Changes from the original
version</a> are only editorial in nature.  The present W3C Math
Working Group is working on further improvements of MathML.</em></p>


<h3>Available formats</h3>
<p>The MathML 1.01 W3C Recommendation is made available in different formats
from the <a HREF="http://www.w3.org/Math">W3C Math WG's site</A>.  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 Recommendation.  At first it is expected that zipped and gzipped
bundles will be made available, but such easily printable formats as
PostScript or PDF may be supplied.</p>

<h3>Available languages</h3>

<p>The English version of this specification is the only normative
version. However, for translations of this document, see
<a href="http://www.w3.org/MarkUp/mathml101-updates/translations.html">
http://www.w3.org/MarkUp/mathml101-updates/translations.html</a>.
</p>


<h3>Errata</h3>

<dl>
<dt>The list of known errors in this specification is available at:
<dd><a href="http://www.w3.org/MarkUp/mathml101-updates/errata.html">
http://www.w3.org/MarkUp/mathml101-updates/errata.html</a>.
</dl>

<p>Please report errors in this document to <a
href="mailto:www-math@w3.org">www-math@w3.org</a>.
</p>

<h2><a name="contents">Table of contents</a></h2>


<p><a href="toc.html"><b>Extended Table of Contents</b></a></p>

<ul>
<li><a href="chapter1.html">Chapter 1. Introduction</a></li>
<li><a href="chapter2.html">Chapter 2. MathML Fundamentals</a></li>
<li><a href="chap3_1.html">Chapter 3. Presentation Markup</a></li>
<li><a href="chap4_1.html">Chapter 4. Content Markup</a></li>
<li><a href="chapter5.html">Chapter 5. Mixing Presentation and Content </a></li>
<li><a href="chapter6.html">Chapter 6. Entities, Characters and Fonts</a></li>
<li><a href="chapter7.html">Chapter 7. Implementing MathML</a></li>
</ul>

<ul>
<li><a href="appendixA.html">Appendix A.
<acronym title="Document Type Definition">DTD</acronym>
 for MathML</a></li>
<li><a href="appendixB.html">Appendix B. Glossary</a></li>
<li><a href="appendixC.html">Appendix C. Operator Dictionary</a></li>
<li><a href="appendixD.html">Appendix D. Working Group Membership</a></li>
<li><a href="appendixE.html">Appendix E. Informal
<acronym title="Extended Backus-Naur Form">EBNF</acronym>
Grammar for Content Elements</a></li>
<li><a href="appendixF.html">Appendix F. Default Semantic Bindings for
Content Elements</a></li>
<li><a href="appendixG.html">Appendix G. MathML 1.0 Changes</a></li>
</ul>
<ul>
<li><a href="refs.html">References</a></li>
</ul>


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