Mathematical markup language

Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web pages and other documents. It is part of HTML5 and is a ISO/IEC standar
ISO/IEC 40314
since 2015.

History

MathML 1 was released as a W3C recommendation in April 1998 as the first XML language to be recommended by the W3C. Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001.

In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C Math Working Group.

MathML was originally designed before the finalization of XML namespaces. However, it was assigned a namespace immediately after the Namespace Recommendation was completed, and for XML use, the elements should be in the namespace with namespace URL http://www.w3.org/1998/Math/MathML. When MathML is used in HTML (as opposed to XML) this namespace is automatically inferred by the HTML parser and need not be specified in the document.

MathML version 3

Version 3 of the MathML specification was released as a W3C recommendation on 20 October 2010. A recommendation of ''A MathML for CSS Profile'' was later released on 7 June 2011; this is a subset of MathML suitable for CSS formatting. Another subset, ''Strict Content MathML'', provides a subset of content MathML with a uniform structure and is designed to be compatible with OpenMath. Other content elements are defined in terms of a transformation to the strict subset. New content elements include which associates bound variables () to expressions, for example a summation index. The new element allows structure sharing.

The development of MathML 3.0 went through a number of stages. In June 2006 the W3C rechartered the MathML Working Group to produce a MathML 3 Recommendation until February 2008 and in November 2008 extended the charter to April 2010. A sixth Working Draft of the MathML 3 revision was published in June 2009. On 10 August 2010 version 3 graduated to become a "Proposed Recommendation" rather than a draft.Mathematical Markup Language Version 3.0 W3C Recommendation
W3.org. Retrieved on 9 May 2012.

The Second Edition of MathML 3.0 was published as a W3C Recommendation on 10 April 2014. The specification was approved as an ISO/IEC international standard 40314:2015 on 23 June 2015.

Presentation and semantics

MathML deals not only with the ''presentation'' but also the ''meaning'' of formula components (the latter part of MathML is known as "Content MathML"). Because the meaning of the equation is preserved separate from the presentation, how the content is communicated can be left up to the user. For example, web pages with MathML embedded in them can be viewed as normal web pages with many browsers, but visually impaired users can also have the same MathML read to them through the use of screen readers (e.g. using the MathPlayer plugin for Internet Explorer or Firefox, Opera 9.50 build 9656+ or the Fire Vox extension for Firefox). Newer versions of JAWS support MathML voicing as well as braille output.

Presentation MathML

Presentation MathML focuses on the display of an equation, and has about 30 elements. The elements' names all begin with . A Presentation MathML expression is built up out of ''tokens'' that are combined using higher-level elements, which control their layout (there are also about 50 attributes, which mainly control fine details).

Token elements generally only contain characters (not other elements). They include:
* – identifiers;
* – operators;
* – numbers.
* – text.

Note, however, that these token elements may be used as extension points, allowing markup in host languages.
MathML in HTML5 allows most inline HTML markup in mtext, and is conforming, with the HTML markup being used within the MathML to mark up the embedded text (making the first word bold in this example).

These are combined using layout elements, that generally contain only elements. They include:
* – a horizontal row of items;
* , , and others – superscripts, limits over and under operators like sums, etc.;
* – fractions;
* and – roots;
* – surrounding content with fences, such as parentheses.

As usual in HTML and XML, many entities are available for specifying special symbols by name, such as and . An interesting feature of MathML is that entities also exist to express normally-invisible operators, such as (or the shorthand ) for implicit multiplication. They are:
* ;
* ;
* ;
* .

The full specification of MathML entities is closely coordinated with the corresponding specifications for use with HTML and XML in general.

Thus, the expression $a x^2+b x+c$ requires two layout elements: one to create the overall horizontal row and one for the superscripted exponent. Including only the layout elements and the (not yet marked up) bare tokens, the structure looks like this:

a ⁢ x 2
+ b ⁢ x
+ c

However, the individual tokens also have to be identified as identifiers (mi), operators (mo), or numbers (mn). Adding the token markup, the full form ends up as

a ⁢ x2
+b⁢x
+c

A valid MathML document typically consists of the XML declaration, DOCTYPE

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