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factoids
Mathematical Markup Language (MathML) is 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 documents. It is a recommendation of the W3C math working group.
History
The specification of 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. In June 2006 the W3C has rechartered the MathML Working Group to produce a MathML 3 Recommendation until February 2008.MathML was originally designed before the finalization of XML namespaces. As such, MathML markup is often not namespaced, and applications that deal with MathML, such as the Mozilla browsers, do not require a namespace. For applications that wish to namespace MathML, the recommended namespace URI isweblink
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, Opera 9.50 build 9656+ or the Fire Vox extension for Firefox).
Presentation MathML
Presentation MathML focuses on the display of an equation, and has about 30 elements, and 50 attributes. The elements all begin with m and include token element: x - identifiers; + - operators; 2 - number. Tokens are combined using layout elements which include: - a row; - superscripts; mfrac - fractions. The attributes mainly control fine details of the presentation. A large number of entities are available which represent letters π, symbols → and some non-visible character such as ⁢ representing multiplication.The expression
a x2+b x+c
could be represented as
a x 2
+ b x + c
Content MathML
Content MathML focuses on the semantic meaning of the expression. Central to Content MathML is the element which represents a function or operator, given in the first child, applied to the remaining child elements. For example x represents
s∈(x)
and x5 represents x+5. The element represents an identifier, a number, and there are over a hundred different elements for different functions and operator. Content MathML only uses a few attributes.The expression
x={-b +- sqrt {b^2 - 4ac}} over 2aThe above equation could be represented in Presentation MathML as an expression tree made up from layout elements like mfrac or msqrt elements:In Content MathML this would be
x ± b
2 b 2
4 a c
2 a
The {{tag1|annotation}} element can be used to embed a semantic annotation in non-XML format, for example to store the formula in the format used by an equation editor. Alternatively, the equation could be represented in Content MathML as an expression tree for the functional structure elements like apply (for function application) or eq (for the equality relation) elements:In the expression tree above, elements like times are defined by the MathML specification and stand for mathematical functions that are applied to sibling expressions that are interpreted as arguments. The csymbol element is a generic extension element that means whatever is specified in the document referred to in the definitionURL attribute. Although less compact than TeX, the XML structuring promises to make it widely usable and allows for instant display in applications such as Web browsers and facilitates a straightforward interpretation of its meaning in mathematical software products. MathML is not intended to be written or edited directly by humans.(1)
Several utilities for converting mathematical expressions to MathML are available, including converters between TeX and MathML.(2) ConTeXt does the reverse and uses TeX for typesetting MathML (usually resulting in PDF documents). MathType from Design Science allows users to create equations in a WYSIWYG window and export them as MathML. Also, Wolfram Research provides a web page to convert typed mathematical expressions to MathML.(3)GNU TeXmacs is a what-you-see-is-what-you-get editor with extensive support for mathematics. Converters exist for presentation MathML in both directions. TeXmacs can be used to write mathematical articles which are exported to XHTML with embedded MathML.Another WYSIWYG MathML-as-is editor, Formulator MathML Weaver(4) provides a means for importing/exporting MathML with support for some abstract entities such as ⅇ and ⅆ.
Web browsers
Of the major web browsers, those that directly support the format are recent versions of Gecko browsers (e.g., Firefox and Camino),(5)(6) and the Opera web browser since version 9.5.For Gecko-based browsers, the user is currently required to download special fonts in order to display MathML correctly; this is likely to change soon with the release of the STIX fonts.Opera, since version 9.5, supports MathML for CSS profile.(7)(8) Before it required User JavaScript to emulate MathML support.(9)Other browsers do not support the format, and require third-party plugins.
Web conversion
ASCIIMath(10) provides a JavaScript library to re-write a convenient Wiki-like text syntax used inline in web pages into MathML on the fly; it works in browsers with MathML support or plug-ins. LaTeXMathML(11) does the same for (a subset of) the standard LaTeX mathematical syntax.Blahtex is a TeX-to-MathML converter intended for use with MediaWiki.Equation Server for .NET from soft4science can be used on the server side (ASP.NET) for TeX-Math(12) (Subset of LaTeX math syntax) to MathML conversion. It can also create bitmap images (Png, Jpg, Gif,...) from TeX-Math or MathML input.
Support of software developers
Support of MathML format accelerates software application development in such various topics, as computer-aided education (distance learning, electronic textbooks and other classroom materials); automated creation of attractive reports; computer algebra systems; authoring, training, publishing tools (both for web and desktop-oriented), and many other applications for mathematics, science, business, economics, etc. Several software vendors propose a component edition of their MathML editors, thus providing the easy way for software developers to insert mathematics rendering/editing/processing functionality in their applications. For example, Formulator ActiveX Control(13) from Hermitech Laboratory can be incorporated into an application as a MathML-as-is editor, Design Science propose a toolkit for building web pages that include interactive math (WebEQ Developers Suite,(14)).
Other standards
Another standard called OpenMath which has been designed (largely by the same people who devised Content MathML) more specifically for storing formulae semantically can also be used to complement MathML.The OMDoc format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, or example, to theories and text books. Formulae in OMDoc documents can either be written in Content MathML or in OpenMath; for presentation, they are converted to Presentation MathML.The Office Open XML (OOXML) standard defines a different XML math syntax, derived from Microsoft Office products. However, it is partially compatible(15) through relatively simple XSL Transformations.
WEB,weblink Mathematical Markup Language (MathML) 1.01 Specification (Abstract), 26 September, 2006, Buswell, Steven, Devitt, Stan; Diaz, Angel; et al, 7 July1999, 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.,
SciWriter — Scientific XML-based WYSIWYM editor with native MathML support; Supports also export to LaTeX
ASCIIMath — A JavaScript library for converting Wiki-like syntax into MathML
LaTeXMathML — A JavaScript program to dynamically translate LaTeX math notation to Presentation MathML
Formulator MathML Suite A Hermitech Laboratory software for authoring mathematical equations in MathML format (both Presentation and Content Markup)
Expressionism — A WYSIWYG browser-based editor (MathML + JavaScript) of mathematical expressions which is also capable of rendering images (e.g. in PNG format).
DragMath, an open-source Java applet for MathML, LaTeX, Maple, Maxima and many more.
MathMagic equation editor, a high-end WYSIWYG equation editor with support for importing and exporting MathML and TeX
