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MathML
please note:
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{short description|Format for expressing mathematical formulae}}- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
factoids | |
---|---|
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 URIweblink 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;WEB, A MathML for CSS Profile,weblink W3C, 25 July 2013, 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 {{tag|bind|o}} which associates bound variables ({{tag|bvar|o}}) to expressions, for example a summation index. The new {{tag|share|o}} 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 April 10, 2014.MathML Version 3.0 2nd Edition. W3.org. Retrieved on 8 July 2014. The specification was approved as an ISO/IEC international standard 40314:2015 on June 23, 2015.W3C MathML 3.0 Approved as ISO/IEC International Standard. W3.org. Retrieved on July 12, 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 â€œContent MathMLâ€). 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. The elements' names all begin with m. 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:- x â€“ identifiers;
- + â€“ operators;
- 2 â€“ numbers.
- non zero â€“ text.
- {{tag|mrow|o}} â€“ a horizontal row of items;
- {{tag|msup|o}}, {{tag|munderover|o}}, and others â€“ superscripts, limits over and under operators like sums, etc.;
- {{tag|mfrac|o}} â€“ fractions;
- {{tag|msqrt|o}} and {{tag|mroot|o}} â€“ roots;
- {{tag|mfenced|o}} - surrounding content with fences, such as parentheses.
a x 2
+ b x
+ c
a x2
+bx
+c
a
x
2
+
b
x
+
c
Content MathML
Content MathML focuses on the semantics, or meaning, of the expression rather than its layout. Central to Content MathML is the {{tag|apply|o}} element that represents function application. The function being applied is the first child element under {{tag|apply|o}}, and its operands or parameters are the remaining child elements. Content MathML uses only a few attributes.Tokens such as identifiers and numbers are individually marked up, much as for Presentation MathML, but with elements such as ci and cn. Rather than being merely another type of token, operators are represented by specific elements, whose mathematical semantics are known to MathML: times, power, etc. There are over a hundred different elements for different functions and operatorweblink example, {{code|2=xml|x}} represents sin(x) and {{code|2=xml|x5}} represents x+5. The elements representing operators and functions are empty elements, because their operands are the other elements under the containing {{tag|apply|o}}.The expression a x^2+b x+c could be represented asa
x
2
b
x
c
(plus
(times a (power x 2))
(times b x)
c)
This reflects the long-known close relationship between XML element structures, and LISP or Scheme S-expressions.Steven DeRose. The SGML FAQ Book: Understanding the Relationship of SGML and XML, Kluwer Academic Publishers, 1997. {{isbn|978-0-7923-9943-8}}.Canonical S-expressions#cite note-0(times a (power x 2))
(times b x)
c)
Wikidata annotation in Content MathML
According to the OM SocietyWEBSITE,weblink , OpenMath Content Dictionaries can be employed as collections of symbols and identifiers with declarations of their semantics - names, descriptions and rules. As proposed inJOURNAL, Moritz Schubotz, Philipp Scharpf, Bela Gipp., Representing Mathematical Formulae in Content MathML using Wikidata.,weblink 2018, Birndl@sigir, , the semantic knowledge-base WikidataWEBSITE,weblink can be used as OpenMath Content Dictionary to link semantic elements of a mathematical formula to unique and language-independent Wikidata items.Example and comparison to other formats
The well-known quadratic formula:
x=frac{-b pm sqrt{b^2 - 4ac}}{2a}
would be marked up using LaTeX syntax like this:x=frac{-b pm sqrt{b^2 - 4ac}}{2a}in troff/eqn like this:
x={-b +- sqrt{b sup 2 â€“ 4ac}} over 2a
in Apache OpenOffice Math and LibreOffice Math like this (all three are valid):
x={-b plusminus sqrt {b^2 â€“ 4 ac}} over {2 a}
x={-b +- sqrt {b^2 â€“ 4ac}} over 2ax={-b Â± sqrt {b^2 â€“ 4ac}} over 2ain AsciiMath like this:
x=(-b +- sqrt(b^2 - 4ac))/(2a)
The above equation could be represented in Presentation MathML as an expression tree made up from layout elements like mfrac or msqrt elements:
x
=
−
b
±
b
2
−
4
a
c
2
a
x=frac{-bpmsqrt{b^2-4ac}}{2a}
x={-b plusminus sqrt {b^2 - 4 ac}} over {2 a}
Embedding MathML in HTML/XHTML files
MathML, being XML, can be embedded inside other XML files such as XHTML files using XML namespaces. Recent browsers such as Firefox 3+ and Opera 9.6+ (support incomplete) can display Presentation MathML embedded in XHTML.Example of MathML embedded in an XHTML file
Example of MathML embedded in an XHTML file
The area of a circle is
π
r
2
.
(File:MathMLxhtml.png|nofloat|435px)
A rendering of the formula for a circle in MathML+XHTML using Firefox 22 on Mac OS X
{{clear}}Inline MathML is also supported in HTML5 files in the current versions of WebKit (Safari and JavaFX/WebView ), Gecko (Firefox). There is no need to specify namespaces like in the XHTML.
Example of MathML embedded in an HTML5 file
Example of MathML embedded in an HTML5 file
The area of a circle is
π
r
2
.
Browser support
Of the major web browsers, Gecko-based browsers (e.g., Firefox and Camino) have the most complete native support for MathML.{{citation |url=https://developer.mozilla.org/en-US/docs/Mozilla_MathML_Project/Status |title=Mozilla MathML Status |first=FrÃ©dÃ©ric |last=Wang |publisher=Mozilla}}{{citation |url=https://www.mozilla.org/projects/mathml/authoring.html |title=Authoring MathML for Mozilla |first=Roger B. |last=Sidje |publisher=Mozilla}}While the WebKit layout engine has a development version of MathML,{{citation |url=https://bugs.webkit.org/show_bug.cgi?id=3251 |title=Bug 3251 â€“ Implement MathML (master bug) |publisher=WebKit}} . . . (However, "see also")weblink this feature is only available in version 5.1 and higher of Safari,{{citation|url=http://www.leancrew.com/all-this/2011/07/safari-5-1-and-math/|title=Safari 5.1 and math}} Chrome 24{{Citation|title=MathML Support Coming To Chrome|url=http://browserfame.com/900/mathml-in-chrome|publisher=BrowserFame|accessdate=16 October 2012|postscript=}}{{Citation|title=Stable Chrome 24 supports MathML and closes security holes |url=http://www.h-online.com/open/news/item/Stable-Chrome-24-supports-MathML-and-closes-security-holes-1781648.html|publisher=The H Online|accessdate=11 January 2013|postscript=}} but not in later versions of Chrome.{{Citation|title=Stable Channel Update |url=http://googlechromereleases.blogspot.ca/2013/02/stable-channel-update_21.html|accessdate=7 April 2013|postscript=}} Google removed support of MathML claiming architectural security issues and low usage do not justify their engineering time.WEB,weblink Google subtracts MathML from Chrome, and anger multiplies, CNET, 22 November 2014, {{As of|October 2013}}, the WebKit/Safari implementation has numerous bugs.WEB,weblink Funding MathML Developments in Gecko and WebKit - Blog de FrÃ©dÃ©ric, FrÃ©dÃ©ric Wang, maths-informatique-jeux.com, 22 November 2014, JavaFX/WebView. Also based on WebKit, the JavaFX embedded web browser supports MathML starting with JavaFX 8 Update 192 and JavaFX 11 versions. Support is broken, in JavaFX 8 previous versions, JavaFX 9 and JavaFX 10.Opera, between version 9.5 and 12, supports MathML for CSS profile,{{citation |url=http://dev.opera.com/articles/view/can-kestrels-do-math-mathml-support-in/ |title=Can Kestrels do Math? MathML support in Opera Kestrel |first=Charles |last=McCathieNevile |date=27 September 2007 |publisher=Opera}}{{citation |url=http://my.opera.com/desktopteam/blog/2007/11/16/even-more-work |title=Even more work |first=Tommy A. |last=Olsen |date=16 November 2007 |publisher=Opera|archiveurl=https://web.archive.org/web/20071118141611weblink |archivedate=18 November 2007}} but is unable to position diacritical marks properly.weblink" title="web.archive.org/web/20081211143506weblink">MathML â€“ The Opera MathML blog. My.opera.com (1 November 2007). Retrieved on 9 May 2012. Prior to version 9.5 it required User JavaScript or custom stylesheets to emulate MathML support.weblink" title="web.archive.org/web/20080928225043weblink">UserJS for MathML 2.0. My.opera.com. Retrieved on 9 May 2012. Starting with Opera 14, Opera drops support for MathML by switching to the Chromium 25 engine.{{citation|url=http://my.opera.com/ODIN/blog/2013/03/05/opera-14-beta-for-android-is-out|title=Opera 14 beta for Android is out|archiveurl=https://web.archive.org/web/20130308155256weblink |archivedate=2013-03-08}}Internet Explorer does not support MathML natively. Support for IE6 through IE9 can be added by installing the MathPlayer plugin.{{citation |url=http://www.dessci.com/en/products/mathplayer/versionhistory.htm |title=MathPlayer â€“ version history}} IE10 has some crashing bugs with MathPlayer and Microsoft decided to completely disable in IE11 the binary plug-in interface that MathPlayer needs.WEB,weblink Microsoft cripples the display of math in IE10 & 11, dessci.com, 22 November 2014, MathPlayer has a license that may limit its use or distribution in commercial webpages and software. Using or distributing the MathPlayer plugin to display HTML content via the WebBrowser control in commercial software may also be forbidden by this license.The KHTML-based Konqueror currently does not provide support for MathML.{{citation |url=http://bugs.kde.org/show_bug.cgi?id=30526 |title=Bug 30526 â€“ MathML support for Konqi}}The quality of rendering of MathML in a browser depends on the installed fonts. The STIX Fonts project have released a comprehensive set of mathematical fonts under an open license. The Cambria Math font supplied with Microsoft Windows had a slightly more limited support.{{Citation|url=https://vismor.com/documents/site_implementation/viewing_mathematics/viewing_mathematics.php|title=Viewing Mathematics on the Internet|accessdate=13 April 2011|first=Timothy|last=Vismor}}According to a member of the MathJax team, none of the major browser makers paid any of their developers for any MathML-rendering work; whatever support exists is overwhelmingly the result of unpaid volunteer time/work.WEB,weblink MathML forges on, Peter Krautzberger, oreilly.com, 22 November 2014, In 2015 the MathML Association was founded to support the adoption of the MathML standard.{{citation|url=http://mathml-association.org/about.html|title=Mondial Association for Tools Handling MathML|accessdate=20 June 2016|author1=Deyan Ginev |author2=Michael Kohlhase |author3=Moritz Schubotz |author4=Raniere Silva |author5=FrÃ©dÃ©ric Wang }}Other standards
Another standard called OpenMath that 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. OpenMath data can be embedded in MathML using the element. OpenMath content dictionaries can be used to define the meaning of elements. The following would define P1(x) to be the first Legendre polynomialP1
x
See also
- CSS
- List of document markup languages
- Comparison of document markup languages
- Formula editors
- LaTeX2HTML
- LaTeXML
- KaTeX - Javascript library that converts latex to mathml
- MathJax - Javascript library that converts latex to mathml
References
{{Reflist|30em}}Further reading
Specifications
- W3C Recommendation: Mathematical Markup Language (MathML) 1.01 Specification
- W3C Recommendation: Mathematical Markup Language (MathML) Version 2.0 (Second Edition)
- W3C Recommendation: Mathematical Markup Language (MathML) Version 3.0 (Third Edition)
External links
- W3C Math Home â€” Contains the specifications, a FAQ, and a list of supporting software.
- WEB,weblink The Mathml Handbook, Pavi, Sandhu, December 12, 2002, Charles River Media, 2015-10-02,
- content above as imported from Wikipedia
- "MathML" does not exist on GetWiki (yet)
- time: 3:52pm EDT - Tue, Oct 15 2019
- "MathML" does not exist on GetWiki (yet)
- time: 3:52pm EDT - Tue, Oct 15 2019
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