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<title>OpenMath</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">OpenMath</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>OpenMath</b> is the name of a <a href="Document_markup_language" class="mw-redirect" title="Document markup language">markup language</a> for specifying the meaning of <a href="Mathematics" title="Mathematics">mathematical</a> <a href="Formulae" class="mw-redirect" title="Formulae">formulae</a>. Among other things, it can be used to complement <a href="MathML" title="MathML">MathML</a>, a standard which mainly focuses on the presentation of formulae, with information about their semantic meaning. OpenMath can be encoded in <a href="Extensible_Markup_Language" class="mw-redirect" title="Extensible Markup Language">XML</a> or in a binary format.

</p>

<div class="mw-heading mw-heading2"><h2 id="Coverage">Coverage</h2></div>

<p>OpenMath consists of the definition of "OpenMath Objects", which is an abstract datatype for describing the logical structure of a mathematical formula and the definition of "OpenMath Content Dictionaries", or collections of names for mathematical concepts. The names available from the latter type of collections are specifically intended for use in extending MathML, and conversely, a basic set of such "Content Dictionaries" has been designed to be compatible with the small set of mathematical concepts defined in Content MathML, the non-presentational subset of MathML.

</p>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>OpenMath has been developed in a long series of workshops and (mostly European) research projects that began in 1993 and continues through today. The OpenMath 1.0 Standard was released in February 2000, and revised as OpenMath 1.1 in October 2002. Two years later, the OpenMath 2.0 Standard was released in June 2004. OpenMath 1 fixed the basic language architecture, while OpenMath2 brought better XML integration, structure sharing and liberalized the notion of OpenMath Content dictionaries.

</p>

<div class="mw-heading mw-heading2"><h2 id="OpenMath_Society">OpenMath Society</h2></div>

<p>The OpenMath Effort is governed by the OpenMath Society, based in <a href="Helsinki" title="Helsinki">Helsinki</a>, <a href="Finland" title="Finland">Finland</a>. The Society brings together tool builders, software suppliers, publishers and authors. Membership is by invitation of the Societies Executive Committee, which welcomes self-nominations of individuals who have worked on OpenMath-related issues in research or application. As of 2007, <a href="Michael_Kohlhase" title="Michael Kohlhase">Michael Kohlhase</a> is president of the OpenMath society. He succeeded Arjeh M. Cohen, who was the first president.

</p>

<div class="mw-heading mw-heading2"><h2 id="Example">Example</h2></div>

<p>The well-known <a href="Quadratic_formula" title="Quadratic formula">quadratic formula</a>:

</p>

<mfrac>

<mrow>

<msqrt>

<msup>

</mrow>

</msup>

</msqrt>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}</annotation>

</semantics>

</math></span><img src="./00c22777378f9c594c71158fea8946f2495f2a28.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:6.176ex;" alt="{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}" loading="lazy"></span></dd></dl>

<p>would be marked up like this in OpenMath (the representation is an expression tree made up from functional elements like <style data-mw-deduplicate="TemplateStyles:r886049734">

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.mw-parser-output .monospaced{font-family:monospace,monospace}

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</style><span class="monospaced">OMA</span> for function application or <span class="monospaced">OMV</span> for variables):

</p>

<div class="mw-highlight mw-highlight-lang-xml mw-content-ltr" dir="ltr"><pre><span class="nt"><OMOBJ</span><span class="w"> </span><span class="na">xmlns=</span><span class="s">"http://www.openmath.org/OpenMath"</span><span class="nt">></span>

<span class="w"> </span><span class="nt"><OMA</span><span class="w"> </span><span class="na">cdbase=</span><span class="s">"http://www.openmath.org/cd"</span><span class="nt">></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"relation1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"eq"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"divide"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cdbase=</span><span class="s">"http://www.example.com/mathops"</span><span class="w"> </span><span class="na">cd=</span><span class="s">"multiops"</span><span class="w"> </span><span class="na">name=</span><span class="s">"plusminus"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"unary_minus"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"root"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"minus"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"power"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"times"</span><span class="nt">/></span>

<span class="w"> </span><span class="nt"><OMS</span><span class="w"> </span><span class="na">cd=</span><span class="s">"arith1"</span><span class="w"> </span><span class="na">name=</span><span class="s">"times"</span><span class="nt">/></span>

</pre></div>

<p>In the expression tree above symbols—i.e. elements like <span class="monospaced"><OMS cd="arith1" name="times"/></span>—stand for mathematical functions that are applied to sibling expressions in an <span class="monospaced">OMA</span> which are interpreted as arguments. The <span class="monospaced">OMS</span> element is a generic extension element that means whatever is specified in the content dictionary referred to in the <span class="monospaced">cd</span> attribute (this document can be found at the URI specified in the innermost <span class="monospaced">cdbase</span> attribute dominating the respective <span class="monospaced">OMS</span> element. In the example above, all symbols come from the content dictionary for arithmetics (<span class="monospaced">arith1</span>, see below), except for the <span class="monospaced">plusminus</span>, which comes from a non-standard place, hence the <span class="monospaced">cdbase</span> attribute here.

</p>

<div class="mw-heading mw-heading2"><h2 id="OpenMath_Content_Dictionaries">OpenMath Content Dictionaries</h2></div>

<p>Content Dictionaries are structured XML documents that define mathematical symbols that can be referred to by OMS elements in OpenMath Objects. The OpenMath 2 standard does not prescribe a canonical encoding for content dictionaries, but only requires an infrastructure sufficient for unique referencing in OMS elements. OpenMath provides a very basic XML encoding that meets these requirements, and a set of specific content dictionaries for some areas of mathematics, in particular covering the K-14 fragment covered by content MathML.

</p><p>For more richly structured content dictionaries (and generally for arbitrary mathematical documents) the <a href="OMDoc" title="OMDoc">OMDoc</a> format extends OpenMath by a “statement level” (including structures like definitions, theorems, proofs and examples, as well as means for interrelating them) and a “theory level”, where a theory is a collection of several contextually related statements. OMDoc's theories are designed to be compatible to OpenMath content dictionaries, but they can also be set into inheritance and import relations.

</p>

<div class="mw-heading mw-heading2"><h2 id="Criticism">Criticism</h2></div>

<p>OpenMath is criticised for being inadequate for general mathematics, exposing not enough formal precision to capture the intricacies of numerics, lacking a proof-of-concept and as an inferior technology to already established approaches of encoding mathematical semantics, amongst other presumed shortcomings.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li><a href="List_of_document_markup_languages" title="List of document markup languages">List of document markup languages</a></li>

<li><a href="Comparison_of_document_markup_languages" title="Comparison of document markup languages">Comparison of document markup languages</a></li>

<li><a href="MathML" title="MathML">MathML</a></li>

<li><a href="OMDoc" title="OMDoc">OMDoc</a></li>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFRichard_J._Fateman2001" class="citation web cs1">Richard J. Fateman (2001-01-17). <a rel="nofollow" class="external text" href="http://www.cs.berkeley.edu/~fateman/papers/openmathcrit.pdf">"A Critique of OpenMath and Thoughts on Encoding Mathematics"</a> <span class="cs1-format">(PDF)</span>. Berkeley: University of California<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-04-25</span></span>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><span class="official-website"><span class="url"><a rel="nofollow" class="external text" href="http://www.openmath.org/">Official website</a></span></span>

<ul><li><a rel="nofollow" class="external text" href="http://www.openmath.org/standard/">Standard definition</a></li>

<li><a rel="nofollow" class="external text" href="http://www.openmath.org/cd/">Content Dictionaries</a></li></ul></li></ul>

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<ul><li><a href="Compound_Document_Format" title="Compound Document Format">Compound Document Format</a></li>

<li><a href="Office_Open_XML" title="Office Open XML">OOXML</a>

<ul><li><a href="SpreadsheetML" title="SpreadsheetML">SpreadsheetML</a></li>

<li><a href="PresentationML" class="mw-redirect" title="PresentationML">PresentationML</a></li>

<li><a href="WordprocessingML" class="mw-redirect" title="WordprocessingML">WordprocessingML</a></li></ul></li>

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<li><a href="XHTML" title="XHTML">XHTML</a></li>

<li><a href="MathML" title="MathML">MathML</a></li>

<li><a href="LaTeX" title="LaTeX">LaTeX</a></li>

<li><a href="Markdown" title="Markdown">Markdown</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lesser-known</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AmigaGuide" title="AmigaGuide">AmigaGuide</a></li>

<li><a href="AsciiDoc" title="AsciiDoc">AsciiDoc</a></li>

<li><a href="BBCode" title="BBCode">BBCode</a></li>

<li><a href="ConTeXt" title="ConTeXt">ConTeXt</a></li>

<li><a href="CrossMark" class="mw-redirect" title="CrossMark">CrossMark</a></li>

<li><a href="DocBook" title="DocBook">DocBook</a></li>

<li><a href="Enriched_text" title="Enriched text">Enriched text</a></li>

<li><a href="FHTML" title="FHTML">FHTML</a></li>

<li><a href="GuideML" class="mw-redirect" title="GuideML">GuideML</a></li>

<li><a href="HyTime" title="HyTime">HyTime</a></li>

<li><a href="LilyPond" title="LilyPond">LilyPond</a></li>

<li><a href="LinuxDoc" title="LinuxDoc">LinuxDoc</a></li>

<li><a href="MusicXML" title="MusicXML">MusicXML</a></li>

<li><a href="OMDoc" title="OMDoc">OMDoc</a></li>

<li><a href="ReStructuredText" title="ReStructuredText">ReStructuredText</a></li>

<li><a href="Setext" title="Setext">Setext</a></li>

<li><a href="Texinfo" title="Texinfo">Texinfo</a></li>

<li><a href="Troff" title="Troff">troff</a></li>

<li><a href="Wiki#Editing" title="Wiki">Wikitext</a></li>

<li><a href="WapTV" title="WapTV">WapTV</a></li>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="List_of_document_markup_languages" title="List of document markup languages">List of document markup languages</a></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2022-12-25" href="https://en.wikipedia.org/wiki/?title=OpenMath&oldid=1129510853">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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