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49-446: Mathematical Markup Language ( MathML ) is a mathematical markup language , an application of XML for describing mathematical notations and capturing both its structure and content, and is one of a number of mathematical markup languages . Its aim is to natively integrate mathematical formulae into World Wide Web pages and other documents. It is part of HTML5 and standardised by ISO /IEC since 2015. Following some experiments in

98-467: A Chromium implementation following a couple of years later, although that implementation was removed from Chromium after less than a year. 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. Also in 2015, the MathML Association was founded to support the adoption of

147-621: A braille device . They do this by applying a wide variety of techniques that include, for example, interacting with dedicated accessibility APIs , using various operating system features (like inter-process communication and querying user interface properties), and employing hooking techniques. Microsoft Windows operating systems have included the Microsoft Narrator screen reader since Windows 2000 , though separate products such as Freedom Scientific 's commercially available JAWS screen reader and ZoomText screen magnifier and

196-504: 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 slightly more limited support. A valid MathML document typically consists of the XML declaration, DOCTYPE declaration, and document element. The document body then contains MathML expressions which appear in < math > elements as needed in

245-425: A different XML math syntax, derived from Microsoft Office products. However, it is partially compatible through XSL Transformations . Mathematical markup language Popular languages for input by humans and interpretation by computers include TeX / LaTeX and eqn . Computer algebra systems such as Macsyma , Mathematica ( Wolfram Language ), Maple , and MATLAB each have their own syntax. When

294-509: A hundred different elements for different functions and operators. For example, <apply><sin/><ci> x </ci></apply> represents sin ⁡ ( x ) {\displaystyle \sin(x)} and <apply><plus/><ci> x </ci><cn> 5 </cn></apply> represents x + 5 {\displaystyle x+5} . The elements representing operators and functions are empty elements, because their operands are

343-553: A mental model of web pages displayed on their computer screen. Based on verbosity settings, a screen-reading program informs users of certain formatting changes, such as when a frame or table begins and ends, where graphics have been inserted into the text, or when a list appears in the document. The verbosity settings can also control the level of descriptiveness of elements, such as lists, tables, and regions. For example, JAWS provides low, medium, and high web verbosity preset levels. The high web verbosity level provides more detail about

392-746: 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. An implementation of MathML 2 landed in WebKit around this same time, with

441-662: A prototype of a talking terminal, known as SAID (for Synthetic Audio Interface Driver), for the IBM 3270 terminal . SAID read the ASCII values of the display in a stream and spoke them through a large vocal track synthesizer the size of a suitcase, and it cost around $ 10,000. Dr. Jesse Wright, a blind research mathematician, and Jim Thatcher , formerly his graduate student from the University of Michigan, working as mathematicians for IBM, adapted this as an internal IBM tool for use by blind people. After

490-572: A small subset, for example superscripting . Ad hoc syntax requires context to interpret ambiguous syntax, for example "<=" could be "is implied by" or "less than or equal to", and "dy/dx" is likely to denote a derivative , but strictly speaking could also mean a finite quantity dy divided by dx . Unicode improves the support for mathematics, compared to ASCII only. Markup languages optimized for computer-to-computer communication include MathML , OpenMath , and OMDoc . These are designed for clarity, parseability and to minimize ambiguity, at

539-440: 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 <bind> which associates bound variables ( <bvar> ) to expressions, for example a summation index. The new <share> element allows structure sharing. The development of MathML 3.0 went through

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588-466: Is a form of assistive technology ( AT ) that renders text and image content as speech or braille output. Screen readers are essential to people who are blind , and are useful to people who are visually impaired , illiterate , or have a learning disability . Screen readers are software applications that attempt to convey what people with normal eyesight see on a display to their users via non-visual means, like text-to-speech , sound icons, or

637-413: Is a significant technical challenge; hooking the low-level messages and maintaining an accurate model are both difficult tasks. Operating system and application designers have attempted to address these problems by providing ways for screen readers to access the display contents without having to maintain an off-screen model. These involve the provision of alternative and accessible representations of what

686-571: Is also supported in HTML5 files. There is no need to specify namespaces as there was in XHTML . Another standard called OpenMath that has been more specifically designed (largely by the same people who devised Content MathML) for storing formulae semantically can be used to complement MathML. OpenMath data can be embedded in MathML using the <annotation-xml encoding= "OpenMath" > element. OpenMath content dictionaries can be used to define

735-412: Is being displayed on the screen accessed through an API . Existing API s include: Screen readers can query the operating system or application for what is currently being displayed and receive updates when the display changes. For example, a screen reader can be told that the current focus is on a button and the button caption to be communicated to the user. This approach is considerably easier for

784-462: 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: As usual in HTML and XML, many entities are available for specifying special symbols by name, such as &pi; and &RightArrow; . An interesting feature of MathML

833-646: 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 VoiceOver in Safari ). JAWS from version 16 onward supports MathML voicing as well as braille output. The quality of rendering of MathML in

882-446: Is not intrinsically inaccessible. Web browsers, word processors, icons and windows and email programs are just some of the applications used successfully by screen reader users. However, according to some users, using a screen reader is considerably more difficult than using a GUI, and many applications have specific problems resulting from the nature of the application (e.g. animations) or failure to comply with accessibility standards for

931-430: Is suitable for browser implementation.” MathML Core set itself apart from MathML 3.0 by including detailed rendering rules and integration with CSS , automated browser support testing resources, and focusing on a fundamental subset of MathML. An implementation was added to Chromium at the beginning of 2023. MathML deals not only with the presentation but also the meaning of formula components (the latter part of MathML

980-483: Is that entities also exist to express normally-invisible operators, such as &InvisibleTimes; (or the shorthand &it; ) 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 {\displaystyle ax^{2}+bx+c} requires two layout elements: one to create

1029-412: Is those who have difficulty reading because of learning disabilities or language barriers. Although functionality remains limited compared to equivalent desktop applications, the major benefit is to increase the accessibility of said websites when viewed on public machines where users do not have permission to install custom software, giving people greater "freedom to roam". This functionality depends on

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1078-425: 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. 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

1127-439: The <annotation> element, which 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 such as StarMath or the markup using LaTeX syntax. The encoding field is usually a MIME type , although most of the equation encodings don't have such a registration; freeform text may be used in such cases. Although less compact than other formats,

1176-687: The Arena browser based on proposals for mathematical markup in HTML, 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. Implementations of the specification appeared in Amaya 1.1 , Mozilla 1.0 and Opera 9.5 . In October 2003,

1225-545: The Office Open XML file formats , they introduced a new equation editor which uses a new format, "Office Math Markup Language" (OMML). The lack of compatibility led some prestigious scientific journals to refuse to accept manuscripts which had been produced using Microsoft Office 2007 . SciWriter is another GUI that can generate MathML and LaTeX. ASCIIMathML , a JavaScript program, can convert ad hoc ASCII notation to MathML. Screen readers A screen reader

1274-534: The SIGIR conference proposed that the semantic knowledge base Wikidata could be used as an OpenMath Content Dictionary to link semantic elements of a mathematical formula to unique and language-independent Wikidata items. The well-known quadratic formula could be represented in Presentation MathML as an expression tree made up from layout elements like <mfrac> or <msqrt> : This example uses

1323-651: The free and open source screen reader NVDA by NV Access are more popular for that operating system. Apple Inc. 's macOS , iOS , and tvOS include VoiceOver as a built-in screen reader, while Google 's Android provides the Talkback screen reader and its ChromeOS can use ChromeVox. Similarly, Android-based devices from Amazon provide the VoiceView screen reader. There are also free and open source screen readers for Linux and Unix-like systems, such as Speakup and Orca . Around 1978, Al Overby of IBM Raleigh developed

1372-458: The MathML standard. At that time, 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 existed was overwhelmingly the result of unpaid volunteer time/work. In August 2021, a new specification called MathML Core was published, described as the “core subset of Mathematical Markup Language, or MathML, that

1421-696: The Research Centre for the Education of the Visually Handicapped ( RCEVH ) at the University of Birmingham developed a Screen Reader for the BBC Micro and NEC Portable. With the arrival of graphical user interfaces ( GUI s), the situation became more complicated. A GUI has characters and graphics drawn on the screen at particular positions, and therefore there is no purely textual representation of

1470-416: The XML structuring of MathML makes its content widely usable and accessible, allows near-instant display in applications such as web browsers , and facilitates an interpretation of its meaning in mathematical software products. MathML is not intended to be written or edited directly by humans. MathML, being XML, can be embedded inside other XML files such as XHTML files using XML namespaces. Inline MathML

1519-399: The contents of a webpage. Some screen readers can read text in more than one language , provided that the language of the material is encoded in its metadata . Screen reading programs like JAWS , NVDA , and VoiceOver also include language verbosity, which automatically detects verbosity settings related to speech output language. For example, if a user navigated to a website based in

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1568-545: The developers of screen readers, but fails when applications do not comply with the accessibility API : for example, Microsoft Word does not comply with the MSAA API , so screen readers must still maintain an off-screen model for Word or find another way to access its contents. One approach is to use available operating system messages and application object models to supplement accessibility API s. Screen readers can be assumed to be able to access all display content that

1617-787: The document. Often, MathML will be embedded in more general documents, such as HTML , DocBook , or other XML -based formats. 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. Finer details of presentation are affected by close to 50 attributes. Token elements generally only contain characters (not other elements). They include: 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 <mtext><b> non </b> zero </mtext>

1666-444: The early IBM Personal Computer (PC) was released in 1981, Thatcher and Wright developed a software equivalent to SAID, called PC-SAID, or Personal Computer Synthetic Audio Interface Driver . This was renamed and released in 1984 as IBM Screen Reader, which became the proprietary eponym for that general class of assistive technology. In early operating systems , such as MS-DOS , which employed command-line interfaces ( CLI s),

1715-695: The expression rather than its layout. Central to Content MathML is the <apply> element that represents function application. The function being applied is the first child element under <apply> , 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

1764-439: The graphical contents of the display. Screen readers were therefore forced to employ new low-level techniques, gathering messages from the operating system and using these to build up an "off-screen model", a representation of the display in which the required text content is stored. For example, the operating system might send messages to draw a command button and its caption. These messages are intercepted and used to construct

1813-578: The many operator and function elements amount to Scheme functions. With this trivial literal transformation, plus un-tagging the individual tokens, the example above becomes: This reflects the long-known close relationship between XML element structures, and LISP or Scheme S-expressions . According to the OM Society, OpenMath Content Dictionaries can be employed as collections of symbols and identifiers with declarations of their semantics – names, descriptions and rules. A 2018 paper presented at

1862-700: The meaning of <csymbol> elements. The following would define P 1 ( x ) to be the first Legendre polynomial : The OMDoc format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, and examples, to complete theories and even entire 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 ISO / IEC standard Office Open XML (OOXML) defines

1911-402: The off-screen model. The user can switch between controls (such as buttons) available on the screen and the captions and control contents will be read aloud and/or shown on a refreshable braille display . Screen readers can also communicate information on menus, controls, and other visual constructs to permit blind users to interact with these constructs. However, maintaining an off-screen model

1960-408: The other elements under the containing <apply> . The expression a x 2 + b x + c {\displaystyle ax^{2}+bx+c} could be represented as Content MathML is nearly isomorphic to expressions in a functional language such as Scheme and other dialects of Lisp . <apply> ... </apply> amounts to Scheme's ( ... ) , and

2009-410: The overall horizontal row and one for the superscripted exponent. 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 complete document that consists of just the MathML example above, is shown here: Content MathML focuses on the semantics, or meaning, of

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2058-664: The phone and does not require special programs or devices on the user side. Virtual assistants can sometimes read out written documents (textual web content, PDF documents, e-mails etc.) The best-known examples are Apple's Siri , Google Assistant , and Amazon Alexa . A relatively new development in the field is web-based applications like Spoken-Web that act as web portals, managing content like news updates, weather, science and business articles for visually-impaired or blind computer users. Other examples are ReadSpeaker or BrowseAloud that add text-to-speech functionality to web content. The primary audience for such applications

2107-442: The platform (e.g. Microsoft Word and Active Accessibility). Some programs and applications have voicing technology built in alongside their primary functionality. These programs are termed self-voicing and can be a form of assistive technology if they are designed to remove the need to use a screen reader. Some telephone services allow users to interact with the internet remotely. For example, TeleTender can read web pages over

2156-424: The price of verbosity. However, the verbosity makes them clumsier for humans to type directly. Many input, rendering, and conversion tools exist. Microsoft Word included Equation Editor , a limited version of MathType , until 2007. These allow entering formulae using a graphical user interface , and converting to standard markup languages such as MathML. With Microsoft's release of Microsoft Office 2007 and

2205-410: The purpose is informal communication with other humans, syntax is often ad hoc, sometimes called "ASCII math notation". Academics sometimes use syntax based on TeX due to familiarity with it from writing papers. Those used to programming languages may also use shorthands like "!" for ¬ {\displaystyle \neg } . Web pages may also use a limited amount of HTML to mark up

2254-450: The quality of the software but also on a logical structure of the text. Use of headings, punctuation, presence of alternate attributes for images, etc. is crucial for a good vocalization. Also a web site may have a nice look because of the use of appropriate two dimensional positioning with CSS but its standard linearization, for example, by suppressing any CSS and Javascript in the browser may not be comprehensible. Most screen readers allow

2303-407: The screen display consisted of characters mapping directly to a screen buffer in memory and a cursor position. Input was by keyboard. All this information could therefore be obtained from the system either by hooking the flow of information around the system and reading the screen buffer or by using a standard hardware output socket and communicating the results to the user. In the 1980s,

2352-542: 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

2401-603: The user to select whether most punctuation is announced or silently ignored. Some screen readers can be tailored to a particular application through scripting . One advantage of scripting is that it allows customizations to be shared among users, increasing accessibility for all. JAWS enjoys an active script-sharing community, for example. Verbosity is a feature of screen reading software that supports vision-impaired computer users. Speech verbosity controls enable users to choose how much speech feedback they wish to hear. Specifically, verbosity settings allow users to construct

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