MathML
1 Mathematical Typesetting
● Mathematical typesetting differs in significant ways from typesetting of ordinary text.
● Mathematical typesetting uses a different font with different spacing between characters than ordinary typesetting.
● It is frequently not line-oriented.
● It has complex alignments both horizontally and vertically.
● It uses a huge character set.
● It has some symbols that change size and have other typesetting around them that depend on the situation
2 XML
● XML stands for Extensible Markup Language. It represents yet another effort by the W3C to divorce content from presentation. Whereas CSS allows us to take most formatting out of a document, but continues to require a restricted set of typesetting commands concerning the structure of the document, XML removes most of the restrictions on the structural commands. XML allows an author to determine the structure of a document, create tags to describe that structure, and leave all the formatting for later.
● XML has a stricter syntax than HTML, but really has very few rules. The only requirements for a well-formed XML file are as follows: 1. Every opening XML tag must have a corresponding closing tag: for example
3 XML
● What are the tags? That is up to us. We can define the tags, their relationship to each other, and the way in which their content will be formatted on a page. As you can see, this means that every XML document actually relies on at least two other files.
● A Data Type Definition (DTD) file contains the rules regarding relationships among the tags we define. We do not really require a DTD, but it allows us to define default values, and enforces our syntax across many different XML documents.
● In addition to a DTD, the presentation of our XML requires an associated style file to tell how it is to be formatted. The style file could be done in CSS - see this sample XML with CSS formatting. As you can see, the control over the appearance is limited. For that reason the X Stylesheet Language was invented - XSL. XSL is a much more versatile language for XML formatting, allowing us to include some typesetting commands in addition to formatting instructions. In short, XSL can handle all procedural matters, while XML is exclusively structural. You can view more examples of that same sample XML file here, here, and here (if you try clicking the links you will see simple web pages, try looking into the source code and you will see XML file. As I mentioned, Ctrl+U is the default shortcut for showing source code in Chrome, Firefox, IE, Edge; for Safari try these steps http://ccm.net/faq/33026-safari-view-the-source-code-of-a-webpage . Also in the header of the file you will see a link to the stylesheet file – try opening this file by simply copying file address, pasting it in your browser’s address line and pressing enter).
4 MathML
● 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.
● Although MathML was officially included by World Wide Web Consortium (W3C) in HTML5 Standard in 2015, currently there is no built-in support for it in such popular browsers as Chrome, Internet Explorer or Edge (it is still possible to render MathML typesetting with those browser, but it requires some additional libraries/extensions, e.g. https://en.wikipedia.org/wiki/MathJax ). Latest versions of Firefox and Safari have built-in support for MathML.
● MathML typesetting may look cumbersome (e.g. this will simply produce x^2).But on the other hand, it appears to be highly structured and meaningful in itself. For example, this give search engines better understanding of what exactly particular formula says.
5 MathML Syntax
● MathML was designed as a small subset of XML, so its syntax is basically that of XML. The rules are simple: 1. MathML commands are tags as with HTML, enclosed in “angle brackets” (less than and greater than signs). 2. MathML tags themselves enclose the text that is to be formatted. 3. There must be a top-level tag that encloses all the content. In MathML that tag is always
● All tags in MathML start from “m” letter, e.g.
6 Basic Elements
● MathML code is inserted into the
element of an HTML document and wrapped with the tag.● The symbols to be represented as a part of expressions and formulas have to be inserted as text into one of the following basic child elements of the
● These basic elements are therefore necessary for every expression in MathML and determine the font style of the inserted symbols. The elements
● Another important element in MathML is
7 Constants, Symbols and Blank Spaces
● Constants and symbols rendering are implemented with character entities (like < or ) together with
● For example
● The MathML
8 Superscripts, Subscripts, Fractions
● Expressions can be written as superscripts or subscripts using tags
● A fraction is generated by the element
9 Square Root, Sum, Limit, Integral
● In MathML the root symbol is generated by the element
●
10 Functions
● Functions are usually displayed in italic letters, thus they should be included into
11 Matrices
● To display matrices, we need to combine 12 Indented Formulas ● A mathematical expression may appear in the running text (“inline mode”) or indented from the running text and centered (“display mode”). These representation modes in MathML are determined by the attribute mode of the 13 Some Sources ● A document with examples for all of the above slides: http://www.math.wsu.edu/students/odykhovychny i/M300/slides/04_MathML/04_MathML_example_doc ument.html ● A nice cheat sheet by Prof. Cooper: http://www.math.wsu.edu/math/kcooper/M300/math mlcheat.php ● More information (references and tutorials) could be found here https://www.w3.org/Math/ ● MathJax library to be used for Chrome or Internet Explorer/Edge: https://www.mathjax.org/ 14 ICE #6 ● Typeset the following page using HTML and MathML: 15, only with the mandatory m prefix in the element name, i.e. table row is defined with