ISO IEC 40314:2016 pdf free download.Information technologv – Mathematical Markup Language ( Math ML ) Version 3.0 Znd Edition.
1.1 Mathematics and its Notation
A distinguishing feature of mathematics is the use of a complex and highly evolved system of two- dimensional symbolic notation. As J. R. Pierce writes in his book on communication theory, mathemalics and its notation should not be viewed as one and the same thing IPicrcelQ6lI, Mathematical ideas can exist indcpendenUy of the notation that represents them. However, the relation between meaning and notation is subtle, and part of the power of mathematics to describe and analyze derives from its ability to represent and manipulate ideas in symbolic form. The challenge before a Mathematical Markup Language (MathML) in enabling mathematics on the Wbrld Wide Web is to capture both notation and content (that is. its meaning) in such a way that documents can utilize the highly evolved notation of written and printed mathematics as well as the new potential for interconnectivity in electmnic media.
Mathematical notation evolves constantly as people continue to innovate in ways of approaching and expressing ideas. Even the common notation of arithmetic has gone through an amazing variety of styles. including many defunct ones advocated by leading mathematical figuresof theirday LCajoril928I. Modem mathematical notation is the product of centuries of refinement, and the notational conventions for high-quality typesetting are quite complicated and subtle. For example. variables and letters which stand for numbers are usually typeset today in a special mathematical italic font subtly distinct from the usual text italic: this seems to have been introduced in Europe in the late sixteenth century. Spacing around symbols for operations such as +, -. x and I is slightly different from thai of text, to reflect conventions about operauw precedence that have evolved over centuries. Entire books have been devoted to the conventions of mathematical typesetting, from the alignment of superscripts and subscripts, to rules for choosing parenthesis sizes, and on to specialized notational practices for sublields of mathematics. The manuals describing the nuances of present-day computer typesetting and composition systems can run to hundreds of pages.
Notational conventions in mathematics, and in printed text in general. guide the eye and make printed expressions much easier to read and understand. Though we usually take them for granted, we, as modern readers, rely on numerous conventions such as paragraphs. capital letters, font families and cases. and even the device of decimal-like numbering of sections such as is used in this document. Such notational conventions are perhaps even more important for electronic media, where one must contend with the difficulties of on-screen reading. Appropriate standards coupled with computers enable a broadening of access to mathematics beyond the world of print. The markup methods for mathematics in use just before the Web rose to prominence importantly included TEX (also written TeX) jKnuthl9l6) and approaches based on SGML (IAAP-mathl, IPoppelierl992l and [lSO-120831).
It is remarkable how widespread the current conventions of mathematical notation have become. The general two-dimensional layout, and most of the same symbols, are used in all modem mathematical communications, whether the participants are, say. European, writing left-to-right, or Middle-Eastern.
HTML. does not support namespace extensibility in the same way. the HTML parser has in-built knowledge of the HTML SVG and MathML namespaces. xmlns attributes arc just treated as nor- mat attributes. Thus when using the HTML serialisation of MathML. prefixed element names must not be used. x lns=”http://www.w3.org/1998/MathlMathNL” may be used on the math elenent. it will be ignored by the HTML parser. which always places math elements and its descendents in the MathML namespace (other than special rules described in Appendix Afor invalid input, and for annotation—xml. If a MathML expression is likely to be in contexts where ii may be parsed by an XML parser or an HTML parser. ii SHOULD use the following form to ensure maximum compatibility:
<math xmlns=9ittp: I/wv .v3. org/1998/Math/MathML”>
2.1.3 Children versus Arguments
Most MathML elements act as ‘containers’; such an element’s children are not distinguished from each other except as individual members of the list of children. Commonly there is no limit imposed on the number of children an element may have. This is the case for most presentation elements and some content elements such as set. But many MathML elements require a specific number of children, or attach a particular meaning to children in certain positions. Such elements are best considered to represent constructors of mathematical objects, and hence thought of as functions of their children. Therefore children of such a MathML element will often be referred to as its arguments instead of merely as children. Examples of this can be found, say. in Section 3.1.3.
There are presentation elements that conceptually accept only a single argument. but which for convenience have been written to accept any number of children: then we infer an mrow containing those children which acts as the argument to the element in question: see Section 3.1.3.1.
In the detailed discussions of element syntax given with each element throughout the MathML specification, the correspondence of children with arguments, the number of arguments required and their order, as well as other constraints on the content. are specified. This information is also tabulated for the presentation elements in Section 3.1.3.
2.1.4 MathML and Rendering
MathML presentation elements only recommend (i.e.. do not require) specific ways of rendering; this is in order to allow for medium-dependent rendering and for individual preferences of style.
Nevertheless, some parts of this specification describe these recommended visual rendering rules in detail: in those descriptions ii is often assumed that the model of rendering used supports the concepts of a well-defined ‘current rendering environment’ which, in particular, specifies a ‘current font’, a ‘current display’ (for pixel size) and a ‘current baseline’. The ‘current font’ provides certain metric properties and an encoding of glyphs.
2.1.5 MathML Attribute Values
MathML elements take attributes with values that further specialize the meaning or effect of the element. Attribute names are shown in a monospaced font throughout this document. The meanings of attributes and their allowed values are described within the specification of each element. The syntax notation explained in this section is used in specifying allowed values.
Except when explicitly forbidden by the specification for an attribute, MathML attribute values may contain any legal characters specified by the XML recommendation. See Chapter 7 for further clarification.