Michel Goossens Sunday, 17 March 2002 This XML document is marked up according the the DocBook schema It shows a few elements of the DocBook vocabulary, as well as a couple of examples of mathematical expressions where we used MathML markup. DocBook proposes an XML model for marking up technical documents. It is particularly well-suited for software reference guides and computer equipment manuals. Docbook contains hundreds of elements to markup up clearly and explicitly the different components of an electronic document (book, article, reference guide, etc.), not only displaying its hierarchical structure but also indicating the semantical meaning of the various elements. The structure of the DTD is optimized to allow for customization, thus making it relatively straightforward to add or eliminate certain elements or attributes, to change the content model for certain structural groups, or to restrict the value that given attributes can take. Norman Walsh developed a set of XSL stylesheets to transform XML documents marked up using the DocBook DTD into HTML or XSL formatting objects. The latter can be interpreted by &PTeX; and &xmltex; to obtain PDF or PostScript output. MathML is a W3C recommendation whose aim is to encode mathematical material for teaching and scientific communication at all levels. MathML consists of two parts: presentation (notation) et contents (meaning). MathML permits the conversion of mathematical information into various representations and output formats, including graphical displays, speech synthesizers, computer algebra programs, other mathematics typesetting languages, such as &TeX;, plain text, printers (PostScript), braille, etc. MathML has support for efficiently browsing long and complex mathematical expressoins and offers an extension mechanism. MathML code is human readable, easy to generate and process by software applications, and well suited for editing (even though MathML syntax might appear unnecessarily verbose and complex to the human reader). The W3C MathMl Working Group released the Second version of the the MathML Specification at the beginning of 2001. Two public initiatives that allow the display of MathML code direcly and that are under active development are W3C's Amaya and Mozilla. Commercial programs, such as IBM's techexplorer (a plugin for Netscape or Microsoft's Internet Explorer) or Design Science Webeq (using the Java applet technology) can display MathML formulae in present day browsers. Several computer algebra programs, e.g., Mathematica, or editors using e.g., mathtype, offer a user-friendly interface to enter, produce or read mathematics material marked up in MathML. The presentation part of MathML discribes the spacial layout of the different elements of a mathematical expression. MathML presenation markup has about thirty elements, that form the basis of a mathematical syntax using classical visual layout model. Some fifty attributes provide precise control on the exact positioning of the various components of the math expression. The list of presentation elements follows. Token elements mi, mn, mo, mtext, mspace/, ms, mchar, mglyph General layout schemata mrow, mfrac, msqrt, mroot, mstyle, merror, mpadded, mphantom, mfenced, menclose Script and limit schemata msub, msup, msubsup, munder, mover, munderover, mmultiscripts Tables and matrices mtable, mtr, mtd, maligngroup/, malignmark/ Enlivening expressions maction A MathML formula can be typeset inline, as here , Einstein's famous equation. An mathematical equation can also be typeset in display mode using DocBook's informalequation element, as is shown in the following example containing a matrix: Note the two attributes open and close on the mfenced element to specify the style of the braces to be used. The MathML Specification contains a detailed list of all possible attributes associated to each presentation element. The meaning of mathematical symbols (e.g., sums, products, integrals) exists independently of their rendering. Moreover the presentation markup of an expression is not necessarily sufficient to evaluate its value and use it in calculations. Therefore, MathML defines content markup to explicitly encode the underlying mathematical structure of an expressoin. It is impossible to cover all of mathematics, so MathML proposes only a relatively small number of commonplace mathematical constructs, chosen carefully to be sufficient in a large number of applications. In addition, it provides a extension mechanism for associating semantics with new notational constructs, thus allowing these to be encoded even when they are not in MathML content element base collection. MathML's basic set of content elements was chosen to allow for simple coding of most of the formulas used in secondary education, through the first year of university. The subject areas targeted are arithmetic, algebra, logic and relations, calculus and vector calculus, set theory, sequences and series, elementary classical functions, and statistics linear algebra. Using this basic sets more complex constructs can be built. The list of the content elements of MathML follows. token elements cn, ci, csymbol (MathML 2.0). basic content elements apply, reln (deprecated), fn (deprecated for externally defined functions) , interval, inverse, sep, condition, declare, lambda, compose, ident. arithmetic, algebra and logic quotient, exp, factorial, divide, max and min, minus, plus, power, rem, times, root, gcd, and, or, xor, not, implies, forall, exists, abs, conjugate, arg (MathML 2.0), real (MathML 2.0), imaginary (MathML 2.0), lcm (MathML 2.0). relations eq, neq, gt, lt, geq, leq, equivalent (MathML 2.0), approx (MathML 2.0). calculus and vector calculus int, diff, partialdiff, lowlimit, uplimit, bvar, degree, divergence (MathML 2.0), grad (MathML 2.0), curl (MathML 2.0), laplacian (MathML 2.0). theory of sets set, list, union, intersect, in, notin, subset, prsubset, notsubset, notprsubset, setdiff, card (MathML 2.0). sequences and series sum, product, limit, tendsto. elementary classical function exp, ln, log, sin, cos, tan, sec, csc, cot, sinh, cosh, tanh, sech, csch, coth, arcsin, arccos, arctan, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsinh, arctanh. statistics mean, sdev, variance, median, mode, moment. linear algebra vector, matrix, matrixrow, determinant, transpose, selector, vectorproduct (MathML 2.0), scalarproduct (MathML 2.0), outerproduct (MathML 2.0). semantic mapping element annotation, semantics, annotation-xml. constant and symbol element (all MathML 2.0) integers, reals, rationals, naturalnumbers, complexes, primes, exponentiale, imaginaryi, notanumber, true, false, emptyset, pi, eulergamma, infinity. The matrix example given in the preceding section in its presentation markup form if recoded here using content markup. <reln> <eq/> <ci>A</ci> <matrix> <matrixrow> <ci>x</ci><ci>y</ci> </matrixrow> <matrixrow> <ci>z</ci><ci>w</ci> </matrixrow> </matrix> </reln> XML98 World Wide Web Consortium Tim Bray Jean Paoli Michael Sperberg-McQueen See also the annotated version of the XML specification. TDG1999 Norman Walsh Leonard Muellner O'Reilly & Associates, Inc. 1999 1-56592-580-7 O'Reilly's catalog entry. You can also consult the online version of the DocBook reference guide and download the Docbook DTD and XSL stylesheets. MATHML2 World Wide Web Consortium David Carlisle Patrick Ion Robert Miner Nico Poppelier