introduction to using mathml

Introduction to Using MathMLIntroduction to Using MathML

Presented by: Robert MinerDirector of New Product Development

Bob MathewsDirector of Training

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What we’ll coverWhat we’ll cover Part I – Understanding MathML

Overview of MathML Presentation and content markup MathML elements Building a MathML expression and inserting into

HTML and XML pages.

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What we’ll coverWhat we’ll cover Part I – Understanding MathML Part II – Magic Incantations

DOCTYPEs & MIME types Namespaces Object Tags and Processing Instructions Universal MathML Stylesheet

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What we’ll coverWhat we’ll cover Part I – Understanding MathML Part II – Magic Incantations Part III – Tools

Design Science WebEQ Design Science MathType with MathPage

technology TeX4ht Amaya

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What we’ll coverWhat we’ll cover Part I – Understanding MathML Part II – Magic Incantations Part III – Tools

Design Science WebEQ Design Science MathType with MathPage

technology TeX4ht Amaya

Now on to Part I – Understanding MathML

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Overview of MathMLOverview of MathML The Mathematical Markup Language

(MathML) was first published as a recommendation in April 1998.

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From the “Math Activity Statement” of the W3C Math Working Group:

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The Mathematical Markup Language (MathML) was first published as a recommendation in April 1998.

From the “Math Activity Statement” of the W3C Math Working Group: “Designed as an XML application, MathML

provides two sets of tags, one for the visual presentation of mathematics and the other associated with the meaning behind equations.”

Overview of MathMLOverview of MathML

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From the “Math Activity Statement” of the W3C Math Working Group: “…two sets of tags…” “MathML is not designed for people to enter by

hand but specialized tools provide the means for typing in and editing mathematical expressions.”

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Anatomy of a MathML expressionAnatomy of a MathML expression About 30 MathML presentation elementselements

which accept about 50 attributesattributes

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Most elements represent templates or patternsfor laying out subexpressions. For example, there is an mfrac element for fractions, and anmsqrt element for square roots.



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Attributes generally specify additional optionalinformation about the element. Each attributehas a name and a value. For example, the mfracelement has an attribute called linethickness.



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which accept about 50 attributesattributes Using presentation markup, it’s possible to

precisely control how an expression will look when displayed.

About 120 content elements, accepting about a dozen attributes.

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Most content elements represent either operatorsor mathematical data types. For example, there is a divide/ element for division, and an emptysetelement to denote the empty set.

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Content markup facilitates applications other than display, like computer algebra and speech synthesis.

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Two types of elementsTwo types of elements Most presentation elements have start and

end tags, similar to the way some HTML has start and end tags.<element_name>…</element_name> These elements can have other data in-between

the start and end tags, such as text, extended characters, or other elements.

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end tags, similar to the way some HTML has start and end tags.<element_name>…</element_name>

The other type of MathML element is an empty element of the form<element_name/> These elements have just one tag.

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The other type of MathML element is an empty element of the form<element_name/> These elements have just one tag. There are only 4 empty presentation elements,

but over 100 empty content elements, used in prefix notation.

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The other type of MathML element is an empty element of the form<element_name/>

Elements can also accept attributes. If an element has both start & end tags, the

attribute immediately precedes the > in the start tag.

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The other type of MathML element is an empty element of the form<element_name/>

Elements can also accept attributes. In empty elements, attributes immediately

precede the />.

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Examples of attributesExamples of attributes

<mfrac linethickness='0'>…

</mfrac>

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</mfrac>

<mspace width='12'/>

Inserts a 12-pt space. For 12 pixels, use “12px”.

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</mfrac>

<mspace width='12'/>

<mtable columnalign="center">…

</mtable>

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Basic presentation elementsBasic presentation elements <mi> – identifier, such as a variable, function

name, constant, etc. example: <mi>x</mi>

rendering: x example: <mi>sin</mi>

rendering: sin

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name, constant, etc. <mo> – operator, such as a summation, fence

(parentheses, brace, etc.), accent, etc. example: <mo>(</mo>

rendering: ( example: <mo>∑</mo>

rendering:

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(parentheses, brace, etc.), accent, etc. example: <mo>(</mo>

rendering: ( example: <mo>∑</mo>

rendering: This is an example of an entity reference. Entity referencesare just keywords in a special format, which representextended characters. Other examples are α (lower-case Greek alpha), and ∞ (infinity).

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(parentheses, brace, etc.), accent, etc. <mn> – number

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(parentheses, brace, etc.), accent, etc. <mn> – number Can you identify this expression?

<mi>x</mi><mo>–</mo><mo>(</mo> <mn>3</mn><mo>+</mo><mi>y</mi><mo>)</mo>

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(parentheses, brace, etc.), accent, etc. <mn> – number Can you identify this expression?

<mi>x</mi><mo>–</mo><mo>(</mo> <mn>3</mn><mo>+</mo><mi>y</mi><mo>)</mo>

x – (3 + y)

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Token elementsToken elements Most MathML elements, like the mfrac

element mentioned earlier, expect to only find other MathML elements in their content…

…but some presentation elements – <mi>, <mo>, and <mn>, for example – are different. They are examples of token elements. Token elements are the only elements which

directly contain character data.

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ScriptsScripts Superscripts and subscripts are ubiquitous in

mathematical notation, and although you won’t be doing much MathML writing manually, it helps to familiarize yourself with the schemata.

MathML contains seven presentation elements for different kinds of scripts, but we’ll take a look at the most common.

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Scripts – sub & superScripts – sub & super These are the first elements we’ve seen in detail

that normally have more than one argument. Subscript: <msub> basebase scriptscript </msub> Superscript: <msup> basebase scriptscript </msup>

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that normally have more than one argument. Subscript: <msub> basebase scriptscript </msub> Superscript: <msup> basebase scriptscript </msup> Usage:

x1 <msub><mi><mi>xx</mi></mi><mn><mn>11</mn></mn></msub>

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Why can’t we code it this way:

<msub> x 1 </msub>?

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Because msub is not a token element. A token elementis the only element that can directly contain character data.

Why can’t we code it this way:

<msub> x 1 </msub>?

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x2 <msup><mi><mi>xx</mi></mi><mn><mn>22</mn></mn></msup>

<msubsup><mi><mi>xx</mi></mi><mn><mn>11</mn></mn><mn><mn>22</mn></mn></msubsup>

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Including MathML in your pageIncluding MathML in your page We need some way to identify the math

markup to our browser, plug-in, or applet. MathML markup is inserted between

<math> and </math>

tags to distinguish MathML from other markup. Although most tags will differ from presentation

markup to content markup, the <math> tag is common to both.

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Coding simple expressionsCoding simple expressions As we stated at the beginning, it is not our

goal in this tutorial to make you proficient at writing MathML. You’ll likely use a software product to produce the

MathML markup rather than write it yourself. Our goal is to familiarize you enough with the

MathML syntax and construction that you can read and understand a block of code, and can perhaps make changes to it by hand.

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Coding simple expressionsCoding simple expressions As we stated at the beginning, it is not our

goal in this tutorial to make you proficient at writing MathML.

That being the case, you know enough MathML now to try your hand at coding a couple of simple expressions…

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Example 1 – try coding this…Example 1 – try coding this…

2b 4

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<math>

</math>

Don’t forget to begin with the <math> start tag and end with the </math> end

tag

Don’t forget to begin with the <math> start tag and end with the </math> end

tag

2b 4

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<math>

<msup>

<mi>b</mi>

<mn>2</mn>

</msup>

<mo>–</mo><mn>4</mn>

</math>

2b 4

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Example 1aExample 1a

2b 4ac

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<math>

<msup>

<mi>b</mi>

<mn>2</mn>

</msup>

<mo>–</mo><mn>4</mn><mi>a</mi><mi>c</mi>

</math>

2b 4ac

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or…2b 4ac

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<math> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo> <mn>4</mn> <mo>⁢<mo> <mi>a</mi> <mo>⁢<mo> <mi>c</mi></math>

Example 1aExample 1aThis entity doesn’t appear in

print, but here we have added

it to facilitate voice synthesisand heuristic evaluation bycomputer algebra systems.

2b 4ac

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<math> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo> <mn>4</mn> <mo>⁢<mo> <mi>a</mi> <mo>⁢<mo> <mi>c</mi> </mrow></math>


24bac−

Horizontal row of expressions aligned on the baseline.

Wrapping an mrow around an element or elements is always

permissible, and often necessary in order to group terms together, for example, for use in a script,

etc.

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€

x2 + y2 = r2

Example 2 – one more…Example 2 – one more…

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Example 2 – one more…Example 2 – one more…<math> <mrow> <msup> <mi>x</mi><mn>2</mn> </msup> <mo>+</mo> <msup> <mi>y</mi><mn>2</mn> </msup> <mo>=</mo> <msup> <mi>r</mi><mn>2</mn> </msup> </mrow></math>

€

x2 + y2 = r2

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Other presentation elementsOther presentation elements Presentation elements are grouped:

Token Elements <mi> identifier <mn> number <mo> operator, fence, or separator <mtext> text

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Token Elements General Layout

<mrow> to group subexpressions <mfrac> form fraction from 2 subexpressions <mroot> radical with a specified index <mfenced> surround content with a pair of fences

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Token Elements General Layout Scripts and Limits

<msub>, <msup>, <msubsup> <munder> attach a script under a base <mover> attach a script over a base <munderover> attach a script both under

and over a base

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Token Elements General Layout Scripts and Limits Tables

<mtable> table or matrix <mtr> row in a table or matrix <mtd> one entry in a table or matrix

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Token Elements General Layout Scripts and Limits Tables Actions

<maction> binds actions to a subexpression

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Content elementsContent elements Most fundamental to content markup is the <apply> element, which enables the explicit application of a function to its argument.

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Content elementsContent elements <apply> application of a function to argument. Token Elements

<cn> content number <ci> content identifier

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Content elementsContent elements <apply> application of a function to argument. Token Elements Basic Content Elements

<inverse/> generic inverse <compose/> compose 2 or more functions <piecewise> piecewise defined function

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Content elementsContent elements <apply> application of a function to argument. Token Elements Basic Content Elements Arithmetic, Algebra, and Logic

<divide/> division <power/> to the power of <root/> nth root <conjugate/> complex conjugate

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Content elementsContent elements <apply> application of a function to argument. Token Elements Basic Content Elements Arithmetic, Algebra, and Logic Relations

<eq/> equal <geq/> greater than or equal <factorof/> the “divides” operator

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Content elementsContent elements <apply> application of a function to argument. Token Elements Basic Content Elements Arithmetic, Algebra, and Logic Relations Calculus and Set Theory

<partialdiff/> partial derivative <lowlimit> lower limit (of integral, etc.) <union/> union or meet

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Content elementsContent elements <apply> application of a function to argument. Token Elements Basic Content Elements Arithmetic, Algebra, and Logic Relations Calculus and Set Theory Further element groups include sequences &

series, elementary classical functions, statistics, linear algebra, semantic mapping elements, and constants.

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Example 3 – content markupExample 3 – content markup We want to code this expression in content

markup:

We know we need to surround the code with the <math>…</math> element…

…but we haven’t seen yet how to combine content elements to create an entire expression, so here goes…

€

cosπ = −1

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Example 3 – content markupExample 3 – content markup

€

cosπ = −1

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Example 3 – content markupExample 3 – content markup

<math> <apply> <eq/> <apply> <cos/> <ci>π</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

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cosπ = −1

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Example 3 – content markupExample 3 – content markup<math> <apply> <eq/> <apply><apply> <cos/> <cos/> <ci>π</ci> <ci>π</ci> </apply> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

to the left of the

to the right of the

€

cosπ = −1

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Example 3 – compareExample 3 – compare<math> <apply> <eq/> <apply> <cos/> <ci>π</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

<math><mi>cos</mi><mi>π</mi><mo>=</mo><mo>–</mo><mn>1</mn>

</math>

€

cosπ = −1

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SummarySummary Presentation markup is for describing math

notation, and content markup is for describing mathematical objects and functions. In presentation markup, expressions are built-up

using layout schemata, which tell how to arrange their subexpressions (i.e., mfrac or msup).

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SummarySummary Presentation markup…& content markup MathML elements either

have start and end tags to enclose their content, or

use a single empty tag.

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SummarySummary Presentation markup…& content markup MathML elements… Attributes may be specified in a start or

empty tag. Attribute values must be enclosed in quotes.

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SummarySummary Presentation markup…& content markup MathML elements… Attributes … in a start or empty tag. All character data must be enclosed in token

elements.

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SummarySummary Presentation markup…& content markup MathML elements… Attributes … in a start or empty tag. All character data … token elements. Extended characters are encoded as entity

references.

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SummarySummary Presentation markup…& content markup MathML elements… Attributes … in a start or empty tag. All character data … token elements. Extended characters as…entity references. We discussed other layout schemata – math, mfrac, mrow, etc.

The next session of the tutorial will deal with displaying MathML in browsers.

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Part II – Magic IncantationsPart II – Magic Incantations

DOCTYPEs & MIME types Namespaces Object Tags and Processing Instructions Universal MathML Stylesheet

Triggering MathML rendering in browsers requires special declarations in the page.

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Which Browsers?Which Browsers? Internet Explorer (requires add-on software)

The main choices are: MathPlayer (IE5.5 or higher under Windows) Techexplorer (IE5 or higher, many platforms) JavaScript/CSS (IE6 Windows, others soon?)

Netscape (add-ons required before NS7 PR1)

Some things to note: MathML doesn’t yet work on the Mac The decision to include MathML isn’t final

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DOCTYPEs and MIME typesDOCTYPEs and MIME types There are two ways browsers determine what

kind of data needs to be displayed. Local files indicate their type with a filename

extension (Windows, Unix) or extra data included in the file (Mac).

Data coming over an http connection doesn’t have a filename. Thus, web servers include extra data about what kind of file is being sent. This extra data is called a MIME type.

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DOCTYPEs and MIME typesDOCTYPEs and MIME types Web servers generally use file extensions to

pick the MIME type. This doesn’t always work…

Netscape 7 is fanatical about using only the MIME type to determine how to display a document.

Internet Explorer is extremely cavalier in using the MIME type, preferring to sniff inside the document to guess its type.

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MIME typesMIME types We are concerned with three kinds of files:

XML files. This includes XHTML files. Netscape 7 will only render MathML in this kind of file.

HTML files. Internet Explorer will only render MathML in HTML files.

XSL files. These are also XML files, but they usually end .xsl instead of .xml, which screws up many/most web servers.

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XHTML vs HTMLXHTML vs HTML

Start and end tags must always match. Things such as <br /> must be empty tags. All attributes must have quotes around them Your code actually has to be correct!

XHTML and HTML are nearly the same. The main difference is that XHTML is picky while HTML is lax.

The most important things are:

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MIME typesMIME typesThe upshot is: To work in Netscape, you need an XML

document. To work in Internet Explorer you need an

HTML document. So, in practice you create an XHTML

document, and fiddle with the MIME type On the server using scripts, etc. On the client using XSL stylesheets.

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DOCTYPEsDOCTYPEs A DOCTYPE is a special declaration at the

beginning of an HTML or XML document that defines what kind of markup is in the document. DOCTYPEs are really for validation, not

identification. DOCTYPEs point to a DTD, which defines the

syntax of the markup in the document.

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DOCTYPEsDOCTYPEs

<!DOCTYPE html SYSTEM "..//xhtml-math11-f.dtd">

<!DOCTYPE html PUBLIC"-//W3C//DTD XHTML 1.0 Strict//EN""../DTD/xhtml1-strict.dtd">

<!DOCTYPE html PUBLIC"-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN""http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd"[ <!ENTITY mathml http://www.w3.org/1998/Math/MathML"> ]>

Typical DOCTYPE declarations look like this:

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DOCTYPEsDOCTYPEs Netscape 7 requires a DOCTYPE, but

doesn’t actually look at the DTD to which it points. Instead the DTD must match one of a few

predefined values.

Internet Explorer doesn’t require a DOCTYPE, but it does download the DTD and use it if there is one.

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DOCTYPEsDOCTYPEsThe upshot is: In your XHTML document, you put a

DOCTYPE, and The W3C Math WG pulls its hair out trying to

make a DTD available that is both correct and works around the bugs in the IE parser.

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NamespacesNamespaces

XML languages are identified by a URI. MathML is http://www.w3.org/1998/Math/MathML XHTML is http://www.w3.org/1999/xhtml

They can be indicated in two ways. By using an xmlns attribute on an element By adding a prefix to element names

Complexities arise when two XML dialects must mix. The case of interest is XHTML + MathML. The solution is to use namepaces.

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<html xmlns="http://www.w3.org/1999/xhtml">

…

<math xmlns="http://www.w3.org/1998/Math/MathML">

<mi>x</mi><mo>+</mo><mn>2</mn>

</math>

…

</html>

Use the xmlns attribute on the outermost element of the embedded markup. This places the element on which the attribute is set, and its children in the indicated namespace.

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<html xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML"> … <m:math> <m:mi>x</m:mi><m:mo>+</m:mo><m:mn>2</m:mn> </m:math> …</html>

To use prefixes, you must Associate a prefix and a namespace using an xmlns:prefix attribute on a containing element.

Use the prefix to identify elements that should be in the namespace.

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Namespaces & DOCTYPEsNamespaces & DOCTYPEs

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "xhtml-math11-f.dtd" [<!ENTITY mathml

http://www.w3.org/1998/Math/MathML">]>

<html xmlns="http://www.w3.org/1999/xhtml" … <math xmlns="&mathml;"> <mi>x</mi><mo>+</mo>< mn>2</mn> </math> …</html>

Since the URIs for namespaces are long, one trick some people like is to declare an entity reference for it in the DOCTYPE:

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Objects and PIsObjects and PIs

The <object> element instructs IE what piece of software to load.

A processing instruction (or PI) is used to assign the add-on software to render markup from a particular namespace.

Two additional declarations are required to trigger add-on software for math rendering in Internet Explorer:

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<OBJECT ID="behave1" CLASSID="clsid:32F66A20-7614-11D4-BD11-00104BD3F987"></OBJECT>

Windows uses a long string of digits and letters called a class id to uniquely identify software components.

The object tag uses an attribute to specify a class id:

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<OBJECT ID="behave1" CLASSID="clsid:32F66A20-7614-11D4-BD11-00104BD3F987"></OBJECT>

<?IMPORT NAMESPACE="M" IMPLEMENTATION="#behave1" ?>

There are many kinds of processing instructions, with different attributes.

For “IE behaviors” one specifies a namespace, and the ID of an object:

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Behaviors are actually triggered by a namespace prefix, and not the namespace itself.

The upshot is, to use add-ons such as MathPlayer or Techexplorer, You must include an OBJECT and PI. You must use the prefix method for namespaces.

One complexity arises from a bug in Internet Explorer behaviors:

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Putting It TogetherPutting It Together

Write XHTML Include a DOCTYPE Include an OBJECT and PI Include a namespace declaration Use namespace prefixes on the MathML

Altogether then, to create a document that works in both IE and Netscape, you must:

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Putting It TogetherPutting It Together

Netscape will only render your document if it is XML.

Internet Explorer will only render it if it is HTML.

The solution? XSL stylesheets…

But wait! Even if you do all that, there is still the insurmountable problem of MIME types:

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The MathML StylesheetThe MathML Stylesheet

You add an XSL stylesheet to an XML document using a PI.

The stylesheet sits on the server with your document.

The stylesheet runs in the client to transform your document for viewing.

An XSL stylesheet is a set of templates for transforming an input document into an output document.

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Detect what browser it is running in and output either XML or HTML accordingly

Detect what add-ons are installed and output the necessary Object and PI declarations

Convert content to presentation markup

XSL is powerful. The W3C Math WG has created a Universal MathML Stylesheet which can:

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<?xml-stylesheet type="text/xsl" href="style/mathml.xsl"?>

The MathML stylesheet PI looks like this:

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Include the stylesheet PI. Write XHTML. Don’t use entity references.

Use numeric references instead. Use namespaces to indicate the MathML. Don’t use Object tags or behavior PIs. It’s not necessary to use a DOCTYPE.

In order to use the MathML stylesheet,

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SummarySummary

The document must be XHTML (NS). It needs a DOCTYPE (NS). The MathML must be in a namespace (both,) and

you have to use the prefix method (IE). You need an <object> element and behavior PI (IE). Serve it as XML for NS, and HTML for IE.

Getting MathML in a document to render in both IE and Netscape is quite a trick. The necessary ingredients are:

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SummarySummary

The document must be XHTML without entity names.

Include the stylesheet PI. The MathML must be in a namespace (either

method). You can omit the DOCTYPE, <object>

element and behavior PI.

A simpler, alternative method which also deals with the MIME types is to use the Universal Math Stylesheet:

introduction to using mathml

Documents

mathml expressionabout

mathml presentation

content elements

attributesmost elements

w3c math

math activity statement

mfrac element

mathematical expressions