MEPresentation1

Mathematical Markup Language : 

Mathematical Markup Language Presented by : SHRADHA .D.MORE

What we’ll cover : 

What we’ll cover Part I – Understanding MathML Overview of MathML Presentation and content markup MathML elements

Overview of MathML : 

Overview of MathML 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 MathML : 

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 MathML

Overview of MathML : 

Overview of MathML 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: “…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.”

Overview of MathML : 

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: “…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.” Overview of MathML

Anatomy of a MathML expression : 

Anatomy of a MathML expression About 30 MathML presentation elements which accept about 50 attributes 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. Content markup facilitates applications other than display, like computer algebra and speech synthesis.

Two types of elements : 

Two 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.

Two types of elements : 

Two 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> 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.

Two types of elements : 

Two 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> 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.

Two types of elements : 

Two 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> 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 />.

Basic presentation elements : 

Basic presentation elements <mi> – identifier, such as a variable, function name, constant, etc. example: <mi>x</mi>rendering: x example: <mi>sin</mi>rendering: sin

Basic presentation elements : 

Basic presentation elements <mi> – identifier, such as a variable, function name, constant, etc. <mo> – operator, such as a summation, fence (parentheses, brace, etc.), accent, etc. example: <mo>(</mo>rendering: ( example: <mo>&sum;</mo>rendering: S

Basic presentation elements : 

Basic presentation elements <mi> – identifier, such as a variable, function name, constant, etc. <mo> – operator, such as a summation, fence (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)

Token elements : 

Token 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.

Scripts : 

Scripts 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.

Scripts – sub & super : 

Scripts – sub & super These are the first elements we’ve seen in detail that normally have more than one argument. Subscript: <msub> base script </msub> Superscript: <msup> base script </msup> Usage:x1 <msub><mi>x</mi><mn>1</mn></msub> x2 <msup><mi>x</mi><mn>2</mn></msup> x1 <msubsup><mi>x</mi> <mn>1</mn> <mn>2</mn></msubsup> 2 Why can’t we code it this way: <msub> x 1 </msub>?

Including MathML in your page : 

Including 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.

Coding simple expressions : 

Coding 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.

Coding simple expressions : 

Coding 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…

Example 1 – try coding this… : 

Example 1 – try coding this… <math> </math>

Example 1 – try coding this… : 

Example 1 – try coding this… <math> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo><mn>4</mn> </math>

Example 1a : 

<math> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo> <mn>4</mn> <mo>&InvisibleTimes;<mo> <mi>a</mi> <mo>&InvisibleTimes;<mo> <mi>c</mi> </mrow></math> Example 1a <math> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo><mn>4</mn><mi>a</mi><mi>c</mi> </math> or… <math> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>–</mo> <mn>4</mn> <mo>&InvisibleTimes;<mo> <mi>a</mi> <mo>&InvisibleTimes;<mo> <mi>c</mi></math> This entity doesn’t appear inprint, but here we have addedit to facilitate voice synthesisand heuristic evaluation bycomputer algebra systems. 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.

Example 2 – one more… : 

Example 2 – one more… <math display='block'> <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>

Other presentation elements : 

Other presentation elements Presentation elements are grouped: Token Elements <mi> identifier <mn> number <mo> operator, fence, or separator <mtext> text

Other presentation elements : 

Other presentation elements Presentation elements are grouped: 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

Other presentation elements : 

Other presentation elements Presentation elements are grouped: 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

Other presentation elements : 

Other presentation elements Presentation elements are grouped: 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

Other presentation elements : 

Other presentation elements Presentation elements are grouped: Token Elements General Layout Scripts and Limits Tables Actions <maction> binds actions to a subexpression

Content elements : 

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

Content elements : 

Content elements <apply> application of a function to argument. Token Elements <cn> content number <ci> content identifier

Content elements : 

Content 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

Content elements : 

Content 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

Content elements : 

Content 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

Content elements : 

Content 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

Content elements : 

Content 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.

Example 3 – content markup : 

Example 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…

Example 3 – content markup : 

Example 3 – content markup <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

Example 3 – content markup : 

Example 3 – content markup <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

Example 3 – content markup : 

Example 3 – content markup <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

Example 3 – content markup : 

Example 3 – content markup <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math> to the left of the = to the right of the =

Example 3 – content markup : 

Example 3 – content markup <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math>

Example 3 – compare : 

Example 3 – compare <math> <apply> <eq/> <apply> <cos/> <ci>&pi;</ci> </apply> <apply> <minus/> <cn>1</cn> </apply> </apply></math> <math> <mi>cos</mi> <mi>&pi;</mi> <mo>=</mo> <mo>–</mo> <mn>1</mn></math>

Summary : 

Summary 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).

Summary : 

Summary Presentation markup…& content markup MathML elements either have start and end tags to enclose their content, or use a single empty tag.

Summary : 

Summary Presentation markup…& content markup MathML elements… Attributes may be specified in a start or empty tag. Attribute values must be enclosed in quotes.

Summary : 

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

Summary : 

Summary 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.

Summary : 

Summary 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.