0.3 Mathml infrastructure

The MathML infrastructure comprises of three important segments of resource base :

Mathml resource base

• Elements
• Unicode character set
• Attributes

Elements

The MathML captures markup requirements for mathematical content display through layered encapsulation of markup design, using three groups of elements (token, layout and table elements).

The underlying philosophy of the mark up design is easily understood in terms of the implementation of a fraction in $\frac{P}{Q}$ form. Once the basic form of the fraction is coded, then second layer of coding is taken up for the numerator expression, followed by third layer of coding for the denominator expression. Thus, we see that coding paradigm for a fraction in the form of $\frac{P}{Q}$ is layered over each other with the core of “mfrac” element. It must be emphasized that we refer layering in reference to the sequence of coding requirements, which should be written one after another and not the display, which is structured in two dimensions. The illustration shown in the figure displays a portion of “Rogers-Ramanujan identity” :

We see that “mfrac” element provides the core structure for nominator and denominator. Subsequently, either of numerator or denominator or both may have elements, which may further require display in two dimensions. Matter of fact, numerator expression, in the illustration above, consists of nested super scripts.

This type of layered coding design is an immense help in generating code for MathML. In contrast to the two dimensional display requirements, the coding requirement is essentially linear. The display of “Rogers-Ramanujan identity” is a point in the case. The figure below outlines the coding sequence. Note that we proceed writing code from left to right, encapsulating two dimensional aspects along the way, such as subscripting and ratio formation with MathML constructors. And we do it all, one after another in sequence.

Unicode character set

The MathML displays data, symbols and text with the help of token elements, which are capable to render a set of certain characters. In all cases of rendering mechanism provided in MathML, the display output is a character or a series of characters. These characters are defined as the Unicode set of characters – about 900 in numbers and growing all the time to meet the requirement of mathematics in conveying special meaning to its expressions. Different font variants of a letter are treated as separate symbols as they may represent different mathematical meaning/ concept/ idea.

There are three ways to encode Unicode characters with token elements specialized in displaying characters:

1: Use the keyboard and type the characters as available on the keyboard.