Introduction to the course in mathml  (Page 2/4)

3: It would not be possible to copy and paste the content and modify the same. This constitues a major handicap in treating mathematical content as picture. We can only select the picture file as a whole - not a part of it. (Try to copy the right hand expression of the equation presented below.)

4: The problem with pictures is that they have an invisible box around them whose color remains that of the background at the time of its capture as picture. The color of the box is, thus, independent of background color of the rendering document. When the background color of the document (rendering system) is changed, mathematical content in ficture fromat pops up with the color of box surrounding it.

The dispay of the same mathematical content as rendendered with MathML encoding is presented here for comparison with the earlier display as picture :

Display with MathML : $${\mathrm{\alpha }}^2+{\mathrm{\beta }}^2+\mathrm{2\alpha \; \beta }$$

Nature of mathematical expression

Mathematical content or expression differs significantly in comparison to normal text. We here present the major differences in the display requirement of the two types of presentation.

Mathematical expression is vastly different in the visual presentation and associated meaning that it conveys. Rendering of normal text in the newspaper or printed books or the ones typed in the standard text editor on the desk top - thanks to the beauty of the structure of the language - is limited to, may be, 50 characters. A change in font and style does not change the the meaning of the text (for exmaple what is said in a paragraph), whereas, mathematical expression is sensitive to the visual forms of font and accompanying style. A particular character style may be attached to the underlying mathematical meaning. For this reason, there are about 900 Unicode characters used in MathML – many of which may not of required in a particular context, but needed in the totality of mathematical expanse.

Normal text flows in horizontal rows. Each character, composing the text, comprises of a base line, which is used as reference for horizontal alignment. In the case of mathematical expressions, the bases of the constituent characters are not at the same level. Consider the limits assigned to an expression involving integration.

$${\int }_a^b{e}^{x}dx$$

This difference in the structural levels of constituents may be repetitive as well :

$$g(z)=e_{}^{-\sum _{i=0}^{\infty }{z}_i^2}$$

The examples shown above highlight the two dimensional aspect of mathematical rendering. In the nutshell, normal text has a linear layout, whereas mathematical expression has two dimensional lay out. This aspect, in turn, introduces the requirement of alignment of characters along multiple horizontal and vertical lines.

Renderdering of expresion in the $\raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$Q$}\right.\hspace{1em}$ format is typical of the requirement of presentation in vertical direction. Presentation of $x=\raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$Q$}\right.\hspace{1em}$ , on the other hand, is actually a combination of single and two dimensional presentations, where linear (x =) and two dimensional elements (nominator and denominator parts above and below horizontal divider) are required to be aligned along a central horizontal line.