(Excerpt from "The MathML Handbook" by Pavi Sandhu)

As we saw under Fundamentals of MathML, Presentation markup, and Content markup, MathML consist of two different markup schemes, each with its own set of tags and attributes. Presentation markup describes the visual structure of mathematical notation. It is useful in contexts that emphasize the visual aspects of mathematics; for example, displaying a technical paper in a Web page. Content markup, on the other hand, describes the symbolic meaning of a mathematical expression. It is useful in contexts where the precise meaning of a mathematical expression has to be communicated; for example, when you are evaluating an equation in a computer algebra system.

In many cases, there is a natural correspondence between the notation for a mathematical expression and its symbolic meaning. Hence, given the presentation encoding for an expression, you can infer its meaning — and therefore its content encoding. However, the correspondence between mathematical notation and meaning is imperfect. As we saw under MathML attributes, the same notation may express more than one mathematical concept; conversely, a given concept can be expressed by different notations. In such cases, there is no simple relationship between the presentation markup and content markup for an expression.

Presentation markup and content markup thus play a complementary role, with each providing a different type of information about a mathematical expression. When authoring a document containing MathML, you can use either presentation or content markup exclusively, depending on the audience for the document and the purpose for which it will be used. However, each of these options has certain limitations. If you use presentation markup, you are limited in the amount of information you can provide about the meaning of the encoded expression. If you use content markup, you cannot directly control how a given expression will be rendered.

To overcome these limitations, MathML also allows a third option, mixing presentation and content tags inside the same math element. This type of markup is called combined markup. It provides a way to specify information about both the presentational and semantic aspects of mathematics, in a single MathML expression, thus allowing a more complete description of any mathematical construct.

Combined markup can be classified into two main types, depending on the structure of the expression tree. If presentation and content tags are mixed together within a single branch of the expression tree, the resulting markup is called mixed markup. If the expression tree contains both content and presentation encodings of the same expression, enclosed in parallel within a semantics element, the resulting markup is called parallel markup. In the rest of this chapter we shall see examples of both types of markup, the situations in which they are useful, and the rules that govern them.


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