The fundamental concept to grasp about Content MathML is that it consists of applying a series of functions and operators to other elements. To do this, Content MathML uses prefix notation. Prefix notation is when the operator comes first and is followed by the operands. Here is how to write "2 plus 3".
<m:apply>
<m:plus/>
<m:ci>2</m:ci>
<m:ci>3</m:ci>
</m:apply>
There are three types of elements in the Content MathML example shown above. First, there is the apply tag, which indicates that an operator (or function) is about to be applied to the operands. Second, there is the function or operator to be applied. In this case the operator, plus, is being applied. Third, the operands follow the operator. In this case the operands are the numbers being added. In summary, the apply tag applies the function (which could be sin or f, etc.) or operator (which could be plus or minus, etc.) to the elements that follow it.
Tokens
Content MathML has three tokens: ci, cn, and csymbol. A token is basically the lowest level element; it contains no other Content MathML. The tokens denote what kind of element you are acting on. The cn tag indicates that the content of the tag is a number. The ci tag indicates that the content of the tag is an identifier. An identifier could be any variable or function; x, y, and f are examples of identifiers. In addition, ci elements can contain Presentation MathML. Tokens, especially ci and cn, are used profusely in Content MathML. Every number, variable, or function is marked by a token.
csymbol is a different type of token from ci and cn. It is used to create a new object that is defined externally. It can take plain text or Presentation MathML. If you find that you need something, such as an operator or function, that is not defined in Content MathML, then you can use csymbol to create it.
Both ci and csymbol can use Presentation MathML to determine how an identifier or a new symbol will be rendered. To learn more about Presentation MathML see Section 3 of the MathML 2.0 Specification. For example, to denote "x with a subscript 2", where the 2 does not have a more semantic meaning, you would use the following code.
<m:ci>
<m:msub>
<m:mi>x</m:mi>
<m:mn>2</m:mn>
</m:msub>
</m:ci>
The ci elements have a type attribute which can be used to provide more information about the content of the element. For example, you can declare the contents of a ci tag to be a function (type='fn'), or a vector (type='vector'), or a complex number (type='complex'), as well as any number of other things. Using the type attribute helps encode the meaning of the math that you are writing.
Functions and Operators
In order to apply a function to a variable, make the function the first argument of an apply. The second argument will be the variable. For example, you would use the following code to encode the meaning, "the function f of x". (Note that you have to include the attribute type='fn' on the ci tag denoting f.)
<m:apply>
<m:ci type='fn'>f</m:ci>
<m:ci>x</m:ci>
</m:apply>
There are also pre-defined functions and operators in Content MathML. For example, sine and cosine are predefined. These predefined functions and operators are all empty tags and they directly follow the apply tag. "the sine of x" is similar to the example above.
<m:apply>
<m:sin/>
<m:ci>x</m:ci>
</m:apply>
You can find a more thorough description of the different predefined functions in the MathML specification.
In addition to the predefined functions, there are also many predefined operators. A few of these are <m:plus/> (for addition), <m:minus/> (for subtraction), <m:times/> (for multiplication), <m:divide/> (for division), <m:power/> (for taking the n-power of something), and <m:root/> (for taking the n-root of something).
Most operators expect a specific number of child tags. For example, the power operator expects two children. The first child is the base and the second is the value in the exponent. However, there are other tags which can take many children. For example, the plus operator merely expects one or more children. It will add together all of its children whether there are two or five.
Representing "the negative of a number" and explicitely representing "the positive of a number" has slightly unusual syntax. In this case you apply the plus or minus operator to the number or variable, etc., in question. The following is the code for "negative x."
<m:apply>
<m:minus/>
<m:ci>x</m:ci>
</m:apply>
To create more complicated expressions, you can nest these bits of apply code within each other. "a times the quantity b plus c" would be written as follows.
<m:apply>
<m:times/>
<m:ci>a</m:ci>
<m:apply>
<m:plus/>
<m:ci>b</m:ci>
<m:ci>c</m:ci>
</m:apply>
</m:apply>
The eq operator is used to write equations. It is used in the same way as any other operator. That is, it is the first child of an apply. It takes two children which are the two quantities that are equal to each other. For example, "a times b plus a times c equals a times the quantity b plus c" would be written as shown.
<m:apply>
<m:eq/>
<m:apply>
<m:plus/>
<m:apply>
<m:times/>
<m:ci>a</m:ci>
<m:ci>b</m:ci>
</m:apply>
<m:apply>
<m:times/>
<m:ci>a</m:ci>
<m:ci>c</m:ci>
</m:apply>
</m:apply>
<m:apply>
<m:times/>
<m:ci>a</m:ci>
<m:apply>
<m:plus/>
<m:ci>b</m:ci>
<m:ci>c</m:ci>
</m:apply>
</m:apply>
</m:apply>
