# Content mathml  (Page 3/3)

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The eq operator is used to write equations. It is used in the same way as any other operator. That is, itis the first child of an apply. It takes two (or more) children which are the two quantities that are equal to eachother. For example, " $a$ times $b$ plus $a$ times $c$ equals $a$ times the quantity $b$ plus $c$ " would be written as shown. <m:math> <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> </m:math> This will display as $ab+ac=a(b+c)$ .

## Integrals

The operator for an integral is int . However, unlike the operators and functions discussed above, it haschildren that define the independent variable that you integrate with respect to ( bvar ) and the interval over which the integral is taken (use either lowlimit and uplimit , or interval , or condition ). lowlimit and uplimit (which go together), interval , and condition are just three different ways of denoting the integrands. Don't forget that the bvar, lowlimit , uplimit , interval , and condition children take token elements as well. The following is "the integral of $f$ of $x$ with respect to $x$ from 0 to $b$ ." <m:math> <m:apply> <m:int/> <m:bvar><m:ci>x</m:ci></m:bvar> <m:lowlimit><m:cn>0</m:cn></m:lowlimit> <m:uplimit><m:ci>b</m:ci></m:uplimit> <m:apply> <m:ci type='fn'>f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\int_{0}^{b} f(x)\,d x$ .

## Derivatives

The derivative operator is diff . The derivative is done in much the same way as the integral. That is, youneed to define a base variable (using bvar ). The following is "the derivative of the function $f$ of $x$ , with respect to $x$ ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> </m:bvar> <m:apply> <m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\frac{d f(x)}{d x}}$ .

To apply a higher level derivative to a function, add a degree tag inside of the bvar tag. The degree tag will contain the order of the derivative. Thefollowing shows "the second derivative of the function $f$ of $x$ , with respect to $x$ ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> <m:degree><m:cn>2</m:cn></m:degree> </m:bvar> <m:apply><m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\frac{d^{2}f(x)}{dx^{2}}$ .

## Vector and matrices

Vectors are created as a combination of other elements using the vector tag. <m:math> <m:vector> <m:apply> <m:plus/> <m:ci>x</m:ci> <m:ci>y</m:ci> </m:apply> <m:ci>z</m:ci> <m:cn>0</m:cn> </m:vector> </m:math> This will display as $\left(\begin{array}{c}x+y\\ z\\ 0\end{array}\right)$ .

Matrices are done in a similar manner. Each matrix element contains several matrixrow elements. Then each matrixrow element contains several other elements. <m:math> <m:matrix> <m:matrixrow> <m:ci>a</m:ci> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>d</m:ci> <m:ci>e</m:ci> <m:ci>f</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>g</m:ci> <m:ci>h</m:ci> <m:ci>j</m:ci> </m:matrixrow> </m:matrix> </m:math> This will display as $\begin{pmatrix}a & b & c\\ d & e & f\\ g & h & j\\ \end{pmatrix}$ .

There are also operators to take the determinant and the transpose of a matrix as well as to select elements fromwithin the matrix.

## Entities

The use of MathML character entity references in Connexions content is deprecated .

MathML defines its own entities for many special characters used in mathematical notation. While the entity references have the advantage of being mnemonic with respect to the characters they stand for, they also entail some technical limitations, and so their use in Connexions content is deprecated. Please use the UTF-8-encoded Unicode characters themselves where possible, or, failing that, the XML Unicode character references for the characters. At some time in the future, the Connexions repository system will likely convert entity references and character references silently to the UTF-8-encoded Unicode characters they stand for. See 6.2.1 Unicode Character Data from the XML Specification for more information. The MathML specification contains a list of character entities with their corresponding Unicode code points .

There are character picker utilities available to help you select and paste UTF-8 characters into applications like Connexions. If you are running Microsoft Windows, the Windows accessory Character Map can help you. The "Lucida Sans Unicode" font seems to have a good selection of mathematical operators and special characters. Under Linux, the charmap utility and GNOME applet provide access to all Unicode characters.

## Other resources

There is a lot more that can be done with Content MathML. Especially if you are planning on writing a lot of ContentMathML, it is well worth your time to take a look at the MathML specification .

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