# Using TeX Notation

Note: You are currently viewing documentation for Moodle 2.2. Up-to-date documentation for the latest stable version is available here: Using TeX Notation.

While there are quite a few notational systems employed for the purpose of representing Math notation, Moodle core provides a TeX filter that can be configured to employ identified latex, dvips and convert binaries to display a gif or png representation of a Tex expression (and hopefully will soon be able to take advantage of newer Tex distributions which will rely on latex and dvipng.) The Moodle core Tex filter falls back to the use of MimeTex if these binaries can't be located. Note that the core TeX filter is not the only way to display Tex expressions in Moodle and the discussion of Mathematics tools address a variety of other solutions. Additionally, the results obtained from the Moodle Tex or algebra filters are dependent on the Tex binaries you have installed.

If you use the Moodle native TeX Notation, you have to realize that this is not the only way of using TeX in Moodle and there are quite a few other "flavors" in the Tex world. You must also accept that the Moodle implementation of TeX is very limited, and a lot of things that work in other varieties of TeX and Latex will not work in TeX Notation. For example, there are three major Tex modes, but the Moodle core Tex filter employs only one. To make matters even more confusing, Moodle Docs now use Tex Live, which uses the delimiters $statement$ to denote TeX statements, yet these pages demonstrate the use of tokens, the $$statement$$ token, that implement TeX in Moodle's native TeX Notation. Essentially, what may work in one Tex implementation, may not work in another - yet a lot of the actual maths coding is exactly the same, no matter how it is denoted.

TeX itself is felt by some to present a significant learning curve, and the internet offers a number of tutorials. A.J. Hildebrand, a Math professor at UIUC offers resources and a tutorial here that you may find helpful. However, the basics of TeX can be mastered quite quickly.

There are a number of Maths tools available and probably one of the more useful tools for using Tex in Moodle (or elsewhere for that matter), is Dragmath which will allow you to use a GUI constructor to build your expression, and then insert it in the format you choose.

There is now, for Moodle 2.x, and Advanced Maths Tools plugin.

## NOTICE

The discussion in these pages is centred entirely upon using the TeX Notation filter in Moodle. The code examples given are proven to work inside Moodle, but much of the discussion that addresses Tex syntax can be generalized to other applications that parse Tex. So far, all items tested work in both Moodle 1.9.x and Moodle 2.0 without change or further refinement.

## Using TeX Notation with the Moodle Tex filter

For the most part, the TeX Notation has been built using a sub-set of characters from the TeX "default" character set. The trouble is there does not seem to be a "default" character set for TeX. This is one of the most confusing aspects of using TeX Notation in Moodle. When we realise that the documentation we are using is related to the creation of printed documents, and we want to use TeX on line, in Moodle, then further problems occur. There are no environment statements to be made. There are few \begins and \ends. If you go to Administration > Modules > Filters > Filter Manager you will see what filters have been enabled. If you then go to the TeX Notation page, the default preamble is editable via the text box. Using this tool you can add in or subtract font packages and other packages, change the default font package, etc.

## Superscripts, Subscripts and Roots

Superscripts are recorded using the caret, ^, symbol. An example for a Maths class might be:

 $$4^2 \ \times \ 4^3 \ = 4^5$$
This is a shorthand way of saying:
(4 x 4) x (4 x 4 x 4) = (4 x 4 x 4 x 4 x 4)
or
16 x 64 = 1024.

$4^2 \ \times \ 4^3 \ = 4^5$


Subscripts are similar, but use the underscore character.

 $$3x_2 \ \times \ 2x_3$$

$3x_2 \ \times \ 2x_3$


This is OK if you want superscripts or subscripts, but square roots are a little different. This uses a control sequence.

 $$\sqrt{64} \ = \ 8$$

$\sqrt{64} \ = \ 8$


You can also take this a little further, but adding in a control character. You may ask a question like:

 $$If \ \sqrt[n]{1024} \ = \ 4, \ what \ is \ the \ value \ of \ n?$$

$If \ \sqrt[n]{1024} \ = \ 4, \ what \ is \ the \ value \ of \ n?$


Using these different commands allows you to develop equations like:

 $$The \sqrt{64} \ \times \ 2 \ \times \ 4^3 \ = \ 1024$$

$The \sqrt{64} \ \times \ 2 \ \times \ 4^3 \ = \ 1024$


Superscripts, Subscripts and roots can also be noted in Matrices.

## Fractions

Fractions in TeX are actually simple, as long as you remember the rules.

 $$\frac{numerator}{denominator}$$ which produces $\frac{numerator}{denominator}$ .


This can be given as:

 $\frac{5}{10} \ is \ equal \ to \ \frac{1}{2}$.


This is entered as:

 $$\frac{5}{10} \ is \ equal \ to \ \frac{1}{2}.$$


With fractions (as with other commands) the curly brackets can be nested so that for example you can implement negative exponents in fractions. As you can see,

 $$\frac {5^{-2}}{3}$$ will produce $\frac {5^{-2}}{3}$

 $$\left(\frac{3}{4}\right)^{-3}$$ will produce $\left(\frac{3}{4}\right)^{-3}$  and

 $$\frac{3}{4^{-3}}$$ will produce $\frac{3}{4^{-3}}$

 You likely do not want to use $$\frac{3}{4}^{-3}$$ as it produces $\frac{3}{4}^{-3}$


You can also use fractions and negative exponents in Matrices.

## Brackets

As students advance through Maths, they come into contact with brackets. Algebraic notation depends heavily on brackets. The usual keyboard values of ( and ) are useful, for example:

  $d = 2 \ \times \ (4 \ - \ j)$


This is written as:

 $$d = 2 \ \times \ (4 \ - \ j)$$


Usually, these brackets are enough for most formulae but they will not be in some circumstances. Consider this:

 $4x^3 \ + \ (x \ + \ \frac{42}{1 + x^4})$


Is OK, but try it this way:

 $4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right)$


This can be achieved by:

 $$4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right)$$


A simple change using the \left( and \right) symbols instead. Note the actual bracket is both named and presented. Brackets are almost essential in Matrices.

## Ellipsis

The Ellipsis is a simple code:

 $x_1, \ x_2, \ \ldots, \ x_n$


Written like:

 $$x_1, \ x_2, \ \ldots, \ x_n$$


A more practical application could be:

Question:

 "Add together all the numbers from 1 $\ldots$ 38.
What is an elegant and simple solution to this problem?
Can you create an algebraic function to explain this solution?
Will your solution work for all numbers?"


Answer: The question uses an even number to demonstrate a mathematical process and generate an algebraic formula.

 Part 1: Part 2. Part 3. $1. \ 1 \ + \ 38 \ = \ 39$ $2. \ 2 \ + \ 37 \ = \ 39$ $3. \ 3 \ + \ 36 \ = \ 39$ $\ldots$ $19. 19 \ + \ 20 \ = \ 39$ $\therefore x \ = \ 39 \ \times \ 19$ $\therefore x \ = \ 741$ An algebraic function might read something like: $t = (1 + n) \times n/2$ Where t = total and n = the last number. The solution is that, using the largest and the smallest numbers, the numbers are added and then multiplied by the number of different combinations to produce the same result adding the first and last numbers. The answer must depend on the number, $\frac{n}{2}$ being a whole number. Therefore, the solution will not work for an odd range of numbers, only an even range.