Mathematical Text and other Special Symbols

Equations can be inserted into your text in several ways. Placing $...$ or \(...\) or \begin{math} ...\end{math} around the mathematical expression or special symbol allows you to place it in a line of normal text. This will use the smaller symbols (see Figure 4), and adjust the size of the formula as necessary. It will also adjust other things. For example, to place $\sum_{i=1}^n$ in a line of text, L^ATEX puts the ``i=1'' to the right of the $\sum$ instead of underneath. Placing \[...\] or \begin{displaymath}... \end{displaymath} around the expression will center it and set it off from the rest of the text, using the larger symbols.

  

Figure 4: Mathematical Symbols

$$\sum$$ $\sum$ \sum

$$\prod$$ $\prod$ \prod

$$\coprod$$ $\coprod$ \coprod

$$\int$$ $\int$ \int

$$\oint$$ $\oint$ \oint

$$\bigcap$$ $\bigcap$ \bigcap

$$\bigcup$$ $\bigcup$ \bigcup

$$\bigsqcup$$ $\bigsqcup$ \bigsqcup

$$\bigvee$$ $\bigvee$ \bigvee

$$\bigwedge$$ $\bigwedge$ \bigwedge

$$\bigodot$$ $\bigodot$ \bigodot

$$\bigotimes$$ $\bigotimes$ \bigotimes

$$\bigoplus$$ $\bigoplus$ \bigoplus

$$\biguplus$$ $\biguplus$ \biguplus

To create a simple equation, for example F=ma, you need only type $ F=ma $. For more advanced formulæ, like E=mc², you need to tell L^ATEX to superscript the 2. The ^ character instructs L^ATEX to superscript, and the _ character instructs L^ATEX to subscript.

For example, $ E=mc^2 $ is used to produce E=mc². Likewise $ x_{k+1} $ is used to produce x_k+1 .

If you want to put more than one character in the superscript or subscript, you need to group them, using { and } as in the examples above. To print something with both superscripts and subscripts, like 238U+4, just type $ _{238}U^{+4} $.21 Anything can go into the brackets, and LATEX will figure out what to do with it: x35+9<<880>>yz+4z1997 requires the hideous expression $x^{35+9^{y_{z}}+4_{z}}_{1997}$, but if you look carefully it should be clear what is happening. To get the prime (') symbol in math mode, type an apostrophe ('). Try some complex expressions of your own, and see how easy they are to create. There are many symbols not found on the keyboard to help you in formatting just about any kind of formula. See Figures 5, 6, 7 and 8 for symbols not found on the keyboard, like $\pm$, $\geq$, and $\wp$.

  

Figure 5: Binary Operations

  

Figure 6: Relations

  

Figure 7: Arrows

  

Figure 8: Miscellaneous Symbols

Of course, not all expressions are polynomials. L^ATEX uses two special cases, \sqrt and \frac to create square roots (radical sign surrounding the entire expression) and fractions (one expression over another with a dividing bar between them) respectively. The term $\sqrt{1-\frac{v^2}{c^2}}$, commonly used in Lorentz transformations, is expressed as $\sqrt{1-\frac{v^2}{c^2}} $ in line. You might want it displayed as

$$\sqrt{1-\frac{v^2}{c^2}}$$

instead, which is generated with \[\sqrt{1-\frac{v^2}{c^2}} \].

If the equation is more interesting, or if you want to refer to it later on, you might want to assign it a number by using the equation environment. The quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ (1)

is displayed by

\begin{equation}
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\end{equation}

You can supply an optional argument to \sqrt, specifying a different root than 2. For example, the fourth root, $\sqrt[4]{1024}$, is expressed as \sqrt[4]{1024}.

Often in a mathematical equation you will want to use symbols instead of the standard italicized letters for variable names. You can add Greek letters by typing the command associated with the particular letter--see Figures 9 and 10.

  

Figure 9: Lowercase Greek

  

Figure 10: Uppercase Greek

Note that if you want to use Greek letters in normal text mode, you must place them in a math environment by surrounding them with $...$. You can also create function names with the $\cal CALLIGRAPHY$ font. This is treated like any type style change such as \bf, but like the Greek letters, you can use it only in math mode. In addition, you only have the 26 upper-case letters available (see Figure 11).

  

Figure 11: Calligraphic Symbols

Sometimes, a formula contains text that should be set in roman type. For example, in the formula `` $\log xy = \log x + \log y$,'' the word ``log'' is not italicized like the variables x and y. It would be inconvenient to have to exit math mode to type the text in normal roman type, so the most common function names are defined as special commands. If the desired command isn't defined, you can use something like $x = \textrm{foo}$ to produce x = foo rather than x = foo. A formula such as $\cos^2 x + \sin^2 x = 1$ would be entered as $\cos^2 x + \sin^2 x = 1$. See Figure 12 for a list of all the special commands which are typeset like this.

The modulo function is slightly different from the other special commands--it has two forms, a binary and a parenthesized one. See Figure 13 for an example of their usage. There are also various types of brackets and other delimiters available in math mode, as shown in figure 14. Certain accents and other diacritical marks are available in math mode. Some of these math mode accents are only available in math mode, while others are modified to work better in math mode. See Figure 15 for examples.

  

Figure 12: Log-like symbols

  

Figure 13: Modulus functions

  

Figure 14: Delimiters

  

Figure 15: Math-mode accents

The symbols in Figure 16 were provided by L^ATEX 2.09, but not by L^ATEX2_e. You can access them by using the latexsym package.

  

Figure 16: Symbols available in the latexsym package