## Hypertext Help with LaTeX

### Delimiters

Delimiters are objects which act logically like parentheses. These can be used only in math mode.

The delimiters recognized by LaTeX include

• ( (left parenthesis)
• ) (right parenthesis)
• [ (left bracket)
• ] (right bracket)
• \{ (left brace)
• \} (right brace)
• | (vertical line)
• \vert (vertical line)
• \| (double vertical lines)
• \Vert (double vertical lines)
• / (slash)
• \backslash (backslash)
• \langle (left angle bracket)
• \rangle (right angle bracket)
• \uparrow (uparrow)
• \downarrow (down arrow)
• \updownarrow (up/down arrow)

### Making delimiters the right size

Delimiters in formulas should be big enough to "fit" around the formulas they delimit (for example arround arrays). To obtain "stretchable" delimiters (LaTeX makes them the appropriate size) type a \left or \right command before the delimiter. \left and \right commands must come in matching pairs, although the delimiters themselves need not be the same. Thus,

    \left \{ ... \right $ produces a legal pair. In cases where only one delimiter is desired, it is possible to make the matching delimiter "invisible" by typing a period (.) after the command, i.e., \left. or \right.. In an eqnarray environment the matching \left and \right cannot be split between lines and it may be necessary to use an "invisible" \right. and \left. to terminate and begin parts on different lines. In this case a second problem may arise, since the size of the delimiters will be chosen only for the local part, so that the size of the visible "left" and "right" delimiters might not match. The solution is to trick LaTeX into thinking that both parts have the same vertical height. This can be done by placing a strut, that is a zero-width \rule. It can also be accomplished with the \vphantom command, which I have not found documented, but which appears to work.  \vphantom{construct}  creates a zero-width object with the height of construct. The argument can contain things such as \frac or the variable size math symbols and should be chosen according to what is in the section with the delimiter you want to match. ### Some examples #### A six-j symbol  \[ \left\{ \begin{array}{ccc} a & b & c \\ d & e & f \end{array} \right\}$


This should be displayed something like (insofar as it can be rendered in "ASCII art"):

    ( a b c )
-       -
( d e f )


Note that the $...$ set this off as Display Math, and that the Array Environment is used to generate the three centered columns inside the braces.

#### A "multiple choice" equation

    $f(x) = \left\{ \begin{array}{l} 0, x < 0 \\ 1, x = 0 \\ 2, x > 0 \end{array} \right.$


will be displayed as

             ( 0, x < 0
f(x) =  - 1, x = 0
( 2, x > 0


Note that the "invisible" \right delimiter is specified using a "period".