# 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)

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".

See also:
See also Math Formulas,
Math Symbols

Back to the LaTeX Table of Contents

Revised: Sheldon Green, 28 Nov 1995.