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<html>
<head>
<title>Delimiters</title>
</head>
<body bgcolor="#ffffff" text="#000000" link="#000099" vlink="#cc0000" alink="#cc0000">
<h1><font size="-2">Hypertext Help with LaTeX</font><br><font color="#cc0000">Delimiters</font></h1>
Delimiters are objects which act logically like parentheses. These can
be used only in math mode.
<p>
The delimiters recognized by LaTeX include
<ul>
<li><tt>(</tt> (left parenthesis)
<li><tt>)</tt> (right parenthesis)
<li><tt>[</tt> (left bracket)
<li><tt>]</tt> (right bracket)
<li><tt>\{</tt> (left brace)
<li><tt>\}</tt> (right brace)
<li><tt>|</tt> (vertical line)
<li><tt>\vert</tt> (vertical line)
<li><tt>\|</tt> (double vertical lines)
<li><tt>\Vert</tt> (double vertical lines)
<li><tt>/</tt> (slash)
<li><tt><a href="ltx-164.html">\backslash</a></tt> (backslash)
<li><tt>\langle</tt> (left angle bracket)
<li><tt>\rangle</tt> (right angle bracket)
<li><tt>\uparrow</tt> (uparrow)
<li><tt>\downarrow</tt> (down arrow)
<li><tt>\updownarrow</tt> (up/down arrow)
</ul>
<h2><a name="big">Making delimiters the right size</a></h2>
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 <tt>\left</tt> or <tt>\right</tt> command before
the delimiter. <tt>\left</tt> and <tt>\right</tt> commands must come in
matching pairs, although the delimiters themselves need not be the same.
Thus, <pre> \left \{ ... \right \[ </pre> 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 (<tt>.</tt>) after the command, i.e.,
<tt>\left.</tt> or <tt>\right.</tt>.
<p>
In an <a href="ltx-223.html">eqnarray environment</a> the matching <tt>\left</tt>
and <tt>\right</tt> cannot be split between lines and it may be necessary to
use an "invisible" <tt>\right.</tt> and <tt>\left.</tt> 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
<strong>local part</strong>, so that the size of the <strong>visible</strong>
"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 <a href="ltx-306.html"><tt>\rule</tt></a>. It
can also be accomplished with the <tt>\vphantom</tt> command, which I have
not found documented, but which appears to work.
<p>
<pre><tt>\vphantom{construct}</tt></pre>
creates a zero-width object with the height of <tt>construct</tt>. The
argument can contain things such as <a href="ltx-235.html"><tt>\frac</tt></a>
or the <a href="ltx-408.html">variable size math symbols</a> and should
be chosen according to what is in the section with the delimiter you want to match.
<h2>Some examples</h2>
<h3>A six-j symbol</h3>
<pre>
<tt>\[ \left<a href="ltx-164.html">\{</a>
\begin{<a href="ltx-202.html">array</a>}{ccc}
a & b & c <a href="ltx-181.html">\\</a>
d & e & f \end{array}
\right<a href="ltx-164.html">\}</a> \]</tt>
</pre>
This should be displayed something like (insofar as it can be rendered in
"ascii art"):
<pre>
( a b c )
- -
( d e f )
</pre>
Note that the <tt>\[ ... \]</tt> set this off as <a href="ltx-421.html">
Display Math</a>, and that the <a href="ltx-202.html">Array Environment</a>
is used to generate the three centered columns inside the braces.
<h3>A "multiple choice" equation</h3>
<pre>
<tt>\[ f(x) =
\left\{ \begin{array}{l}
0, x < 0 \\ 1, x = 0 \\
2, x > 0 \end{array} \right. \]</tt>
</pre>
will be displayed as
<pre>
<tt> ( 0, x < 0
f(x) = - 1, x = 0
( 2, x > 0</tt>
</pre>
Note that the "invisible" <tt>\right</tt> delimiter is specified using
a "period".
<hr>
See also:
See also <a href="ltx-115.html">Math Formulas</a>,
<a href="ltx-117.html">Math Symbols</a>
<ul>
<li><a href="ltx-404.html">Binary and relational operators</a>
<li><a href="ltx-115.html">Math formulas</a>,
<li><a href="ltx-202.html">Arrays</a>
<li><a href="ltx-406.html">Arrows</a>
<li><a href="ltx-408.html">Variable size symbols (sums, integrals, etc.)</a>
</ul>
<hr>
Back to the <a href="ltx-2.html">LaTeX Table of Contents</a>
<hr>
<address>
Revised: Sheldon Green, 28 Nov 1995.
</address>
</body>
</html>
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