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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>\[ \left<a href="ltx-164.html">\{</a>
- \begin{<a href="ltx-202.html">array</a>}{ccc}
- a &amp; b &amp; c <a href="ltx-181.html">\\</a>
- d &amp; e &amp; f \end{array}
- \right<a href="ltx-164.html">\}</a> \]</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>\[ f(x) =
- \left\{ \begin{array}{l}
- 0, x &lt; 0 \\ 1, x = 0 \\
- 2, x &gt; 0 \end{array} \right. \]</tt>
-</pre>
-will be displayed as
-<pre>
-<tt> ( 0, x &lt; 0
- f(x) = - 1, x = 0
- ( 2, x &gt; 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>
-