[latexrefman-commits] [SCM] latexrefman updated: r645 - in trunk: . graphics

jimhefferon at gnu.org.ua jimhefferon at gnu.org.ua
Sun Jun 10 01:37:34 CEST 2018


Author: jimhefferon
Date: 2018-06-10 02:37:33 +0300 (Sun, 10 Jun 2018)
New Revision: 645

Modified:
   trunk/ChangeLog
   trunk/graphics/README
   trunk/latex2e.html
   trunk/latex2e.info
   trunk/latex2e.pdf
   trunk/latex2e.texi
Log:
math miscellany

Modified: trunk/ChangeLog
===================================================================
--- trunk/ChangeLog	2018-06-08 16:55:33 UTC (rev 644)
+++ trunk/ChangeLog	2018-06-09 23:37:33 UTC (rev 645)
@@ -1,3 +1,11 @@
+2018-06-09  Jim Hefferon  <jhefferon at smcvt.edu>
+
+	* latex2e.texi (Math miscellany)  Move dots to separate subsection
+	under Math symbols.  Move \overline, etc. to separate subsection
+	after Math accents.  Move \imath and \jmath to Math symbols.
+	Change rest to a menu, with synopses and examples, and error
+	messages where appropriate.  Adjust wording.
+
 2018-06-07  Jim Hefferon  <jhefferon at smcvt.edu>
 
 	* latex2e.texi (\pagestyle)  Add description of mechanism,

Modified: trunk/graphics/README
===================================================================
--- trunk/graphics/README	2018-06-08 16:55:33 UTC (rev 644)
+++ trunk/graphics/README	2018-06-09 23:37:33 UTC (rev 645)
@@ -1,5 +1,8 @@
 This directory contains the source for the graphics used in the document.
 
-Note that different TeXinfo output formats require different graphic
-formats.  TeXinfo wants them in ../latex2e-figures/.
+The asy/ directory contains the source for graphics produced with
+Asymptote.
 
+TeXinfo wants the graphics in ../latex2e-figures/.  Note that
+different TeXinfo output formats require different graphic formats.
+

Modified: trunk/latex2e.html
===================================================================
--- trunk/latex2e.html	2018-06-08 16:55:33 UTC (rev 644)
+++ trunk/latex2e.html	2018-06-09 23:37:33 UTC (rev 645)
@@ -346,11 +346,21 @@
       <li><a name="toc-Blackboard-bold-1" href="#Blackboard-bold">16.2.1 Blackboard bold</a></li>
       <li><a name="toc-Calligraphic-1" href="#Calligraphic">16.2.2 Calligraphic</a></li>
       <li><a name="toc-_005cboldmath-_0026-_005cunboldmath-1" href="#g_t_005cboldmath-_0026-_005cunboldmath">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></a></li>
+      <li><a name="toc-Ellipses-1" href="#Ellipses">16.2.4 Ellipses</a></li>
     </ul></li>
     <li><a name="toc-Math-functions-1" href="#Math-functions">16.3 Math functions</a></li>
     <li><a name="toc-Math-accents-1" href="#Math-accents">16.4 Math accents</a></li>
-    <li><a name="toc-Spacing-in-math-mode-1" href="#Spacing-in-math-mode">16.5 Spacing in math mode</a></li>
-    <li><a name="toc-Math-miscellany-1" href="#Math-miscellany">16.6 Math miscellany</a></li>
+    <li><a name="toc-Over_002d-and-Underlining-1" href="#Over_002d-and-Underlining">16.5 Over- and Underlining</a></li>
+    <li><a name="toc-Spacing-in-math-mode-1" href="#Spacing-in-math-mode">16.6 Spacing in math mode</a></li>
+    <li><a name="toc-Math-miscellany-1" href="#Math-miscellany">16.7 Math miscellany</a>
+    <ul class="no-bullet">
+      <li><a name="toc-Colon-character-_003a-_0026-_005ccolon" href="#Colon-character-_0026-_005ccolon">16.7.1 Colon character <code>:</code> & <code>\colon</code></a></li>
+      <li><a name="toc-_005c_002a-1" href="#g_t_005c_002a">16.7.2 <code>\*</code></a></li>
+      <li><a name="toc-_005cfrac-1" href="#g_t_005cfrac">16.7.3 <code>\frac</code></a></li>
+      <li><a name="toc-_005cleft-_0026-_005cright-1" href="#g_t_005cleft-_0026-_005cright">16.7.4 <code>\left</code> & <code>\right</code></a></li>
+      <li><a name="toc-_005csqrt-1" href="#g_t_005csqrt">16.7.5 <code>\sqrt</code></a></li>
+      <li><a name="toc-_005cstackrel-1" href="#g_t_005cstackrel">16.7.6 <code>\stackrel</code></a></li>
+    </ul></li>
   </ul></li>
   <li><a name="toc-Modes-1" href="#Modes">17 Modes</a>
   <ul class="no-bullet">
@@ -5434,7 +5444,8 @@
 </pre></div>
 
 <p>or
-</p><div class="example">
+</p>
+<div class="example">
 <pre class="example">\item[<var>optional-label</var>] text of item
 </pre></div>
 
@@ -5570,7 +5581,7 @@
 \end{minipage}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\begin{minipage}[<var>position</var>][<var>height</var>][<var>inner-pos</var>]{<var>width</var>}
@@ -6838,7 +6849,7 @@
 \end{table}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\begin{table}[<var>placement</var>]
@@ -7448,7 +7459,7 @@
 <pre class="example">\bibitem{<var>cite_key</var>}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\bibitem[<var>label</var>]{<var>cite_key</var>}
@@ -7525,7 +7536,7 @@
 <pre class="example">\cite{<var>keys</var>}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\cite[<var>subcite</var>]{<var>keys</var>}
@@ -7955,10 +7966,17 @@
 blank lines to separate the stanzas.
 </p>
 <div class="example">
-<pre class="example">A poem is a piece of poetry.
-
-And don't let the head of the poetry society \\
-tell you diff'rent.
+<pre class="example">\begin{verse}
+\makebox[\linewidth][c]{\textit{Shut Not Your Doors} ---Walt Whitman}
+  \\[1\baselineskip]
+Shut not your doors to me proud libraries,                  \\
+For that which was lacking on all your well-fill'd shelves, \\
+\qquad yet needed most, I bring,                             \\
+Forth from the war emerging, a book I have made,            \\
+The words of my book nothing, the drift of it every thing,  \\
+A book separate, not link'd with the rest nor felt by the intellect, \\
+But you ye untold latencies will thrill to every page.
+\end{verse}
 </pre></div>
 
 <p>The output has margins indented on the left and the right, paragraphs
@@ -8031,7 +8049,7 @@
 \\[<var>morespace</var>]
 </pre></div>
 
-<p>or one of: 
+<p>or one of these. 
 </p>
 <div class="example">
 <pre class="example">\\*
@@ -8394,7 +8412,7 @@
 \linebreak[<var>zero-to-four</var>]
 </pre></div>
 
-<p>or one of:
+<p>or one of these.
 </p>
 <div class="example">
 <pre class="example">\nolinebreak
@@ -8496,7 +8514,7 @@
 <pre class="example">\clearpage
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\cleardoublepage
@@ -8645,7 +8663,7 @@
 \pagebreak[<var>zero-to-four</var>]
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\nopagebreak
@@ -9139,7 +9157,7 @@
 \newcommand*{\<var>cmd</var>}[<var>nargs</var>][<var>optargdefault</var>]{<var>defn</var>}
 </pre></div>
 
-<p>or one of:
+<p>or one of these.
 </p>
 <div class="example">
 <pre class="example">\renewcommand{\<var>cmd</var>}[<var>nargs</var>]{<var>defn</var>}
@@ -9488,7 +9506,7 @@
 \newenvironment*{<var>env</var>}[<var>nargs</var>][<var>optargdefault</var>]{<var>begdef</var>}{<var>enddef</var>}
 </pre></div>
 
-<p>or one of:
+<p>or one of these.
 </p>
 <div class="example">
 <pre class="example">\renewenvironment{<var>env</var>}{<var>begdef</var>}{<var>enddef</var>}
@@ -10859,7 +10877,7 @@
 <pre class="example">\indent
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\noindent
@@ -11122,13 +11140,15 @@
 <p>The two mathematics modes are similar, but there are some differences.
 One involves the placement of subscripts and superscripts; in display
 math mode they are further apart and in inline math mode they are closer
-together.  Sometimes you want the display math treatment to happen in
-the inline math mode.  For this, the <code>\displaystyle</code> declaration
-forces the size and style of the formula to be that of
-<code>displaymath</code>.  Thus <code>\(\displaystyle \sum_{n=0}^\infty
-x_n\)</code> will have the limits above and below the summation sign, not next
-to it.  Another example is that
+together.
 </p>
+<p>Sometimes you want the display math treatment to happen in the inline
+math mode.  For this, the <code>\displaystyle</code> declaration forces the
+size and style of the formula to be that of <code>displaymath</code>.  Thus
+<code>\(\displaystyle \sum_{n=0}^\infty x_n\)</code> will have the limits
+above and below the summation sign, not next to it.  Another example is
+that
+</p>
 <div class="example">
 <pre class="example">\begin{tabular}{r|cc}
   \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
@@ -11153,10 +11173,12 @@
 </td></tr>
 <tr><td align="left" valign="top">• <a href="#Math-accents" accesskey="4">Math accents</a>:</td><td>  </td><td align="left" valign="top">Accents in math.
 </td></tr>
-<tr><td align="left" valign="top">• <a href="#Spacing-in-math-mode" accesskey="5">Spacing in math mode</a>:</td><td>  </td><td align="left" valign="top">Thick, medium, thin, and negative spaces.
+<tr><td align="left" valign="top">• <a href="#Over_002d-and-Underlining" accesskey="5">Over- and Underlining</a>:</td><td>  </td><td align="left" valign="top">Things over or under formulas.
 </td></tr>
-<tr><td align="left" valign="top">• <a href="#Math-miscellany" accesskey="6">Math miscellany</a>:</td><td>  </td><td align="left" valign="top">Stuff that doesn’t fit anywhere else.
+<tr><td align="left" valign="top">• <a href="#Spacing-in-math-mode" accesskey="6">Spacing in math mode</a>:</td><td>  </td><td align="left" valign="top">Thick, medium, thin, and negative spaces.
 </td></tr>
+<tr><td align="left" valign="top">• <a href="#Math-miscellany" accesskey="7">Math miscellany</a>:</td><td>  </td><td align="left" valign="top">Stuff that doesn’t fit anywhere else.
+</td></tr>
 </table>
 
 
@@ -11181,7 +11203,7 @@
 <pre class="example"><var>base</var>^<var>exp</var>
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example"><var>base</var>_<var>exp</var>
@@ -11728,6 +11750,13 @@
 <dd><p>&#x2111; Imaginary part (ordinary).  See: real part <code>\Re</code>.
 </p>
 </dd>
+<dt><code>\imath</code>
+<a name="index-_005cimath"></a>
+</dt>
+<dd><a name="index-dotless-i_002c-math"></a>
+<p>Dotless i; used when you are putting an accent on an i (see <a href="#Math-accents">Math accents</a>).
+</p>
+</dd>
 <dt><code>\in</code>
 <a name="index-_005cin"></a>
 </dt>
@@ -11761,6 +11790,13 @@
 TeX.
 </p>
 </dd>
+<dt><code>\jmath</code>
+<a name="index-_005cjmath"></a>
+</dt>
+<dd><a name="index-dotless-j_002c-math"></a>
+<p>Dotless j; used when you are putting an accent on a j (see <a href="#Math-accents">Math accents</a>).
+</p>
+</dd>
 <dt><code>\kappa</code>
 <a name="index-_005ckappa"></a>
 </dt>
@@ -12780,6 +12816,42 @@
 </dd>
 </dl>
 
+<p>The following symbols are most often used in plain text but LaTeX
+provides versions to use in mathematical text.
+</p>
+<dl compact="compact">
+<dt><code>\mathdollar</code>
+<a name="index-_005cmathdollar"></a>
+</dt>
+<dd><p>Dollar sign in math mode: $.
+</p>
+</dd>
+<dt><code>\mathparagraph</code>
+<a name="index-_005cmathparagraph"></a>
+</dt>
+<dd><p>Paragraph sign (pilcrow) in math mode, &#x00B6;.
+</p>
+</dd>
+<dt><code>\mathsection</code>
+<a name="index-_005cmathsection"></a>
+</dt>
+<dd><p>Section sign in math mode &#x00A7;.
+</p>
+</dd>
+<dt><code>\mathsterling</code>
+<a name="index-_005cmathsterling"></a>
+</dt>
+<dd><p>Sterling sign in math mode: £.
+</p>
+</dd>
+<dt><code>\mathunderscore</code>
+<a name="index-_005cmathunderscore"></a>
+</dt>
+<dd><p>Underscore in math mode: _.
+</p>
+</dd>
+</dl>
+
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#Blackboard-bold" accesskey="1">Blackboard bold</a>:</td><td>  </td><td align="left" valign="top">Doublestruck characters.
 </td></tr>
@@ -12787,6 +12859,8 @@
 </td></tr>
 <tr><td align="left" valign="top">• <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="3">\boldmath & \unboldmath</a>:</td><td>  </td><td align="left" valign="top">Symbols in boldface.
 </td></tr>
+<tr><td align="left" valign="top">• <a href="#Ellipses" accesskey="4">Ellipses</a>:</td><td>  </td><td align="left" valign="top">Dots.
+</td></tr>
 </table>
 
 
@@ -12867,7 +12941,7 @@
 <a name="g_t_005cboldmath-_0026-_005cunboldmath"></a>
 <div class="header">
 <p>
-Previous: <a href="#Calligraphic" accesskey="p" rel="prev">Calligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+Next: <a href="#Ellipses" accesskey="n" rel="next">Ellipses</a>, Previous: <a href="#Calligraphic" accesskey="p" rel="prev">Calligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
 </div>
 <a name="g_t_005cboldmath-_0026-_005cunboldmath-1"></a>
 <h4 class="subsection">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></h4>
@@ -12889,7 +12963,6 @@
 <pre class="example">\unboldmath \( <var>math</var> \)
 </pre></div>
 
-
 <a name="index-_005cboldmath-1"></a>
 <a name="index-_005cunboldmath-1"></a>
 <p>Declarations to change the letters and symbols in <var>math</var> to be in
@@ -12933,6 +13006,95 @@
 </p>
 
 <hr>
+<a name="Ellipses"></a>
+<div class="header">
+<p>
+Previous: <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="p" rel="prev">\boldmath & \unboldmath</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="Ellipses-1"></a>
+<h4 class="subsection">16.2.4 Ellipses</h4>
+
+<a name="index-ellipses"></a>
+<a name="index-dots"></a>
+
+<p>Ellipses are the three dots (usually three) indicating that a pattern
+continues.
+</p>
+<div class="example">
+<pre class="example">\begin{array}{cccc}
+  a_{0,0}    &a_{0,1}   &a_{0,2} &\ldots \\
+  a_{1,0}    &\ddots                     \\
+  \vdots
+\end{array}
+</pre></div>
+
+<p>LaTeX provides these.
+</p>
+<dl compact="compact">
+<dt><code>\cdots</code>
+<a name="index-_005ccdots"></a>
+</dt>
+<dd><p>Horizontal ellipsis with the dots raised to the center of the line, as
+in &#x22EF;.  Used as: <code>\( a_0\cdot a_1\cdots a_{n-1}
+\)</code>.
+</p>
+</dd>
+<dt><code>\ddots</code>
+<a name="index-_005cddots"></a>
+</dt>
+<dd><p>Diagonal ellipsis, &#x22F1;.  See the above example for a
+usage.
+</p>
+</dd>
+<dt><code>\ldots</code>
+<a name="index-_005cldots"></a>
+</dt>
+<dd><p>Ellipsis on the baseline, &#x2026;.  Used as: <code>\(
+x_0,\ldots x_{n-1} \)</code>.  A synonym is <code>\mathellipsis</code>.  A synonym
+from the <samp>amsmath</samp> package is <code>\hdots</code>.
+</p>
+<p>You can also use this command outside of mathematical text, as in
+<code>The gears, brakes, \ldots{} are all broken</code>.  (In a text mode a
+synonym for <code>\ldots</code> is <code>\dots</code>.)
+</p>
+</dd>
+<dt><code>\vdots</code>
+<a name="index-_005cvdots"></a>
+</dt>
+<dd><p>Vertical ellipsis, &#x22EE;.  See the above example for a
+usage.
+</p>
+</dd>
+</dl>
+
+<a name="index-package_002c-amsmath-4"></a>
+<a name="index-amsmath-package-4"></a>
+
+<p>The <samp>amsmath</samp> package has the command <code>\dots</code> to semantically
+mark up ellipses.  This example produces two different-looking outputs
+for the first two uses of the <code>\dots</code> command.
+</p>
+<div class="example">
+<pre class="example">\usepackage{amsmath}  % in preamble
+  ...
+Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes.
+Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a multiple of any \( p_i \).
+Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).
+</pre></div>
+
+<p>In the first line LaTeX looks to the comma following <code>\dots</code> to
+determine that it should output an ellipsis on the baseline.  The second
+line has a <code>\cdot</code> following <code>\dots</code> so LaTeX outputs an
+ellipsis that is on the math axis, vertically centered.  However, the
+third usage has no follow-on character so you have to tell LaTeX what
+to do.  You can use one of the commands: <code>\dotsc</code> if you need the
+ellipsis appropriate for a comma following, <code>\dotsb</code> if you need
+the ellipses that fits when the dots are followed by a binary operator
+or relation symbol, <code>\dotsi</code> for dots with integrals, or
+<code>\dotso</code> for others.
+</p>
+
+<hr>
 <a name="Math-functions"></a>
 <div class="header">
 <p>
@@ -13154,8 +13316,8 @@
 </dd>
 </dl>
 
-<a name="index-package_002c-amsmath-4"></a>
-<a name="index-amsmath-package-4"></a>
+<a name="index-package_002c-amsmath-5"></a>
+<a name="index-amsmath-package-5"></a>
 <p>The <samp>amsmath</samp> package adds improvements on some
 of these, and also allows you to define your own.  See the full
 documentation on CTAN, but
@@ -13169,7 +13331,7 @@
 <a name="Math-accents"></a>
 <div class="header">
 <p>
-Next: <a href="#Spacing-in-math-mode" accesskey="n" rel="next">Spacing in math mode</a>, Previous: <a href="#Math-functions" accesskey="p" rel="prev">Math functions</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+Next: <a href="#Over_002d-and-Underlining" accesskey="n" rel="next">Over- and Underlining</a>, Previous: <a href="#Math-functions" accesskey="p" rel="prev">Math functions</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
 </div>
 <a name="Math-accents-1"></a>
 <h3 class="section">16.4 Math accents</h3>
@@ -13242,20 +13404,6 @@
 <p>Math hat (circumflex) accent
 </p>
 </dd>
-<dt><code>\imath</code>
-<a name="index-_005cimath"></a>
-</dt>
-<dd><a name="index-dotless-i_002c-math"></a>
-<p>Math dotless i
-</p>
-</dd>
-<dt><code>\jmath</code>
-<a name="index-_005cjmath"></a>
-</dt>
-<dd><a name="index-dotless-j_002c-math"></a>
-<p>Math dotless j
-</p>
-</dd>
 <dt><code>\mathring</code>
 <a name="index-_005cmathring"></a>
 </dt>
@@ -13292,15 +13440,93 @@
 </dd>
 </dl>
 
+<p>When you are putting an accent on an i or a j, the tradition is to use
+one without a dot, <code>\imath</code> or <code>jmath</code> (see <a href="#Math-symbols">Math symbols</a>).
+</p>
 
 <hr>
+<a name="Over_002d-and-Underlining"></a>
+<div class="header">
+<p>
+Next: <a href="#Spacing-in-math-mode" accesskey="n" rel="next">Spacing in math mode</a>, Previous: <a href="#Math-accents" accesskey="p" rel="prev">Math accents</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="Over_002d-and-Underlining-1"></a>
+<h3 class="section">16.5 Over- and Underlining</h3>
+
+<a name="index-overlining"></a>
+<a name="index-underlining"></a>
+
+<p>LaTeX provides commands for making overlines or underlines, or
+putting braces over or under some material.
+</p>
+<dl compact="compact">
+<dt><code>\underline{<var>text</var>}</code>
+<a name="index-_005cunderline_007btext_007d"></a>
+</dt>
+<dd><p>Underline <var>text</var>.  Works inside math mode, and outside.
+The line is always completely below the text, taking account of
+descenders, so in <code>\(\underline{y}\)</code> the line is lower than in
+<code>\(\underline{x}\)</code>.  This command is fragile (see <a href="#g_t_005cprotect">\protect</a>).
+</p>
+<a name="index-package_002c-ulem"></a>
+<a name="index-ulem-package"></a>
+
+<p>Note that the package <samp>ulem</samp> does text mode underlining and allows
+line breaking as well as a number of other features.  See the
+documentation is on CTAN.
+</p>        
+</dd>
+<dt><code>\overline{<var>text</var>}</code>
+<a name="index-_005coverline_007btext_007d"></a>
+</dt>
+<dd><p>Put a horizontal line over <var>tex</var>.  Works inside math mode, and
+outside.  For example, <code>\overline{x+y}</code>.
+Note that this differs from the command <code>\bar</code> (see <a href="#Math-accents">Math accents</a>).
+</p>
+</dd>
+<dt><code>\underbrace{<var>math</var>}</code>
+<a name="index-_005cunderbrace_007bmath_007d"></a>
+</dt>
+<dd><p>Put a brace under <var>math</var>. For example, this
+<code>(1-\underbrace{1/2)+(1/2}-1/3)</code> emphasizes the telescoping part.
+Attach text to the brace by using subscript, <code>_</code>, or superscript,
+<code>^</code>, as here.
+</p>
+<div class="example">
+<pre class="example">\begin{displaymath}
+  1+1/2+\underbrace{1/3+1/4}_{>1/2}+
+       \underbrace{1/5+1/6+1/7+1/8}_{>1/2}+\cdots
+\end{displaymath}
+</pre></div>
+
+<p>The superscript appears on top of the expression, and so can look
+unconnected to the underbrace.
+</p>
+</dd>
+<dt><code>\overbrace{<var>math</var>}</code>
+<a name="index-_005coverbrace_007bmath_007d"></a>
+</dt>
+<dd><p>Put a brace over <var>math</var>; see also <code>\underbrace</code>.  An example is
+<code>\overbrace{x+x+\cdots+x}^{\mbox{\(k\) times}}</code>.
+</p>
+</dd>
+</dl>
+
+<a name="index-package_002c-mathtools-1"></a>
+<a name="index-mathtools-package-1"></a>
+
+<p>The package <samp>mathtools</samp> adds an over- and underbrace, as well as
+some improvements on the braces.  See the documentation on CTAN.
+</p>
+
+<hr>
 <a name="Spacing-in-math-mode"></a>
 <div class="header">
 <p>
-Next: <a href="#Math-miscellany" accesskey="n" rel="next">Math miscellany</a>, Previous: <a href="#Math-accents" accesskey="p" rel="prev">Math accents</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+Next: <a href="#Math-miscellany" accesskey="n" rel="next">Math miscellany</a>, Previous: <a href="#Over_002d-and-Underlining" accesskey="p" rel="prev">Over- and Underlining</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
 </div>
 <a name="Spacing-in-math-mode-1"></a>
-<h3 class="section">16.5 Spacing in math mode</h3>
+<h3 class="section">16.6 Spacing in math mode</h3>
 
 <a name="index-spacing-within-math-mode"></a>
 <a name="index-math-mode_002c-spacing"></a>
@@ -13376,167 +13602,236 @@
 Previous: <a href="#Spacing-in-math-mode" accesskey="p" rel="prev">Spacing in math mode</a>, Up: <a href="#Math-formulas" accesskey="u" rel="up">Math formulas</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
 </div>
 <a name="Math-miscellany-1"></a>
-<h3 class="section">16.6 Math miscellany</h3>
+<h3 class="section">16.7 Math miscellany</h3>
 
 <a name="index-math-miscellany"></a>
 
-<dl compact="compact">
-<dt><code>\*</code>
-<a name="index-_005c_002a"></a>
-</dt>
-<dd><a name="index-discretionary-multiplication"></a>
-<a name="index-multiplication-symbol_002c-discretionary-line-break"></a>
-<p>A <em>discretionary</em> multiplication symbol, at which a line break is
-allowed. Without the break multiplication is implicitly indicated by a
-space, while in the case of a break a &#x00D7; symbol is
-printed immediately before the break. So
+<p>LaTeX contains a wide variety of mathematics facilities.  Here are
+some that don’t fit into other categories.
 </p>
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">• <a href="#Colon-character-_0026-_005ccolon" accesskey="1">Colon character & \colon</a>:</td><td>  </td><td align="left" valign="top">Colon.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005c_002a" accesskey="2">\*</a>:</td><td>  </td><td align="left" valign="top">Discretionary multiplication.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005cfrac" accesskey="3">\frac</a>:</td><td>  </td><td align="left" valign="top">Fraction.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005cleft-_0026-_005cright" accesskey="4">\left & \right</a>:</td><td>  </td><td align="left" valign="top">Paired delimiters.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005csqrt" accesskey="5">\sqrt</a>:</td><td>  </td><td align="left" valign="top">Radicals.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005cstackrel" accesskey="6">\stackrel</a>:</td><td>  </td><td align="left" valign="top">Text over a relation.
+</td></tr>
+</table>
+
+
+<hr>
+<a name="Colon-character-_0026-_005ccolon"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005c_002a" accesskey="n" rel="next">\*</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="Colon-character-_003a-_0026-_005ccolon"></a>
+<h4 class="subsection">16.7.1 Colon character <code>:</code> & <code>\colon</code></h4>
+
+<a name="index-_003a"></a>
+<a name="index-colon-character"></a>
+<a name="index-_003a-1"></a>
+<a name="index-_005ccolon"></a>
+
+<p>Synopsis, one of:
+</p>
 <div class="example">
-<pre class="example">\documentclass{article}
-\begin{document}
-Now \(A_3 = 0\), hence the product of all terms \(A_1\) 
-through \(A_4\), that is \(A_1\* A_2\* A_3 \* A_4\), is 
-equal to zero.
-\end{document}
+<pre class="example">:
+\colon
 </pre></div>
 
-<p>will make that sort of output <!-- /@w -->(the ellipsis ‘<samp>[…]</samp>’ is here to show the line break at
-the same place as in a TeX output):
+<p>In mathematics, the colon character, <code>:</code>, is a relation.
 </p>
-<blockquote class="indentedblock">
-<p>Now <em>A_3 = 0</em>,
-[…]
-<em>A_1</em>
-through <em>A_4</em>, that is <em>A_1 A_2 \times</em><br><em>A_3 A_4</em>, is
-equal to zero.
-</p></blockquote>
+<div class="example">
+<pre class="example">With side ratios \( 3:4 \) and \( 4:5 \), the triangle is right.
+</pre></div>
 
-</dd>
-<dt><code>\cdots</code>
-<a name="index-_005ccdots"></a>
-</dt>
-<dd><p>A horizontal ellipsis with the dots raised to the center of the line.
+<a name="index-package_002c-amsmath-6"></a>
+<a name="index-amsmath-package-6"></a>
+
+<p>Ordinary LaTeX defines <code>\colon</code> to produce the
+colon character with the spacing appropriate for punctuation, as in
+set-builder notation <code>\{x\colon 0\leq x<1\}</code>.
 </p>
-</dd>
-<dt><code>\ddots</code>
-<a name="index-_005cddots"></a>
-</dt>
-<dd><p>A diagonal ellipsis: <em>\ddots</em>.
+<a name="index-package_002c-amsmath-7"></a>
+<a name="index-amsmath-package-7"></a>
+
+<p>But the widely-used <samp>amsmath</samp> package defines <code>\colon</code> for use
+in the definition of functions <code>f\colon D\to C</code>.  So if you want
+the colon character as a punctuation then use <code>\mathpunct{:}</code>.
 </p>
-</dd>
-<dt><code>\frac{<var>num</var>}{<var>den</var>}</code>
-<a name="index-_005cfrac_007bnum_007d_007bden_007d"></a>
-</dt>
-<dd><a name="index-_005cfrac"></a>
-<p>Produces the fraction <var>num</var> divided by <var>den</var>.
+
+<hr>
+<a name="g_t_005c_002a"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005cfrac" accesskey="n" rel="next">\frac</a>, Previous: <a href="#Colon-character-_0026-_005ccolon" accesskey="p" rel="prev">Colon character & \colon</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005c_002a-1"></a>
+<h4 class="subsection">16.7.2 <code>\*</code></h4>
+
+<a name="index-multiplication_002c-discretionary"></a>
+<a name="index-muiltiplication_002c-line-breaks"></a>
+<a name="index-multiplication-symbol_002c-discretionary-line-break"></a>
+<a name="index-_005c_002a"></a>
+
+<p>Synopsis:
 </p>
+<div class="example">
+<pre class="example">\*
+</pre></div>
 
-</dd>
-<dt><code>\left <var>delim1</var> ... \right <var>delim2</var></code>
-<a name="index-_005cleft-delim1-_002e_002e_002e-_005cright-delim2"></a>
-</dt>
-<dd><a name="index-_005cright"></a>
-<a name="index-null-delimiter"></a>
-<p>The two delimiters need not match; ‘<samp>.</samp>’ acts as a <em>null delimiter</em>,
-producing no output.  The delimiters are sized according to the math
-in between.  Example: <code>\left( \sum_{i=1}^{10} a_i \right]</code>.
+<p>A multiplication symbol that allows a line break.  If there is a break
+then LaTeX puts a <code>\times</code> symbol, &#x00D7;, before
+that break.
 </p>
-</dd>
-<dt><code>\mathdollar</code>
-<a name="index-_005cmathdollar"></a>
-</dt>
-<dd><p>Dollar sign in math mode: $.
+<p>In <code>\( A_1\* A_2\* A_3\* A_4 \)</code>, if there is no line break then
+LaTeX outputs it as though it were <code>\( A_1 A_2 A_3 A_4 \)</code>.  If
+a line break does happen, for example between the two middle ones, then
+LaTeX sets it like <code>\( A_1 A_2 \times \)</code>, followed by the
+break, followed by <code>\( A_3 A_4 \)</code>.
 </p>
-</dd>
-<dt><code>\mathellipsis</code>
-<a name="index-_005cmathellipsis"></a>
-</dt>
-<dd><p>Ellipsis (spaced for text) in math mode: …
+
+<hr>
+<a name="g_t_005cfrac"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005cleft-_0026-_005cright" accesskey="n" rel="next">\left & \right</a>, Previous: <a href="#g_t_005c_002a" accesskey="p" rel="prev">\*</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005cfrac-1"></a>
+<h4 class="subsection">16.7.3 <code>\frac</code></h4>
+
+<a name="index-fraction"></a>
+<a name="index-_005cfrac"></a>
+
+<p>Synopsis:
 </p>
-</dd>
-<dt><code>\mathparagraph</code>
-<a name="index-_005cmathparagraph"></a>
-</dt>
-<dd><p>Paragraph sign (pilcrow) in math mode: &#x00B6;.
+<div class="example">
+<pre class="example">\frac{<var>numerator</var>}{<var>denominator</var>}
+</pre></div>
+
+<p>Produces the fraction <var>numerator</var> divided by <var>denominator</var>.
+Used as: <code>\begin{displaymath} \frac{1}{\sqrt{2\pi\sigma}}
+\end{displaymath}</code>.  In inline math mode it comes out small; see the
+discussion of <code>\displaystyle</code> (see <a href="#Math-formulas">Math formulas</a>).
 </p>
-</dd>
-<dt><code>\mathsection</code>
-<a name="index-_005cmathsection"></a>
-</dt>
-<dd><p>Section sign in math mode.
+
+<hr>
+<a name="g_t_005cleft-_0026-_005cright"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005csqrt" accesskey="n" rel="next">\sqrt</a>, Previous: <a href="#g_t_005cfrac" accesskey="p" rel="prev">\frac</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005cleft-_0026-_005cright-1"></a>
+<h4 class="subsection">16.7.4 <code>\left</code> & <code>\right</code></h4>
+
+<a name="index-delimiters_002c-paired"></a>
+<a name="index-paired-delimiters"></a>
+<a name="index-matching-parentheses"></a>
+<a name="index-matching-brackets"></a>
+<a name="index-null-delimiter"></a>
+<a name="index-_005cleft"></a>
+<a name="index-_005cright"></a>
+
+<p>Synopsis:
 </p>
-</dd>
-<dt><code>\mathsterling</code>
-<a name="index-_005cmathsterling"></a>
-</dt>
-<dd><p>Sterling sign in math mode: £.
+<div class="example">
+<pre class="example">\left <var>delimiter1</var> ... \right <var>delimiter2</var>
+</pre></div>
+
+<p>Make matching parentheses, braces, or other delimiters.  The delimiters
+are sized according to the math they enclose.  This makes a unit vector
+surrounded by appropriate-height parentheses.
 </p>
-</dd>
-<dt><code>\mathunderscore</code>
-<a name="index-_005cmathunderscore"></a>
-</dt>
-<dd><p>Underscore in math mode: _.
+<div class="example">
+<pre class="example">\begin{equation}
+  \left(\begin{array}{c}
+    1   \\
+    0   \\
+  \end{array}\right)
+</pre></div>
+
+<p>Every <code>\left</code> must have a matching <code>\right</code>.  Leaving out the
+<code>\left(</code> in the above gets ‘<samp>Extra \right</samp>’.  Leaving off the
+<code>\right)</code> gets ‘<samp>You can't use `\eqno' in math mode</samp>’.
 </p>
-</dd>
-<dt><code>\overbrace{<var>math</var>}</code>
-<a name="index-_005coverbrace_007bmath_007d"></a>
-</dt>
-<dd><p>Generates a brace over <var>math</var>.
-For example, <code>\overbrace{x+\cdots+x}^{k \;\textrm{times}}</code>.
-</p>        
-</dd>
-<dt><code>\overline{<var>text</var>}</code>
-<a name="index-_005coverline_007btext_007d"></a>
-</dt>
-<dd><p>Generates a horizontal line over <var>tex</var>.
-For example, <code>\overline{x+y}</code>.
+<p>However, the two delimiters <var>delimiter1</var> and <var>delimiter2</var> need
+not match.  A common case is that you want an unmatched brace, as
+below. Use a period, ‘<samp>.</samp>’, as a null delimiter.
 </p>
-</dd>
-<dt><code>\sqrt[<var>root</var>]{<var>arg</var>}</code>
-<a name="index-_005csqrt_005broot_005d_007barg_007d"></a>
-</dt>
-<dd><p>Produces the representation of the square root of <var>arg</var>.  The
-optional argument <var>root</var> determines what root to produce.  For
-example, the cube root of <code>x+y</code> would be typed as
-<code>\sqrt[3]{x+y}</code>.
+<div class="example">
+<pre class="example">\begin{equation}
+  f(n)=\left\{\begin{array}{ll}
+                1             &\mbox{--if \(n=0\)} \\
+                f(n-1)+3n^2   &\mbox{--else}       
+       \end{array}\right.
+\end{equation}
+</pre></div>
+
+<p>Note that to get a curly brace as a delimiter you must prefix it with a
+backslash, <code>\{</code>.
 </p>
-</dd>
-<dt><code>\stackrel{<var>text</var>}{<var>relation</var>}</code>
-<a name="index-_005cstackrel_007btext_007d_007brelation_007d"></a>
-</dt>
-<dd><p>Puts <var>text</var> above <var>relation</var>.  For example,
-<code>\stackrel{f}{\longrightarrow}</code>.
+
+<hr>
+<a name="g_t_005csqrt"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005cstackrel" accesskey="n" rel="next">\stackrel</a>, Previous: <a href="#g_t_005cleft-_0026-_005cright" accesskey="p" rel="prev">\left & \right</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005csqrt-1"></a>
+<h4 class="subsection">16.7.5 <code>\sqrt</code></h4>
+
+<a name="index-square-root"></a>
+<a name="index-roots"></a>
+<a name="index-radical"></a>
+<a name="index-_005csqrt"></a>
+
+<p>Synopsis, one of:
 </p>
-</dd>
-<dt><code>\underbrace{<var>math</var>}</code>
-<a name="index-_005cunderbrace_007bmath_007d"></a>
-</dt>
-<dd><p>Generates <var>math</var> with a brace underneath. For example, <code>\underbrace{x+y+z}_{>\,0}</code>
+<div class="example">
+<pre class="example">\sqrt{<var>arg</var>}
+\sqrt[<var>root-number</var>]{<var>arg</var>}
+</pre></div>
+
+<p>The square root, or optionally other roots, of <var>arg</var>.  The optional
+argument <var>root-number</var> gives the root, i.e., enter the cube root of
+<code>x+y</code> as <code>\sqrt[3]{x+y}</code>.
+The radical grows with the size of <var>arg</var> (as the height of the
+radical grows, the angle on the leftmost part gets steeper, until for
+a large enough <code>arg</code>, it is vertical).
 </p>
-<a name="index-package_002c-ulem"></a>
-<a name="index-ulem-package"></a>
+<p>LaTeX has a separate <code>\surd</code> character (see <a href="#Math-symbols">Math symbols</a>).
+</p>
 
-</dd>
-<dt><code>\underline{<var>text</var>}</code>
-<a name="index-_005cunderline_007btext_007d"></a>
-</dt>
-<dd><p>Causes <var>text</var>, which may be either math mode or not, to be
-underlined.  The line is always below the text, taking account of
-descenders.
-(The package <samp>ulem</samp> does underlining and allows line breaking as
-well as a number of other underline-related features.  The documentation
-is on CTAN.)
+<hr>
+<a name="g_t_005cstackrel"></a>
+<div class="header">
+<p>
+Previous: <a href="#g_t_005csqrt" accesskey="p" rel="prev">\sqrt</a>, Up: <a href="#Math-miscellany" accesskey="u" rel="up">Math miscellany</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005cstackrel-1"></a>
+<h4 class="subsection">16.7.6 <code>\stackrel</code></h4>
+
+<a name="index-stack-math"></a>
+<a name="index-relation_002c-text-above"></a>
+<a name="index-_005cstackrel"></a>
+
+<p>Synopsis, one of:
 </p>
-</dd>
-<dt><code>\vdots</code>
-<a name="index-_005cvdots"></a>
-</dt>
-<dd><p>Vertical ellipsis.
+<div class="example">
+<pre class="example">\stackrel{<var>text</var>}{<var>relation</var>}
+</pre></div>
+
+<p>Put <var>text</var> above <var>relation</var>.  To put a function name above an
+arrow enter <code>\stackrel{f}{\longrightarrow}</code>.
 </p>
-</dd>
-</dl>
 
-
 <hr>
 <a name="Modes"></a>
 <div class="header">
@@ -13903,10 +14198,10 @@
 <a name="index-fancyhdr-package-1"></a>
 
 <p>A discussion with an example is below.  Note first that the package
-<samp>fancyhdr</samp> is the standard way to manipulate headers and footers
-because it makes it immensely easier.  New documents that need to do
-anything other than one of the standard options below should use this
-package.  See its documentation on CTAN.
+<samp>fancyhdr</samp> is now the standard way to manipulate headers and
+footers.  New documents that need to do anything other than one of the
+standard options below should use this package.  See its documentation
+on CTAN.
 </p>
 <p>Values for <var>style</var>:
 </p>
@@ -14736,7 +15031,7 @@
 <pre class="example">\parbox{<var>width</var>}{<var>contents</var>}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\parbox[<var>position</var>][<var>height</var>][<var>inner-pos</var>]{<var>width</var>}{<var>contents</var>}
@@ -14807,7 +15102,7 @@
 <pre class="example">\raisebox{<var>distance</var>}{<var>text</var>}
 </pre></div>
 
-<p>or:
+<p>or
 </p>
 <div class="example">
 <pre class="example">\raisebox{<var>distance</var>}[<var>height</var>][<var>depth</var>]{<var>text</var>}
@@ -16563,7 +16858,7 @@
 </p>
 </dd>
 <dt><code>\ldots</code>
-<a name="index-_005cldots"></a>
+<a name="index-_005cldots-1"></a>
 </dt>
 <dt><code>\dots</code>
 <a name="index-_005cdots"></a>
@@ -18673,8 +18968,10 @@
    
 <a class="summary-letter" href="#Concept-Index_cp_symbol-2"><b>.</b></a>
    
-<a class="summary-letter" href="#Concept-Index_cp_symbol-3"><b>`</b></a>
+<a class="summary-letter" href="#Concept-Index_cp_symbol-3"><b>:</b></a>
    
+<a class="summary-letter" href="#Concept-Index_cp_symbol-4"><b>`</b></a>
+   
 <br>
 <a class="summary-letter" href="#Concept-Index_cp_letter-A"><b>A</b></a>
    
@@ -18739,7 +19036,10 @@
 <tr><td></td><td valign="top"><a href="#index-_002eidx-file"><samp>.idx</samp> file</a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002eind-file"><samp>.ind</samp> file</a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Concept-Index_cp_symbol-3">`</a></th><td></td><td></td></tr>
+<tr><th><a name="Concept-Index_cp_symbol-3">:</a></th><td></td><td></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_003a">:</a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td colspan="4"> <hr></td></tr>
+<tr><th><a name="Concept-Index_cp_symbol-4">`</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_0060see_0027-and-_0060see-also_0027-index-entries">‘see’ and ‘see also’ index entries</a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-A">A</a></th><td></td><td></td></tr>
@@ -18760,7 +19060,10 @@
 <tr><td></td><td valign="top"><a href="#index-amsmath-package-1"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package-2"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package-3"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-amsmath-package-4"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-4"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-5"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-6"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-7"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package_002c-replacing-eqnarray">amsmath <span class="roman">package, replacing <code>eqnarray</code></span></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsthm-package"><code>amsthm</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-appendix_002c-creating">appendix, creating</a>:</td><td> </td><td valign="top"><a href="#Sectioning">Sectioning</a></td></tr>
@@ -18861,6 +19164,7 @@
 <tr><td></td><td valign="top"><a href="#index-closing-letters">closing letters</a>:</td><td> </td><td valign="top"><a href="#g_t_005cclosing">\closing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-closing-quote">closing quote</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-code_002c-typesetting">code, typesetting</a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-colon-character">colon character</a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-color">color</a>:</td><td> </td><td valign="top"><a href="#Color">Color</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-color-1">color</a>:</td><td> </td><td valign="top"><a href="#Define-colors">Define colors</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-color-2">color</a>:</td><td> </td><td valign="top"><a href="#Colored-text">Colored text</a></td></tr>
@@ -18919,13 +19223,13 @@
 <tr><td></td><td valign="top"><a href="#index-defining-new-fonts">defining new fonts</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewfont">\newfont</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-defining-new-theorems">defining new theorems</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewtheorem">\newtheorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-definitions">definitions</a>:</td><td> </td><td valign="top"><a href="#Definitions">Definitions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-delimiters_002c-paired">delimiters, paired</a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-description-lists_002c-creating">description lists, creating</a>:</td><td> </td><td valign="top"><a href="#description">description</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-design-size_002c-in-font-definitions">design size, in font definitions</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewfont">\newfont</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-Didot-point">Didot point</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dieresis-accent">dieresis accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-difference-between-class-and-package">difference between class and package</a>:</td><td> </td><td valign="top"><a href="#Class-and-package-construction">Class and package construction</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-discretionary-hyphenation">discretionary hyphenation</a>:</td><td> </td><td valign="top"><a href="#g_t_005cdiscretionary">\discretionary</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-discretionary-multiplication">discretionary multiplication</a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-display-math-mode">display math mode</a>:</td><td> </td><td valign="top"><a href="#Modes">Modes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-displaying-quoted-text-with-paragraph-indentation">displaying quoted text with paragraph indentation</a>:</td><td> </td><td valign="top"><a href="#quotation-_0026-quote">quotation & quote</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-displaying-quoted-text-without-paragraph-indentation">displaying quoted text without paragraph indentation</a>:</td><td> </td><td valign="top"><a href="#quotation-_0026-quote">quotation & quote</a></td></tr>
@@ -18940,9 +19244,10 @@
 <tr><td></td><td valign="top"><a href="#index-dot_002dover-accent">dot-over accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dot_002dunder-accent">dot-under accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dotless-i">dotless i</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-dotless-i_002c-math">dotless i, math</a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-dotless-i_002c-math">dotless i, math</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-dotless-j">dotless j</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-dotless-j_002c-math">dotless j, math</a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-dotless-j_002c-math">dotless j, math</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-dots">dots</a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-angle-quotation-marks">double angle quotation marks</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-dagger_002c-in-text">double dagger, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-dagger_002c-in-text-1">double dagger, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -18959,6 +19264,7 @@
 <tr><th><a name="Concept-Index_cp_letter-E">E</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-e_002ddash">e-dash</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-e_002dTeX">e-TeX</a>:</td><td> </td><td valign="top"><a href="#TeX-engines">TeX engines</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-ellipses">ellipses</a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-ellipsis">ellipsis</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-em">em</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-em_002ddash">em-dash</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -19035,6 +19341,7 @@
 <tr><td></td><td valign="top"><a href="#index-formulas_002c-math">formulas, math</a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-forward-reference">forward reference</a>:</td><td> </td><td valign="top"><a href="#Cross-references">Cross references</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-forward-references_002c-resolving">forward references, resolving</a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-fraction">fraction</a>:</td><td> </td><td valign="top"><a href="#g_t_005cfrac">\frac</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-fragile-commands">fragile commands</a>:</td><td> </td><td valign="top"><a href="#g_t_005cprotect">\protect</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-French-quotation-marks">French quotation marks</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-functions_002c-math">functions, math</a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
@@ -19196,6 +19503,8 @@
 <tr><td></td><td valign="top"><a href="#index-making-paragraphs">making paragraphs</a>:</td><td> </td><td valign="top"><a href="#Making-paragraphs">Making paragraphs</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-marginal-notes">marginal notes</a>:</td><td> </td><td valign="top"><a href="#Marginal-notes">Marginal notes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-masculine-ordinal-symbol">masculine ordinal symbol</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-matching-brackets">matching brackets</a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-matching-parentheses">matching parentheses</a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math-accents">math accents</a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math-formulas">math formulas</a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math-functions">math functions</a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
@@ -19206,6 +19515,7 @@
 <tr><td></td><td valign="top"><a href="#index-math-symbols">math symbols</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math_002c-bold">math, bold</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mathtools-package"><code>mathtools</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-mathtools-package-1"><code>mathtools</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mfirstuc-package"><code>mfirstuc</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mhchem-package"><code>mhchem</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-Millimeter">Millimeter</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
@@ -19217,10 +19527,12 @@
 <tr><td></td><td valign="top"><a href="#index-moving-arguments">moving arguments</a>:</td><td> </td><td valign="top"><a href="#g_t_005cprotect">\protect</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mpfootnote-counter">mpfootnote counter</a>:</td><td> </td><td valign="top"><a href="#g_t_005cfootnote">\footnote</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mu_002c-math-unit">mu, math unit</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-muiltiplication_002c-line-breaks">muiltiplication, line breaks</a>:</td><td> </td><td valign="top"><a href="#g_t_005c_002a">\*</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-multicolumn-text">multicolumn text</a>:</td><td> </td><td valign="top"><a href="#g_t_005ctwocolumn">\twocolumn</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-multilingual-support">multilingual support</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-multind-package"><code>multind</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-multiplication-symbol_002c-discretionary-line-break">multiplication symbol, discretionary line break</a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-multiplication-symbol_002c-discretionary-line-break">multiplication symbol, discretionary line break</a>:</td><td> </td><td valign="top"><a href="#g_t_005c_002a">\*</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-multiplication_002c-discretionary">multiplication, discretionary</a>:</td><td> </td><td valign="top"><a href="#g_t_005c_002a">\*</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-N">N</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-nested-_005cinclude_002c-not-allowed">nested <code>\include</code>, not allowed</a>:</td><td> </td><td valign="top"><a href="#g_t_005cinclude-_0026-_005cincludeonly">\include & \includeonly</a></td></tr>
@@ -19235,7 +19547,7 @@
 <tr><td></td><td valign="top"><a href="#index-new-page_002c-starting">new page, starting</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewpage">\newpage</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-non_002dEnglish-characters">non-English characters</a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-notes-in-the-margin">notes in the margin</a>:</td><td> </td><td valign="top"><a href="#Marginal-notes">Marginal notes</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-null-delimiter">null delimiter</a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-null-delimiter">null delimiter</a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-numbered-items_002c-specifying-counter">numbered items, specifying counter</a>:</td><td> </td><td valign="top"><a href="#g_t_005cusecounter">\usecounter</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-numerals_002c-old_002dstyle">numerals, old-style</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
@@ -19260,6 +19572,7 @@
 <tr><td></td><td valign="top"><a href="#index-outer-paragraph-mode">outer paragraph mode</a>:</td><td> </td><td valign="top"><a href="#Modes">Modes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-overbar-accent">overbar accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-overdot-accent_002c-math">overdot accent, math</a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-overlining">overlining</a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-overview-of-LaTeX">overview of LaTeX</a>:</td><td> </td><td valign="top"><a href="#Overview">Overview</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-P">P</a></th><td></td><td></td></tr>
@@ -19272,7 +19585,10 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-1"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-2"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-3"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-4"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-4"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-5"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-6"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-7"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsthm"><span class="roman">package</span>, <code>amsthm</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-babel"><span class="roman">package</span>, <code>babel</code></a>:</td><td> </td><td valign="top"><a href="#thebibliography">thebibliography</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-babel-1"><span class="roman">package</span>, <code>babel</code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
@@ -19302,6 +19618,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-macros2e"><span class="roman">package</span>, <code>macros2e</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmakeatletter-and-_005cmakeatother">\makeatletter and \makeatother</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-makeidx"><span class="roman">package</span>, <code>makeidx</code></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mathtools"><span class="roman">package</span>, <code>mathtools</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-mathtools-1"><span class="roman">package</span>, <code>mathtools</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mfirstuc"><span class="roman">package</span>, <code>mfirstuc</code></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mhchem"><span class="roman">package</span>, <code>mhchem</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-minted"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
@@ -19313,7 +19630,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-symbols"><span class="roman">package</span>, <code>symbols</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-textcase"><span class="roman">package</span>, <code>textcase</code></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-textcomp"><span class="roman">package</span>, <code>textcomp</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-package_002c-ulem"><span class="roman">package</span>, <code>ulem</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-ulem"><span class="roman">package</span>, <code>ulem</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-url"><span class="roman">package</span>, <code>url</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-verbatimbox"><span class="roman">package</span>, <code>verbatimbox</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-xspace"><span class="roman">package</span>, <code>xspace</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_0028SPACE_0029-after-control-sequence">\(SPACE) after control sequence</a></td></tr>
@@ -19327,6 +19644,7 @@
 <tr><td></td><td valign="top"><a href="#index-page-style_002c-this-page">page style, this page</a>:</td><td> </td><td valign="top"><a href="#g_t_005cthispagestyle">\thispagestyle</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-page-styles">page styles</a>:</td><td> </td><td valign="top"><a href="#Page-styles">Page styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-page_002c-colored">page, colored</a>:</td><td> </td><td valign="top"><a href="#Colored-pages">Colored pages</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-paired-delimiters">paired delimiters</a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-paragraph-indentation">paragraph indentation</a>:</td><td> </td><td valign="top"><a href="#g_t_005cparindent-_0026-_005cparskip">\parindent & \parskip</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-paragraph-indentation_002c-in-minipage">paragraph indentation, in minipage</a>:</td><td> </td><td valign="top"><a href="#minipage">minipage</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-paragraph-indentations-in-quoted-text">paragraph indentations in quoted text</a>:</td><td> </td><td valign="top"><a href="#quotation-_0026-quote">quotation & quote</a></td></tr>
@@ -19374,6 +19692,7 @@
 <tr><td></td><td valign="top"><a href="#index-quoted-text-without-paragraph-indentation_002c-displaying">quoted text without paragraph indentation, displaying</a>:</td><td> </td><td valign="top"><a href="#quotation-_0026-quote">quotation & quote</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-R">R</a></th><td></td><td></td></tr>
+<tr><td></td><td valign="top"><a href="#index-radical">radical</a>:</td><td> </td><td valign="top"><a href="#g_t_005csqrt">\sqrt</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-ragged-left-text">ragged left text</a>:</td><td> </td><td valign="top"><a href="#g_t_005craggedleft">\raggedleft</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-ragged-left-text_002c-environment-for">ragged left text, environment for</a>:</td><td> </td><td valign="top"><a href="#flushright">flushright</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-ragged-right-text">ragged right text</a>:</td><td> </td><td valign="top"><a href="#g_t_005craggedright">\raggedright</a></td></tr>
@@ -19382,6 +19701,7 @@
 <tr><td></td><td valign="top"><a href="#index-reference_002c-forward">reference, forward</a>:</td><td> </td><td valign="top"><a href="#Cross-references">Cross references</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-references_002c-resolving-forward">references, resolving forward</a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-registered-symbol">registered symbol</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-relation_002c-text-above">relation, text above</a>:</td><td> </td><td valign="top"><a href="#g_t_005cstackrel">\stackrel</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-remarks-in-the-margin">remarks in the margin</a>:</td><td> </td><td valign="top"><a href="#Marginal-notes">Marginal notes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-reporting-bugs">reporting bugs</a>:</td><td> </td><td valign="top"><a href="#About-this-document">About this document</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-reserved-characters">reserved characters</a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
@@ -19401,6 +19721,7 @@
 <tr><td></td><td valign="top"><a href="#index-robust-commands">robust commands</a>:</td><td> </td><td valign="top"><a href="#g_t_005cprotect">\protect</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-roman-font">roman font</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-root-file">root file</a>:</td><td> </td><td valign="top"><a href="#Splitting-the-input">Splitting the input</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-roots">roots</a>:</td><td> </td><td valign="top"><a href="#g_t_005csqrt">\sqrt</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-rotating-graphics">rotating graphics</a>:</td><td> </td><td valign="top"><a href="#g_t_005crotatebox">\rotatebox</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-rotating-text">rotating text</a>:</td><td> </td><td valign="top"><a href="#g_t_005crotatebox">\rotatebox</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-rotation">rotation</a>:</td><td> </td><td valign="top"><a href="#g_t_005crotatebox">\rotatebox</a></td></tr>
@@ -19452,6 +19773,8 @@
 <tr><td></td><td valign="top"><a href="#index-special-insertions">special insertions</a>:</td><td> </td><td valign="top"><a href="#Special-insertions">Special insertions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-specifier_002c-float-placement">specifier, float placement</a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-splitting-the-input-file">splitting the input file</a>:</td><td> </td><td valign="top"><a href="#Splitting-the-input">Splitting the input</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-square-root">square root</a>:</td><td> </td><td valign="top"><a href="#g_t_005csqrt">\sqrt</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-stack-math">stack math</a>:</td><td> </td><td valign="top"><a href="#g_t_005cstackrel">\stackrel</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-star_002dvariants_002c-commands">star-variants, commands</a>:</td><td> </td><td valign="top"><a href="#g_t_005c_0040ifstar">\@ifstar</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-starred-form_002c-defining-new-commands">starred form, defining new commands</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewcommand-_0026-_005crenewcommand">\newcommand & \renewcommand</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-starting-a-new-page">starting a new page</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewpage">\newpage</a></td></tr>
@@ -19522,9 +19845,10 @@
 <tr><td></td><td valign="top"><a href="#index-typewriter-labels-in-lists">typewriter labels in lists</a>:</td><td> </td><td valign="top"><a href="#description">description</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-U">U</a></th><td></td><td></td></tr>
-<tr><td></td><td valign="top"><a href="#index-ulem-package"><code>ulem</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-ulem-package"><code>ulem</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-umlaut-accent">umlaut accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-underbar">underbar</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-underlining">underlining</a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-underscore_002c-in-text">underscore, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-Unicode-input_002c-native">Unicode input, native</a>:</td><td> </td><td valign="top"><a href="#TeX-engines">TeX engines</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-units_002c-of-length">units, of length</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
@@ -19570,8 +19894,10 @@
    
 <a class="summary-letter" href="#Concept-Index_cp_symbol-2"><b>.</b></a>
    
-<a class="summary-letter" href="#Concept-Index_cp_symbol-3"><b>`</b></a>
+<a class="summary-letter" href="#Concept-Index_cp_symbol-3"><b>:</b></a>
    
+<a class="summary-letter" href="#Concept-Index_cp_symbol-4"><b>`</b></a>
+   
 <br>
 <a class="summary-letter" href="#Concept-Index_cp_letter-A"><b>A</b></a>
    
@@ -19640,16 +19966,18 @@
    
 <a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>1</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>[</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>:</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>\</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>[</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>^</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>\</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>_</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>^</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>{</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>_</b></a>
    
+<a class="summary-letter" href="#Command-Index_fn_symbol-10"><b>{</b></a>
+   
 <br>
 <a class="summary-letter" href="#Command-Index_fn_letter-A"><b>A</b></a>
    
@@ -19720,10 +20048,13 @@
 <tr><td></td><td valign="top"><a href="#index-11pt-option"><code>11pt <span class="roman">option</span></code></a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-12pt-option"><code>12pt <span class="roman">option</span></code></a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-5">[</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-5">:</a></th><td></td><td></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_003a-1"><code>:</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
+<tr><td colspan="4"> <hr></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-6">[</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005b_002e_002e_002e_005d-for-optional-arguments"><code>[...] <span class="roman">for optional arguments</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-6">\</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-7">\</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c-character-starting-commands"><code>\ <span class="roman">character starting commands</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0021"><code>\!</code></a>:</td><td> </td><td valign="top"><a href="#Spacing-in-math-mode">Spacing in math mode</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0022-_0028umlaut-accent_0029"><code>\" <span class="roman">(umlaut accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
@@ -19734,7 +20065,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005c_0027-_0028acute-accent_0029"><code>\' <span class="roman">(acute accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0027-_0028tabbing_0029"><code>\' <span class="roman">(tabbing)</span></code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0028SPACE_0029"><code>\(SPACE)</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_0028SPACE_0029-and-_005c_0040">\(SPACE) and \@</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005c_002a"><code>\*</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005c_002a"><code>\*</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_002a">\*</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002b"><code>\+</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002c"><code>\,</code></a>:</td><td> </td><td valign="top"><a href="#Spacing-in-math-mode">Spacing in math mode</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002d"><code>\-</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
@@ -19856,7 +20187,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005ccaption-1"><code>\caption</code></a>:</td><td> </td><td valign="top"><a href="#table">table</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccc"><code>\cc</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ccc">\cc</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccdot"><code>\cdot</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005ccdots"><code>\cdots</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005ccdots"><code>\cdots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccentering"><code>\centering</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ccentering">\centering</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cchapter"><code>\chapter</code></a>:</td><td> </td><td valign="top"><a href="#Sectioning">Sectioning</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccheck"><code>\check</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
@@ -19876,6 +20207,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005ccline"><code>\cline</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ccline">\cline</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cclosing"><code>\closing</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cclosing">\closing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cclubsuit"><code>\clubsuit</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005ccolon"><code>\colon</code></a>:</td><td> </td><td valign="top"><a href="#Colon-character-_0026-_005ccolon">Colon character & \colon</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccolumnsep"><code>\columnsep</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ctwocolumn">\twocolumn</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccolumnsep-1"><code>\columnsep</code></a>:</td><td> </td><td valign="top"><a href="#Page-layout-parameters">Page layout parameters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ccolumnsep-2"><code>\columnsep</code></a>:</td><td> </td><td valign="top"><a href="#Page-layout-parameters">Page layout parameters</a></td></tr>
@@ -19912,7 +20244,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cddag"><code>\ddag</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cddagger"><code>\ddagger</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cddot"><code>\ddot</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cddots"><code>\ddots</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cddots"><code>\ddots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareGraphicsExtensions"><code>\DeclareGraphicsExtensions</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cDeclareGraphicsExtensions">\DeclareGraphicsExtensions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareGraphicsRule"><code>\DeclareGraphicsRule</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cDeclareGraphicsRule">\DeclareGraphicsRule</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cDeclareOption"><code>\DeclareOption</code></a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
@@ -19991,8 +20323,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cfootskip"><code>\footskip</code></a>:</td><td> </td><td valign="top"><a href="#Page-layout-parameters">Page layout parameters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cfootskip-1"><code>\footskip</code></a>:</td><td> </td><td valign="top"><a href="#Page-layout-parameters">Page layout parameters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cforall"><code>\forall</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cfrac"><code>\frac</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cfrac_007bnum_007d_007bden_007d"><code>\frac{<var>num</var>}{<var>den</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cfrac"><code>\frac</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cfrac">\frac</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cframe"><code>\frame</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cframe">\frame</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cframebox"><code>\framebox</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cframebox-_0028picture_0029">\framebox (picture)</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cframebox-1"><code>\framebox</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cfbox-and-_005cframebox">\fbox and \framebox</a></td></tr>
@@ -20044,7 +20375,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cij-_0028ij_0029"><code>\ij (ij)</code></a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cIJ-_0028IJ_0029"><code>\IJ (IJ)</code></a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cIm"><code>\Im</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cimath"><code>\imath</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cimath"><code>\imath</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cin"><code>\in</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cinclude"><code>\include</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cinclude-_0026-_005cincludeonly">\include & \includeonly</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cincludegraphics"><code>\includegraphics</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cincludegraphics">\includegraphics</a></td></tr>
@@ -20070,7 +20401,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005citemsep"><code>\itemsep</code></a>:</td><td> </td><td valign="top"><a href="#list">list</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005citshape"><code>\itshape</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cj-_0028dotless-j_0029"><code>\j <span class="roman">(dotless j)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cjmath"><code>\jmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cjmath"><code>\jmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cJoin"><code>\Join</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ck-_0028ogonek_0029"><code>\k <span class="roman">(ogonek)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ckappa"><code>\kappa</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -20101,10 +20432,11 @@
 <tr><td></td><td valign="top"><a href="#index-_005clbrace"><code>\lbrace</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005clbrack"><code>\lbrack</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005clceil"><code>\lceil</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cldots"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cldots"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cldots-1"><code>\ldots</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cle"><code>\le</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cleadsto"><code>\leadsto</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cleft-delim1-_002e_002e_002e-_005cright-delim2"><code>\left <var>delim1</var> ... \right <var>delim2</var></code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cleft"><code>\left</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cLeftarrow"><code>\Leftarrow</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cleftarrow"><code>\leftarrow</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005clefteqn"><code>\lefteqn</code></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
@@ -20171,17 +20503,16 @@
 <tr><td></td><td valign="top"><a href="#index-_005cmarkright_007bright_007d"><code>\markright{<var>right</var>}</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cpagestyle">\pagestyle</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathbf"><code>\mathbf</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathcal"><code>\mathcal</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathdollar"><code>\mathdollar</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathellipsis"><code>\mathellipsis</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cmathdollar"><code>\mathdollar</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathnormal"><code>\mathnormal</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathparagraph"><code>\mathparagraph</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cmathparagraph"><code>\mathparagraph</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathring"><code>\mathring</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathrm"><code>\mathrm</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathsection"><code>\mathsection</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cmathsection"><code>\mathsection</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathsf"><code>\mathsf</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathsterling"><code>\mathsterling</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cmathsterling"><code>\mathsterling</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathtt"><code>\mathtt</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cmathunderscore"><code>\mathunderscore</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cmathunderscore"><code>\mathunderscore</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmathversion"><code>\mathversion</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmax"><code>\max</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cmbox"><code>\mbox</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmbox">\mbox</a></td></tr>
@@ -20258,8 +20589,8 @@
 <tr><td></td><td valign="top"><a href="#index-_005coslash"><code>\oslash</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cotimes"><code>\otimes</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005coval"><code>\oval</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005coval">\oval</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005coverbrace_007bmath_007d"><code>\overbrace{<var>math</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005coverline_007btext_007d"><code>\overline{<var>text</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005coverbrace_007bmath_007d"><code>\overbrace{<var>math</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005coverline_007btext_007d"><code>\overline{<var>text</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cowns"><code>\owns</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cP"><code>\P</code></a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cPackageError"><code>\PackageError</code></a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
@@ -20349,7 +20680,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005crfloor"><code>\rfloor</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005crhd"><code>\rhd</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005crho"><code>\rho</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cright"><code>\right</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cright"><code>\right</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cleft-_0026-_005cright">\left & \right</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cRightarrow"><code>\Rightarrow</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005crightarrow"><code>\rightarrow</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005crightharpoondown"><code>\rightharpoondown</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -20404,14 +20735,14 @@
 <tr><td></td><td valign="top"><a href="#index-_005cspadesuit"><code>\spadesuit</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqcap"><code>\sqcap</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqcup"><code>\sqcup</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005csqrt_005broot_005d_007barg_007d"><code>\sqrt[<var>root</var>]{<var>arg</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005csqrt"><code>\sqrt</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005csqrt">\sqrt</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqsubset"><code>\sqsubset</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqsubseteq"><code>\sqsubseteq</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqsupset"><code>\sqsupset</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005csqsupseteq"><code>\sqsupseteq</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005css-_0028ss_0029"><code>\ss (ß)</code></a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cSS-_0028SS_0029"><code>\SS (SS)</code></a>:</td><td> </td><td valign="top"><a href="#Additional-Latin-letters">Additional Latin letters</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cstackrel_007btext_007d_007brelation_007d"><code>\stackrel{<var>text</var>}{<var>relation</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cstackrel"><code>\stackrel</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cstackrel">\stackrel</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cstar"><code>\star</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cstepcounter"><code>\stepcounter</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cstepcounter">\stepcounter</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cstop"><code>\stop</code></a>:</td><td> </td><td valign="top"><a href="#Command-line">Command line</a></td></tr>
@@ -20541,8 +20872,8 @@
 <tr><td></td><td valign="top"><a href="#index-_005cunboldmath"><code>\unboldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunboldmath-1"><code>\unboldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunderbar"><code>\underbar</code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cunderbrace_007bmath_007d"><code>\underbrace{<var>math</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cunderline_007btext_007d"><code>\underline{<var>text</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cunderbrace_007bmath_007d"><code>\underbrace{<var>math</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cunderline_007btext_007d"><code>\underline{<var>text</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Over_002d-and-Underlining">Over- and Underlining</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunitlength"><code>\unitlength</code></a>:</td><td> </td><td valign="top"><a href="#picture">picture</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunlhd"><code>\unlhd</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunrhd"><code>\unrhd</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -20569,7 +20900,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005cvarsigma"><code>\varsigma</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvartheta"><code>\vartheta</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvdash"><code>\vdash</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cvdots"><code>\vdots</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cvdots"><code>\vdots</code></a>:</td><td> </td><td valign="top"><a href="#Ellipses">Ellipses</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvec"><code>\vec</code></a>:</td><td> </td><td valign="top"><a href="#Math-accents">Math accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvector"><code>\vector</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cvector">\vector</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cvee"><code>\vee</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
@@ -20613,13 +20944,13 @@
 <tr><td></td><td valign="top"><a href="#index-_005c_007e"><code>\~</code></a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_007e-_0028tilde-accent_0029"><code>\~ <span class="roman">(tilde accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-7">^</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-8">^</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005e"><code>^</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-8">_</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-9">_</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005f"><code>_</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-9">{</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-10">{</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_007b_002e_002e_002e_007d-for-required-arguments"><code>{...} <span class="roman">for required arguments</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Command-Index_fn_letter-A">A</a></th><td></td><td></td></tr>
@@ -20806,16 +21137,18 @@
    
 <a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>1</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>[</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>:</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>\</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>[</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>^</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>\</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>_</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>^</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>{</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>_</b></a>
    
+<a class="summary-letter" href="#Command-Index_fn_symbol-10"><b>{</b></a>
+   
 <br>
 <a class="summary-letter" href="#Command-Index_fn_letter-A"><b>A</b></a>
    

Modified: trunk/latex2e.info
===================================================================
--- trunk/latex2e.info	2018-06-08 16:55:33 UTC (rev 644)
+++ trunk/latex2e.info	2018-06-09 23:37:33 UTC (rev 645)
@@ -2410,7 +2410,7 @@
        ...
      \end{array}
 
-   or
+or
 
      \begin{array}[POS]{COLS}
        COLUMN 1 ENTRY &COLUMN 2 ENTRY ... &COLUMN N ENTRY \\
@@ -2476,7 +2476,7 @@
        ... text ...
      \end{center}
 
-   or
+or
 
      \begin{center}
        text on first line \\
@@ -2531,7 +2531,7 @@
 
      {\centering ... }
 
-   or
+or
 
      \begin{group}
        \centering ...
@@ -2810,7 +2810,7 @@
        ...
      \end{eqnarray}
 
-   or
+or
 
      \begin{eqnarray*}
        FIRST FORMULA LEFT  &FIRST FORMULA MIDDLE  &FIRST FORMULA RIGHT \\
@@ -2882,7 +2882,7 @@
        \label{LABEL}              % optional
      \end{figure}
 
-   or
+or
 
      \begin{figure*}[PLACEMENT]
        figure body
@@ -2938,7 +2938,7 @@
        TEXT
      \end{filecontents}
 
-   or
+or
 
      \begin{filecontents*}{FILENAME}
        TEXT
@@ -3024,7 +3024,7 @@
 
      {\raggedright  ... }
 
-   or
+or
 
      \begin{ENVIRONMENT} \raggedright
        ...
@@ -3084,7 +3084,7 @@
 
      {\raggedleft  ... }
 
-   or
+or
 
      \begin{ENVIRONMENT} \raggedleft
        ...
@@ -3498,7 +3498,8 @@
 
      \item text of item
 
-   or
+or
+
      \item[OPTIONAL-LABEL] text of item
 
    An entry in a list.  The entries are prefixed by a label, whose
@@ -3595,7 +3596,7 @@
        CONTENTS
      \end{minipage}
 
-   or:
+or
 
      \begin{minipage}[POSITION][HEIGHT][INNER-POS]{WIDTH}
        CONTENTS
@@ -3737,7 +3738,7 @@
         PICTURE COMMANDS
      \end{picture}
 
-   or
+or
 
      \begin{picture}(WIDTH,HEIGHT)(XOFFSET,YOFFSET)
        PICTURE COMMANDS
@@ -4304,7 +4305,7 @@
        TEXT
      \end{quotation}
 
-   or
+or
 
      \begin{quote}
        TEXT
@@ -4488,7 +4489,7 @@
        TABLE BODY
      \end{table}
 
-   or:
+or
 
      \begin{table}[PLACEMENT]
        TABLE BODY
@@ -4959,7 +4960,7 @@
 
      \bibitem{CITE_KEY}
 
-   or:
+or
 
      \bibitem[LABEL]{CITE_KEY}
 
@@ -5021,7 +5022,7 @@
 
      \cite{KEYS}
 
-   or:
+or
 
      \cite[SUBCITE]{KEYS}
 
@@ -5315,11 +5316,18 @@
    Separate the lines of each stanza with '\\', and use one or more
 blank lines to separate the stanzas.
 
-     A poem is a piece of poetry.
+     \begin{verse}
+     \makebox[\linewidth][c]{\textit{Shut Not Your Doors} ---Walt Whitman}
+       \\[1\baselineskip]
+     Shut not your doors to me proud libraries,                  \\
+     For that which was lacking on all your well-fill'd shelves, \\
+     \qquad yet needed most, I bring,                             \\
+     Forth from the war emerging, a book I have made,            \\
+     The words of my book nothing, the drift of it every thing,  \\
+     A book separate, not link'd with the rest nor felt by the intellect, \\
+     But you ye untold latencies will thrill to every page.
+     \end{verse}
 
-     And don't let the head of the poetry society \\
-     tell you diff'rent.
-
    The output has margins indented on the left and the right, paragraphs
 are not indented, and the text is not right-justified.
 
@@ -5365,7 +5373,7 @@
      \\
      \\[MORESPACE]
 
-   or one of:
+or one of these.
 
      \\*
      \\*[MORESPACE]
@@ -5634,7 +5642,7 @@
      \linebreak
      \linebreak[ZERO-TO-FOUR]
 
-   or one of:
+or one of these.
 
      \nolinebreak
      \nolinebreak[ZERO-TO-FOUR]
@@ -5707,7 +5715,7 @@
 
      \clearpage
 
-   or:
+or
 
      \cleardoublepage
 
@@ -5816,7 +5824,7 @@
      \pagebreak
      \pagebreak[ZERO-TO-FOUR]
 
-   or:
+or
 
      \nopagebreak
      \nopagebreak[ZERO-TO-FOUR]
@@ -6170,7 +6178,7 @@
      \newcommand*{\CMD}[NARGS]{DEFN}
      \newcommand*{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}
 
-   or one of:
+or one of these.
 
      \renewcommand{\CMD}[NARGS]{DEFN}
      \renewcommand{\CMD}[NARGS]{DEFN}
@@ -6428,7 +6436,7 @@
      \newenvironment*{ENV}[NARGS]{BEGDEF}{ENDDEF}
      \newenvironment*{ENV}[NARGS][OPTARGDEFAULT]{BEGDEF}{ENDDEF}
 
-   or one of:
+or one of these.
 
      \renewenvironment{ENV}{BEGDEF}{ENDDEF}
      \renewenvironment{ENV}[NARGS]{BEGDEF}{ENDDEF}
@@ -6755,7 +6763,7 @@
 
      \ignorespaces
 
-   or
+or
 
      \ignorespacesafterend
 
@@ -7414,7 +7422,7 @@
 
      \indent
 
-   or:
+or
 
      \noindent
 
@@ -7593,13 +7601,14 @@
    The two mathematics modes are similar, but there are some
 differences.  One involves the placement of subscripts and superscripts;
 in display math mode they are further apart and in inline math mode they
-are closer together.  Sometimes you want the display math treatment to
-happen in the inline math mode.  For this, the '\displaystyle'
-declaration forces the size and style of the formula to be that of
-'displaymath'.  Thus '\(\displaystyle \sum_{n=0}^\infty x_n\)' will have
-the limits above and below the summation sign, not next to it.  Another
-example is that
+are closer together.
 
+   Sometimes you want the display math treatment to happen in the inline
+math mode.  For this, the '\displaystyle' declaration forces the size
+and style of the formula to be that of 'displaymath'.  Thus
+'\(\displaystyle \sum_{n=0}^\infty x_n\)' will have the limits above and
+below the summation sign, not next to it.  Another example is that
+
      \begin{tabular}{r|cc}
        \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
        Arithmetic     &\( a+(a+b)+(a+2b)+\cdots+(a+(n-1)b) \)
@@ -7619,6 +7628,7 @@
 * Math symbols::                Various mathematical squiggles.
 * Math functions::              Math function names like sin and exp.
 * Math accents::                Accents in math.
+* Over- and Underlining::       Things over or under formulas.
 * Spacing in math mode::        Thick, medium, thin, and negative spaces.
 * Math miscellany::             Stuff that doesn't fit anywhere else.
 
@@ -7632,7 +7642,7 @@
 
      BASE^EXP
 
-   or:
+or
 
      BASE_EXP
 
@@ -7949,6 +7959,10 @@
 '\Im'
      U+2111 Imaginary part (ordinary).  See: real part '\Re'.
 
+'\imath'
+     Dotless i; used when you are putting an accent on an i (*note Math
+     accents::).
+
 '\in'
      U+2208 Set element (relation).  See also: lower case lunate
      epsilon '\epsilon'U+03F5 and small letter script
@@ -7967,6 +7981,10 @@
      U+2A1D Condensed bowtie symbol (relation).  Not available in Plain
      TeX.
 
+'\jmath'
+     Dotless j; used when you are putting an accent on a j (*note Math
+     accents::).
+
 '\kappa'
      U+03BA Lower case Greek letter (ordinary).
 
@@ -8555,11 +8573,30 @@
 '\zeta'
      U+03B6 Lower case Greek letter (ordinary).
 
+   The following symbols are most often used in plain text but LaTeX
+provides versions to use in mathematical text.
+
+'\mathdollar'
+     Dollar sign in math mode: $.
+
+'\mathparagraph'
+     Paragraph sign (pilcrow) in math mode, U+00B6.
+
+'\mathsection'
+     Section sign in math mode U+00A7.
+
+'\mathsterling'
+     Sterling sign in math mode: #.
+
+'\mathunderscore'
+     Underscore in math mode: _.
+
 * Menu:
 
 * Blackboard bold::            Doublestruck characters.
 * Calligraphic::               Cursive characters.
 * \boldmath & \unboldmath::    Symbols in boldface.
+* Ellipses::                   Dots.
 
 
 File: latex2e.info,  Node: Blackboard bold,  Next: Calligraphic,  Up: Math symbols
@@ -8612,7 +8649,7 @@
 outputs a plus sign.
 
 
-File: latex2e.info,  Node: \boldmath & \unboldmath,  Prev: Calligraphic,  Up: Math symbols
+File: latex2e.info,  Node: \boldmath & \unboldmath,  Next: Ellipses,  Prev: Calligraphic,  Up: Math symbols
 
 16.2.3 '\boldmath' & '\unboldmath'
 ----------------------------------
@@ -8621,7 +8658,7 @@
 
      \boldmath \( MATH \)
 
-   or
+or
 
      \unboldmath \( MATH \)
 
@@ -8655,6 +8692,62 @@
    strongly suggests that it is an improvement over '\boldmath'.
 
 
+File: latex2e.info,  Node: Ellipses,  Prev: \boldmath & \unboldmath,  Up: Math symbols
+
+16.2.4 Ellipses
+---------------
+
+Ellipses are the three dots (usually three) indicating that a pattern
+continues.
+
+     \begin{array}{cccc}
+       a_{0,0}    &a_{0,1}   &a_{0,2} &\ldots \\
+       a_{1,0}    &\ddots                     \\
+       \vdots
+     \end{array}
+
+   LaTeX provides these.
+
+'\cdots'
+     Horizontal ellipsis with the dots raised to the center of the line,
+     as in U+22EF. Used as: '\( a_0\cdot a_1\cdots a_{n-1} \)'.
+
+'\ddots'
+     Diagonal ellipsis, U+22F1.  See the above example for a usage.
+
+'\ldots'
+     Ellipsis on the baseline, U+2026.  Used as: '\( x_0,\ldots x_{n-1}
+     \)'.  A synonym is '\mathellipsis'.  A synonym from the 'amsmath'
+     package is '\hdots'.
+
+     You can also use this command outside of mathematical text, as in
+     'The gears, brakes, \ldots{} are all broken'.  (In a text mode a
+     synonym for '\ldots' is '\dots'.)
+
+'\vdots'
+     Vertical ellipsis, U+22EE. See the above example for a usage.
+
+   The 'amsmath' package has the command '\dots' to semantically mark up
+ellipses.  This example produces two different-looking outputs for the
+first two uses of the '\dots' command.
+
+     \usepackage{amsmath}  % in preamble
+       ...
+     Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes.
+     Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a multiple of any \( p_i \).
+     Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).
+
+   In the first line LaTeX looks to the comma following '\dots' to
+determine that it should output an ellipsis on the baseline.  The second
+line has a '\cdot' following '\dots' so LaTeX outputs an ellipsis that
+is on the math axis, vertically centered.  However, the third usage has
+no follow-on character so you have to tell LaTeX what to do.  You can
+use one of the commands: '\dotsc' if you need the ellipsis appropriate
+for a comma following, '\dotsb' if you need the ellipses that fits when
+the dots are followed by a binary operator or relation symbol, '\dotsi'
+for dots with integrals, or '\dotso' for others.
+
+
 File: latex2e.info,  Node: Math functions,  Next: Math accents,  Prev: Math symbols,  Up: Math formulas
 
 16.3 Math functions
@@ -8773,7 +8866,7 @@
 traditional with '\lim', '\sup', or '\max'.
 
 
-File: latex2e.info,  Node: Math accents,  Next: Spacing in math mode,  Prev: Math functions,  Up: Math formulas
+File: latex2e.info,  Node: Math accents,  Next: Over- and Underlining,  Prev: Math functions,  Up: Math formulas
 
 16.4 Math accents
 =================
@@ -8806,12 +8899,6 @@
 '\hat'
      Math hat (circumflex) accent
 
-'\imath'
-     Math dotless i
-
-'\jmath'
-     Math dotless j
-
 '\mathring'
      Math ring accent
 
@@ -8827,10 +8914,58 @@
 '\widetilde'
      Math wide tilde accent
 
+   When you are putting an accent on an i or a j, the tradition is to
+use one without a dot, '\imath' or 'jmath' (*note Math symbols::).
+
 
-File: latex2e.info,  Node: Spacing in math mode,  Next: Math miscellany,  Prev: Math accents,  Up: Math formulas
+File: latex2e.info,  Node: Over- and Underlining,  Next: Spacing in math mode,  Prev: Math accents,  Up: Math formulas
 
-16.5 Spacing in math mode
+16.5 Over- and Underlining
+==========================
+
+LaTeX provides commands for making overlines or underlines, or putting
+braces over or under some material.
+
+'\underline{TEXT}'
+     Underline TEXT.  Works inside math mode, and outside.  The line is
+     always completely below the text, taking account of descenders, so
+     in '\(\underline{y}\)' the line is lower than in
+     '\(\underline{x}\)'.  This command is fragile (*note \protect::).
+
+     Note that the package 'ulem' does text mode underlining and allows
+     line breaking as well as a number of other features.  See the
+     documentation is on CTAN.
+
+'\overline{TEXT}'
+     Put a horizontal line over TEX.  Works inside math mode, and
+     outside.  For example, '\overline{x+y}'.  Note that this differs
+     from the command '\bar' (*note Math accents::).
+
+'\underbrace{MATH}'
+     Put a brace under MATH.  For example, this
+     '(1-\underbrace{1/2)+(1/2}-1/3)' emphasizes the telescoping part.
+     Attach text to the brace by using subscript, '_', or superscript,
+     '^', as here.
+
+          \begin{displaymath}
+            1+1/2+\underbrace{1/3+1/4}_{>1/2}+
+                 \underbrace{1/5+1/6+1/7+1/8}_{>1/2}+\cdots
+          \end{displaymath}
+
+     The superscript appears on top of the expression, and so can look
+     unconnected to the underbrace.
+
+'\overbrace{MATH}'
+     Put a brace over MATH; see also '\underbrace'.  An example is
+     '\overbrace{x+x+\cdots+x}^{\mbox{\(k\) times}}'.
+
+   The package 'mathtools' adds an over- and underbrace, as well as some
+improvements on the braces.  See the documentation on CTAN.
+
+
+File: latex2e.info,  Node: Spacing in math mode,  Next: Math miscellany,  Prev: Over- and Underlining,  Up: Math formulas
+
+16.6 Spacing in math mode
 =========================
 
 When typesetting mathematics, LaTeX puts in spacing according to the
@@ -8877,93 +9012,149 @@
 
 File: latex2e.info,  Node: Math miscellany,  Prev: Spacing in math mode,  Up: Math formulas
 
-16.6 Math miscellany
+16.7 Math miscellany
 ====================
 
-'\*'
-     A "discretionary" multiplication symbol, at which a line break is
-     allowed.  Without the break multiplication is implicitly indicated
-     by a space, while in the case of a break a U+00D7 symbol is printed
-     immediately before the break.  So
+LaTeX contains a wide variety of mathematics facilities.  Here are some
+that don't fit into other categories.
 
-          \documentclass{article}
-          \begin{document}
-          Now \(A_3 = 0\), hence the product of all terms \(A_1\)
-          through \(A_4\), that is \(A_1\* A_2\* A_3 \* A_4\), is
-          equal to zero.
-          \end{document}
+* Menu:
 
-     will make that sort of output (the ellipsis '[...]' is here to show
-     the line break at the same place as in a TeX output):
+* Colon character & \colon::    Colon.
+* \*::                            Discretionary multiplication.
+* \frac::                         Fraction.
+* \left & \right::                Paired delimiters.
+* \sqrt::                         Radicals.
+* \stackrel::                     Text over a relation.
 
-          Now A_3 = 0, [...] A_1 through A_4, that is A_1 A_2 \times
-          A_3 A_4, is equal to zero.
+
+File: latex2e.info,  Node: Colon character & \colon,  Next: \*,  Up: Math miscellany
 
-'\cdots'
-     A horizontal ellipsis with the dots raised to the center of the
-     line.
+16.7.1 Colon character ':' & '\colon'
+-------------------------------------
 
-'\ddots'
-     A diagonal ellipsis: \ddots.
+Synopsis, one of:
 
-'\frac{NUM}{DEN}'
-     Produces the fraction NUM divided by DEN.
+     :
+     \colon
 
-'\left DELIM1 ... \right DELIM2'
-     The two delimiters need not match; '.' acts as a "null delimiter",
-     producing no output.  The delimiters are sized according to the
-     math in between.  Example: '\left( \sum_{i=1}^{10} a_i \right]'.
+   In mathematics, the colon character, ':', is a relation.
 
-'\mathdollar'
-     Dollar sign in math mode: $.
+     With side ratios \( 3:4 \) and \( 4:5 \), the triangle is right.
 
-'\mathellipsis'
-     Ellipsis (spaced for text) in math mode: ...
+Ordinary LaTeX defines '\colon' to produce the colon character with the
+spacing appropriate for punctuation, as in set-builder notation
+'\{x\colon 0\leq x<1\}'.
 
-'\mathparagraph'
-     Paragraph sign (pilcrow) in math mode: U+00B6.
+   But the widely-used 'amsmath' package defines '\colon' for use in the
+definition of functions 'f\colon D\to C'.  So if you want the colon
+character as a punctuation then use '\mathpunct{:}'.
 
-'\mathsection'
-     Section sign in math mode.
+
+File: latex2e.info,  Node: \*,  Next: \frac,  Prev: Colon character & \colon,  Up: Math miscellany
 
-'\mathsterling'
-     Sterling sign in math mode: #.
+16.7.2 '\*'
+-----------
 
-'\mathunderscore'
-     Underscore in math mode: _.
+Synopsis:
 
-'\overbrace{MATH}'
-     Generates a brace over MATH.  For example,
-     '\overbrace{x+\cdots+x}^{k \;\textrm{times}}'.
+     \*
 
-'\overline{TEXT}'
-     Generates a horizontal line over TEX.  For example,
-     '\overline{x+y}'.
+   A multiplication symbol that allows a line break.  If there is a
+break then LaTeX puts a '\times' symbol, U+00D7, before that break.
 
-'\sqrt[ROOT]{ARG}'
-     Produces the representation of the square root of ARG.  The
-     optional argument ROOT determines what root to produce.  For
-     example, the cube root of 'x+y' would be typed as '\sqrt[3]{x+y}'.
+   In '\( A_1\* A_2\* A_3\* A_4 \)', if there is no line break then
+LaTeX outputs it as though it were '\( A_1 A_2 A_3 A_4 \)'.  If a line
+break does happen, for example between the two middle ones, then LaTeX
+sets it like '\( A_1 A_2 \times \)', followed by the break, followed by
+'\( A_3 A_4 \)'.
 
-'\stackrel{TEXT}{RELATION}'
-     Puts TEXT above RELATION.  For example,
-     '\stackrel{f}{\longrightarrow}'.
+
+File: latex2e.info,  Node: \frac,  Next: \left & \right,  Prev: \*,  Up: Math miscellany
 
-'\underbrace{MATH}'
-     Generates MATH with a brace underneath.  For example,
-     '\underbrace{x+y+z}_{>\,0}'
+16.7.3 '\frac'
+--------------
 
-'\underline{TEXT}'
-     Causes TEXT, which may be either math mode or not, to be
-     underlined.  The line is always below the text, taking account of
-     descenders.  (The package 'ulem' does underlining and allows line
-     breaking as well as a number of other underline-related features.
-     The documentation is on CTAN.)
+Synopsis:
 
-'\vdots'
-     Vertical ellipsis.
+     \frac{NUMERATOR}{DENOMINATOR}
 
+   Produces the fraction NUMERATOR divided by DENOMINATOR.  Used as:
+'\begin{displaymath} \frac{1}{\sqrt{2\pi\sigma}} \end{displaymath}'.  In
+inline math mode it comes out small; see the discussion of
+'\displaystyle' (*note Math formulas::).
+
 
+File: latex2e.info,  Node: \left & \right,  Next: \sqrt,  Prev: \frac,  Up: Math miscellany
+
+16.7.4 '\left' & '\right'
+-------------------------
+
+Synopsis:
+
+     \left DELIMITER1 ... \right DELIMITER2
+
+   Make matching parentheses, braces, or other delimiters.  The
+delimiters are sized according to the math they enclose.  This makes a
+unit vector surrounded by appropriate-height parentheses.
+
+     \begin{equation}
+       \left(\begin{array}{c}
+         1   \\
+         0   \\
+       \end{array}\right)
+
+   Every '\left' must have a matching '\right'.  Leaving out the
+'\left(' in the above gets 'Extra \right'.  Leaving off the '\right)'
+gets 'You can't use `\eqno' in math mode'.
+
+   However, the two delimiters DELIMITER1 and DELIMITER2 need not match.
+A common case is that you want an unmatched brace, as below.  Use a
+period, '.', as a null delimiter.
+
+     \begin{equation}
+       f(n)=\left\{\begin{array}{ll}
+                     1             &\mbox{--if \(n=0\)} \\
+                     f(n-1)+3n^2   &\mbox{--else}
+            \end{array}\right.
+     \end{equation}
+
+   Note that to get a curly brace as a delimiter you must prefix it with
+a backslash, '\{'.
+
+
+File: latex2e.info,  Node: \sqrt,  Next: \stackrel,  Prev: \left & \right,  Up: Math miscellany
+
+16.7.5 '\sqrt'
+--------------
+
+Synopsis, one of:
+
+     \sqrt{ARG}
+     \sqrt[ROOT-NUMBER]{ARG}
+
+   The square root, or optionally other roots, of ARG.  The optional
+argument ROOT-NUMBER gives the root, i.e., enter the cube root of 'x+y'
+as '\sqrt[3]{x+y}'.  The radical grows with the size of ARG (as the
+height of the radical grows, the angle on the leftmost part gets
+steeper, until for a large enough 'arg', it is vertical).
+
+   LaTeX has a separate '\surd' character (*note Math symbols::).
+
+
+File: latex2e.info,  Node: \stackrel,  Prev: \sqrt,  Up: Math miscellany
+
+16.7.6 '\stackrel'
+------------------
+
+Synopsis, one of:
+
+     \stackrel{TEXT}{RELATION}
+
+   Put TEXT above RELATION.  To put a function name above an arrow enter
+'\stackrel{f}{\longrightarrow}'.
+
+
 File: latex2e.info,  Node: Modes,  Next: Page styles,  Prev: Math formulas,  Up: Top
 
 17 Modes
@@ -9216,10 +9407,9 @@
 typeset, from the current page onwards.
 
    A discussion with an example is below.  Note first that the package
-'fancyhdr' is the standard way to manipulate headers and footers because
-it makes it immensely easier.  New documents that need to do anything
-other than one of the standard options below should use this package.
-See its documentation on CTAN.
+'fancyhdr' is now the standard way to manipulate headers and footers.
+New documents that need to do anything other than one of the standard
+options below should use this package.  See its documentation on CTAN.
 
    Values for STYLE:
 
@@ -9798,7 +9988,7 @@
 
      \parbox{WIDTH}{CONTENTS}
 
-   or:
+or
 
      \parbox[POSITION][HEIGHT][INNER-POS]{WIDTH}{CONTENTS}
 
@@ -9851,7 +10041,7 @@
 
      \raisebox{DISTANCE}{TEXT}
 
-   or:
+or
 
      \raisebox{DISTANCE}[HEIGHT][DEPTH]{TEXT}
 
@@ -10071,7 +10261,7 @@
      \textcolor{NAME}{...}
      \textcolor[COLOR MODEL]{COLOR SPECIFICATION}{...}
 
-   or
+or
 
      \color{NAME}
      \color[COLOR MODEL]{SPECIFICATION}
@@ -10140,7 +10330,7 @@
      \colorbox{NAME}{...}
      \colorbox[MODEL NAME]{BOX BACKGROUND COLOR SPECIFICATION}{...}
 
-   or
+or
 
      \fcolorbox{FRAME COLOR}{BOX BACKGROUND COLOR}{...}
      \fcolorbox[MODEL NAME]{FRAME COLOR SPECIFICATION}{BOX BACKGROUND COLOR SPECIFICATION}{...}
@@ -10249,7 +10439,7 @@
 
      \usepackage[COMMA-SEPARATED OPTION LIST]{graphics}
 
-   or
+or
 
      \usepackage[COMMA-SEPARATED OPTION LIST]{graphicx}
 
@@ -12426,6 +12616,8 @@
 * .glo file:                             Glossaries.          (line   8)
 * .idx file:                             Indexes.             (line   9)
 * .ind file:                             Indexes.             (line  23)
+* ::                                     Colon character & \colon.
+                                                              (line   6)
 * 'see' and 'see also' index entries:    Indexes.             (line  16)
 * abstracts:                             abstract.            (line   6)
 * accents:                               Accents.             (line   6)
@@ -12446,7 +12638,12 @@
 * amsmath package <1>:                   displaymath.         (line  22)
 * amsmath package <2>:                   theorem.             (line  28)
 * amsmath package <3>:                   Math formulas.       (line  21)
-* amsmath package <4>:                   Math functions.      (line 111)
+* amsmath package <4>:                   Ellipses.            (line  36)
+* amsmath package <5>:                   Math functions.      (line 111)
+* amsmath package <6>:                   Colon character & \colon.
+                                                              (line  15)
+* amsmath package <7>:                   Colon character & \colon.
+                                                              (line  19)
 * amsmath package, replacing eqnarray:   eqnarray.            (line   6)
 * amsthm package:                        theorem.             (line  28)
 * appendix, creating:                    Sectioning.          (line  37)
@@ -12563,6 +12760,8 @@
 * closing letters:                       \closing.            (line   6)
 * closing quote:                         Text symbols.        (line  55)
 * code, typesetting:                     verbatim.            (line   6)
+* colon character:                       Colon character & \colon.
+                                                              (line   6)
 * color:                                 Color.               (line   6)
 * color <1>:                             Define colors.       (line   6)
 * color <2>:                             Colored text.        (line   6)
@@ -12631,6 +12830,7 @@
 * defining new fonts:                    \newfont.            (line   6)
 * defining new theorems:                 \newtheorem.         (line   6)
 * definitions:                           Definitions.         (line   6)
+* delimiters, paired:                    \left & \right.      (line   6)
 * description lists, creating:           description.         (line   6)
 * design size, in font definitions:      \newfont.            (line  19)
 * Didot point:                           Units of length.     (line  30)
@@ -12638,7 +12838,6 @@
 * difference between class and package:  Class and package construction.
                                                               (line  15)
 * discretionary hyphenation:             \discretionary.      (line   6)
-* discretionary multiplication:          Math miscellany.     (line   7)
 * display math mode:                     Modes.               (line  28)
 * displaying quoted text with paragraph indentation: quotation & quote.
                                                               (line   6)
@@ -12657,9 +12856,10 @@
 * dot-over accent:                       Accents.             (line  25)
 * dot-under accent:                      Accents.             (line  55)
 * dotless i:                             Accents.             (line  63)
-* dotless i, math:                       Math accents.        (line  35)
+* dotless i, math:                       Math symbols.        (line 271)
 * dotless j:                             Accents.             (line  66)
-* dotless j, math:                       Math accents.        (line  38)
+* dotless j, math:                       Math symbols.        (line 294)
+* dots:                                  Ellipses.            (line   6)
 * double angle quotation marks:          Text symbols.        (line  30)
 * double dagger, in text:                Text symbols.        (line  18)
 * double dagger, in text <1>:            Text symbols.        (line 107)
@@ -12675,6 +12875,7 @@
 * doublestruck:                          Blackboard bold.     (line   6)
 * e-dash:                                Text symbols.        (line 116)
 * e-TeX:                                 TeX engines.         (line  12)
+* ellipses:                              Ellipses.            (line   6)
 * ellipsis:                              Text symbols.        (line  36)
 * em:                                    Units of length.     (line  38)
 * em-dash:                               Text symbols.        (line 113)
@@ -12769,6 +12970,7 @@
 * formulas, math:                        Math formulas.       (line   6)
 * forward reference:                     Cross references.    (line  27)
 * forward references, resolving:         Output files.        (line  33)
+* fraction:                              \frac.               (line   6)
 * fragile commands:                      \protect.            (line   6)
 * French quotation marks:                Text symbols.        (line  30)
 * functions, math:                       Math functions.      (line   6)
@@ -12941,6 +13143,8 @@
 * making paragraphs:                     Making paragraphs.   (line   6)
 * marginal notes:                        Marginal notes.      (line   6)
 * masculine ordinal symbol:              Text symbols.        (line 135)
+* matching brackets:                     \left & \right.      (line   6)
+* matching parentheses:                  \left & \right.      (line   6)
 * math accents:                          Math accents.        (line   6)
 * math formulas:                         Math formulas.       (line   6)
 * math functions:                        Math functions.      (line   6)
@@ -12952,6 +13156,8 @@
 * math symbols:                          Math symbols.        (line   6)
 * math, bold:                            Font styles.         (line 130)
 * mathtools package:                     Math formulas.       (line  21)
+* mathtools package <1>:                 Over- and Underlining.
+                                                              (line  42)
 * mfirstuc package:                      Upper and lower case.
                                                               (line  45)
 * mhchem package:                        Subscripts & superscripts.
@@ -12965,11 +13171,12 @@
 * moving arguments:                      \protect.            (line  19)
 * mpfootnote counter:                    \footnote.           (line  62)
 * mu, math unit:                         Units of length.     (line  49)
+* muiltiplication, line breaks:          \*.                  (line   6)
 * multicolumn text:                      \twocolumn.          (line   6)
 * multilingual support:                  Accents.             (line   6)
 * multind package:                       Indexes.             (line  39)
-* multiplication symbol, discretionary line break: Math miscellany.
-                                                              (line   7)
+* multiplication symbol, discretionary line break: \*.        (line   6)
+* multiplication, discretionary:         \*.                  (line   6)
 * nested \include, not allowed:          \include & \includeonly.
                                                               (line  99)
 * new class commands:                    Class and package construction.
@@ -12989,7 +13196,7 @@
 * non-English characters:                Additional Latin letters.
                                                               (line   6)
 * notes in the margin:                   Marginal notes.      (line   6)
-* null delimiter:                        Math miscellany.     (line  36)
+* null delimiter:                        \left & \right.      (line   6)
 * numbered items, specifying counter:    \usecounter.         (line   6)
 * numerals, old-style:                   Font styles.         (line 134)
 * oblique font:                          Font styles.         (line  89)
@@ -13021,6 +13228,8 @@
 * outer paragraph mode:                  Modes.               (line  46)
 * overbar accent:                        Accents.             (line  29)
 * overdot accent, math:                  Math accents.        (line  26)
+* overlining:                            Over- and Underlining.
+                                                              (line   6)
 * overview of LaTeX:                     Overview.            (line   6)
 * package file layout:                   Class and package structure.
                                                               (line   6)
@@ -13034,7 +13243,12 @@
 * package, amsmath <1>:                  displaymath.         (line  22)
 * package, amsmath <2>:                  theorem.             (line  28)
 * package, amsmath <3>:                  Math formulas.       (line  21)
-* package, amsmath <4>:                  Math functions.      (line 111)
+* package, amsmath <4>:                  Ellipses.            (line  36)
+* package, amsmath <5>:                  Math functions.      (line 111)
+* package, amsmath <6>:                  Colon character & \colon.
+                                                              (line  15)
+* package, amsmath <7>:                  Colon character & \colon.
+                                                              (line  19)
 * package, amsthm:                       theorem.             (line  28)
 * package, babel:                        thebibliography.     (line  53)
 * package, babel <1>:                    Accents.             (line   6)
@@ -13070,6 +13284,8 @@
                                                               (line  39)
 * package, makeidx:                      Indexes.             (line  28)
 * package, mathtools:                    Math formulas.       (line  21)
+* package, mathtools <1>:                Over- and Underlining.
+                                                              (line  42)
 * package, mfirstuc:                     Upper and lower case.
                                                               (line  45)
 * package, mhchem:                       Subscripts & superscripts.
@@ -13085,7 +13301,8 @@
 * package, textcase:                     Upper and lower case.
                                                               (line  42)
 * package, textcomp:                     Font styles.         (line 134)
-* package, ulem:                         Math miscellany.     (line  79)
+* package, ulem:                         Over- and Underlining.
+                                                              (line  15)
 * package, url:                          \verb.               (line  30)
 * package, verbatimbox:                  verbatim.            (line  37)
 * package, xspace:                       \(SPACE) after control sequence.
@@ -13103,6 +13320,7 @@
 * page style, this page:                 \thispagestyle.      (line   6)
 * page styles:                           Page styles.         (line   6)
 * page, colored:                         Colored pages.       (line   6)
+* paired delimiters:                     \left & \right.      (line   6)
 * paragraph indentation:                 \parindent & \parskip.
                                                               (line   6)
 * paragraph indentation, in minipage:    minipage.            (line 108)
@@ -13157,6 +13375,7 @@
                                                               (line   6)
 * quoted text without paragraph indentation, displaying: quotation & quote.
                                                               (line   6)
+* radical:                               \sqrt.               (line   6)
 * ragged left text:                      \raggedleft.         (line   6)
 * ragged left text, environment for:     flushright.          (line   6)
 * ragged right text:                     \raggedright.        (line   6)
@@ -13166,6 +13385,7 @@
 * reference, forward:                    Cross references.    (line  27)
 * references, resolving forward:         Output files.        (line  33)
 * registered symbol:                     Text symbols.        (line 163)
+* relation, text above:                  \stackrel.           (line   6)
 * remarks in the margin:                 Marginal notes.      (line   6)
 * reporting bugs:                        About this document. (line  21)
 * reserved characters:                   Reserved characters. (line   6)
@@ -13182,10 +13402,11 @@
 * right-justifying text:                 \raggedleft.         (line   6)
 * right-justifying text, environment for: flushright.         (line   6)
 * ring accent:                           Accents.             (line  75)
-* ring accent, math:                     Math accents.        (line  41)
+* ring accent, math:                     Math accents.        (line  35)
 * robust commands:                       \protect.            (line   6)
 * roman font:                            Font styles.         (line  80)
 * root file:                             Splitting the input. (line  10)
+* roots:                                 \sqrt.               (line   6)
 * rotating graphics:                     \rotatebox.          (line   6)
 * rotating text:                         \rotatebox.          (line   6)
 * rotation:                              \rotatebox.          (line   6)
@@ -13243,6 +13464,8 @@
 * special insertions:                    Special insertions.  (line   6)
 * specifier, float placement:            Floats.              (line  31)
 * splitting the input file:              Splitting the input. (line   6)
+* square root:                           \sqrt.               (line   6)
+* stack math:                            \stackrel.           (line   6)
 * star-variants, commands:               \@ifstar.            (line   6)
 * starred form, defining new commands:   \newcommand & \renewcommand.
                                                               (line  25)
@@ -13301,7 +13524,7 @@
 * three-quarters em-dash:                Text symbols.        (line 169)
 * tie-after accent:                      Accents.             (line  81)
 * tilde accent:                          Accents.             (line  43)
-* tilde accent, math:                    Math accents.        (line  44)
+* tilde accent, math:                    Math accents.        (line  38)
 * tilde, ASCII, in text:                 Text symbols.        (line  67)
 * title page, separate or run-in:        Document class options.
                                                               (line  71)
@@ -13320,9 +13543,12 @@
 * typefaces:                             Fonts.               (line   6)
 * typewriter font:                       Font styles.         (line  92)
 * typewriter labels in lists:            description.         (line  34)
-* ulem package:                          Math miscellany.     (line  79)
+* ulem package:                          Over- and Underlining.
+                                                              (line  15)
 * umlaut accent:                         Accents.             (line  16)
 * underbar:                              Accents.             (line  89)
+* underlining:                           Over- and Underlining.
+                                                              (line   6)
 * underscore, in text:                   Text symbols.        (line 178)
 * Unicode input, native:                 TeX engines.         (line   6)
 * units, of length:                      Units of length.     (line   6)
@@ -13334,7 +13560,7 @@
 * using BibTeX:                          Using BibTeX.        (line   6)
 * UTF-8:                                 TeX engines.         (line   6)
 * variables, a list of:                  Counters.            (line   6)
-* vector symbol, math:                   Math accents.        (line  47)
+* vector symbol, math:                   Math accents.        (line  41)
 * verbatim text:                         verbatim.            (line   6)
 * verbatim text, inline:                 \verb.               (line   6)
 * verbatimbox package:                   verbatim.            (line  37)
@@ -13350,8 +13576,8 @@
 * weights, of fonts:                     Low-level font commands.
                                                               (line  58)
 * white space:                           Spaces.              (line   6)
-* wide hat accent, math:                 Math accents.        (line  50)
-* wide tilde accent, math:               Math accents.        (line  53)
+* wide hat accent, math:                 Math accents.        (line  44)
+* wide tilde accent, math:               Math accents.        (line  47)
 * widths, of fonts:                      Low-level font commands.
                                                               (line  70)
 * writing external files:                filecontents.        (line   6)
@@ -13391,6 +13617,8 @@
                                                               (line  14)
 * 12pt option:                           Document class options.
                                                               (line  14)
+* ::                                     Colon character & \colon.
+                                                              (line   6)
 * [...] for optional arguments:          LaTeX command syntax.
                                                               (line   6)
 * \ character starting commands:         LaTeX command syntax.
@@ -13405,7 +13633,7 @@
 * \' (acute accent):                     Accents.             (line  20)
 * \' (tabbing):                          tabbing.             (line  87)
 * \(SPACE):                              \(SPACE) and \@.     (line   6)
-* \*:                                    Math miscellany.     (line   6)
+* \*:                                    \*.                  (line   6)
 * \+:                                    tabbing.             (line  79)
 * \,:                                    Spacing in math mode.
                                                               (line  31)
@@ -13547,7 +13775,7 @@
 * \caption <1>:                          table.               (line  47)
 * \cc:                                   \cc.                 (line   6)
 * \cdot:                                 Math symbols.        (line 126)
-* \cdots:                                Math miscellany.     (line  25)
+* \cdots:                                Ellipses.            (line  17)
 * \centering:                            \centering.          (line   6)
 * \chapter:                              Sectioning.          (line   9)
 * \check:                                Math accents.        (line  19)
@@ -13576,6 +13804,8 @@
 * \cline:                                \cline.              (line   6)
 * \closing:                              \closing.            (line   6)
 * \clubsuit:                             Math symbols.        (line 137)
+* \colon:                                Colon character & \colon.
+                                                              (line   6)
 * \columnsep:                            \twocolumn.          (line  22)
 * \columnsep <1>:                        Page layout parameters.
                                                               (line   6)
@@ -13619,7 +13849,7 @@
 * \ddag:                                 Text symbols.        (line  17)
 * \ddagger:                              Math symbols.        (line 164)
 * \ddot:                                 Math accents.        (line  22)
-* \ddots:                                Math miscellany.     (line  29)
+* \ddots:                                Ellipses.            (line  21)
 * \DeclareGraphicsExtensions:            \DeclareGraphicsExtensions.
                                                               (line   6)
 * \DeclareGraphicsRule:                  \DeclareGraphicsRule.
@@ -13720,8 +13950,7 @@
 * \footskip <1>:                         Page layout parameters.
                                                               (line  27)
 * \forall:                               Math symbols.        (line 224)
-* \frac:                                 Math miscellany.     (line  33)
-* \frac{NUM}{DEN}:                       Math miscellany.     (line  32)
+* \frac:                                 \frac.               (line   6)
 * \frame:                                \frame.              (line   6)
 * \framebox:                             \framebox (picture). (line   6)
 * \framebox <1>:                         \fbox and \framebox. (line   6)
@@ -13784,8 +14013,8 @@
 * \IJ (IJ):                              Additional Latin letters.
                                                               (line  32)
 * \Im:                                   Math symbols.        (line 267)
-* \imath:                                Math accents.        (line  34)
-* \in:                                   Math symbols.        (line 270)
+* \imath:                                Math symbols.        (line 270)
+* \in:                                   Math symbols.        (line 274)
 * \include:                              \include & \includeonly.
                                                               (line   6)
 * \includegraphics:                      \includegraphics.    (line   6)
@@ -13796,14 +14025,14 @@
 * \indexentry:                           Indexes.             (line  12)
 * \indexspace:                           Indexes.             (line  32)
 * \inf:                                  Math functions.      (line  57)
-* \infty:                                Math symbols.        (line 276)
+* \infty:                                Math symbols.        (line 280)
 * \input:                                \input.              (line   6)
 * \InputIfFileExists:                    Class and package commands.
                                                               (line 127)
-* \int:                                  Math symbols.        (line 279)
+* \int:                                  Math symbols.        (line 283)
 * \intextsep:                            Floats.              (line 118)
 * \intextsep <1>:                        Floats.              (line 119)
-* \iota:                                 Math symbols.        (line 282)
+* \iota:                                 Math symbols.        (line 286)
 * \it:                                   Font styles.         (line  76)
 * \item:                                 description.         (line  29)
 * \item <1>:                             enumerate.           (line  29)
@@ -13813,10 +14042,10 @@
 * \itemsep:                              list.                (line  82)
 * \itshape:                              Font styles.         (line  33)
 * \j (dotless j):                        Accents.             (line  66)
-* \jmath:                                Math accents.        (line  37)
-* \Join:                                 Math symbols.        (line 285)
+* \jmath:                                Math symbols.        (line 293)
+* \Join:                                 Math symbols.        (line 289)
 * \k (ogonek):                           Accents.             (line  70)
-* \kappa:                                Math symbols.        (line 289)
+* \kappa:                                Math symbols.        (line 297)
 * \ker:                                  Math functions.      (line  60)
 * \kill:                                 tabbing.             (line 107)
 * \l (/l):                               Additional Latin letters.
@@ -13834,27 +14063,28 @@
 * \labelitemiv:                          itemize.             (line  34)
 * \labelsep:                             list.                (line  94)
 * \labelwidth:                           list.                (line  99)
-* \Lambda:                               Math symbols.        (line 292)
-* \lambda:                               Math symbols.        (line 295)
-* \land:                                 Math symbols.        (line 298)
-* \langle:                               Math symbols.        (line 303)
+* \Lambda:                               Math symbols.        (line 300)
+* \lambda:                               Math symbols.        (line 303)
+* \land:                                 Math symbols.        (line 306)
+* \langle:                               Math symbols.        (line 311)
 * \large:                                Font sizes.          (line  11)
 * \Large:                                Font sizes.          (line  11)
 * \LARGE:                                Font sizes.          (line  11)
 * \LaTeX:                                Text symbols.        (line  20)
 * \LaTeXe:                               Text symbols.        (line  23)
-* \lbrace:                               Math symbols.        (line 308)
-* \lbrack:                               Math symbols.        (line 312)
-* \lceil:                                Math symbols.        (line 316)
-* \ldots:                                Text symbols.        (line  33)
-* \le:                                   Math symbols.        (line 320)
-* \leadsto:                              Math symbols.        (line 324)
-* \left DELIM1 ... \right DELIM2:        Math miscellany.     (line  35)
-* \Leftarrow:                            Math symbols.        (line 331)
-* \leftarrow:                            Math symbols.        (line 336)
+* \lbrace:                               Math symbols.        (line 316)
+* \lbrack:                               Math symbols.        (line 320)
+* \lceil:                                Math symbols.        (line 324)
+* \ldots:                                Ellipses.            (line  24)
+* \ldots <1>:                            Text symbols.        (line  33)
+* \le:                                   Math symbols.        (line 328)
+* \leadsto:                              Math symbols.        (line 332)
+* \left:                                 \left & \right.      (line   6)
+* \Leftarrow:                            Math symbols.        (line 339)
+* \leftarrow:                            Math symbols.        (line 344)
 * \lefteqn:                              eqnarray.            (line  46)
-* \leftharpoondown:                      Math symbols.        (line 340)
-* \leftharpoonup:                        Math symbols.        (line 343)
+* \leftharpoondown:                      Math symbols.        (line 348)
+* \leftharpoonup:                        Math symbols.        (line 351)
 * \leftmargin:                           itemize.             (line  53)
 * \leftmargin <1>:                       list.                (line 119)
 * \leftmargini:                          itemize.             (line  53)
@@ -13863,12 +14093,12 @@
 * \leftmarginiv:                         itemize.             (line  53)
 * \leftmarginv:                          itemize.             (line  53)
 * \leftmarginvi:                         itemize.             (line  53)
-* \Leftrightarrow:                       Math symbols.        (line 346)
-* \leftrightarrow:                       Math symbols.        (line 351)
-* \leq:                                  Math symbols.        (line 356)
-* \lfloor:                               Math symbols.        (line 360)
+* \Leftrightarrow:                       Math symbols.        (line 354)
+* \leftrightarrow:                       Math symbols.        (line 359)
+* \leq:                                  Math symbols.        (line 364)
+* \lfloor:                               Math symbols.        (line 368)
 * \lg:                                   Math functions.      (line  63)
-* \lhd:                                  Math symbols.        (line 363)
+* \lhd:                                  Math symbols.        (line 371)
 * \lim:                                  Math functions.      (line  66)
 * \liminf:                               Math functions.      (line  69)
 * \limsup:                               Math functions.      (line  72)
@@ -13885,20 +14115,20 @@
 * \listoffigures:                        Tables of contents.  (line  16)
 * \listoftables:                         Tables of contents.  (line  16)
 * \listparindent:                        list.                (line 136)
-* \ll:                                   Math symbols.        (line 371)
+* \ll:                                   Math symbols.        (line 379)
 * \ln:                                   Math functions.      (line  75)
-* \lnot:                                 Math symbols.        (line 375)
+* \lnot:                                 Math symbols.        (line 383)
 * \LoadClass:                            Class and package commands.
                                                               (line 144)
 * \LoadClassWithOptions:                 Class and package commands.
                                                               (line 144)
 * \location:                             \location.           (line   6)
 * \log:                                  Math functions.      (line  78)
-* \longleftarrow:                        Math symbols.        (line 378)
-* \longleftrightarrow:                   Math symbols.        (line 383)
-* \longmapsto:                           Math symbols.        (line 387)
-* \longrightarrow:                       Math symbols.        (line 392)
-* \lor:                                  Math symbols.        (line 397)
+* \longleftarrow:                        Math symbols.        (line 386)
+* \longleftrightarrow:                   Math symbols.        (line 391)
+* \longmapsto:                           Math symbols.        (line 395)
+* \longrightarrow:                       Math symbols.        (line 400)
+* \lor:                                  Math symbols.        (line 405)
 * \lq:                                   Text symbols.        (line  39)
 * \makebox:                              \makebox.            (line   6)
 * \makebox (for picture):                \makebox (picture).  (line   6)
@@ -13907,7 +14137,7 @@
 * \makelabel:                            list.                (line  55)
 * \makelabels:                           \makelabels.         (line   6)
 * \maketitle:                            \maketitle.          (line   6)
-* \mapsto:                               Math symbols.        (line 400)
+* \mapsto:                               Math symbols.        (line 408)
 * \marginpar:                            Marginal notes.      (line   6)
 * \marginparpush:                        Page layout parameters.
                                                               (line  40)
@@ -13924,21 +14154,20 @@
                                                               (line  41)
 * \marginsep <1>:                        Page layout parameters.
                                                               (line  43)
-* \markboth{LEFT-HEAD}{RIGHT-HEAD}:      \pagestyle.          (line  76)
-* \markright{RIGHT}:                     \pagestyle.          (line  85)
+* \markboth{LEFT-HEAD}{RIGHT-HEAD}:      \pagestyle.          (line  75)
+* \markright{RIGHT}:                     \pagestyle.          (line  84)
 * \mathbf:                               Font styles.         (line 112)
 * \mathcal:                              Font styles.         (line 128)
-* \mathdollar:                           Math miscellany.     (line  40)
-* \mathellipsis:                         Math miscellany.     (line  43)
+* \mathdollar:                           Math symbols.        (line 914)
 * \mathnormal:                           Font styles.         (line 125)
-* \mathparagraph:                        Math miscellany.     (line  46)
-* \mathring:                             Math accents.        (line  40)
+* \mathparagraph:                        Math symbols.        (line 917)
+* \mathring:                             Math accents.        (line  34)
 * \mathrm:                               Font styles.         (line 109)
-* \mathsection:                          Math miscellany.     (line  49)
+* \mathsection:                          Math symbols.        (line 920)
 * \mathsf:                               Font styles.         (line 115)
-* \mathsterling:                         Math miscellany.     (line  52)
+* \mathsterling:                         Math symbols.        (line 923)
 * \mathtt:                               Font styles.         (line 118)
-* \mathunderscore:                       Math miscellany.     (line  55)
+* \mathunderscore:                       Math symbols.        (line 926)
 * \mathversion:                          Font styles.         (line 130)
 * \max:                                  Math functions.      (line  81)
 * \mbox:                                 \mbox.               (line   6)
@@ -13949,24 +14178,24 @@
                                                               (line  15)
 * \medspace:                             Spacing in math mode.
                                                               (line  27)
-* \mho:                                  Math symbols.        (line 404)
-* \mid:                                  Math symbols.        (line 409)
+* \mho:                                  Math symbols.        (line 412)
+* \mid:                                  Math symbols.        (line 417)
 * \min:                                  Math functions.      (line  84)
-* \models:                               Math symbols.        (line 419)
+* \models:                               Math symbols.        (line 427)
 * \month:                                \day \month \year.   (line   6)
-* \mp:                                   Math symbols.        (line 424)
-* \mu:                                   Math symbols.        (line 427)
+* \mp:                                   Math symbols.        (line 432)
+* \mu:                                   Math symbols.        (line 435)
 * \multicolumn:                          \multicolumn.        (line   6)
 * \multiput:                             \multiput.           (line   6)
-* \nabla:                                Math symbols.        (line 430)
+* \nabla:                                Math symbols.        (line 438)
 * \name:                                 \name.               (line   6)
-* \natural:                              Math symbols.        (line 433)
-* \ne:                                   Math symbols.        (line 436)
-* \nearrow:                              Math symbols.        (line 439)
+* \natural:                              Math symbols.        (line 441)
+* \ne:                                   Math symbols.        (line 444)
+* \nearrow:                              Math symbols.        (line 447)
 * \NeedsTeXFormat:                       Class and package commands.
                                                               (line 176)
-* \neg:                                  Math symbols.        (line 442)
-* \neq:                                  Math symbols.        (line 446)
+* \neg:                                  Math symbols.        (line 450)
+* \neq:                                  Math symbols.        (line 454)
 * \newcommand:                           \newcommand & \renewcommand.
                                                               (line   6)
 * \newcounter:                           \newcounter.         (line   6)
@@ -13984,7 +14213,7 @@
                                                               (line  40)
 * \NG:                                   Additional Latin letters.
                                                               (line  40)
-* \ni:                                   Math symbols.        (line 449)
+* \ni:                                   Math symbols.        (line 457)
 * \nocite:                               \nocite.             (line   6)
 * \nocorr:                               Font styles.         (line  21)
 * \nocorrlist:                           Font styles.         (line  21)
@@ -14000,10 +14229,10 @@
 * \normalmarginpar:                      Marginal notes.      (line  23)
 * \normalsfcodes:                        \normalsfcodes.      (line   6)
 * \normalsize:                           Font sizes.          (line  11)
-* \not:                                  Math symbols.        (line 454)
-* \notin:                                Math symbols.        (line 462)
-* \nu:                                   Math symbols.        (line 466)
-* \nwarrow:                              Math symbols.        (line 469)
+* \not:                                  Math symbols.        (line 462)
+* \notin:                                Math symbols.        (line 470)
+* \nu:                                   Math symbols.        (line 474)
+* \nwarrow:                              Math symbols.        (line 477)
 * \o (/o):                               Additional Latin letters.
                                                               (line  44)
 * \O (/O):                               Additional Latin letters.
@@ -14016,27 +14245,29 @@
                                                               (line  66)
 * \oddsidemargin <2>:                    Page layout parameters.
                                                               (line  68)
-* \odot:                                 Math symbols.        (line 472)
+* \odot:                                 Math symbols.        (line 480)
 * \oe (oe):                              Additional Latin letters.
                                                               (line  48)
 * \OE (OE):                              Additional Latin letters.
                                                               (line  48)
-* \oint:                                 Math symbols.        (line 477)
+* \oint:                                 Math symbols.        (line 485)
 * \oldstylenums:                         Font styles.         (line 134)
-* \Omega:                                Math symbols.        (line 481)
-* \omega:                                Math symbols.        (line 484)
-* \ominus:                               Math symbols.        (line 487)
+* \Omega:                                Math symbols.        (line 489)
+* \omega:                                Math symbols.        (line 492)
+* \ominus:                               Math symbols.        (line 495)
 * \onecolumn:                            \onecolumn.          (line   6)
 * \opening:                              \opening.            (line   6)
-* \oplus:                                Math symbols.        (line 490)
+* \oplus:                                Math symbols.        (line 498)
 * \OptionNotUsed:                        Class and package commands.
                                                               (line 192)
-* \oslash:                               Math symbols.        (line 494)
-* \otimes:                               Math symbols.        (line 497)
+* \oslash:                               Math symbols.        (line 502)
+* \otimes:                               Math symbols.        (line 505)
 * \oval:                                 \oval.               (line   6)
-* \overbrace{MATH}:                      Math miscellany.     (line  58)
-* \overline{TEXT}:                       Math miscellany.     (line  62)
-* \owns:                                 Math symbols.        (line 502)
+* \overbrace{MATH}:                      Over- and Underlining.
+                                                              (line  38)
+* \overline{TEXT}:                       Over- and Underlining.
+                                                              (line  19)
+* \owns:                                 Math symbols.        (line 510)
 * \P:                                    Text symbols.        (line  42)
 * \PackageError:                         Class and package commands.
                                                               (line  41)
@@ -14063,7 +14294,7 @@
                                                               (line  86)
 * \par:                                  \par.                (line   6)
 * \paragraph:                            Sectioning.          (line  14)
-* \parallel:                             Math symbols.        (line 507)
+* \parallel:                             Math symbols.        (line 515)
 * \parbox:                               \parbox.             (line   6)
 * \parindent:                            minipage.            (line 108)
 * \parindent <1>:                        \indent & \noindent. (line   6)
@@ -14074,7 +14305,7 @@
                                                               (line   6)
 * \parskip example:                      itemize.             (line  72)
 * \part:                                 Sectioning.          (line   8)
-* \partial:                              Math symbols.        (line 510)
+* \partial:                              Math symbols.        (line 518)
 * \partopsep:                            list.                (line 151)
 * \PassOptionsToClass:                   Class and package commands.
                                                               (line 198)
@@ -14084,26 +14315,26 @@
                                                               (line  40)
 * \pdfpagewidth:                         Document class options.
                                                               (line  40)
-* \perp:                                 Math symbols.        (line 513)
-* \phi:                                  Math symbols.        (line 518)
-* \Pi:                                   Math symbols.        (line 522)
-* \pi:                                   Math symbols.        (line 525)
-* \pm:                                   Math symbols.        (line 529)
+* \perp:                                 Math symbols.        (line 521)
+* \phi:                                  Math symbols.        (line 526)
+* \Pi:                                   Math symbols.        (line 530)
+* \pi:                                   Math symbols.        (line 533)
+* \pm:                                   Math symbols.        (line 537)
 * \pmod:                                 Math functions.      (line  87)
 * \poptabs:                              tabbing.             (line 113)
 * \poptabs <1>:                          tabbing.             (line 114)
 * \pounds:                               Text symbols.        (line  46)
 * \Pr:                                   Math functions.      (line  90)
-* \prec:                                 Math symbols.        (line 532)
-* \preceq:                               Math symbols.        (line 535)
-* \prime:                                Math symbols.        (line 540)
+* \prec:                                 Math symbols.        (line 540)
+* \preceq:                               Math symbols.        (line 543)
+* \prime:                                Math symbols.        (line 548)
 * \printindex:                           Indexes.             (line  28)
 * \ProcessOptions:                       Class and package commands.
                                                               (line 232)
 * \ProcessOptions*:                      Class and package commands.
                                                               (line 232)
-* \prod:                                 Math symbols.        (line 549)
-* \propto:                               Math symbols.        (line 552)
+* \prod:                                 Math symbols.        (line 557)
+* \propto:                               Math symbols.        (line 560)
 * \protect:                              \protect.            (line   6)
 * \providecommand:                       \providecommand.     (line   6)
 * \ProvidesClass:                        Class and package commands.
@@ -14113,8 +14344,8 @@
 * \ProvidesPackage:                      Class and package commands.
                                                               (line 270)
 * \ps:                                   \ps.                 (line   6)
-* \Psi:                                  Math symbols.        (line 555)
-* \psi:                                  Math symbols.        (line 558)
+* \Psi:                                  Math symbols.        (line 563)
+* \psi:                                  Math symbols.        (line 566)
 * \pushtabs:                             tabbing.             (line 116)
 * \put:                                  \put.                (line   6)
 * \qbezier:                              \qbezier.            (line   6)
@@ -14129,11 +14360,11 @@
 * \raggedleft:                           \raggedleft.         (line   6)
 * \raggedright:                          \raggedright.        (line   6)
 * \raisebox:                             \raisebox.           (line   6)
-* \rangle:                               Math symbols.        (line 561)
-* \rbrace:                               Math symbols.        (line 565)
-* \rbrack:                               Math symbols.        (line 569)
-* \rceil:                                Math symbols.        (line 573)
-* \Re:                                   Math symbols.        (line 576)
+* \rangle:                               Math symbols.        (line 569)
+* \rbrace:                               Math symbols.        (line 573)
+* \rbrack:                               Math symbols.        (line 577)
+* \rceil:                                Math symbols.        (line 581)
+* \Re:                                   Math symbols.        (line 584)
 * \ref:                                  \ref.                (line   6)
 * \reflectbox:                           \scalebox.           (line   6)
 * \refstepcounter:                       \refstepcounter.     (line   6)
@@ -14146,18 +14377,18 @@
 * \resizebox:                            \resizebox.          (line   6)
 * \restorecr:                            \obeycr & \restorecr.
                                                               (line   6)
-* \restriction:                          Math symbols.        (line 581)
-* \revemptyset:                          Math symbols.        (line 586)
+* \restriction:                          Math symbols.        (line 589)
+* \revemptyset:                          Math symbols.        (line 594)
 * \reversemarginpar:                     Marginal notes.      (line  23)
-* \rfloor:                               Math symbols.        (line 591)
-* \rhd:                                  Math symbols.        (line 595)
-* \rho:                                  Math symbols.        (line 602)
-* \right:                                Math miscellany.     (line  36)
-* \Rightarrow:                           Math symbols.        (line 606)
-* \rightarrow:                           Math symbols.        (line 610)
-* \rightharpoondown:                     Math symbols.        (line 615)
-* \rightharpoonup:                       Math symbols.        (line 618)
-* \rightleftharpoons:                    Math symbols.        (line 621)
+* \rfloor:                               Math symbols.        (line 599)
+* \rhd:                                  Math symbols.        (line 603)
+* \rho:                                  Math symbols.        (line 610)
+* \right:                                \left & \right.      (line   6)
+* \Rightarrow:                           Math symbols.        (line 614)
+* \rightarrow:                           Math symbols.        (line 618)
+* \rightharpoondown:                     Math symbols.        (line 623)
+* \rightharpoonup:                       Math symbols.        (line 626)
+* \rightleftharpoons:                    Math symbols.        (line 629)
 * \rightmargin:                          list.                (line 166)
 * \rm:                                   Font styles.         (line  79)
 * \rmfamily:                             Font styles.         (line  30)
@@ -14175,7 +14406,7 @@
 * \scalebox:                             \scalebox.           (line   6)
 * \scriptsize:                           Font sizes.          (line  11)
 * \scshape:                              Font styles.         (line  51)
-* \searrow:                              Math symbols.        (line 624)
+* \searrow:                              Math symbols.        (line 632)
 * \sec:                                  Math functions.      (line  93)
 * \section:                              Sectioning.          (line  11)
 * \seename:                              Indexes.             (line  20)
@@ -14183,62 +14414,62 @@
                                                               (line 131)
 * \setcounter:                           \setcounter.         (line   6)
 * \setlength:                            \setlength.          (line   6)
-* \setminus:                             Math symbols.        (line 627)
+* \setminus:                             Math symbols.        (line 635)
 * \settodepth:                           \settodepth.         (line   6)
 * \settoheight:                          \settoheight.        (line   6)
 * \settowidth:                           \settowidth.         (line   6)
 * \sf:                                   Font styles.         (line  85)
 * \sffamily:                             Font styles.         (line  48)
-* \sharp:                                Math symbols.        (line 633)
+* \sharp:                                Math symbols.        (line 641)
 * \shortstack:                           \shortstack.         (line   6)
-* \Sigma:                                Math symbols.        (line 636)
-* \sigma:                                Math symbols.        (line 639)
+* \Sigma:                                Math symbols.        (line 644)
+* \sigma:                                Math symbols.        (line 647)
 * \signature:                            \signature.          (line  11)
-* \sim:                                  Math symbols.        (line 643)
-* \simeq:                                Math symbols.        (line 646)
+* \sim:                                  Math symbols.        (line 651)
+* \simeq:                                Math symbols.        (line 654)
 * \sin:                                  Math functions.      (line  96)
 * \sinh:                                 Math functions.      (line  99)
 * \sl:                                   Font styles.         (line  88)
 * \sloppy:                               \fussy & \sloppy.    (line   6)
 * \slshape:                              Font styles.         (line  45)
 * \small:                                Font sizes.          (line  11)
-* \smallint:                             Math symbols.        (line 649)
+* \smallint:                             Math symbols.        (line 657)
 * \smallskip:                            \bigskip \medskip \smallskip.
                                                               (line  19)
 * \smallskipamount:                      \bigskip \medskip \smallskip.
                                                               (line  20)
-* \smile:                                Math symbols.        (line 653)
+* \smile:                                Math symbols.        (line 661)
 * \spacefactor:                          \spacefactor.        (line  10)
-* \spadesuit:                            Math symbols.        (line 656)
-* \sqcap:                                Math symbols.        (line 659)
-* \sqcup:                                Math symbols.        (line 663)
-* \sqrt[ROOT]{ARG}:                      Math miscellany.     (line  66)
-* \sqsubset:                             Math symbols.        (line 667)
-* \sqsubseteq:                           Math symbols.        (line 672)
-* \sqsupset:                             Math symbols.        (line 677)
-* \sqsupseteq:                           Math symbols.        (line 682)
+* \spadesuit:                            Math symbols.        (line 664)
+* \sqcap:                                Math symbols.        (line 667)
+* \sqcup:                                Math symbols.        (line 671)
+* \sqrt:                                 \sqrt.               (line   6)
+* \sqsubset:                             Math symbols.        (line 675)
+* \sqsubseteq:                           Math symbols.        (line 680)
+* \sqsupset:                             Math symbols.        (line 685)
+* \sqsupseteq:                           Math symbols.        (line 690)
 * \ss (ss):                              Additional Latin letters.
                                                               (line  52)
 * \SS (SS):                              Additional Latin letters.
                                                               (line  52)
-* \stackrel{TEXT}{RELATION}:             Math miscellany.     (line  71)
-* \star:                                 Math symbols.        (line 686)
+* \stackrel:                             \stackrel.           (line   6)
+* \star:                                 Math symbols.        (line 694)
 * \stepcounter:                          \stepcounter.        (line   6)
 * \stop:                                 Command line.        (line  18)
 * \subparagraph:                         Sectioning.          (line  15)
 * \subsection:                           Sectioning.          (line  12)
-* \subset:                               Math symbols.        (line 693)
-* \subseteq:                             Math symbols.        (line 696)
+* \subset:                               Math symbols.        (line 701)
+* \subseteq:                             Math symbols.        (line 704)
 * \subsubsection:                        Sectioning.          (line  13)
-* \succ:                                 Math symbols.        (line 699)
-* \succeq:                               Math symbols.        (line 703)
-* \sum:                                  Math symbols.        (line 708)
+* \succ:                                 Math symbols.        (line 707)
+* \succeq:                               Math symbols.        (line 711)
+* \sum:                                  Math symbols.        (line 716)
 * \sup:                                  Math functions.      (line 102)
 * \suppressfloats:                       Floats.              (line  87)
-* \supset:                               Math symbols.        (line 712)
-* \supseteq:                             Math symbols.        (line 715)
-* \surd:                                 Math symbols.        (line 718)
-* \swarrow:                              Math symbols.        (line 723)
+* \supset:                               Math symbols.        (line 720)
+* \supseteq:                             Math symbols.        (line 723)
+* \surd:                                 Math symbols.        (line 726)
+* \swarrow:                              Math symbols.        (line 731)
 * \symbol:                               Symbols by font position.
                                                               (line   6)
 * \t (tie-after accent):                 Accents.             (line  81)
@@ -14248,7 +14479,7 @@
 * \tableofcontents:                      Tables of contents.  (line   6)
 * \tan:                                  Math functions.      (line 105)
 * \tanh:                                 Math functions.      (line 108)
-* \tau:                                  Math symbols.        (line 726)
+* \tau:                                  Math symbols.        (line 734)
 * \telephone:                            \telephone.          (line   6)
 * \TeX:                                  Text symbols.        (line  60)
 * \textascendercompwordmark:             Text symbols.        (line  98)
@@ -14325,7 +14556,7 @@
 * \TH (TH):                              Additional Latin letters.
                                                               (line  56)
 * \thanks{TEXT}:                         \maketitle.          (line  56)
-* \theta:                                Math symbols.        (line 729)
+* \theta:                                Math symbols.        (line 737)
 * \thicklines:                           \thicklines.         (line   6)
 * \thickspace:                           Spacing in math mode.
                                                               (line  22)
@@ -14334,13 +14565,13 @@
                                                               (line  31)
 * \thinspace <1>:                        \thinspace.          (line   6)
 * \thispagestyle:                        \thispagestyle.      (line   6)
-* \tilde:                                Math accents.        (line  43)
-* \times:                                Math symbols.        (line 733)
+* \tilde:                                Math accents.        (line  37)
+* \times:                                Math symbols.        (line 741)
 * \tiny:                                 Font sizes.          (line  11)
 * \title{TEXT}:                          \maketitle.          (line  63)
-* \to:                                   Math symbols.        (line 737)
+* \to:                                   Math symbols.        (line 745)
 * \today:                                \today.              (line   6)
-* \top:                                  Math symbols.        (line 741)
+* \top:                                  Math symbols.        (line 749)
 * \topfraction:                          Floats.              (line 107)
 * \topfraction <1>:                      Floats.              (line 108)
 * \topmargin:                            Page layout parameters.
@@ -14351,9 +14582,9 @@
 * \topskip <1>:                          Page layout parameters.
                                                               (line 131)
 * \totalheight:                          Predefined lengths.  (line  12)
-* \triangle:                             Math symbols.        (line 746)
-* \triangleleft:                         Math symbols.        (line 749)
-* \triangleright:                        Math symbols.        (line 755)
+* \triangle:                             Math symbols.        (line 754)
+* \triangleleft:                         Math symbols.        (line 757)
+* \triangleright:                        Math symbols.        (line 763)
 * \tt:                                   Font styles.         (line  91)
 * \ttfamily:                             Font styles.         (line  54)
 * \twocolumn:                            \twocolumn.          (line   6)
@@ -14365,20 +14596,22 @@
 * \unboldmath <1>:                       \boldmath & \unboldmath.
                                                               (line  14)
 * \underbar:                             Accents.             (line  89)
-* \underbrace{MATH}:                     Math miscellany.     (line  75)
-* \underline{TEXT}:                      Math miscellany.     (line  79)
+* \underbrace{MATH}:                     Over- and Underlining.
+                                                              (line  24)
+* \underline{TEXT}:                      Over- and Underlining.
+                                                              (line   9)
 * \unitlength:                           picture.             (line  25)
-* \unlhd:                                Math symbols.        (line 761)
-* \unrhd:                                Math symbols.        (line 768)
-* \Uparrow:                              Math symbols.        (line 775)
-* \uparrow:                              Math symbols.        (line 779)
-* \Updownarrow:                          Math symbols.        (line 783)
-* \updownarrow:                          Math symbols.        (line 788)
-* \upharpoonright:                       Math symbols.        (line 793)
-* \uplus:                                Math symbols.        (line 798)
+* \unlhd:                                Math symbols.        (line 769)
+* \unrhd:                                Math symbols.        (line 776)
+* \Uparrow:                              Math symbols.        (line 783)
+* \uparrow:                              Math symbols.        (line 787)
+* \Updownarrow:                          Math symbols.        (line 791)
+* \updownarrow:                          Math symbols.        (line 796)
+* \upharpoonright:                       Math symbols.        (line 801)
+* \uplus:                                Math symbols.        (line 806)
 * \upshape:                              Font styles.         (line  42)
-* \Upsilon:                              Math symbols.        (line 805)
-* \upsilon:                              Math symbols.        (line 808)
+* \Upsilon:                              Math symbols.        (line 813)
+* \upsilon:                              Math symbols.        (line 816)
 * \usebox:                               \usebox.             (line   6)
 * \usecounter:                           \usecounter.         (line   6)
 * \usefont:                              Low-level font commands.
@@ -14386,34 +14619,34 @@
 * \usepackage:                           Additional packages. (line   6)
 * \v (breve accent):                     Accents.             (line  97)
 * \value:                                \value.              (line   6)
-* \vanothing:                            Math symbols.        (line 816)
-* \varepsilon:                           Math symbols.        (line 811)
-* \varphi:                               Math symbols.        (line 821)
-* \varpi:                                Math symbols.        (line 825)
-* \varrho:                               Math symbols.        (line 829)
-* \varsigma:                             Math symbols.        (line 833)
-* \vartheta:                             Math symbols.        (line 837)
-* \vdash:                                Math symbols.        (line 841)
-* \vdots:                                Math miscellany.     (line  86)
-* \vec:                                  Math accents.        (line  46)
+* \vanothing:                            Math symbols.        (line 824)
+* \varepsilon:                           Math symbols.        (line 819)
+* \varphi:                               Math symbols.        (line 829)
+* \varpi:                                Math symbols.        (line 833)
+* \varrho:                               Math symbols.        (line 837)
+* \varsigma:                             Math symbols.        (line 841)
+* \vartheta:                             Math symbols.        (line 845)
+* \vdash:                                Math symbols.        (line 849)
+* \vdots:                                Ellipses.            (line  33)
+* \vec:                                  Math accents.        (line  40)
 * \vector:                               \vector.             (line   6)
-* \vee:                                  Math symbols.        (line 845)
+* \vee:                                  Math symbols.        (line 853)
 * \verb:                                 \verb.               (line   6)
-* \Vert:                                 Math symbols.        (line 850)
-* \vert:                                 Math symbols.        (line 866)
+* \Vert:                                 Math symbols.        (line 858)
+* \vert:                                 Math symbols.        (line 874)
 * \vfill:                                \vfill.              (line   6)
 * \vline:                                \vline.              (line   6)
 * \vspace:                               \vspace.             (line   6)
-* \wedge:                                Math symbols.        (line 884)
-* \widehat:                              Math accents.        (line  49)
-* \widetilde:                            Math accents.        (line  52)
+* \wedge:                                Math symbols.        (line 892)
+* \widehat:                              Math accents.        (line  43)
+* \widetilde:                            Math accents.        (line  46)
 * \width:                                Predefined lengths.  (line   6)
-* \wp:                                   Math symbols.        (line 888)
-* \wr:                                   Math symbols.        (line 891)
-* \Xi:                                   Math symbols.        (line 894)
-* \xi:                                   Math symbols.        (line 897)
+* \wp:                                   Math symbols.        (line 896)
+* \wr:                                   Math symbols.        (line 899)
+* \Xi:                                   Math symbols.        (line 902)
+* \xi:                                   Math symbols.        (line 905)
 * \year:                                 \day \month \year.   (line   6)
-* \zeta:                                 Math symbols.        (line 900)
+* \zeta:                                 Math symbols.        (line 908)
 * \\ (for center):                       center.              (line  22)
 * \\ (for eqnarray):                     eqnarray.            (line  29)
 * \\ (for flushright):                   flushright.          (line  12)
@@ -14651,222 +14884,230 @@
 Node: Environments94665
 Node: abstract96668
 Node: array98257
-Node: center100655
-Node: \centering102386
-Node: description103833
-Node: displaymath106020
-Node: document107798
-Node: \AtBeginDocument108228
-Node: \AtEndDocument108852
-Node: enumerate109496
-Node: eqnarray112293
-Node: equation114291
-Node: figure114919
-Node: filecontents116993
-Node: flushleft118746
-Node: \raggedright119675
-Node: flushright120876
-Node: \raggedleft121539
-Node: itemize122332
-Node: letter125799
-Node: list126037
-Node: \item138855
-Node: trivlist140108
-Node: math141636
-Node: minipage141942
-Node: picture146803
-Node: \put153230
-Node: \multiput153708
-Node: \qbezier154428
-Node: \graphpaper155356
-Node: \line156153
-Node: \linethickness157932
-Node: \thinlines158381
-Node: \thicklines158792
-Node: \circle159176
-Node: \oval159716
-Node: \shortstack160695
-Node: \vector162089
-Node: \makebox (picture)162932
-Node: \framebox (picture)163853
-Node: \frame164650
-Node: \dashbox165051
-Node: quotation & quote165777
-Node: tabbing166676
-Node: table172681
-Node: tabular174706
-Node: \multicolumn181956
-Node: \vline185841
-Node: \cline187186
-Node: \hline187870
-Node: thebibliography188552
-Node: \bibitem190965
-Node: \cite193247
-Node: \nocite194904
-Node: Using BibTeX195393
-Node: theorem197340
-Node: titlepage198262
-Node: verbatim199545
-Node: \verb201055
-Node: verse202524
-Node: Line breaking203252
-Node: \\204618
-Node: \obeycr & \restorecr207064
-Node: \newline207864
-Node: \- (hyphenation)208802
-Node: \discretionary210443
-Node: \fussy & \sloppy211331
-Node: sloppypar212113
-Node: \hyphenation213252
-Node: \linebreak & \nolinebreak213838
-Node: Page breaking214906
-Node: \clearpage & \cleardoublepage216935
-Node: \newpage218417
-Node: \enlargethispage219710
-Node: \pagebreak & \nopagebreak220666
-Node: Footnotes222253
-Node: \footnote223399
-Node: \footnotemark226347
-Node: \footnotetext228692
-Node: Footnotes in section headings229293
-Node: Footnotes in a table230120
-Node: Footnotes of footnotes232998
-Node: Definitions233702
-Node: \newcommand & \renewcommand234579
-Node: \providecommand239790
-Node: \newcounter240939
-Node: \newlength242684
-Node: \newsavebox243544
-Node: \newenvironment & \renewenvironment244488
-Node: \newtheorem249599
-Node: \newfont253127
-Node: \protect254423
-Node: \ignorespaces & \ignorespacesafterend256809
-Node: Counters259558
-Node: \alph \Alph \arabic \roman \Roman \fnsymbol261231
-Node: \usecounter264060
-Node: \value264923
-Node: \setcounter265852
-Node: \addtocounter266454
-Node: \refstepcounter266919
-Node: \stepcounter267577
-Node: \day \month \year267919
-Node: Lengths268464
-Node: Units of length270254
-Node: \setlength271748
-Node: \addtolength272525
-Node: \settodepth273499
-Node: \settoheight274254
-Node: \settowidth275013
-Node: Predefined lengths275796
-Node: Making paragraphs276311
-Node: \par277966
-Node: \indent & \noindent279648
-Node: \parindent & \parskip281204
-Node: Marginal notes282243
-Node: Math formulas284042
-Node: Subscripts & superscripts287963
-Node: Math symbols290076
-Node: Blackboard bold315845
-Node: Calligraphic316621
-Node: \boldmath & \unboldmath317194
-Node: Math functions318713
-Node: Math accents320321
-Node: Spacing in math mode321141
-Node: Math miscellany322688
-Node: Modes325387
-Node: \ensuremath328001
-Node: Page styles328718
-Node: \maketitle329481
-Node: \pagenumbering332492
-Node: \pagestyle334430
-Node: \thispagestyle337968
-Node: Spaces338355
-Node: \hspace339225
-Node: \hfill340180
-Node: \spacefactor340572
-Node: \(SPACE) and \@343284
-Ref: \AT343427
-Node: \frenchspacing344904
-Node: \normalsfcodes345520
-Node: \(SPACE) after control sequence345709
-Node: \thinspace346620
-Node: \/347012
-Node: \hrulefill \dotfill348194
-Node: \addvspace349187
-Node: \bigskip \medskip \smallskip350233
-Node: \vfill351125
-Node: \vspace351994
-Node: Boxes352987
-Node: \mbox353699
-Node: \fbox and \framebox353986
-Node: lrbox354790
-Node: \makebox355148
-Node: \parbox355868
-Node: \raisebox357979
-Node: \savebox358592
-Node: \sbox359007
-Node: \usebox359456
-Node: Color359717
-Node: Color package options360561
-Node: Color models362207
-Node: Commands for color364516
-Node: Define colors364931
-Node: Colored text365646
-Node: Colored boxes368021
-Node: Colored pages369460
-Node: Graphics370153
-Node: Graphics package options372280
-Node: Graphics package configuration375036
-Node: \graphicspath375838
-Node: \DeclareGraphicsExtensions378761
-Node: \DeclareGraphicsRule380558
-Node: Commands for graphics383747
-Node: \includegraphics384252
-Node: \rotatebox397221
-Node: \scalebox400016
-Node: \resizebox401068
-Node: Special insertions402260
-Node: Reserved characters403064
-Node: Upper and lower case404265
-Node: Symbols by font position406180
-Node: Text symbols406800
-Node: Accents410248
-Node: Additional Latin letters412790
-Ref: Non-English characters412961
-Node: \rule413978
-Node: \today414407
-Node: Splitting the input415161
-Node: \endinput416641
-Node: \include & \includeonly417908
-Node: \input421944
-Node: Front/back matter422652
-Node: Tables of contents422857
-Node: \addcontentsline423918
-Node: \addtocontents424936
-Node: Glossaries425469
-Node: Indexes425988
-Node: Letters427621
-Node: \address431287
-Node: \cc432098
-Node: \closing432516
-Node: \encl432793
-Node: \location433208
-Node: \makelabels433472
-Node: \name435624
-Node: \opening435865
-Node: \ps436146
-Node: \signature436435
-Node: \telephone437652
-Node: Terminal input/output438017
-Node: \typein438282
-Node: \typeout438867
-Node: Command line439490
-Node: Document templates440442
-Node: beamer template440849
-Node: book template441500
-Node: tugboat template441868
-Node: Concept Index444232
-Node: Command Index512529
+Node: center100652
+Node: \centering102380
+Node: description103824
+Node: displaymath106011
+Node: document107789
+Node: \AtBeginDocument108219
+Node: \AtEndDocument108843
+Node: enumerate109487
+Node: eqnarray112284
+Node: equation114279
+Node: figure114907
+Node: filecontents116978
+Node: flushleft118728
+Node: \raggedright119657
+Node: flushright120855
+Node: \raggedleft121518
+Node: itemize122308
+Node: letter125775
+Node: list126013
+Node: \item138831
+Node: trivlist140082
+Node: math141610
+Node: minipage141916
+Node: picture146773
+Node: \put153197
+Node: \multiput153675
+Node: \qbezier154395
+Node: \graphpaper155323
+Node: \line156120
+Node: \linethickness157899
+Node: \thinlines158348
+Node: \thicklines158759
+Node: \circle159143
+Node: \oval159683
+Node: \shortstack160662
+Node: \vector162056
+Node: \makebox (picture)162899
+Node: \framebox (picture)163820
+Node: \frame164617
+Node: \dashbox165018
+Node: quotation & quote165744
+Node: tabbing166640
+Node: table172645
+Node: tabular174666
+Node: \multicolumn181916
+Node: \vline185801
+Node: \cline187146
+Node: \hline187830
+Node: thebibliography188512
+Node: \bibitem190925
+Node: \cite193203
+Node: \nocite194856
+Node: Using BibTeX195345
+Node: theorem197292
+Node: titlepage198214
+Node: verbatim199497
+Node: \verb201007
+Node: verse202476
+Node: Line breaking203706
+Node: \\205072
+Node: \obeycr & \restorecr207521
+Node: \newline208321
+Node: \- (hyphenation)209259
+Node: \discretionary210900
+Node: \fussy & \sloppy211788
+Node: sloppypar212570
+Node: \hyphenation213709
+Node: \linebreak & \nolinebreak214295
+Node: Page breaking215366
+Node: \clearpage & \cleardoublepage217395
+Node: \newpage218873
+Node: \enlargethispage220166
+Node: \pagebreak & \nopagebreak221122
+Node: Footnotes222705
+Node: \footnote223851
+Node: \footnotemark226799
+Node: \footnotetext229144
+Node: Footnotes in section headings229745
+Node: Footnotes in a table230572
+Node: Footnotes of footnotes233450
+Node: Definitions234154
+Node: \newcommand & \renewcommand235031
+Node: \providecommand240245
+Node: \newcounter241394
+Node: \newlength243139
+Node: \newsavebox243999
+Node: \newenvironment & \renewenvironment244943
+Node: \newtheorem250057
+Node: \newfont253585
+Node: \protect254881
+Node: \ignorespaces & \ignorespacesafterend257267
+Node: Counters260013
+Node: \alph \Alph \arabic \roman \Roman \fnsymbol261686
+Node: \usecounter264515
+Node: \value265378
+Node: \setcounter266307
+Node: \addtocounter266909
+Node: \refstepcounter267374
+Node: \stepcounter268032
+Node: \day \month \year268374
+Node: Lengths268919
+Node: Units of length270709
+Node: \setlength272203
+Node: \addtolength272980
+Node: \settodepth273954
+Node: \settoheight274709
+Node: \settowidth275468
+Node: Predefined lengths276251
+Node: Making paragraphs276766
+Node: \par278421
+Node: \indent & \noindent280103
+Node: \parindent & \parskip281655
+Node: Marginal notes282694
+Node: Math formulas284493
+Node: Subscripts & superscripts288480
+Node: Math symbols290589
+Node: Blackboard bold316988
+Node: Calligraphic317764
+Node: \boldmath & \unboldmath318337
+Node: Ellipses319870
+Node: Math functions322017
+Node: Math accents323625
+Node: Over- and Underlining324524
+Node: Spacing in math mode326256
+Node: Math miscellany327812
+Node: Colon character & \colon328371
+Node: \*329064
+Node: \frac329648
+Node: \left & \right330061
+Node: \sqrt331238
+Node: \stackrel331833
+Node: Modes332106
+Node: \ensuremath334720
+Node: Page styles335437
+Node: \maketitle336200
+Node: \pagenumbering339211
+Node: \pagestyle341149
+Node: \thispagestyle344654
+Node: Spaces345041
+Node: \hspace345911
+Node: \hfill346866
+Node: \spacefactor347258
+Node: \(SPACE) and \@349970
+Ref: \AT350113
+Node: \frenchspacing351590
+Node: \normalsfcodes352206
+Node: \(SPACE) after control sequence352395
+Node: \thinspace353306
+Node: \/353698
+Node: \hrulefill \dotfill354880
+Node: \addvspace355873
+Node: \bigskip \medskip \smallskip356919
+Node: \vfill357811
+Node: \vspace358680
+Node: Boxes359673
+Node: \mbox360385
+Node: \fbox and \framebox360672
+Node: lrbox361476
+Node: \makebox361834
+Node: \parbox362554
+Node: \raisebox364661
+Node: \savebox365270
+Node: \sbox365685
+Node: \usebox366134
+Node: Color366395
+Node: Color package options367239
+Node: Color models368885
+Node: Commands for color371194
+Node: Define colors371609
+Node: Colored text372324
+Node: Colored boxes374696
+Node: Colored pages376132
+Node: Graphics376825
+Node: Graphics package options378952
+Node: Graphics package configuration381705
+Node: \graphicspath382507
+Node: \DeclareGraphicsExtensions385430
+Node: \DeclareGraphicsRule387227
+Node: Commands for graphics390416
+Node: \includegraphics390921
+Node: \rotatebox403890
+Node: \scalebox406685
+Node: \resizebox407737
+Node: Special insertions408929
+Node: Reserved characters409733
+Node: Upper and lower case410934
+Node: Symbols by font position412849
+Node: Text symbols413469
+Node: Accents416917
+Node: Additional Latin letters419459
+Ref: Non-English characters419630
+Node: \rule420647
+Node: \today421076
+Node: Splitting the input421830
+Node: \endinput423310
+Node: \include & \includeonly424577
+Node: \input428613
+Node: Front/back matter429321
+Node: Tables of contents429526
+Node: \addcontentsline430587
+Node: \addtocontents431605
+Node: Glossaries432138
+Node: Indexes432657
+Node: Letters434290
+Node: \address437956
+Node: \cc438767
+Node: \closing439185
+Node: \encl439462
+Node: \location439877
+Node: \makelabels440141
+Node: \name442293
+Node: \opening442534
+Node: \ps442815
+Node: \signature443104
+Node: \telephone444321
+Node: Terminal input/output444686
+Node: \typein444951
+Node: \typeout445536
+Node: Command line446159
+Node: Document templates447111
+Node: beamer template447518
+Node: book template448169
+Node: tugboat template448537
+Node: Concept Index450901
+Node: Command Index521741
 
 End Tag Table

Modified: trunk/latex2e.pdf
===================================================================
(Binary files differ)

Modified: trunk/latex2e.texi
===================================================================
--- trunk/latex2e.texi	2018-06-08 16:55:33 UTC (rev 644)
+++ trunk/latex2e.texi	2018-06-09 23:37:33 UTC (rev 645)
@@ -3143,7 +3143,7 @@
 \end@{array@}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{array@}[@var{pos}]@{@var{cols}@}
@@ -3225,7 +3225,7 @@
 \end@{center@}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{center@}
@@ -3292,7 +3292,7 @@
 @{\centering ... @}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{group@}
@@ -3632,7 +3632,7 @@
 \end@{eqnarray@}
 @end example
 
-or 
+ at noindent or 
 
 @example
 \begin@{eqnarray*@} 
@@ -3721,7 +3721,7 @@
 \end@{figure@}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{figure*@}[@var{placement}]
@@ -3789,7 +3789,7 @@
 \end@{filecontents@}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{filecontents*@}@{@var{filename}@}
@@ -3894,7 +3894,7 @@
 @{\raggedright  ... @}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{@var{environment}@} \raggedright
@@ -3970,7 +3970,7 @@
 @{\raggedleft  ... @}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{@var{environment}@} \raggedleft
@@ -4431,7 +4431,8 @@
 \item text of item
 @end example
 
-or
+ at noindent or
+
 @example
 \item[@var{optional-label}] text of item
 @end example
@@ -4547,7 +4548,7 @@
 \end@{minipage@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \begin@{minipage@}[@var{position}][@var{height}][@var{inner-pos}]@{@var{width}@}
@@ -4715,7 +4716,7 @@
 \end@{picture@}
 @end example
 
-or
+ at noindent or
 
 @example
 \begin@{picture@}(@var{width}, at var{height})(@var{xoffset}, at var{yoffset})
@@ -5388,7 +5389,7 @@
 \end@{quotation@}
 @end example
 
-or 
+ at noindent or 
 
 @example
 \begin@{quote@}
@@ -5609,7 +5610,7 @@
 \end@{table@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \begin@{table@}[@var{placement}]
@@ -5687,8 +5688,7 @@
 \end@{tabular@}
 @end example
 
- at noindent
-or
+ at noindent or
 
 @example
 \begin@{tabular*@}@{@var{width}@}[@var{pos}]@{@var{cols}@}
@@ -6145,7 +6145,7 @@
 \bibitem@{@var{cite_key}@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \bibitem[@var{label}]@{@var{cite_key}@}
@@ -6216,7 +6216,7 @@
 \cite@{@var{keys}@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \cite[@var{subcite}]@{@var{keys}@}
@@ -6576,10 +6576,17 @@
 blank lines to separate the stanzas.
 
 @example
-A poem is a piece of poetry.
-
-And don't let the head of the poetry society \\
-tell you diff'rent.
+\begin@{verse@}
+\makebox[\linewidth][c]@{\textit@{Shut Not Your Doors@} ---Walt Whitman@}
+  \\[1\baselineskip]
+Shut not your doors to me proud libraries,                  \\
+For that which was lacking on all your well-fill'd shelves, \\
+\qquad yet needed most, I bring,                             \\
+Forth from the war emerging, a book I have made,            \\
+The words of my book nothing, the drift of it every thing,  \\
+A book separate, not link'd with the rest nor felt by the intellect, \\
+But you ye untold latencies will thrill to every page.
+\end@{verse@}
 @end example
 
 The output has margins indented on the left and the right, paragraphs
@@ -6632,7 +6639,7 @@
 \\[@var{morespace}]
 @end example
 
-or one of: 
+ at noindent or one of these. 
 
 @example
 \\*
@@ -6948,7 +6955,7 @@
 \linebreak[@var{zero-to-four}]
 @end example
 
-or one of:
+ at noindent or one of these.
 
 @example
 \nolinebreak
@@ -7035,7 +7042,7 @@
 \clearpage
 @end example
 
-or:
+ at noindent or
 
 @example
 \cleardoublepage
@@ -7167,7 +7174,7 @@
 \pagebreak[@var{zero-to-four}]
 @end example
 
-or:
+ at noindent or
 
 @example
 \nopagebreak
@@ -7583,7 +7590,7 @@
 \newcommand*@{\@var{cmd}@}[@var{nargs}][@var{optargdefault}]@{@var{defn}@}
 @end example
 
-or one of:
+ at noindent or one of these.
 
 @example
 \renewcommand@{\@var{cmd}@}[@var{nargs}]@{@var{defn}@}
@@ -7898,7 +7905,7 @@
 \newenvironment*@{@var{env}@}[@var{nargs}][@var{optargdefault}]@{@var{begdef}@}@{@var{enddef}@}
 @end example
 
-or one of:
+ at noindent or one of these.
 
 @example
 \renewenvironment@{@var{env}@}@{@var{begdef}@}@{@var{enddef}@}
@@ -8288,7 +8295,7 @@
 \ignorespaces
 @end example
 
-or
+ at noindent or
 
 @example
 \ignorespacesafterend
@@ -9086,7 +9093,7 @@
 \indent
 @end example
 
-or:
+ at noindent or
 
 @example
 \noindent
@@ -9314,13 +9321,15 @@
 The two mathematics modes are similar, but there are some differences.
 One involves the placement of subscripts and superscripts; in display
 math mode they are further apart and in inline math mode they are closer
-together.  Sometimes you want the display math treatment to happen in
-the inline math mode.  For this, the @code{\displaystyle} declaration
-forces the size and style of the formula to be that of
- at code{displaymath}.  Thus @code{\(\displaystyle \sum_@{n=0@}^\infty
-x_n\)} will have the limits above and below the summation sign, not next
-to it.  Another example is that
+together.
 
+Sometimes you want the display math treatment to happen in the inline
+math mode.  For this, the @code{\displaystyle} declaration forces the
+size and style of the formula to be that of @code{displaymath}.  Thus
+ at code{\(\displaystyle \sum_@{n=0@}^\infty x_n\)} will have the limits
+above and below the summation sign, not next to it.  Another example is
+that
+
 @example
 \begin@{tabular@}@{r|cc@}
   \textsc@{Name@}  &\textsc@{Series@}  &\textsc@{Sum@}  \\  \hline
@@ -9341,6 +9350,7 @@
 * Math symbols::                Various mathematical squiggles.
 * Math functions::              Math function names like sin and exp.
 * Math accents::                Accents in math.
+* Over- and Underlining::       Things over or under formulas.
 * Spacing in math mode::        Thick, medium, thin, and negative spaces.
 * Math miscellany::             Stuff that doesn't fit anywhere else.
 @end menu
@@ -9361,7 +9371,7 @@
 @var{base}^@var{exp}
 @end example
 
-or:
+ at noindent or
 
 @example
 @var{base}_ at var{exp}
@@ -9702,6 +9712,11 @@
 @item \Im
 @BES{2111,\Im} Imaginary part (ordinary).  See: real part at tie{}@code{\Re}.
 
+ at item \imath
+ at cindex dotless i, math
+Dotless i; used when you are putting an accent on an i (@pxref{Math
+accents}).
+
 @item \in
 @BES{2208,\in} Set element (relation).  See also: lower case lunate
 epsilon at tie{}@code{\epsilon}@BES{03F5,\epsilon} and small letter script
@@ -9720,6 +9735,11 @@
 @BESU{2A1D,Join} Condensed bowtie symbol (relation).  Not available in Plain
 @TeX{}.
 
+ at item \jmath
+ at cindex dotless j, math
+Dotless j; used when you are putting an accent on a j (@pxref{Math
+accents}).
+
 @item \kappa
 @BES{03BA,\kappa} Lower case Greek letter (ordinary).
 
@@ -10315,10 +10335,32 @@
 
 @end ftable
 
+The following symbols are most often used in plain text but @LaTeX{}
+provides versions to use in mathematical text.
+
+ at ftable @code
+ at item \mathdollar
+Dollar sign in math mode: $.
+
+ at item \mathparagraph
+Paragraph sign (pilcrow) in math mode, @BES{00B6,\P}.
+
+ at item \mathsection
+Section sign in math mode @BES{00A7,\S}.
+
+ at item \mathsterling
+Sterling sign in math mode: @pounds{}.
+
+ at item \mathunderscore
+Underscore in math mode: _.
+
+ at end ftable
+
 @menu
 * Blackboard bold::            Doublestruck characters.
 * Calligraphic::               Cursive characters.
 * \boldmath & \unboldmath::    Symbols in boldface.
+* Ellipses::                   Dots.
 @end menu
 
 
@@ -10397,13 +10439,12 @@
 \boldmath \( @var{math} \)
 @end example
 
-or
+ at noindent or
 
 @example
 \unboldmath \( @var{math} \)
 @end example
 
-
 @findex \boldmath
 @findex \unboldmath
 @c xx Refer to package bm: https://tex.stackexchange.com/q/595/121234
@@ -10445,6 +10486,75 @@
 strongly suggests that it is an improvement over @code{\boldmath}.
 
 
+ at node Ellipses
+ at subsection Ellipses
+
+ at cindex ellipses
+ at cindex dots
+
+Ellipses are the three dots (usually three) indicating that a pattern
+continues.
+
+ at example
+\begin@{array@}@{cccc@}
+  a_@{0,0@}    &a_@{0,1@}   &a_@{0,2@} &\ldots \\
+  a_@{1,0@}    &\ddots                     \\
+  \vdots
+\end@{array@}
+ at end example
+
+ at LaTeX{} provides these.
+
+ at ftable @code
+ at item \cdots
+Horizontal ellipsis with the dots raised to the center of the line, as
+in @BES{22EF,\cdots}.  Used as: @code{\( a_0\cdot a_1\cdots a_@{n-1@}
+\)}.
+
+ at item \ddots
+Diagonal ellipsis, @BES{22F1,\ddots}.  See the above example for a
+usage.
+
+ at item \ldots
+Ellipsis on the baseline, @BES{2026,\ldots}.  Used as: @code{\(
+x_0,\ldots x_@{n-1@} \)}.  A synonym is @code{\mathellipsis}.  A synonym
+from the @file{amsmath} package is @code{\hdots}.
+
+You can also use this command outside of mathematical text, as in
+ at code{The gears, brakes, \ldots@{@} are all broken}.  (In a text mode a
+synonym for @code{\ldots} is @code{\dots}.)
+
+ at item \vdots
+Vertical ellipsis, @BES{22EE,\vdots}.  See the above example for a
+usage.
+
+ at end ftable
+
+ at PkgIndex{amsmath}
+The @file{amsmath} package has the command @code{\dots} to semantically
+mark up ellipses.  This example produces two different-looking outputs
+for the first two uses of the @code{\dots} command.
+
+ at example
+\usepackage@{amsmath@}  % in preamble
+  ...
+Suppose that \( p_0, p_1, \dots, p_@{n-1@} \) lists all of the primes.
+Observe that \( p_0\cdot p_1 \dots \cdot p_@{n-1@} +1 \) is not a multiple of any \( p_i \).
+Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).
+ at end example
+
+In the first line @LaTeX{} looks to the comma following @code{\dots} to
+determine that it should output an ellipsis on the baseline.  The second
+line has a @code{\cdot} following @code{\dots} so @LaTeX{} outputs an
+ellipsis that is on the math axis, vertically centered.  However, the
+third usage has no follow-on character so you have to tell @LaTeX{} what
+to do.  You can use one of the commands: @code{\dotsc} if you need the
+ellipsis appropriate for a comma following, @code{\dotsb} if you need
+the ellipses that fits when the dots are followed by a binary operator
+or relation symbol, @code{\dotsi} for dots with integrals, or
+ at code{\dotso} for others.
+
+
 @node Math functions
 @section Math functions
 
@@ -10748,14 +10858,6 @@
 @math{\hat{x}}
 @end iftex
 
- at item \imath
- at cindex dotless i, math
-Math dotless i
-
- at item \jmath
- at cindex dotless j, math
-Math dotless j
-
 @item \mathring
 @cindex ring accent, math
 Math ring accent  @c don't bother implementing in texinfo
@@ -10793,7 +10895,77 @@
 
 @end ftable
 
+When you are putting an accent on an i or a j, the tradition is to use
+one without a dot, @code{\imath} or @code{jmath} (@pxref{Math symbols}).
 
+
+ at node Over- and Underlining
+ at section Over- and Underlining
+
+ at cindex overlining
+ at cindex underlining
+
+ at LaTeX{} provides commands for making overlines or underlines, or
+putting braces over or under some material.
+
+ at ftable @code
+
+ at item \underline@{@var{text}@}
+Underline @var{text}.  Works inside math mode, and outside.
+ at ifset HAS-MATH
+The result of @code{\underline@{xyz@}} is @math{\underline{xyz}}.
+ at end ifset
+The line is always completely below the text, taking account of
+descenders, so in @code{\(\underline@{y@}\)} the line is lower than in
+ at code{\(\underline@{x@}\)}.  This command is fragile (@pxref{\protect}).
+
+ at PkgIndex{ulem}
+Note that the package @file{ulem} does text mode underlining and allows
+line breaking as well as a number of other features.  See the
+documentation is on CTAN.
+        
+ at item \overline@{@var{text}@}
+Put a horizontal line over @var{tex}.  Works inside math mode, and
+outside.  For example, @code{\overline@{x+y@}}.
+ at ifset HAS-MATH
+The result looks like: @math{\overline{x+y}}.
+ at end ifset
+Note that this differs from the command @code{\bar} (@pxref{Math
+accents}).
+
+ at item \underbrace@{@var{math}@}
+Put a brace under @var{math}. For example, this
+ at code{(1-\underbrace@{1/2)+(1/2@}-1/3)} emphasizes the telescoping part.
+ at ifset HAS-MATH
+The result looks like this: @math{(1-\underbrace{1/2)+(1/2}-1/3)}.
+ at end ifset
+Attach text to the brace by using subscript, @code{_}, or superscript,
+ at code{^}, as here.
+
+ at example
+\begin@{displaymath@}
+  1+1/2+\underbrace@{1/3+1/4@}_@{>1/2@}+
+       \underbrace@{1/5+1/6+1/7+1/8@}_@{>1/2@}+\cdots
+\end@{displaymath@}
+ at end example
+
+The superscript appears on top of the expression, and so can look
+unconnected to the underbrace.
+
+ at item \overbrace@{@var{math}@}
+Put a brace over @var{math}; see also @code{\underbrace}.  An example is
+ at code{\overbrace@{x+x+\cdots+x@}^@{\mbox@{\(k\) times@}@}}.
+ at c @ifset HAS-MATH
+ at c The result is @math{\overbrace{x+x+\cdots+x}^{\mbox{\(k\) times}}}.
+ at c @end ifset
+
+ at end ftable
+
+ at PkgIndex{mathtools}
+The package @file{mathtools} adds an over- and underbrace, as well as
+some improvements on the braces.  See the documentation on CTAN.
+
+
 @node Spacing in math mode
 @section Spacing in math mode
 
@@ -10863,143 +11035,192 @@
 
 @cindex math miscellany
 
- at ftable @code
- at item \*
- at cindex discretionary multiplication
+ at LaTeX{} contains a wide variety of mathematics facilities.  Here are
+some that don't fit into other categories.
+
+ at menu
+* Colon character & \colon::    Colon.
+* \*::                            Discretionary multiplication.
+* \frac::                         Fraction.
+* \left & \right::                Paired delimiters.
+* \sqrt::                         Radicals.
+* \stackrel::                     Text over a relation.
+ at end menu
+
+
+ at node Colon character & \colon  
+ at subsection Colon character @code{:} & @code{\colon}
+
+ at cindex :
+ at cindex colon character
+ at findex :
+ at findex \colon
+
+Synopsis, one of:
+
+ at example
+:
+\colon
+ at end example
+
+In mathematics, the colon character, @code{:}, is a relation.
+
+ at example
+With side ratios \( 3:4 \) and \( 4:5 \), the triangle is right.
+ at end example
+
+ at PkgIndex{amsmath}
+ at noindent Ordinary @LaTeX{} defines @code{\colon} to produce the
+colon character with the spacing appropriate for punctuation, as in
+set-builder notation @code{\@{x\colon 0\leq x<1\@}}.
+
+ at PkgIndex{amsmath}
+But the widely-used @file{amsmath} package defines @code{\colon} for use
+in the definition of functions @code{f\colon D\to C}.  So if you want
+the colon character as a punctuation then use @code{\mathpunct@{:@}}.
+
+
+ at node \* 
+ at subsection @code{\*}
+
+ at cindex multiplication, discretionary
+ at cindex muiltiplication, line breaks
 @cindex multiplication symbol, discretionary line break
-A @dfn{discretionary} multiplication symbol, at which a line break is
-allowed. Without the break multiplication is implicitly indicated by a
-space, while in the case of a break a @BES{00D7,\times} symbol is
-printed immediately before the break. So
+ at findex \*
 
+Synopsis:
+
 @example
-\documentclass@{article@}
-\begin@{document@}
-Now \(A_3 = 0\), hence the product of all terms \(A_1\) 
-through \(A_4\), that is \(A_1\* A_2\* A_3 \* A_4\), is 
-equal to zero.
-\end@{document@}
+\*
 @end example
 
-will make that sort of output at c
- at ifnottex
- at w{ }(the ellipsis @samp{[@dots{}]} is here to show the line break at
-the same place as in a @TeX{} output)@c
- at end ifnottex
-:
+A multiplication symbol that allows a line break.  If there is a break
+then @LaTeX{} puts a @code{\times} symbol, @BES{00D7,\times}, before
+that break.
 
- at indentedblock
-Now @math{A_3 = 0},
- at iftex
-hence the product of all terms
- at end iftex
- at ifnottex
-[@dots{}]
- at end ifnottex
- at math{A_1}
-through @math{A_4}, that is @math{A_1 A_2 \times}@*@math{A_3 A_4}, is
-equal to zero.
- at end indentedblock
+In @code{\( A_1\* A_2\* A_3\* A_4 \)}, if there is no line break then
+ at LaTeX{} outputs it as though it were @code{\( A_1 A_2 A_3 A_4 \)}.  If
+a line break does happen, for example between the two middle ones, then
+ at LaTeX{} sets it like @code{\( A_1 A_2 \times \)}, followed by the
+break, followed by @code{\( A_3 A_4 \)}.
 
- at item \cdots
-A horizontal ellipsis with the dots raised to the center of the line.
- at tex
-As in: `$\cdots$'.
- at end tex
 
- at item \ddots
-A diagonal ellipsis: @math{\ddots}.
+ at node \frac
+ at subsection @code{\frac} 
 
- at item \frac@{@var{num}@}@{@var{den}@}
+ at cindex fraction
 @findex \frac
-Produces the fraction @var{num} divided by @var{den}.
 
- at ifset HAS-MATH
-eg. @math{{1}\over{4}}
- at end ifset
+Synopsis:
 
- at item \left @var{delim1} ... \right @var{delim2}
+ at example
+\frac@{@var{numerator}@}@{@var{denominator}@}
+ at end example
+
+Produces the fraction @var{numerator} divided by @var{denominator}.
+Used as: @code{\begin@{displaymath@} \frac@{1@}@{\sqrt@{2\pi\sigma@}@}
+\end@{displaymath@}}.  In inline math mode it comes out small; see the
+discussion of @code{\displaystyle} (@pxref{Math formulas}).
+
+
+ at node \left & \right
+ at subsection @code{\left} & @code{\right}
+
+ at cindex delimiters, paired
+ at cindex paired delimiters
+ at cindex matching parentheses
+ at cindex matching brackets
+ at cindex null delimiter
+ at findex \left
 @findex \right
- at cindex null delimiter
-The two delimiters need not match; @samp{.} acts as a @dfn{null delimiter},
-producing no output.  The delimiters are sized according to the math
-in between.  Example: @code{\left( \sum_@{i=1@}^@{10@} a_i \right]}.
 
- at item \mathdollar
-Dollar sign in math mode: $.
+Synopsis:
 
- at item \mathellipsis
-Ellipsis (spaced for text) in math mode: @dots{}
+ at example
+\left @var{delimiter1} ... \right @var{delimiter2}
+ at end example
 
- at item \mathparagraph
-Paragraph sign (pilcrow) in math mode: @BES{00B6,\P}.
+Make matching parentheses, braces, or other delimiters.  The delimiters
+are sized according to the math they enclose.  This makes a unit vector
+surrounded by appropriate-height parentheses.
 
- at item \mathsection
-Section sign in math mode.
+ at example
+\begin@{equation@}
+  \left(\begin@{array@}@{c@}
+    1   \\
+    0   \\
+  \end@{array@}\right)
+ at end example
 
- at item \mathsterling
-Sterling sign in math mode: @pounds{}.
+Every @code{\left} must have a matching @code{\right}.  Leaving out the
+ at code{\left(} in the above gets @samp{Extra \right}.  Leaving off the
+ at code{\right)} gets @samp{You can't use `\eqno' in math mode}.
 
- at item \mathunderscore
-Underscore in math mode: _.
+However, the two delimiters @var{delimiter1} and @var{delimiter2} need
+not match.  A common case is that you want an unmatched brace, as
+below. Use a period, @samp{.}, as a null delimiter.
 
- at item \overbrace@{@var{math}@}
-Generates a brace over @var{math}.
-For example, @code{\overbrace@{x+\cdots+x@}^@{k \;\textrm@{times@}@}}.
- at ifset HAS-MATH
-The result looks like: @math{\overbrace{x+\cdots+x}^{k \rm\;times}}
- at end ifset
-        
- at item \overline@{@var{text}@}
-Generates a horizontal line over @var{tex}.
-For example, @code{\overline@{x+y@}}.
- at ifset HAS-MATH
-The result looks like: @math{\overline{x+y}}.
- at end ifset
+ at example
+\begin@{equation@}
+  f(n)=\left\@{\begin@{array@}@{ll@}
+                1             &\mbox@{--if \(n=0\)@} \\
+                f(n-1)+3n^2   &\mbox@{--else@}       
+       \end@{array@}\right.
+\end@{equation@}
+ at end example
 
- at item \sqrt[@var{root}]@{@var{arg}@}
-Produces the representation of the square root of @var{arg}.  The
-optional argument @var{root} determines what root to produce.  For
-example, the cube root of @code{x+y} would be typed as
- at code{\sqrt[3]@{x+y@}}.
- at ifset HAS-MATH
-The result looks like this: @math{\root 3 \of {x+y}}.
- at end ifset
+Note that to get a curly brace as a delimiter you must prefix it with a
+backslash, @code{\@{}.
 
- at item \stackrel@{@var{text}@}@{@var{relation}@}
-Puts @var{text} above @var{relation}.  For example,
- at code{\stackrel@{f@}@{\longrightarrow@}}.
- at ifset HAS-MATH
- The result looks like this: @math{\buildrel f \over \longrightarrow}.
- at end ifset
 
- at item \underbrace@{@var{math}@}
-Generates @var{math} with a brace underneath. For example, @code{\underbrace@{x+y+z@}_@{>\,0@}}
- at ifset HAS-MATH
-The result looks like this: @math{\underbrace{x+y+z}_{>\,0}}.
- at end ifset
+ at node \sqrt
+ at subsection @code{\sqrt}
 
- at PkgIndex{ulem}
- at item \underline@{@var{text}@}
-Causes @var{text}, which may be either math mode or not, to be
-underlined.  The line is always below the text, taking account of
-descenders.
+ at cindex square root
+ at cindex roots
+ at cindex radical
+ at findex \sqrt
+
+Synopsis, one of:
+
+ at example
+\sqrt@{@var{arg}@}
+\sqrt[@var{root-number}]@{@var{arg}@}
+ at end example
+
+The square root, or optionally other roots, of @var{arg}.  The optional
+argument @var{root-number} gives the root, i.e., enter the cube root of
+ at code{x+y} as @code{\sqrt[3]@{x+y@}}.
 @ifset HAS-MATH
-The result looks like this: @math{\underline{xyz}}
+It comes out like this: @math{\root 3 \of {x+y}}.
 @end ifset
-(The package @file{ulem} does underlining and allows line breaking as
-well as a number of other underline-related features.  The documentation
-is on CTAN.)
+The radical grows with the size of @var{arg} (as the height of the
+radical grows, the angle on the leftmost part gets steeper, until for
+a large enough @code{arg}, it is vertical).
 
- at item \vdots
-Vertical ellipsis.
+ at LaTeX{} has a separate @code{\surd} character (@pxref{Math symbols}).
+
+
+ at node \stackrel
+ at subsection @code{\stackrel}
+
+ at cindex stack math
+ at cindex relation, text above
+ at findex \stackrel
+
+Synopsis, one of:
+
+ at example
+\stackrel@{@var{text}@}@{@var{relation}@}
+ at end example
+
+Put @var{text} above @var{relation}.  To put a function name above an
+arrow enter @code{\stackrel@{f@}@{\longrightarrow@}}.
 @ifset HAS-MATH
-The result looks like this: @math{\vdots}.
+ The result looks like this: @math{\buildrel f \over \longrightarrow}.
 @end ifset
 
- at end ftable
 
-
 @node Modes
 @chapter Modes
 
@@ -11305,10 +11526,10 @@
 
 @PkgIndex{fancyhdr}
 A discussion with an example is below.  Note first that the package
- at file{fancyhdr} is the standard way to manipulate headers and footers
-because it makes it immensely easier.  New documents that need to do
-anything other than one of the standard options below should use this
-package.  See its documentation on CTAN.
+ at file{fancyhdr} is now the standard way to manipulate headers and
+footers.  New documents that need to do anything other than one of the
+standard options below should use this package.  See its documentation
+on CTAN.
 
 Values for @var{style}:
 
@@ -11970,7 +12191,7 @@
 \parbox@{@var{width}@}@{@var{contents}@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \parbox[@var{position}][@var{height}][@var{inner-pos}]@{@var{width}@}@{@var{contents}@}
@@ -12035,7 +12256,7 @@
 \raisebox@{@var{distance}@}@{@var{text}@}
 @end example
 
-or:
+ at noindent or
 
 @example
 \raisebox@{@var{distance}@}[@var{height}][@var{depth}]@{@var{text}@}
@@ -12287,7 +12508,7 @@
 \textcolor[@var{color model}]@{@var{color specification}@}@{...@}
 @end example
 
-or
+ at noindent or
 
 @example
 \color@{@var{name}@}
@@ -12378,7 +12599,7 @@
 \colorbox[@var{model name}]@{@var{box background color specification}@}@{...@}
 @end example
 
-or
+ at noindent or
 
 @example
 \fcolorbox@{@var{frame color}@}@{@var{box background color}@}@{...@}
@@ -12510,7 +12731,7 @@
 \usepackage[@var{comma-separated option list}]@{graphics@}
 @end example
 
-or
+ at noindent or
 
 @example
 \usepackage[@var{comma-separated option list}]@{graphicx@}



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