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+<!--
+ ****************************************************************************
+ * Copyright(c) 2002-2012, John Forkosh Associates, Inc. All rights reserved.
+ * http://www.forkosh.com mailto: john@forkosh.com
+ * ==========================================================================
+ * This file is part of mimeTeX, which is free software. You may redistribute
+ * and/or modify it under the terms of the GNU General Public License,
+ * version 3 or later, as published by the Free Software Foundation.
+ * MimeTeX is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY, not even the implied warranty of MERCHANTABILITY.
+ * See the GNU General Public License for specific details.
+ * By using mimeTeX, you warrant that you have read, understood and
+ * agreed to these terms and conditions, and that you possess the legal
+ * right and ability to enter into this agreement and to use mimeTeX
+ * in accordance with it.
+ * Your mimetex.zip distribution file should contain the file COPYING,
+ * an ascii text copy of the GNU General Public License, version 3.
+ * If not, point your browser to http://www.gnu.org/licenses/
+ * or write to the Free Software Foundation, Inc.,
+ * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
+ ****************************************************************************
+ -->
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+ <!-- "http://www.forkosh.com/loose.dtd" -->
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Preamble
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<html>
+ <head>
+ <title> mimeTeX user's manual </title>
+ <meta HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
+ <style type="text/css">
+ body { background-image: none; /* none; or url(); */
+ /*background-repeat: repeat-y;*/
+ /*background-attachment: fixed;*/ /* fixed; or scroll; */
+ background-color: #ffffff; color: #000000;
+ margin-left: 0.5em; margin-right: 0.1em;
+ font-size: large; /* or medium */
+ clear: both }
+ A:active { color: blue/*#0000FF*/; text-decoration: none }
+ A:link { color: blue/*#0000FF*/; text-decoration: none }
+ A:visited { color: blue/*#0000FF*/; text-decoration: none }
+ A:hover { color: red/*#FF0000*/; text-decoration: underline
+ /*font-style: italic; font-weight: bold;*/
+ /*font-size: normal; line-height: normal*/ }
+ h1 { color: maroon; text-decoration: underline;
+ font-style: normal; /* italic oblique */
+ font-size: xx-large;
+ padding-top: 2.0em;
+ letter-spacing: 0.25em }
+ h2 { color: maroon; text-decoration: underline;
+ font-style: normal; /* italic oblique */
+ font-size: x-large;
+ padding-top: 1.0em;
+ letter-spacing: 0.20em }
+ h3 { color: maroon; /*black; text-decoration: underline;*/
+ font-style: normal; /* italic oblique */
+ font-size: large;
+ margin-left: 1em;
+ padding-top: 0.5em;
+ letter-spacing: 0.15em }
+ center { padding-top: -0.1em; padding-bottom: -0.1em; }
+ table { font-size: large }
+ table.medium { font-size: medium }
+ dl { font-size: large;
+ margin-left: 3.0em; margin-right: 2.5em }
+ ol { margin-left: 3.0em; margin-right: 2.5em }
+ ul { margin-left: 3.0em; margin-right: 2.5em;
+ list-style-type: square }
+ ul ul { margin-left: -0.5em; margin-right: 3.5em;
+ list-style-type: disc }
+ pre { margin-left: 3.0em; font-size: medium; font-weight: bold }
+ pre.nobold { margin-left:3.0em; font-size:medium; font-weight:normal }
+ p { margin-left: 2.0em; margin-right: 1.5em }
+ p:first-letter
+ { font-size: x-large; font-weight: bold;
+ color: maroon }
+ p.continue { margin-left: 2.0em; margin-right: 1.5em;
+ padding-top: -0.1em }
+ p.continue:first-letter
+ { font-size: large; font-weight: normal;
+ color: black }
+ p.warning { color: red } /* defines p class=warning */
+ </style>
+ <style type="text/css">
+ a.info{
+ position:relative;
+ z-index:24;
+ /*background-color:#8692A5;*/
+ visibility: inherit;
+ text-decoration: none; }
+ a.info:hover{
+ z-index:25;
+ /*background-color:#999999;
+ color: #FFFF00;*/
+ text-decoration: none; }
+ a.info span{
+ display: none;
+ /*color: #FFFF00;*/ }
+ a.info:hover span{
+ display:block;
+ position:absolute;
+ top:2em;
+ left:2em;
+ /*width:15em;*/
+ border:1px solid #330066;
+ background-color:#FFFF99;
+ color:#660000;
+ text-align: left;
+ font-size: 13px;
+ font-weight: normal;
+ margin: 3px;
+ padding: 6px; }
+ a.info:link {
+ text-decoration: none;
+ /*color: #FFFF00;*/ /*themecolour1%0;*/ }
+ a.info:visited {
+ text-decoration: none;
+ /*color: #FFFF00;*/ /*themecolour1%0;*/ }
+ </style>
+ <script type="text/javascript">
+ <!--
+ // add/clear text to expression
+ function eqntext(eqn)
+ { var eqnSrc = document.getElementById(eqn).src;
+ var texSrc = eqnSrc.substring(eqnSrc.indexOf('?')+1,eqnSrc.length);
+ addtext(texSrc); }
+ function addtext(text)
+ { cleartext();
+ document.expression.formdata.value += unescape(text);
+ document.expression.formdata.focus(); }
+ function cleartext()
+ { document.expression.formdata.value = "";
+ //document.inlineframe.value = "";
+ document.expression.formdata.focus(); }
+ -->
+ </script>
+
+ <!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ + php functions to use Vertical-Align: info from mimetex
+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <?php
+ //$mimetexurl = "../cgi-bin/mimetex.cgi?";
+ $mimetexurl = "http://www.forkosh.com/mimetex.cgi?";
+ //$mimetexurl = "http://psi2star/cgi-bin/mimetex.cgi?";
+ function verticalalign( $expression ) {
+ global $mimetexurl;
+ // note: curl_init() stops at the first whitespace char in $url argument
+ $expression = ereg_replace(" ","~",$expression); // remove whitespace
+ $url = $mimetexurl . "\depth~" . $expression;
+ $valign = "0";
+ $options = array(
+ CURLOPT_RETURNTRANSFER => true, // return web page
+ CURLOPT_HEADER => true); // return headers
+ $ch = curl_init( $url );
+ //curl_setopt_array( $ch, $options );
+ curl_setopt( $ch, CURLOPT_RETURNTRANSFER, true );
+ curl_setopt( $ch, CURLOPT_HEADER, true );
+ $gif = curl_exec( $ch );
+ $errno = curl_errno( $ch );
+ $error = curl_error( $ch );
+ //$info = curl_getinfo( $ch );
+ curl_close( $ch );
+ //echo '<br> url= ',$url,'<br>',"\n";
+ //echo '<br> gif=<br>',$gif,'<br>',"\n";
+ if ( $errno == 0 ) {
+ $fields = explode("Vertical-Align:",$gif);
+ $vfield = trim($fields[1]);
+ $fldlen = strspn($vfield,"+-0123456789");
+ $valign = substr($vfield,0,$fldlen); }
+ else {
+ echo 'verticalalign> errno ',$errno,' = ',$error,'<br><br>',"\n"; }
+ return $valign;
+ }
+ function mimetextag( $label, $expression ) {
+ global $mimetexurl;
+ $valign = verticalalign($expression);
+ $url = $mimetexurl . $expression;
+ //echo ' valign=',$valign,' ',"\n";
+ echo '<a href="#preview" class="info"><img id="',$label,'" ';
+ echo ' onclick="eqntext(',"'",$label,"'",')" ';
+ echo ' src="',$url,'" ';
+ echo ' style="Vertical-Align:',$valign,'px" ';
+ echo ' alt="" border=0>';
+ echo '<span>',$expression,'</span>';
+ echo '</a>', "\n";
+ }
+ ?>
+
+ <!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ + javascript from mathtran.org to render <img alt="tex:math expression">
+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <!-- script type="text/javascript"
+ src="http://www.mathtran.org/js/mathtran_img.js"></script -->
+ </head>
+<body>
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Banner across top of page, containing title and two example mimeTeX images.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<br>
+<hr size=4>
+<center>
+ <table cellspacing=10>
+ <tr>
+ <td align="center">
+ <a href="#preview"><img id="imageBanr1" onclick="eqntext('imageBanr1')"
+ src="../cgi-bin/mimetex.cgi?\Large f=b_o+\frac{a_1}{b_1+\frac{a_2}
+ {b_2+\frac{a_3}{b_3+a_4}}}" alt="" border=0 align=middle></a> </td>
+ <td align="center" valign="middle">
+ <center> <font color="maroon" size=4>
+ <b><nobr>m i m e T e X &nbsp; m a n u a l</nobr></b> <br>
+ <font size=3>( for mimeTeX version
+ <a href="#preview"><img id="imageVer1" onclick="eqntext('imageVer1')"
+ src="../cgi-bin/mimetex.cgi?\small\versionnumber"
+ alt="" border=0 align=bottom></a> )</font> <br>
+ <font size=3> <b>Click for:</b>&nbsp;
+ <!-- <a href="http://www.forkosh.com" target="_top">homepage</a>, &nbsp;
+ <a href="http://www.forkosh.com/resume.html" target="_top">resume</a> -->
+ <a href="http://www.forkosh.com/mimetextutorial.html" target="_top">
+ LaTeX tutorial</a><br>
+ <a href="http://www.forkosh.com/mimetex.html" target="_top">
+ mimeTeX QuickStart</a><br>
+
+ <a href="http://www.forkosh.com/cgi-bin/weblist.cgi?-t=weblist
+ &-f=sources/weblistemplate.html&files=@sources/sourcecode/mimetex.lis
+ &copyright=2002-2011&counter=mimetex
+ &title=mimetex&description=m i m e T e X S o u r c e L i s t i n g"
+ target="_top">mimeTeX Source Listing</a><br>
+ <a href="http://www.forkosh.com/mimetex.zip">
+ <!-- jfa <a href="ftp://ftp.tex.ac.uk/tex-archive/support/mimetex/mimetex.zip"></a> -->
+ <font size=4>download&nbsp;mimeTeX</font></a></font>
+ </font> </center> </td>
+ <td align="center">
+ <a href="#preview"><img id="imageBanr2" onclick="eqntext('imageBanr2')"
+ src="../cgi-bin/mimetex.cgi?\Large\scr{J}^{ij}=\frac12\varepsilon_{ijk}
+ \left[\begin{array}{cc}\sigma_k&0\\0&\sigma_k\end{array}\right]"
+ alt="" border=0 align=middle></a> <br>
+ <a href="#examples">more_examples...</a> </td>
+ </tr>
+ <tr> <td align="center" colspan="3">
+ This page discusses mimeTeX, a program that displays math on the web.<br>
+ (<font size=3>See
+ <a href="http://www.americanscientist.org/issues/pub/2009/3/writing-math-on-the-web/1"
+ target="_top">Writing&nbsp;Math&nbsp;on&nbsp;the&nbsp;Web</a>
+ for a more general discussion.</font>)
+ </td> </tr>
+ </table>
+</center>
+<hr size=4>
+<center><b><font color="maroon" size=3>
+Copyright <font size=5>&copy;</font> 2002-2012,
+<a href="http://www.forkosh.com">John Forkosh Associates, Inc.</a> <br>
+email: <a href="mailto:john&#64;forkosh&#46;com">john&#64;forkosh&#46;com</a>
+</font></b> <br><br>
+<a href="#preview"><img id="timestamp1" onclick="eqntext('timestamp1')"
+src="../cgi-bin/mimetex.cgi?\normalsize\blue\begin{matrix}
+\large\today\\\normalsize\today[3]\end{matrix}"
+alt="" border=0 align=middle></a> </center>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Table of Contents
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<br> <center><b><font color="maroon" size=6>
+ <u> &nbsp; &nbsp; &nbsp; &nbsp; C o n t e n t s &nbsp; &nbsp; &nbsp; &nbsp;
+ </u></font></b> <br>
+<table cellspacing=0 class="medium">
+ <tr>
+ <td valign="top" align="center" width=150>
+ <font size=3><b>- - - T u t o r i a l - - -</b></font> </td>
+ <td valign="top" align="center" colspan=3 width=450><font size=3><b>
+ - - - - - - - - - - - - - - R e f e r e n c e - - - - - - - - - - - - - -
+ </b></font></td>
+ </tr>
+ <tr>
+ <td valign="top" align="center" width=150> <font size=3>
+ <a href="#introduction">&nbsp; (I) Introduction &nbsp;</a><br>
+ <a href="#quickstart"> a. Quick Start </a><br>
+ <a href="#examples"> b. Examples </a><br>
+ <a href="#scripts"> c. Scripts&amp;Plugins </a><br>
+ <a href="#gpl"> d. GPL License </a> </font> </td>
+ <td valign="top" align="center" width=150> <font size=3>
+ <a href="#build">&nbsp; (II) Building mimeTeX &nbsp;</a><br>
+ <a href="#compile"> a. Compile </a><br>
+ <a href="#install"> b. Install </a><br>
+ <a href="#options"> c. Compile Options </a><br>
+ <a href="#cmdline"> d. Command Line </a> </font> </td>
+ <td valign="top" align="center" width=150> <font size=3>
+ <a href="#reference">&nbsp; (III) Syntax Reference &nbsp;</a><br>
+ <a href="#spaces"> a. Math & White Space </a><br>
+ <a href="#symbols"> b. Symbols, Sizes, Modes </a><br>
+ <a href="#delimiters"> c. Delimiters </a><br>
+ <a href="#accents"> d. Accents, Arrows, etc. </a><br>
+ <a href="#array"> e. \begin{array} </a><br>
+ <a href="#picture"> f. \picture(&nbsp;){&nbsp;} </a><br>
+ <a href="#commands"> g. Other Commands </a><br>
+ <a href="#exceptions"> h. Other Exceptions </a><br>
+ <a href="#messages"> i. Errors and Messages </a> </font> </td>
+ <td valign="top" align="center" width=150> <font size=3>
+ <a href="#appendices">&nbsp; &nbsp; (IV) Appendices &nbsp; &nbsp;</a><br>
+ <a href="#fonts"> a. Fonts </a><br>
+ <a href="#makeraster"> b. make_raster() </a><br>
+ <a href="#gifsave"> c. gifsave.c </a>
+ <br><a href="#remarks"> &nbsp; Remarks &nbsp; </a> </font> </td>
+ </tr>
+</table>
+</center>
+
+<!-- br -->
+<p style="margin-left:3em;margin-right:3em;">
+ <font color="blue" size=3> This page contains more information
+ than you'll probably need to read. If you follow the
+ <font color="maroon">Installation&nbsp;and&nbsp;Usage&nbsp;Summary</font>
+ below, try installing mimeTeX immediately. <!-- If you need
+ more information, --> Or continue reading until you feel comfortable
+ trying to install mimeTeX. <!-- Return to this page as needed. -->
+ Prerequisites are: some knowledge of your OS's shell,
+ of installing cgi's, of LaTeX. </font>
+ <font color="maroon" size=3> <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>&quot</b><i>Computers are like Old Testament gods<b>:</b>
+ lots of rules and no mercy.</i><b>&quot</b><br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>&#150;&#150;</b> Joseph Campbell, The Power of Myth &nbsp;
+ (Doubleday 1988, page 18) </font> </p>
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++ Installation and Usage Summary
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<!-- br -->
+<center>
+<table border="0">
+<tr> <!-- banner -->
+ <td align="left">
+ <!-- <b><font color="maroon" size=4>
+ <u> &nbsp; &nbsp; &nbsp; &nbsp; I n s t a l l a t i o n &nbsp;
+ a n d &nbsp; U s a g e &nbsp; S u m m a r y &nbsp; &nbsp; &nbsp; &nbsp;
+ </u></font></b> -->
+ <font size=4 color="maroon"><b>- - - - - - I n s t a l l a t i o n &nbsp;
+ a n d &nbsp; U s a g e &nbsp; S u m m a r y - - - - - -</b></font>
+ </td> </tr>
+<tr>
+ <td valign="top"> <!-- summary -->
+ <table border="0" cellpadding="0" cellspacing="0" hspace="0" vspace="0">
+ <tr><td align="right" valign="top"> &nbsp; &nbsp; &nbsp;
+ <a href="#build">Installation</a>: &nbsp; &nbsp; </td>
+ <td><font size=4> Download <a href="http://www.forkosh.com/mimetex.zip">
+ mimetex.zip</a> and then type <br>
+ <b> &nbsp; &nbsp; unzip mimetex.zip</b> <br>
+ <b> &nbsp; &nbsp; cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi</b>
+ <br>Now just <b>mv</b> mimetex.cgi to your <b>cgi-bin/</b>
+ directory, <br> set permissions as necessary, and you're all done.
+ </font></td></tr>
+ <tr><td colspan="2"> <font size="2">&nbsp;</font> </td></tr>
+ <tr><td align="right" valign="top">
+ <a href="#introduction">Usage</a>: &nbsp; &nbsp; </td>
+ <td><font size=4> To see the image <br> &nbsp; &nbsp;
+ <a href="#preview"><img id="summary1" onclick="eqntext('summary1')"
+ src="../cgi-bin/mimetex.cgi?x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}"
+ alt="" border=0 align=middle></a> <br>
+ just write the tag <br>
+ <b> &nbsp; &nbsp; &lt;img&nbsp;src="/cgi-bin/mimetex.cgi?<br>
+ &nbsp; &nbsp; x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}"&gt;</b>
+ </font></td></tr>
+ </table>
+ </td>
+</tr>
+</table>
+</center>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+SECTION I. INTRODUCTION
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h1> <a name="introduction">(I) Introduction</a> &nbsp; </h1>
+
+<p> <font color="maroon">MimeTeX, licensed under the
+ <a href="http://www.gnu.org/licenses/gpl.html" target="_top">gpl</a>,
+ lets you easily embed LaTeX math in your html pages.</font>
+ It parses a LaTeX math expression and immediately emits the
+ corresponding gif image, rather than the usual TeX dvi.
+ And mimeTeX is an entirely separate little program that doesn't use
+ TeX or its fonts in any way. It's just one cgi that you put in your
+ site's cgi-bin/ directory, with no other dependencies. So mimeTeX
+ is very easy to <a href="#build">install</a>. <br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp;
+ Just download <a href="http://www.forkosh.com/mimetex.zip">
+ mimetex.zip</a> and then type </nobr> <br>
+ <nobr><b> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ unzip mimetex.zip</b></nobr> <br>
+ <nobr><b> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ cc &#150;DAA mimetex.c gifsave.c
+ &#150;lm &#150;o mimetex.cgi</b></nobr> <br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp;
+ Now just <b>mv</b> mimetex.cgi to your <b>cgi-bin/</b>
+ directory, </nobr> <br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp;
+ set permissions as necessary, and you're all done. </nobr> <br>
+ <br>
+ And mimeTeX is equally easy to <a href="#quickstart">use</a><b>:</b>
+ &nbsp; just place an html &lt;img&gt; tag in your document
+ wherever you want to see the corresponding LaTeX expression. <br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp;
+ For example, the &lt;img&gt tag </nobr> <br>
+ <nobr><b> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ &lt;img&nbsp;
+ src="../cgi-bin/mimetex.cgi?f(x)=\int_{-\infty}^xe^{-t^2}dt" &gt;</b></nobr><br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp;
+ immediately generates the corresponding gif image on-the-fly,</nobr><br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ displaying &nbsp;
+ <?php mimetextag('imageI1',
+ '\normalsize f(x)=\int\limits_{-\infty}^xe^{-t^2}dt'); ?>
+ &nbsp; wherever you put that tag.</nobr><br>
+ <br>
+ MimeTeX doesn't need intermediate dvi-to-gif conversion, and it doesn't
+ create separate gif files for each converted expression.
+ (But you can enable image caching with mimeTeX's
+ &nbsp; <b>-DCACHEPATH=\&quot;<i>path/</i>\&quot;</b> &nbsp;
+ <a href="#options">compile&nbsp;option</a>.)
+ &nbsp; And there's no inherent need to repeatedly write the
+ cumbersome &lt;img&gt; tag illustrated above.
+ You can write your own
+ <a href="#scripts">wrapper&nbsp;scripts</a>,
+ discussed below, around mimeTeX to simplify the notation. </p>
+
+<h3> <a name="alternatives">
+Alternative solutions<font size=5>...</font></a> </h3>
+<p> MimeTeX's benefit over similar math-on-the-web solutions is, as
+ mentioned above, its easy installation. But if that's not a
+ problem for you, and if your site's server already has a LaTeX
+ distribution installed, and suitable image conversion utilities like
+ <a href="http://www.imagemagick.org" target="_top">ImageMagick</a>,
+ then you may prefer to look at a math rendering script like
+ <a href="http://www.mayer.dial.pipex.com/tex.htm#latexrender"
+ target="_top">latexrender</a>
+ which uses LaTeX to create higher quality images than mimeTeX
+ produces. For comparison,
+ <?php mimetextag('imageI2',
+ '\small f(x)=\int\limits_{-\infty}^xe^{-t^2}dt'); ?>,
+ with arbitrary mean
+ <?php mimetextag('imageI3','\normalsize\mu'); ?> and standard deviation
+ <?php mimetextag('imageI4','\normalsize\sigma'); ?>,
+ and at mimeTeX's next larger font size, looks like </p>
+ <center>
+ <table>
+ <tr align="center">
+ <td> <font size="4">latexrender</font> </td>
+ <td> <img src="../cgi-bin/mimetex.cgi?\hspace{30}"
+ alt="" border=0> </td>
+ <td> <font size="4">mimeTeX</font> </td>
+ </tr>
+ <tr align="center">
+ <td> <img src="http://www.forkosh.com/lrender.gif"
+ alt="" border=0 align=middle> </td>
+ <td> &nbsp; </td>
+ <td>
+ <?php mimetextag('imageI5',
+ '\normalsize f(x)={\Large\frac1{\sigma\sqrt{2\pi}}}
+ \int_{\small-\infty}^xe^{-\small\frac{(t-\mu)^2}{2\sigma^2}}dt'); ?>
+ </td>
+ </tr>
+ </table>
+ </center>
+<p> Similar LaTeX-based solutions that you may want to look at are
+ <a href="http://www.mathtran.org" target="_top">mathtran</a>,
+ <a href="http://www.fourmilab.ch/webtools/textogif/textogif.html"
+ target="_top">textogif</a> and
+ <a href="http://www.math.uio.no/~martingu/gladtex/"
+ target="_top">gladTeX</a>. Additional discussion and several more
+ links are at <a href="http://www.tug.org/interest.html#web"
+ target="_top">www.tug.org/interest.html</a> and in the
+ <a href="http://www.tex.ac.uk/cgi-bin/texfaq2html?label=LaTeX2HTML"
+ target="_top">tex-faq</a>. </p>
+
+<p> For example, <a href="http://www.mathtran.org" target="_top">mathtran</a>
+ is a public LaTeX web service that's
+ particularly easy to use by following these simple
+ <a href="http://www.mathtran.org/wiki/index.php/TeX_image"
+ target="_top">instructions</a>. In the &lt;head&gt; of your
+ html page, place the tag <br>
+ &nbsp; &nbsp;
+ &lt;script type="text/javascript" <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ src="http://www.mathtran.org/js/mathtran_img.js"&gt;&lt;/script&gt;<br>
+ and in the &lt;body&gt;, wherever you want to see latex images,
+ place tags like <br>
+ &nbsp; &nbsp;
+ &lt;img alt=<b>"</b>tex:<i>any latex math expression</i><b>"</b>&gt;<br>
+ For comparison, <br>
+ &nbsp; &nbsp;
+ &lt;img alt="tex: f(x) = \frac1{\sigma\sqrt{2\pi}} <br>
+ &nbsp; &nbsp;
+ \int_{-\infty}^x e^{-\frac{(t-\mu)^2}{2\sigma^2}}dt"&gt; <br>
+ looks like </p>
+ <center>
+ <table>
+ <tr align="center">
+ <td> <font size="4">mathtran</font> </td>
+ <td> <img src="../cgi-bin/mimetex.cgi?\hspace{30}"
+ alt="" border=0> </td>
+ <td> <font size="4">mimeTeX</font> </td>
+ </tr>
+ <tr align="center">
+ <td> unavailable
+ <!-- img alt="tex:\displaystyle f(x) = \frac1{\sigma\sqrt{2\pi}}
+ \int_{-\infty}^x e^{-\frac{(t-\mu)^2}{2\sigma^2}}dt" --> <br> </td>
+ <td> &nbsp; </td>
+ <td>
+ <a href="#preview"><img id="imageP3" onclick="eqntext('imageP3')"
+ src="../cgi-bin/mimetex.cgi?\large
+ f(x)={\Large\frac1{\sigma\sqrt{2\pi}}}
+ \int_{\small-\infty}^xe^{-\small\frac{(t-\mu)^2}{2\sigma^2}}dt"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ </table>
+ </center>
+
+<!--
+<p> The remainder of this introductory mimeTeX tutorial section contains </p>
+ <ul>
+ <li> First, a concise <a href="#quickstart">Quickstart</a> providing
+ just enough information for you to try rendering your own
+ expressions by <a href="#preview">Submitting&nbsp;Queries</a>
+ right from this page. </li>
+ <li> Then, a variety of additional <a href="#examples">Examples</a>
+ that more fully illustrate mimeTeX's capabilities
+ (later on, Section III comprises a more complete mimeTeX
+ <a href="#reference">Syntax&nbsp;Reference</a>). </li>
+ <li> Finally, the <a href="#gpl">gpl</a> license, whose terms
+ and conditions you must agree to before using mimeTeX.</li>
+ </ul>
+-->
+<p> You may now want to browse the additional <a href="#examples">Examples</a>
+ below before proceeding, to make sure mimeTeX suits your needs before you
+ spend more time learning to use it. </p>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+QUICKSTART
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h2> <a name="quickstart"> (Ia) Quick Start &nbsp; </a> </h2>
+
+ <p> <!-- Unlike MathML, --> MimeTeX is as TeX-like as possible (though
+ not 100% compliant), and you must already be familiar with LaTeX
+ math markup to use it. If you're not, many online LaTeX
+ <a href="http://www.tug.org/begin.html#doc" target="_top">turorials</a>
+ are readily available. You may also want to browse Andrew Roberts'
+ <a href="http://www.andy-roberts.net/misc/latex/latextutorial9.html"
+ target="_top">Latex&nbsp;Math&nbsp;I</a> and
+ <a href="http://www.andy-roberts.net/misc/latex/latextutorial10.html"
+ target="_top">Latex&nbsp;Math&nbsp;II</a>, or my own
+ <a href="http://www.forkosh.com/mimetextutorial.html" target="_top">
+ LaTeX&nbsp;math&nbsp;tutorial</a>.
+ Then, instead of continuing to read this page, you can <!-- may prefer
+ to play with mimeTeX yourself. In that case, --> just Submit any LaTeX
+ math expression you like in the Query Box below. I've started
+ you out with a little example already in the box, or <!-- , instead, -->
+ you can Click any of the <a href="#examples">Examples</a> below
+ to place that corresponding expression in the Query Box. </p>
+
+ <p> Meanwhile, here are just a few quickstart tips for Submitting
+ your own mimeTeX expressions in the Query Box below: </p>
+ <ul>
+ <li> MimeTeX currently has eight font sizes selected by
+ one of the usual directives &nbsp; <b>\tiny</b>
+ or <b>\small</b> or <b>\normalsize</b>&nbsp;,
+ or <b>\large</b>&nbsp;(default) or <b>\Large</b>
+ or <b>\LARGE</b>&nbsp;, or <b>\huge</b> or <b>\Huge</b>&nbsp;.
+ &nbsp; &nbsp; Unlike standard LaTeX, font size directives may
+ appear within math&nbsp;mode expressions. They affect everything
+ to their right, except that their scope will be limited to any
+ <b>{&nbsp;}</b>-enclosed subexpression in which they occur.
+ For example, &nbsp; "<b>a+\small&nbsp;b+c</b>"
+ &nbsp; renders &nbsp;
+ <a href="#preview"> <img id="imageBu" onclick="eqntext('imageBu')"
+ src="../cgi-bin/mimetex.cgi?\large a+\small b+c"
+ alt="" border=0 style="Vertical-Align:-2px"></a>, &nbsp;
+ whereas &nbsp; "<b>\small&nbsp;a+{\Large&nbsp;b+}c</b>" &nbsp;
+ renders &nbsp;
+ <a href="#preview"> <img id="imageBv" onclick="eqntext('imageBv')"
+ src="../cgi-bin/mimetex.cgi?\small a+{\Large b+}c"
+ alt="" border=0 style="Vertical-Align:-2px"></a>. </li>
+<!-- <li> At smaller font sizes, try preceding your expression with &nbsp;
+ <b>\light</b> &nbsp; which adjusts mimeTeX's anti-aliasing
+ parameters to produce thinner lines that you may feel are
+ more legible, e.g.,<br> &nbsp; &nbsp;
+ <a href="#preview"><img id="imageIA1" onclick="eqntext('imageIA1')"
+ src="../cgi-bin/mimetex.cgi?\light\small\displaystyle
+ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}" alt="" border=0
+ align=middle> </a> &nbsp versus &nbsp;
+ <a href="#preview"><img id="imageIA2" onclick="eqntext('imageIA2')"
+ src="../cgi-bin/mimetex.cgi?\small\displaystyle
+ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}" alt="" border=0
+ align=middle> </a> </li> -->
+ <li> <!-- For displaystyle math mode limits illustrated above,
+ write either &nbsp;
+ <b>\displaystyle&nbsp;e^x=\sum_{n=0}^\infty\frac{x^n}{n!}</b>
+ &nbsp; or &nbsp; <b>e^x=\sum\limits_{n=0}^\infty\frac{x^n}{n!}</b>
+ &nbsp; in the usual way (ditto for <b>\int</b>, <b>\prod</b>,
+ <b>\cup</b>, <b>\cap</b>, etc). --> <!-- MimeTeX also recognizes
+ <b>\Bigint</b>, <b>\Bigsum</b>, <b>\Bigprod</b>, and several
+ similar extra symbols which are a little bigger, and which
+ automatically render displaystyle limits. -->
+ <!-- MimeTeX default-renders limits displaystyle at sizes
+ <b>\large</b> and larger (see the <b>-DDISPLAYSIZE=<i>n</i></b>
+ <a href="#options">compile&nbsp;option</a> below to change the
+ default). &nbsp; <b>\textstyle</b> overrides this default for
+ your entire expression, or <b>\nolimits</b> overrides it
+ for a single operator. -->
+ By default, mimeTeX renders limits textstyle &nbsp;
+ <a href="#preview"> <img id="imageB1" onclick="eqntext('imageB1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\textstyle
+ \sum_{n=0}^\infty\frac{x^n}{n!}" alt="" border=0
+ style="Vertical-Align:-5px"></a> &nbsp;
+ at sizes <b>\normalsize</b> and smaller,
+ and renders them displaystyle &nbsp;
+ <a href="#preview"> <img id="imageB2" onclick="eqntext('imageB2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \sum_{n=0}^\infty\frac{x^n}{n!}" alt="" border=0
+ style="Vertical-Align:-15px"></a> &nbsp;
+ at sizes <b>\large</b> and larger.
+ The LaTeX directives <b>\displaystyle</b> or <b>\textstyle</b>,
+ and <b>\limits</b> or <b>\nolimits</b>, override mimeTeX's default
+ in the usual way. Or see the <b>-DDISPLAYSIZE=<i>n</i></b>
+ <a href="#options">compile&nbsp;option</a> below to change
+ the default. </li>
+ <!-- <li> As discussed in the <a href="#introduction">Introduction</a>,
+ you can replace cumbersome &lt;img&gt; tags with your own custom
+ tags or wrapper scripts. </li> -->
+ <li> <!-- And --> There are occasional exceptions where I couldn't
+ program mimeTeX to recognize valid LaTeX syntax.
+ One particular "gotcha" is that mimeTeX bindings
+ are pretty much left-to-right. Thus, for example, although
+ mimeTeX correctly interprets <b>\frac12</b> as well as
+ <b>\frac1{x^2}</b>, etc, the legal LaTeX expression
+ <b>x^\frac12</b> must be written <b>x^{\frac12}</b>.
+ Otherwise, mimeTeX interprets it as <b>{x^\frac}12</b>, i.e.,
+ the same way <b>x^\alpha12</b> would be interpreted, which is
+ nonsense for <b>\frac</b>. The same "gotcha" also applies to
+ other combinations of commands, e.g., you must write
+ <b>\sqrt{\frac\alpha\beta}</b>, or
+ <b>\frac\alpha{\sqrt\beta}</b>, etc.
+ The <a href="#reference">Syntax&nbsp;Reference</a> section
+ contains much additional information. <!-- Or you can just begin
+ playing with mimeTeX for yourself to see if it might have
+ any potential usefulness for you. --> </li>
+ <li> And there are various additional syntactic and cosmetic
+ differences between LaTeX and mimeTeX. For example,
+ bounding boxes for mimeTeX's character bitmaps don't
+ accommodate italic corrections. Therefore, an expression
+ like <b>\int\nolimits_a^b</b> renders
+ <a href="#preview"><img id="gotcha1" onclick="eqntext('gotcha1')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\displaystyle\int\nolimits_a^b"
+ alt="" border=0 align=middle></a> rather than
+ <a href="#preview"><img id="gotcha2" onclick="eqntext('gotcha2')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\displaystyle\smashmargin{2}{\int\nolimits_a}^b"
+ alt="" border=0 align=middle></a><b>.</b>
+ To render the latter image you have to write the somewhat
+ cumbersome expression <b>{\smashmargin2{\int\nolimits_a}^b}</b>
+ instead (see <a href="#smash">smash</a> below). </li>
+ <li> Besides such exceptions, mimeTeX
+ also provides various LaTeX extensions <!-- , i.e., LaTeX errors
+ permitted by mimetex. --> (such as font size
+ directives like <b>\Large</b> permitted within mimeTeX
+ math&nbsp;mode expressions, as discussed above).
+ <!-- , but flagged as errors by LaTeX. -->
+ <!-- But note well: if you take advantage of mimeTeX extensions,
+ your math&nbsp;mode expressions will no longer be accepted by
+ standard TeX engines. --> </li>
+ </ul>
+ <p> <a name="forminput"> </a> <a name="preview"> </a>
+ Now enter your own LaTeX expression, use the sample provided,
+ or Click any of the <a href="#examples">Examples</a>.
+ Then press the Submit button, and mimeTeX's rendering should be
+ displayed in the little window immediately below it. </p>
+ <center>
+ <table border="2" cellpadding="5" cellspacing="0">
+ <tr align="center"><td>
+ <form name="expression" action="../cgi-bin/mimetex.cgi"
+ method="get" target="inlineframe">
+ <table border="0" cellpadding="0" cellspacing="1">
+ <tr align="left"><td align="center">
+ <b>First enter your own LaTeX expression,
+ or Click any example...</b> <br>
+ <textarea name="formdata" rows="5" cols="72"
+ >\Large f(x)=\int_{-\infty}^x e^{-t^2}dt</textarea> <br>
+ </td></tr>
+ <tr align="center"><td>
+ <font size="-1"> <input type="button" onClick="cleartext()"
+ value="Clear Expression"> &nbsp; &nbsp;
+ &nbsp; <input type="submit" value="Submit Expression"> </font>
+ </td></tr>
+ </table>
+ </form> </td></tr> <tr align="left"><td align="center">
+ <b>Now click Submit to see it rendered below...</b> <br>
+ <iframe name="inlineframe" align="middle" width="85%" height="110">
+ &lt;p&gt;iframe's not supported if you see this.&lt;/p&gt;
+ </iframe>
+ </td></tr>
+ </table>
+ </center>
+ <p> You should see &nbsp;
+ <a href="#preview"><img id="imageIA3" onclick="eqntext('imageIA3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize
+ f(x)=\int\limits_{-\infty}^x e^{-t^2}dt"
+ alt="" border=0 style="Vertical-Align:-11px"></a> &nbsp;
+ if you submit the sample expression already in the box.
+ Or see <a href="#messages">error&nbsp;messages</a> whenever an
+ unexpected image is displayed instead. &nbsp; And (as discussed
+ above) the &lt;img&gt; tag to embed this same integral anywhere
+ in your own document is <br>
+ <nobr><b> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ &lt;img&nbsp;
+ src="../cgi-bin/mimetex.cgi?f(x)=\int_{-\infty}^xe^{-t^2}dt" &gt;</b></nobr><br>
+ </p>
+ <!-- p class="continue">
+ And recall that the typical mimeTeX &lt;img&gt; tag has the form </p>
+<pre> &lt;img&nbsp;src="../cgi-bin/mimetex.cgi?any valid LaTeX/mimeTeX expression"
+ alt="" border=0 align=middle&gt;</pre> <p class="continue">
+ where <b>../cgi-bin/mimetex.cgi</b> is the relative path from your html
+ page containing these tags to your compiled mimetex.cgi program, and
+ where <b>any&nbsp;valid&nbsp;LaTeX/mimeTeX&nbsp;expression</b>
+ is pretty much any valid LaTeX math expression: </p -->
+
+<!-- ++++++++
+ <h3> <a name="errormessages">
+ Error messages<font size=5>...</font></a> </h3>
+ <p> Any (La)TeX error is typically also a mimeTeX error.
+ However, mimeTeX has no command line interface or
+ <b>.</b>log file for reporting errors. Its only
+ communication with you is through the mimeTeX image
+ rendered by your browser. So error messages are embedded
+ in that image whenever feasible. For example,
+ suppose you want to see
+ <a href="#preview"><img id="messages1" onclick="eqntext('messages1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\alpha\beta\gamma\delta"
+ alt="" border=0 align="bottom"></a>
+ but you mistakenly type &nbsp; <b>\alpha\bethe\gamma\delta</b> &nbsp;
+ instead. Then the image rendered is
+ <a href="#preview"><img id="messages2" onclick="eqntext('messages2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\alpha\bethe\gamma\delta"
+ alt="" border=0 align="bottom"></a>
+ indicating the unrecognized <b>[\bethe?]</b> where you wanted to type
+ &nbsp; <b>\beta</b> &nbsp; and had hoped to see &nbsp;
+ <a href="#preview"><img id="messages3" onclick="eqntext('messages3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\bf\beta"
+ alt="" border=0 align="bottom"></a><b>.</b> &nbsp;
+ If your expression contains some unprintable character
+ (meaning any character mimeTeX has no bitmap for),
+ then just &nbsp;
+ <a href="#preview"><img id="messages4" onclick="eqntext('messages4')"
+ src="../cgi-bin/mimetex.cgi?\small\bf[?]"
+ alt="" border=0 align="bottom"></a> &nbsp;
+ is displayed in the corresponding position. </p>
+
+ <p> The preceding example illustrates a pretty trivial error.
+ Any non-trivial errors in your expression are likely to
+ go unrecognized and unreported by mimeTeX, and to render
+ unexpected images. While checking your input expression
+ for syntax errors, keep in mind the following points
+ about mimeTeX's behavior: </p>
+ <ul>
+ <li> An unmatched left brace &nbsp; <b>{</b> &nbsp; is matched
+ by mimeTeX with a "phantom" right brace &nbsp; <b>}</b> &nbsp;
+ that's imagined to be at the end of your expression. </li>
+ <li> Likewise, an unmatched &nbsp; <b>\left(</b>, &nbsp;
+ or <b>\left\{</b> &nbsp; or <b>\left\</b><i>anything</i>, &nbsp;
+ is matched by mimeTeX with a "phantom" &nbsp; <b>\right.</b>
+ &nbsp; at the end of your expression. </li>
+ <li> On the other hand, an unmatched right brace &nbsp; <b>}</b>
+ &nbsp; is displayed in place, as if you had typed \rbrace. </li>
+ <li> But an unmatched &nbsp; <b>\right\</b><i>anything</i> &nbsp;
+ is interpreted as an
+ <a href="http://www.forkosh.com/mimetexmanual.html?abbreviations"
+ target="_top">abbreviation</a> for <b>\</b>rightarrow
+ followed by <b>\</b><i>anything</i>. For example, &nbsp;
+ <b>\leff(&nbsp;abc&nbsp;\right)&nbsp;def</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="messages5"
+ onclick="eqntext('messages5')"
+ src="../cgi-bin/mimetex.cgi?\small\leff(abc\right)def"
+ alt="" border=0 align="bottom"></a>.
+ </li>
+ </ul>
+++++++++ -->
+
+<!-- ++++++++
+ <h3> <a name="infomessages">
+ Informational messages<font size=5>...</font></a> </h3>
+ <p> The latest release of mimeTeX is version
+ <a href="#preview"><img id="messages11" onclick="eqntext('messages11')"
+ src="../cgi-bin/mimetex.cgi?\small\versionnumber"
+ alt="" border=0 align="bottom"></a>
+ which was last revised
+ <a href="#preview"><img id="messages12" onclick="eqntext('messages12')"
+ src="../cgi-bin/mimetex.cgi?\small\revisiondate"
+ alt="" border=0 align="bottom"></a>.
+ The special mimeTeX directive &nbsp; <b>\version</b> &nbsp;
+ displays that same information, </p>
+ <center>
+ <a href="#preview"><img id="messages13" onclick="eqntext('messages13')"
+ src="../cgi-bin/mimetex.cgi?\version"
+ alt="" border=0 align=middle></a>
+ </center>
+ <p> To check that your own release of mimeTeX is current,
+ type a url into your browser's locator window something like <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>http://www.<i>yourdomain</i>.com/cgi-bin/mimetex.cgi?\version</b> <br>
+ which will display the version and revision date of
+ mimeTeX installed on your server. </p>
+++++++++ -->
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+EXAMPLES
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h2> <a name="examples"> (Ib) Examples &nbsp; </a> </h2>
+
+ <p> Here are various additional random examples further illustrating
+ mimeTeX's features and usage. To see how they're done, Click any
+ one of them to place its corresponding expression in the
+ <a href="#preview">Query&nbsp;Box</a> above. Then press Submit
+ to re-render it, or you can edit the expression first to suit
+ your own purposes. </p>
+
+<table cellspacing=15>
+<!-- first example: taylor series for e^x at various font sizes and colors
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5><a name="example1">(1)</a></font> &nbsp;&nbsp;&nbsp; </td>
+ <td align="left" colspan=4>
+ <a href="#preview">
+ <img id="example1a" onclick="eqntext('example1a')"
+ src="../cgi-bin/mimetex.cgi?\red\normalsize\displaystyle
+ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}"
+ alt="" border=0 align=middle></a> &nbsp &nbsp
+ <a href="#preview">
+ <img id="example1b" onclick="eqntext('example1b')"
+ src="../cgi-bin/mimetex.cgi?\green\large\displaystyle
+ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}"
+ alt="" border=0 align=middle></a> &nbsp &nbsp
+ <a href="#preview">
+ <img id="example1c" onclick="eqntext('example1c')"
+ src="../cgi-bin/mimetex.cgi?\blue\Large
+ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}"
+ alt="" border=0 align=middle></a> &nbsp &nbsp
+ <a href="#preview">
+ <img id="example1d" onclick="eqntext('example1d')"
+ src="../cgi-bin/mimetex.cgi?\reverse\opaque
+ \LARGE e^x=\sum_{n=0}^\infty\frac{x^n}{n!}"
+ alt="" border=0 align=middle></a> &nbsp &nbsp
+ <a href="#preview">
+ <img id="example1e" onclick="eqntext('example1e')"
+ src="../cgi-bin/mimetex.cgi?\LARGE
+ e^x=\lim_{n\to\infty} \left(1+\frac xn\right)^n"
+ alt="" border=0 align=middle></a>
+ </td>
+ </tr>
+
+<!-- second example
++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(2)</font> </td>
+ <td align="left" colspan=4>
+ <a href="#preview">
+ <img id="example2" onclick="eqntext('example2')"
+ src="../cgi-bin/mimetex.cgi?\Large\frac{dv^m}{ds}=-\Gamma^m_{oo}v^{o^2}
+ =-g^{mn}\Gamma_{noo}v^{o^2}=\frac12g^{mn}g_{oo,n}v^{o^2}"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+
+<!-- third example
+++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(3)</font> </td>
+ <td align="left" colspan=4>
+ <a href="#preview">
+ <img id="example3" onclick="eqntext('example3')"
+ src="../cgi-bin/mimetex.cgi?\Large\varepsilon=\sum_{i=1}^{n-1}
+ \frac1{\Delta x}\int_{x_i}^{x_{i+1}}\left\{\frac1{\Delta x}\big[
+ (x_{i+1}-x)y_i^\ast+(x-x_i)y_{i+1}^\ast\big]-f(x)\right\}^2dx"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+
+<!-- fourth example: solution to quadratic, definition of derivative
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(4)</font> </td>
+ <td align="left" colspan=4>
+ <table>
+ <tr>
+ <td align="left">
+ <a href="#preview">
+ <img id="example4a" onclick="eqntext('example4a')"
+ src="../cgi-bin/mimetex.cgi?\LARGE x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ solution for quadratic </td>
+ </tr>
+ <tr> <td> <br> </td> </tr>
+ <tr>
+ <td align="left">
+ <a href="#preview">
+ <img id="example4b" onclick="eqntext('example4b')"
+ src="../cgi-bin/mimetex.cgi?\large f^\prime(x)\ =
+ \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ definition of derivative </td>
+ </tr>
+ </table> </td>
+ </tr>
+
+<!-- fifth example: continued fraction
++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(5)</font> </td>
+ <td align="left">
+ <a href="#preview">
+ <img id="example5" onclick="eqntext('example5')"
+ src="../cgi-bin/mimetex.cgi?\LARGE f=b_o+\frac{a_1}{b_1+
+ \frac{a_2}{b_2+\frac{a_3}{b_3+a_4}}}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ illustrating <b>\frac{}{}</b> for continued fraction </td>
+ </tr>
+
+<!-- sixth example: demonstrating \left\{ ... \right.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(6)</font> </td>
+ <td align="left">
+ <a href="#preview">
+ <img id="example6" onclick="eqntext('example6')"
+ src="../cgi-bin/mimetex.cgi?\LARGE\tilde y=\left\{
+ {\ddot x\text{ if \vec x odd}\atop\hat{\,\bar x+1}\text{ if even}}\right."
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ illustrating <b>\left\{...\right<font size=5>.</font></b>
+ <!-- we may write <b>\{...\.</b> --> <br>
+ and note the accents </td>
+ </tr>
+
+<!-- seventh example: demonstrating \overbrace \underbrace
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(7)</font> </td>
+ <td align="center">
+ <a href="#preview">
+ <img id="example7" onclick="eqntext('example7')"
+ src="../cgi-bin/mimetex.cgi?\large\overbrace{a,...,a}^{\text{k a^,s}},
+ \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}
+ \normalsize\underbrace{\overbrace{a...a}^{\text{k a^,s}},
+ \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ <b>\overbrace{}^{}</b> and <b>\underbrace{}_{}</b> <br>
+ (TeXbook page 181, Exercise 18.41) </td>
+ </tr>
+
+<!-- eighth example: demonstrating \begin{array}
++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(8)</font> </td>
+ <td align="left" colspan=3>
+ <table>
+ <tr>
+ <td align="left" colspan=2>
+ <a href="#preview">
+ <img id="example8a" onclick="eqntext('example8a')"
+ src="../cgi-bin/mimetex.cgi?\large\scr{J}^{i0}=+\frac i2
+ \left[\begin{array}{cc}\sigma_i&0\\0&-\sigma_i\end{array}\right]
+ \hspace{10}\scr{J}^{ij}=\frac12\varepsilon_{ijk}
+ \left[\begin{array}{cc}\sigma_k&0\\0&\sigma_k\end{array}\right]"
+ alt="" border=0 align=middle> </a> </td>
+ </tr>
+ <tr> <td> <br> </td> </tr>
+ <tr>
+ <td align="left">
+ <a href="#preview">
+ <img id="example8b" onclick="eqntext('example8b')"
+ src="../cgi-bin/mimetex.cgi?\large A\ =\ \normalsize\left(
+ \begin{array}{c.cccc}&1&2&\cdots&n\\
+ \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\
+ 2&a_{21}&a_{22}&\cdots&a_{2n}\\
+ \vdots&\vdots&\vdots&\ddots&\vdots\\
+ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ demonstrating <a href="#array">\begin{array}</a>'s dashed lines </td>
+ </tr>
+ </table> </td>
+ </tr>
+
+<!-- ninth example: block diagonal form using nested arrays
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5><a name="example9">(9)</a></font> </td>
+ <td align="left" colspan="2">
+ <a href="#preview">
+ <img id="example9c" onclick="eqntext('example9c')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \left(\large\begin{array}{GC+45}
+ \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\
+ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\large=}
+ \ \left[\begin{array}{CC}
+ \begin{array}\frac1{E_{\fs{+1}x}}
+ &-\frac{\nu_{xy}}{E_{\fs{+1}x}}
+ &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\
+ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\
+ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}&
+ -\frac{\nu_{zy}}{E_{\fs{+1}z}}
+ &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\
+ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\
+ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array}
+ \end{array}\right]
+ \ \left(\large\begin{array}
+ \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz}
+ \end{array}\right)"
+ alt="" border=0 align=middle></a> </td>
+ <td align="left">
+ Block diagonal form using nested <b>\begin{array}</b>'s.<br>
+ Also, note rows aligned across all three arrays.
+ </td>
+ </tr>
+
+<!-- tenth example: demonstrating \begin{eqnarray} to align equations
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(10)</font> </td>
+ <td align="center">
+ <a href="#preview">
+ <img id="example10" onclick="eqntext('example10')"
+ src="../cgi-bin/mimetex.cgi?\large\left.\begin{eqnarray}
+ x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ using <a href="#array">\begin{eqnarray}</a> to align equations </td>
+ </tr>
+
+<!-- eleventh example: demonstrating commutative diagram
+using \longxxxarrow[] and \begin{array}
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(11)</font> </td>
+ <td align="center">
+ <a href="#preview">
+ <img id="example11" onclick="eqntext('example11')"
+ src="../cgi-bin/mimetex.cgi?\Large\begin{array}{rccclBCB}
+ &f&\longrightarrow[75]^{\alpha:{\normalsize f\rightarrow g}}&g\\
+ \large\gamma&\longdownarrow[50]&&\longdownarrow[50]&\large\gamma\\
+ &u&\longrightarrow[75]_\beta&v\end{array}"
+ alt="" border=0 align=middle></a> </td>
+ <td>
+ commutative diagram using <a href="#array">\begin{array}</a> </td>
+ </tr>
+
+<!-- twelfth example: demonstrating \picture
++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(12)</font> </td>
+ <td align="left">
+ <a href="#preview">
+ <img id="example12" onclick="eqntext('example12')"
+ src="../cgi-bin/mimetex.cgi?\large\hspace{5}\unitlength{1}
+ \picture(175,100){ (50,50){\circle(100)}
+ (1,50){\overbrace{\line(46)}^{3$\;\;a}}
+ (52,50){\line(125)} (50,52;115;2){\mid} (52,55){\longleftar[60]}
+ (130,56){\longrightar[35]} (116,58){\small r}
+ (c85,50;80;2){\small\bullet} (c85,36){\small -q} (c165,36){\small q}
+ (42,29){\underbrace{\line(32)}_{\scriptsize a^2/r\;\;\;}} }"
+ alt="" border=0 align=middle></a> </td>
+ <td valign="middle">
+ mimeTeX <a href="#picture">\picture(size){pic_elems}</a>
+ "environment", illustrating the image charge <b>- q</b>
+ for a grounded conducting sphere of radius <b>a</b> with
+ a charge <b>q</b> at distance <b>r &gt; a</b> outside it. </td>
+ </tr>
+
+<!-- thirteenth example: demonstrating \picture
++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+ <tr>
+ <td>
+ <font size=5>(13)</font> </td>
+ <td align="left">
+ <a href="#preview">
+ <img id="example13" onclick="eqntext('example13')"
+ src="../cgi-bin/mimetex.cgi?\small\hspace{10}\unitlength{.75}
+ \picture(120,220){ (60,200){\circle(120,40)} (0,20){\line(0,180)}
+ (5,189;0,-30){\pict(110,20){(c20,10;70;2){
+ \pict(40,20){(20,10){\circle(40,20)}(c10,10)+(c30,10)-}} } }
+ (119,20){\line(0,180)} (60,20){\circle(120,40;34)}}"
+ alt="" border=0 align=middle></a> </td>
+ <td valign="middle"> <a href="#picture">\picture</a> "environment"
+ illustrating the surface polarization charge induced by a uniform
+ electric field. Inside the slab of material, the volume polarization
+ charge clearly vanishes. <br><br> The little
+ <img src="../cgi-bin/mimetex.cgi?\small\unitlength{.75} \pict(40,20){(20,10)
+ {\circle(40,20)}(c10,10)+(c30,10)-}" alt="" border=0 align=middle>
+ dipole image is drawn only once, then multiput across two columns, and
+ then that result is further multiput down the rows. MimeTeX \picture's
+ can be used as picture elements in other pictures, nested to any level.
+ The image at left is picture-in-picture-in-picture. </td>
+ </tr>
+</table>
+
+<!-- font examples
+++++++++++++++++++ -->
+<!-- font-size-examples-commented-out ---
+<br><br>
+<h3> Some font examples <font size=5>...</font></a> </h3>
+ <p> Finally, illustrated below are some examples of fonts and symbols
+ available with mimeTeX. All symbols and sizes from cmr, cmmi,
+ cmmib (use <b>\mathbf{&nbsp;}</b>), cmsy, cmex, bbold (use
+ <b>\mathbb{&nbsp;}</b>), rsfs (use <b>\mathscr{&nbsp;}</b>),
+ stmary and cyrillic wncyr (use <b>{\cyr&nbsp;&nbsp;}</b> or
+ <b>\cyr{&nbsp;}</b>) should be available, but they're not all shown.
+ And also not shown are various "constructed symbols" like \sqrt,
+ accents, etc. The illustrated font sizes are numbered 4=\Large,
+ 3=\large and 2=\normalsize (not shown are 7=\Huge, 6=\huge,
+ 5=\LARGE, 1=\small and 0=\tiny). </p>
+
+<h3>cmmi latin uppercase, and lowercase</h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$A&4$B&4$C&4$D,&4$a&4$b&4$c&4$d\\
+2$\rm~3:~&3$E&3$F&3$G&3$H&3$I&3$J&3$K&3$L,&3$e&3$f&3$g&3$h&3$i&3$j&3$k&3$l\\
+2$\rm~2:~&2$M&2$N&2$O&2$P&2$Q&2$R&2$S&2$T&2$U&2$V&2$W&2$X&2$Y&2$Z,&
+2$m&2$n&2$o&2$p&2$q&2$r&2$s&2$t&2$u&2$v&2$w&2$x&2$y&2$z}"
+alt="" border=0 align=middle> </p>
+
+<h3>calligraphic, and rsfs (<b>\cal{A}, \scr{B}, etc</b>)</h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\calA&4$\calB&4$\calC&4$\calD&4$\calE&4$\calF&4$\calG,&
+4$\scrA&4$\scrB&4$\scrC&4$\scrD&4$\scrE&4$\scrF&4$\scrG\\
+2$\rm~3:~&3$\calH&3$\calI&3$\calJ&3$\calK&3$\calL&3$\calM&3$\calN&3$\calO&
+3$\calP,&
+3$\scrH&3$\scrI&3$\scrJ&3$\scrK&3$\scrL&3$\scrM&3$\scrN&3$\scrO&3$\scrP\\
+2$\rm~2:~&2$\calQ&2$\calR&2$\calS&2$\calT&2$\calU&
+2$\calV&2$\calW&2$\calX&2$\calY&2$\calZ,&
+2$\scrQ&2$\scrR&2$\scrS&2$\scrT&2$\scrU&2$\scrV&2$\scrW&
+2$\scrX&2$\scrY&2$\scrZ}"
+alt="" border=0 align=middle> </p>
+
+<h3>cmmi greek uppercase, and \var lowercase</h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\Gamma&4$\Delta&4$\Theta&4$\Lambda&4$\Xi&4$\Pi&4$\Sigma&
+4$\Upsilon&4$\Phi&4$\Psi&4$\Omega,&4$\rm~~&4$\varepsilon&4$\vartheta&4$\varpi&
+4$\varrho&4$\varsigma&4$\varphi\\
+2$\rm~3:~&3$\Gamma&3$\Delta&3$\Theta&3$\Lambda&3$\Xi&3$\Pi&3$\Sigma&
+3$\Upsilon&3$\Phi&3$\Psi&3$\Omega,&~&3$\varepsilon&3$\vartheta&3$\varpi&
+3$\varrho&3$\varsigma&3$\varphi\\
+2$\rm~2:~&2$\Gamma&2$\Delta&2$\Theta&2$\Lambda&2$\Xi&2$\Pi&2$\Sigma&
+2$\Upsilon&2$\Phi&2$\Psi&2$\Omega,&~&2$\varepsilon&2$\vartheta&2$\varpi&
+2$\varrho&2$\varsigma&2$\varphi}"
+alt="" border=0 align=middle> </p>
+
+<h3>cmmi greek lowercase</h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\alpha&4$\beta&4$\gamma&4$\delta&4$\epsilon&4$\zeta&
+4$\eta&4$\theta&4$\iota&4$\kappa&4$\lambda&4$\mu&4$\nu&4$\xi&4$%%\omicron%%&
+4$\pi&4$\rho&4$\sigma&4$\tau&4$\upsilon&4$\phi&4$\chi&4$\psi&4$\omega\\
+2$\rm~3:~&3$\alpha&3$\beta&3$\gamma&3$\delta&3$\epsilon&3$\zeta&
+3$\eta&3$\theta&3$\iota&3$\kappa&3$\lambda&3$\mu&3$\nu&3$\xi&3$%%\omicron%%&
+3$\pi&3$\rho&3$\sigma&3$\tau&3$\upsilon&3$\phi&3$\chi&3$\psi&3$\omega\\
+2$\rm~2:~&2$\alpha&2$\beta&2$\gamma&2$\delta&2$\epsilon&2$\zeta&
+2$\eta&2$\theta&2$\iota&2$\kappa&2$\lambda&2$\mu&2$\nu&2$\xi&2$%%\omicron%%&
+2$\pi&2$\rho&2$\sigma&2$\tau&2$\upsilon&2$\phi&2$\chi&2$\psi&2$\omega}"
+alt="" border=0 align=middle> </p>
+
+<h3>cmsy symbols at mimeTeX font size 3<br>
+<font size="3">(operators shown large are automatically "promoted"<br>
+to the larger size in \displaystyle mode)</font> </h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{3,r$1$\rm~chars~\\
+1$\rm~0-15:~&-&\cdot&\times&\ast&\div&\diamond&\pm&\mp&
+\oplus&\ominus&\otimes&\oslash&\odot&\bigcirc&\circ&\bullet\\
+1$\rm~16-31:~&\asymp&\equiv&\subseteq&\supseteq&\leq&\geq&\preceq&\succeq&
+\sim&\approx&\subset&\supset&\ll&\gg&\prec&\succ\\
+1$\rm~32-47:~&\leftar&\rightar&\uparr&\downar&\leftrightar&\near&\sear&
+\simeq&\Leftar&\Rightar&\Upar&\Downar&\Leftrightar&\nwar&\swar&\propto\\
+1$\rm~48-63:~&\prime&\infty&\in&\ni&\triangle&\bigtriangledo&/&\'&
+\forall&\exists&\neg&\emptyset&\Re&\Im&\top&\bot\\
+1$\rm~64-100:~&\aleph&&\calA&4$.\,.\,.&\calZ&&\cup&\cap&
+\uplus&\wedge&\vee&\vdash&\dashv&\lfloor&\rfloor&\lceil\\
+1$\rm~101-116:~&\rceil&\lbrace&\rbrace&\langle&\rangle&\mid&\parallel&
+\updownar&\Updownar&\setminus&\wr&\surd&\amalg&\nabla&\int&\sqcup\\
+1$\rm~117-127:~&\sqcap&\sqsubseteq&\sqsupseteq&\S&\dag&\ddag&\P&\clubsuit&
+\Diamond&\Heart&\spadesuit}" alt="" border=0 align=middle> </p>
+
+<h3>a few other cmmi, cmr, stmary and wncyr symbols
+at mimeTeX font size 4</h3>
+<p> <img src="../cgi-bin/mimetex.cgi?\array{4,r$
+1$\rm~cmmi:~&\leftharpoonup&\leftharpoondo&\rightharpoonup&\rightharpoondo&
+\triangleright&\triangleleft&\star&\partial&
+\flat&\natural&\sharp&\smile&\frown&\ell&\imath&\jmath&\wp&\vec\\
+1$\rm~cmr:~&\ss&\ae&\oe&\AE&\OE \\
+1$\rm~stmary:~&\moo&\Lbag&\Rbag&\lightning&\llbracket&\rrbracket&
+\subsetpluseq&\supsetpluseq&\Yup&\Ydown\\
+1$\rm~wncyr:~&\cyr A&\cyr a&\cyr B&\cyr b&\cyr V&\cyr v&\cyr G&\cyr g&
+\cyr D&\cyr d&\cyr Dj&\cyr dj&\cyr\=E&\cyr\=e&\cyr Zh&\cyr zh}"
+alt="" border=0 align=middle> </p>
+--- end-of-font-size-examples-commented-out -->
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+SCRIPTS & PLUGINS
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h2> <a name="scripts"> (Ic) Scripts &amp; Plugins &nbsp; </a> </h2>
+
+<p> Some useful scripts that automatically construct
+ mimeTeX &lt;img&gt; tags for you are illustrated below.
+ And you can also write your own scripts to simplify
+ the HTML notation required to incorporate mimeTeX
+ math images in your pages. </p>
+
+<h3> <a name="plugins">
+mimeTeX plugins<font size=5>...</font></a> </h3>
+<!-- p> There's no inherent need to repeatedly write the cumbersome
+ &lt;img&gt; tag illustrated above. You can write your own <a href=
+ "http://java.sun.com/j2ee/1.4/docs/tutorial/doc/JSPIntro9.html#wp73314"
+ target="_top">custom&nbsp;tags</a>,
+ or write a wrapper&nbsp;script around mimeTeX to simplify the
+ notation. </p -->
+
+<p style="margin-bottom:0"> <!-- For example, -->
+ The following javascript snippet (based on
+ <a href="http://www.mathtran.org" target="_top">mathtran</a>'s
+ <a href="http://www.mathtran.org/js/mathtran_img.js"
+ target="_top">mathtran_img.js</a>) lets you just write &nbsp;
+ <b>&lt;img&nbsp;alt="mimetex:c=\sqrt{a^2+b^2}"&gt;</b> &nbsp;
+ wherever you want to see&nbsp;<a href="#preview"><img id="imageJS1"
+ onclick="eqntext('imageJS1')" src="../cgi-bin/mimetex.cgi?
+ \normalsize c=\sqrt{a^2+b^2}" alt="" border=0
+ style="Vertical-Align:-1px"></a>&nbsp; </p>
+ <pre class="medium" style="margin-top:0;margin-bottom:0"
+> &lt;script type="text/javascript"&gt;
+ &lt;!--
+ // Create a namespace to hold variables and functions
+ mimetex = new Object();
+ // Change this to use your server
+ mimetex.imgSrc = "http://www.<i>yourdomain</i>.com/cgi-bin/mimetex.cgi?";
+ // Transform the whole document: add src to each img with
+ // alt text starting with "mimetex:", unless img already has a src.
+ mimetex.init = function () {
+ if (! document.getElementsByTagName) return;
+ var objs = document.getElementsByTagName("img");
+ var len = objs.length;
+ for (i=0; i&lt;len; i++) {
+ var img = objs[i];
+ if (img.alt.substring(0,8) == 'mimetex:')
+ if (!img.src) {
+ var tex_src = img.alt.substring(8);
+ img.src = mimetex.imgSrc + encodeURIComponent(tex_src);
+ // Append TEX to the class of the IMG.
+ img.className +=' tex'; }
+ }
+ mimetex.hideElementById("mimetex.error"); }
+ // Utility function
+ mimetex.hideElementById = function (id) {
+ var obj = document.getElementById(id);
+ if (obj) obj.style.display = 'none'; }
+ // resolve a cross-browser issue (see <a href="http://scottandrew.com/weblog/articles/cbs-events" target="_top">CBS&nbsp;events</a>)
+ mimetex.addEvent = function (obj, evType, fn, useCapture) {
+ if (obj.addEventListener) { //For Mozilla.
+ obj.addEventListener(evType, fn, useCapture);
+ return true; }
+ else if (obj.attachEvent) { //For Internet Explorer.
+ var r = obj.attachEvent("on"+evType, fn);
+ return r; }
+ }
+ // Initialize after entire document is loaded
+ mimetex.addEvent(window, 'load', mimetex.init, false);
+ --&gt;
+ &lt;/script&gt;</pre>
+
+<p style="margin-bottom:0">
+ Bulletin boards, wikis, etc, can also incorporate mimeTeX images
+ with short scripts. For example, if you're using
+ <a href="http://www.phpbb.com" target="_top">phpBB2</a>, then
+ <a href="http://www.themathforum.com/" target="_top">Jameson</a>
+ contributed the following typical one-line mod that lets you write
+ <b>[tex]&nbsp;c=\sqrt{a^2+b^2}&nbsp;[/tex]</b> to obtain the
+ same&nbsp;<a href="#preview"><img id="imageJS2"
+ onclick="eqntext('imageJS2')" src="../cgi-bin/mimetex.cgi?
+ \normalsize c=\sqrt{a^2+b^2}" alt="" border=0
+ style="Vertical-Align:-1px"></a> image illustrated above&nbsp; </p>
+ <pre class="medium" style="margin-top:0;margin-bottom:0"
+> #--------[open]-----------------------------------------------------
+ /includes/bbcode.php
+ #--------[find]-----------------------------------------------------
+ // Remove our padding from the string..
+ #--------[before, add]----------------------------------------------
+ $text = preg_replace('/\[tex\](.*?)\[\/tex\]/ie',
+ "'&lt;img src=\"/cgi-bin/mimetex.cgi?'.rawurlencode('$1').'\" align=\"middle\" /&gt;'",
+ $text);</pre>
+<p class="continue" style="margin-top:0"> If you're using
+ <a href="http://www.phpbb.com" target="_top">phpBB3</a>,
+ then no mod is even needed.
+ Just click Postings from the Administrator Control Panel,
+ and add the custom BBCode&nbsp;<b>[tex]{TEXT}[/tex]</b> &nbsp;
+ with the HTML replacement
+ <b>&lt;img&nbsp;src="/cgi-bin/mimetex.cgi?{TEXT}"&nbsp;align=middle&gt;</b></p>
+
+<p> Similarly, <a href="http://www.pmwiki.org/" target="_top">PmWiki</a>
+ also has a
+ <a href="http://www.pmwiki.org/wiki/Cookbook/MimeTeX" target="_top">
+ mimeTeX&nbsp;plugin</a> that lets you just write
+ <b>{$&nbsp;f(x)=\int_{-\infty}^xe^{-t^2}dt&nbsp;$}</b>
+ to obtain that same image. &nbsp; Several other packages
+ also have similar mimeTeX plugins: </p>
+ <center><table>
+ <tr> <td align=center> <u>&nbsp;<b>Package</b>&nbsp;</u> </td>
+ <td> &nbsp; </td>
+ <td align=center> <u>&nbsp;&nbsp;<b>Plugin</b>&nbsp;&nbsp;</u> </td>
+ </tr>
+ <tr> <td align=center>
+ <a href="http://www.pmwiki.org" target="_top">
+ PmWiki</a> </td> <td> &nbsp; </td>
+ <td align=center>
+ <a href="http://www.pmwiki.org/wiki/Cookbook/MimeTeX"
+ target="_top">mimeTeX&nbsp;plugin</a> </td> </tr>
+ <tr> <td align=center>
+ <!-- a href="http://www.wikimedia.org/wiki/Main_Page" -->
+ <!-- a href="http://www.wikimediafoundation.org/wiki/Main_Page" -->
+ <a href="http://www.mediawiki.org/wiki/MediaWiki"
+ target="_top">MediaWiki</a> </td>
+ <td align=center> &nbsp; </td>
+ <td align=center>
+ <!-- a href="http://meta.wikimedia.org/wiki/Mimetex_alternative" -->
+ <a href="http://www.mediawiki.org/wiki/Mimetex_alternative"
+ target="_top">&quot;mimeTeX&nbsp;alternative&quot;</a> </td> </tr>
+<!-- ***redirect loop***
+ <tr> <td align=center>
+ <a href="http://www.unitorganizer.com/mathwiki/index.php/Main_Page"
+ target="_top">MathWiki</a> </td> <td> &nbsp; </td>
+ <td align=center> <a href=
+ "http://www.unitorganizer.com/mathwiki/index.php/MimetexParser"
+ target="_top">&quot;mimeTeX&nbsp;Parser&quot;</a> </td> </tr>
+-->
+ <tr> <td align=center>
+ <a href="http://forums.punbb.org/" target="_top">PunBB</a> </td>
+ <td> &nbsp; </td> <td align=center>
+ <a href="http://www.math-linux.com/spip.php?article44"
+ target="_top">mimeTeX&nbsp;plugin</a> </td> </tr>
+ <tr> <td align=center>
+ <!-- a href="http://www.sixapart.com/movabletype/" -->
+ <a href="http://www.movabletype.com/"
+ target="_top">Movable&nbsp;Type</a> </td> <td> &nbsp; </td>
+ <td align=center> <a href=
+ "http://www.unitorganizer.com/myblog/2006/08/creating_equations_in_movable.html"
+ target="_top">mimeTeX&nbsp;plugin</a> </td> </tr>
+ <tr> <td align=center>
+ <a href="http://wordpress.org/" target="_top">WordPress</a> </td>
+ <td> &nbsp; </td> <td align=center> <a href=
+ "http://www.anlak.com/?page_id=66" target="_top">
+ <!-- "http://sixthform.info/steve/wordpress/index.php?p=13&page=2" -->
+ mimeTeX&nbsp;plugin</a> <!-- &nbsp; (see item 9) --> </td> </tr>
+ <tr> <td align=center>
+ <a href="http://www.joomla.org/"
+ target="_top">Joomla</a> </td> <td> &nbsp; </td>
+ <td align=center> <a href=
+ "http://extensions.joomla.org/component/option,com_mtree/task,viewlink/link_id,5932/Itemid,35/"
+ target="_top">mimeTeX&nbsp;plugin</a> </td> </tr>
+ <tr> <td align=center>
+ <a href="http://mambo-foundation.org/"
+ target="_top">Mambo</a> </td> <td> &nbsp; </td>
+ <td align=center> <a href=
+ "http://webscripts.softpedia.com/script/Modules/Joomla-Mambo-Modules/MimeTeX-Bot-9250.html"
+ target="_top">&quot;mimeTeX&nbsp;bot&quot;</a> </td> </tr>
+ <!--- dead links --->
+ <!-- tr> <td align=center>
+ <a href="http://www.phpbb.com" target="_top">phpBB</a> </td>
+ <td> &nbsp; </td> <td align=center>
+ <a href=
+ "http://www.themathforum.com/math/showthread.php?p=621#post621"
+ target="_top">mimeTeX&nbsp;plugin</a> </td> </tr -->
+ <!-- tr> <td align=center>
+ <a href="http://www.mamboserver.com/" target="_top">Mambo</a> </td>
+ <td> &nbsp; </td> <td align=center>
+ <a href="http://mamboxchange.com/projects/mimetexbot/"
+ target="_top">&quot;mimeTeX&nbsp;bot&quot;</a> </td> </tr -->
+ </table></center>
+
+<p> <b>Please note:</b> If you're writing your own plugin for mimeTeX,
+ please don't write php code using <b>system(&nbsp;)</b>, or any other
+ shell escape mechanism, just to cache images. Use mimeTeX's
+ &nbsp; <b>-DCACHEPATH=\&quot;<i>path/</i>\&quot;</b> &nbsp;
+ <a href="#options">compile&nbsp;option</a> instead.
+ <b>system(&nbsp;)</b> raises security
+ issues, either real ones if used carelessly, or just in the minds of
+ system administrators. Either way, I've received many emails from
+ people unable to use mimeTeX because of unnecessary <b>system(&nbsp;)</b>
+ calls prohibited by security-conscious sysadmins. MimeTeX itself poses
+ minimal risk when used as illustrated above, but you're responsible
+ for any plugin/wrapper script you write around it. </p>
+
+<h3> <a name="valignment">
+Vertical alignment<font size=5>...</font></a> </h3>
+<p> An image like
+ <a href="#preview"><img id="imageAV1" onclick="eqntext('imageAV1')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize f(x)=\int\limits_{-\infty}^xe^{-t^2}dt"
+ alt="" border=0 align=middle></a>
+ doesn't look as good as the same image
+ <a href="#preview"><img id="imageAV2" onclick="eqntext('imageAV2')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize f(x)=\int\limits_{-\infty}^xe^{-t^2}dt"
+ alt="" border=0 style="Vertical-Align:-26px"></a>
+ that's vertically aligned with your surrounding text.
+ Along with several standard
+ <a href="http://www.w3.org/Protocols/rfc2616/rfc2616-sec14.html">
+ HTTP&nbsp;header&nbsp;fields</a>, mimeTeX also emits a special
+ &nbsp; <b>Vertical-Align:&nbsp;&#150;<i>nn</i></b> &nbsp;
+ header, where <b>&#150;<i>nn</i></b> is the number of pixels
+ (usually negative as illustrated) needed for a
+ &nbsp; <b>style="Vertical-Align:&nbsp;&#150;<i>nn</i>&nbsp;px"</b>
+ &nbsp; attribute in the <b>&lt;img&gt;</b>&nbsp;tag used to
+ render your expression. This Vertical-Align:&nbsp;header
+ is obtained by placing the directive &nbsp;<b>\depth</b>&nbsp;
+ anywhere in your expression. </p>
+
+<p> But mimeTeX's special Vertical-Align: header
+ is unrecognized and ignored by your browser. You have to get the
+ header, interpret it, and write the corresponding &lt;img&gt; tag.
+ The only feasible way to do all this is using a scripting language,
+ as illustrated by the following, rather naive, php code </p>
+ <pre class="medium" style="margin-top:.5em;margin-bottom:.5em"
+> &lt;?php
+ $mimetexurl = "http://www.<i>yourdomain</i>.com/cgi-bin/mimetex.cgi?";
+ function verticalalign( $expression ) {
+ global $mimetexurl;
+ // note: curl_init() stops at the first whitespace char in $url argument
+ $expression = ereg_replace(" ","~",$expression); // so remove whitespace
+ $url = $mimetexurl . "\depth~" . $expression;
+ $valign = "0";
+ $ch = curl_init( $url );
+ curl_setopt( $ch, CURLOPT_RETURNTRANSFER, true );
+ curl_setopt( $ch, CURLOPT_HEADER, true );
+ $gif = curl_exec( $ch );
+ $errno = curl_errno( $ch );
+ curl_close( $ch );
+ if ( $errno == 0 ) {
+ $fields = explode("Vertical-Align:",$gif);
+ $vfield = trim($fields[1]);
+ $fldlen = strspn($vfield,"+-0123456789");
+ $valign = substr($vfield,0,$fldlen); }
+ return $valign;
+ }
+ function mimetextag( $expression ) {
+ global $mimetexurl;
+ $valign = verticalalign($expression);
+ $url = $mimetexurl . "\depth~" . $expression;
+ echo ' &lt;img src="',$url,'" ';
+ echo ' style="Vertical-Align:',$valign,'px" ';
+ echo ' alt="" border=0&gt;', "\n";
+ }
+ ?&gt;</pre>
+
+<p> Now you can write &nbsp;
+ &lt;?php&nbsp;mimetextag('\frac12\left(a^2+b^2\right)');&nbsp;?&gt;
+ wherever you want to see
+ <a href="#preview"><img id="imageAV5" onclick="eqntext('imageAV5')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\frac12\left(a^2+b^2\right)"
+ alt="" border=0 style="Vertical-Align:-7px"></a>
+ correctly aligned. Note that the php code automatically
+ prepends &nbsp;<b>\depth</b>&nbsp; to your expression for you.
+ <!-- Besides making you escape backslashes
+ (each&nbsp;&#092;&nbsp;must be written&nbsp;&#092;&#092;), -->
+ (Also note that this code calls mimeTeX twice to render each
+ expression, once to get the Vertical-Align: header and build
+ an &lt;img&gt; tag, and then again to render that tag.
+ If you're a good php programmer and write better code,
+ please email me a copy.) </p>
+
+<p> If you're using mimeTeX's
+ &nbsp; <b>-DCACHEPATH=\&quot;<i>path</i>/\&quot;</b> &nbsp;
+ <a href="#options">compile&nbsp;option</a>, you can request
+ that all images be cached with Vertical-Align:&nbsp;headers,
+ whether or not they contain the \depth directive. Prefix your
+ <b><i>path</i>/</b> with a leading&nbsp;<b>&#037;</b> and write &nbsp;
+ <b>-DCACHEPATH=\&quot;&#037;<i>path</i>/\&quot;</b> &nbsp; instead.
+ That leading&nbsp;<b>&#037;</b> won't become part of your cache
+ directory's <b><i>path</i>/</b>, but it will signal mimeTeX
+ to cache headers along with each image. (In this case,
+ the directive &nbsp;<b>\nodepth</b>&nbsp; suppresses
+ mimeTeX's header caching for that image.)
+ <!-- Otherwise, the Vertical-Align: information is lost,
+ and attempts to align cached images will fail. --> </p>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+GPL
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h2> <a name="gpl"> (Id) GPL License &nbsp; </a> </h2>
+
+<font color="black">
+<b>&quot</b><i>My grandfather once told me there are two kinds of people:<br>
+&nbsp &nbsp Those who do the work and those who take the credit.<br>
+&nbsp &nbsp He told me to try to be in the first group; there was much
+less competition.</i><b>&quot</b><br>
+Indira Gandhi, the late Prime Minister of India</font> <br>
+
+ <p> MimeTeX's copyright is registered by me with the US Copyright Office,
+ and I hereby license it to you under the terms and conditions of the
+ <a href="http://www.gnu.org/licenses/gpl.html" target="_top">GPL</a>.
+ There is no official support of any kind whatsoever,
+ and you use mimeTeX entirely at your own risk, with no guarantee
+ of any kind, in particular with no warranty of merchantability. </p>
+
+ <p> By using mimeTeX, you warrant that you have read, understood
+ and agreed to these terms and conditions, and that you <!-- are at least
+ 18 years of age and --> possess the legal right and ability to enter
+ into this agreement and to use mimeTeX in accordance with it. </p>
+
+ <p> Hopefully, the law and ethics regarding computer programs will
+ evolve to make this kind of obnoxious banter unnecessary.
+ In the meantime, please forgive me my paranoia. </p>
+
+ <p> To protect your own intellectual property, I recommend (both are pdf)
+ <a href="http://www.copyright.gov/circs/circ01.pdf"
+ target="_top">Copyright&nbsp;Basics</a> from The Library of Congress,
+ in particular <a href="http://www.copyright.gov/circs/circ61.pdf"
+ target="_top">Circular&nbsp;61</a>, Copyright Registration for
+ Computer Programs.
+ <!-- and similarly,
+ <a href="http://www.abanet.org/intelprop/comm106/106copy.html"
+ target="_top">Copyright Basics</a> from The American Bar Association. -->
+ Very briefly, download
+ <a href="http://www.copyright.gov/forms/formtxi.pdf">Form&nbsp;TX</a>
+ and follow the included instructions.
+ In principle, you automatically own the copyright
+ to anything you write the moment it's on paper. In practice,
+ if the matter comes under dispute, the courts look _very_ favorably
+ on you for demonstrating your intent by registering the copyright.
+ <!-- For example, courts will stop unauthorized use of unregistered
+ material, but monetary damages are awarded _only_ if you
+ register the copyright before infringement occurs. --> </p>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+SECTION II. BUILDING MIMETEX
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h1> <a name="build"> (II) Building mimeTeX &nbsp; </a> </h1>
+
+<!-- <center> -->
+ <table border="0" cellpadding="0" cellspacing="0">
+ <tr><td><center><hr size="2">Very quickly &nbsp; --- &nbsp; download
+ <a href="http://www.forkosh.com/mimetex.zip">
+ <!-- jfa <a href="ftp://ftp.tex.ac.uk/tex-archive/support/mimetex/mimetex.zip"></a> -->
+ mimetex.zip</a> and then type
+ <table border="0" cellpadding="0" cellspacing="0">
+ <tr align="left">
+ <td><img src="../cgi-bin/mimetex.cgi?\hspace{50}" alt="" border=0></td>
+ <td><b>unzip mimetex.zip</b> <br>
+ <b>cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi</b></td>
+ </tr></table>
+ &nbsp; &nbsp; &nbsp; Now <b>mv</b> mimetex.cgi to your <b>cgi-bin/</b>
+ directory, and you're all done. &nbsp; &nbsp; &nbsp; <br>
+ Read the rest of this section for more detailed
+ information.<hr size="2"></center></td>
+ <td><img src="../cgi-bin/mimetex.cgi?\hspace{150}" alt="" border=0></td>
+ </tr></table>
+<!-- </center> -->
+
+<p> I've built and run mimeTeX under Linux and NetBSD using gcc. The source
+ code is ansi-standard C, and should compile and run under all
+ environments without change. Instructions below
+ are for Unix. Modify them as necessary for your particular situation
+ (note the -DWINDOWS switch if applicable). </p>
+
+<h2> <a name="compile"> (IIa) Download and Compile &nbsp; </a> </h2>
+
+ <p> The steps needed to download and compile mimeTeX are </p>
+ <ul>
+ <li> Download and unzip
+ <a href="http://www.forkosh.com/mimetex.zip">
+ <!-- jfa <a href="ftp://ftp.tex.ac.uk/tex-archive/support/mimetex/mimetex.zip"></a> -->
+ mimetex.zip</a> in any convenient working directory.
+ Your working directory should now contain <center>
+ <table cellpadding=0 cellspacing=0>
+ <tr><td width=100>README</td> <td>mimeTeX release notes</td></tr>
+ <tr><td>COPYING</td> <td>GPL license, under which you may use
+ mimeTeX</td></tr>
+ <tr><td>mimetex.c</td> <td>mimeTeX source program and all required
+ functions</td></tr>
+ <tr><td>mimetex.h</td> <td>header file for mimetex.c (and for
+ gfuntype.c)</td></tr>
+ <tr><td>gfuntype.c</td> <td>parses output from <b>gftype -i</b>
+ and writes bitmap data</td></tr>
+ <tr><td>texfonts.h</td> <td>output from several <b>gfuntype</b> runs,
+ needed by mimetex.c</td></tr>
+ <tr><td>gifsave.c</td> <td>gif library by Sverre H. Huseby
+ <a href="http://shh.thathost.com"
+ target="_top">http://shh.thathost.com</a>
+ </td></tr>
+ <tr><td>mimetex.html</td> <td>this file, the mimeTeX
+ user's manual</td></tr>
+ </table></center>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ Note: all files use Unix line termination, i.e., linefeeds
+ (without carriage returns) signal line endings. Conversion for
+ Windows PC's, Macs, VMS, etc, can usually be accomplished by
+ unzip's&nbsp;-a option, i.e., unzip&nbsp;-a&nbsp;mimetex.zip
+ <br> <br> </li>
+ <li> To compile an executable that emits anti-aliased gif images
+ (which is recommended for most uses), just type the following
+ command from the Unix shell <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi</b> </li>
+ <li> Or, to compile an executable that emit gif images
+ without anti-aliasing <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>cc -DGIF mimetex.c gifsave.c -lm -o mimetex.cgi</b> </li>
+ <li> Alternatively, to compile an executable that emits mime xbitmaps<br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>cc -DXBITMAP mimetex.c -lm -o mimetex.cgi</b> </li>
+ <li> Compile Notes: <ul>
+ <li> If (and only if) you're compiling a Windows executable with
+ the <b>-DAA</b> or <b>-DGIF</b> option (but not -DXBITMAP), then
+ add <b>-DWINDOWS</b>&nbsp;. For example, <br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp; <b>gcc -DAA -DWINDOWS
+ mimetex.c gifsave.c -lm -o mimetex.exe</b> </nobr> <br>
+ The above Unix-like syntax works with
+ <a href="http://www.mingw.org" target="_top">MinGW</a> and
+ <a href="http://www.delorie.com/djgpp/" target="_top">djgpp</a>
+ Windows compilers, but probably not with most others,
+ where it's only intended as a "template". <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ Explanation: mimeTeX writes gif bytes directly to stdout, as usual
+ for cgi's. But Windows treats stdout as a character stream,
+ interpreting any hex 0A byte as an &lt;lf&gt;, and automatically
+ preceding it with a spurious hex 0D &nbsp; &lt;cr&gt; byte. The
+ -DWINDOWS switch compiles in a non-portable, Windows-specific
+ _setmode() call that sets stdout to binary mode. </li>
+ <li> If you're compiling for Windows and would prefer
+ to install mimeTeX as a Win32 DLL, see the
+ <a href="http://www.codeproject.com/dotnet/Eq2Img.asp">
+ Code&nbsp;Project</a> developed by
+ <a href="http://www.shitalshah.com">Shital&nbsp;Shah</a>, and
+ download <a href="http://www.shitalshah.com/dev/eq2img_all.zip">
+ eq2img_all.zip</a> containing Shital's latest code. </li>
+ <li> If you install mimeTeX on one server and try to use it
+ from another, you may instead see messages like <br>
+ <img src="../cgi-bin/mimetex.cgi?\message{3}"
+ alt="" align="middle" border=0> <br>
+ In this case, compile mimetex.cgi with the -DNOREFCHECK switch,
+ <i>e.g.</i>,<br>
+ <nobr> &nbsp; &nbsp; &nbsp; &nbsp; <b>cc -DAA -DNOREFCHECK
+ mimetex.c gifsave.c -lm -o mimetex.cgi</b> </nobr> <br>
+ and read the -DREFLEVELS=<i>n</i> discussion under
+ <a href="#options">compile&nbsp;options</a> below. </li>
+ <!-- <li> If you're compiling on Sun or VMS, and see about a zillion
+ irritating warnings, try adding <b>-DSIGNEDCHAR</b>
+ (for VMS, that's cc/define=(AA,SIGNEDCHAR)&nbsp;mimetex.c) </li> -->
+ </ul> <br> </li>
+ <li> The gfuntype program is only needed if you plan to change the
+ font information in texfonts.h, as explained in
+ <a href="#fonts">Appendix IVa</a> below.
+ In that case, compile gfuntype with the command <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>cc gfuntype.c mimetex.c -lm -o gfuntype</b> </li>
+ </ul>
+ <p> That's all there is to compiling mimeTeX.
+ Several other optional compile-line <a href="#options">options</a>
+ available for mimetex.c are discussed below. </p>
+
+ <p> Immediately after compiling mimeTeX, test your new executable
+ by typing &nbsp; <b>./mimetex.cgi&nbsp;"x^2+y^2"</b> &nbsp;
+ from the Unix shell (or &nbsp; <b>mimetex&nbsp;"x^2+y^2"</b>
+ &nbsp; from the Windows Command Prompt), which should emit
+ two "ascii&nbsp;rasters" something like the following </p> <pre>
+Ascii dump of bitmap image... Hex dump of colormap indexes...
+...........**....................**... ..........1**1...................1**1..
+..........*..*......*...........*..*.. ..........*23*......*............*23*..
+.............*......*..............*.. .............*......*...............*..
+....****.....*......*.....*..*.....*.. ...1****....2*......*.....2*..*....2*..
+...*.*.*....*.......*....**..*....*... ...*.*.*...1*.......*.....**..*...1*...
+.....*.....*.*..********..*..*...*.*.. ....1*1...2*.*..********..3*..*..2*.*..
+.....*....****......*.....*..*..****.. ....2*2...****......*......*12*..****..
+..*.*.*.............*.....*.*......... ..*.*.*.............*......*.*2........
+...****.............*.....***......... ..1****.............*......***.........
+....................*.......*......... ....................*........*.........
+.........................*.*.......... ..........................*.*1.........
+.........................**........... ..........................**1..........
+ The 5 colormap indexes denote rgb vals...
+ .-->255 1-->196 2-->186 3-->177 *-->0</pre>
+ <p class="continue"> <b>(</b>The right-hand illustration shows asterisks
+ in the same positions as the left-hand one, along with anti-aliased
+ grayscale colormap indexes assigned to neighboring pixels, and with
+ the rgb value for each index.<b>)</b> Just typing <b>./mimetex.cgi</b>
+ without an argument should produce ascii rasters for the default
+ expression <b>f(x)=x^2</b>. If you see these two ascii rasters then
+ your binary's good. Otherwise, you must find and fix the problem
+ before proceeding. </p>
+
+
+<h2> <a name="install"> (IIb) Install &nbsp; </a> </h2>
+
+ <p> Once you've successfully tested mimetex.cgi from the Unix shell
+ (or mimetex.exe from the Windows Command Prompt),
+ the steps needed to install mimeTeX are </p>
+ <ul>
+ <li> <b>mv</b> mimetex.cgi &nbsp; (or <b>move</b> mimetex.exe) &nbsp;
+ to your server's <b>cgi-bin/</b> directory, wherever cgi
+ programs are expected. </li>
+ <li> Now you may need to <b>chmod&nbsp;755&nbsp;mimetex.cgi</b> &nbsp;
+ and/or <b>chown</b> it, too, depending on your server's
+ requirements. Contact your system administrator or ISP
+ if you're not already familiar with this information. </li>
+ <li> Once mimetex.cgi is moved to your server's <b>cgi-bin/</b>
+ directory, with permissions and owner set as necessary,
+ you're all done. </li>
+ </ul>
+
+ <p> Immediately after installing mimeTeX, test your new mimetex.cgi
+ by typing a url into your browser's locator window something like <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>http://www.<i>yourdomain</i>.com/cgi-bin/mimetex.cgi?x^2+y^2</b> <br>
+ which should display &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?\normalsize x^2+y^2" alt="" border=0
+ style="Vertical-Align:-3px"> &nbsp;
+ in the upper-left corner of your window,
+ just like clicking this link does, which tests my mimetex.cgi, <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <a href="http://www.forkosh.com/cgi-bin/mimetex.cgi?x^2+y^2"
+ target="_top">http://www.forkosh.com/cgi-bin/mimetex.cgi?x^2+y^2</a><br>
+ If you see the same &nbsp; <img src="../cgi-bin/mimetex.cgi?
+ \normalsize x^2+y^2" alt="" border=0 style="Vertical-Align:-3px"> &nbsp;
+ image from the <b><i>yourdomain</i></b> link, then you've completed
+ a successful mimeTeX installation. </p>
+
+ <p> If you don't see the image, then your installation failed.
+ If your earlier post-compilation "ascii&nbsp;raster" test
+ succeeeded, then the problem is probably some server-specific
+ installation requirement. First make sure you installed mimetex.cgi
+ in the correct <b>cgi-bin/</b> directory, set the correct <b>chmod</b>
+ permissions, and typed the correct url into your browser's locator
+ window. Then contact your system administrator or ISP,
+ and ask how to install cgi programs on your server. </p>
+
+ <p> After you've successfully installed mimeTeX, and both preceeding tests
+ have succeeded, you can optionally &quot;regression&nbsp;test&quot;
+ all mimeTeX features as follows: </p>
+ <ul>
+ <li> <b>mv</b> mimetex.html (this file) to your server's
+ <b>htdocs/</b> directory </li>
+ <li> Paths to <b>cgi-bin/</b> and <b>htdocs/</b> directories
+ are typically <b><i>path</i>/www/cgi-bin/</b> and
+ <b><i>path</i>/www/htdocs/</b>, so I set up mimtex.html
+ to access mimetex.cgi from the relative path <b>../cgi-bin/</b>.
+ If your directories are non-conforming, you may have to edit
+ the few dozen occurrences of <b>../cgi-bin/mimetex.cgi</b>
+ in your mimetex.html page. Sometimes a suitable symlink works;
+ if not, you'll have to edit. Globally changing
+ <b>../cgi-bin/mimetex.cgi</b> usually works. </li>
+ <li> Now visit your page &nbsp;
+ <b>http://www.<i>yourdomain</i>.com/mimetex.html</b> </li>
+ <li> Once your mimetex.html displays properly, you can assume
+ everything is working, and can begin authoring html documents
+ using mimetex.cgi to render your own math. </li>
+ </ul>
+
+ <p> That's all there is to installing mimeTeX. </p>.
+
+
+<h2> <a name="options"> (IIc) Additional Compile-Line Options &nbsp; </a></h2>
+
+ <p> In addition to -DAA or -DGIF or -DXBITMAP (along with -DWINDOWS
+ when necessary) on the mimetex.c compile line, as discussed above,
+ you may also optionally include the following -D switches,
+ whose functionality is discussed below. </p>
+ <dl>
+ <dt> <b>-DAA</b> </dt>
+ <dd> As already discussed, -DAA turns on anti-aliasing.
+ It also sets default values for individual anti-aliasing
+ parameters discussed below. If you specify -DAA
+ then you needn't specify the individual parameters unless
+ you want to override the defaults. <br>
+ &nbsp; &nbsp; &nbsp; Anti-aliasing can't be applied to mime
+ xbitmaps, so don't specify -DAA if you also specify -DXBITMAP. <br>
+ &nbsp; &nbsp; &nbsp; And mimeTeX's anti-aliasing only works
+ well on white (or light gray) backgrounds. Your html file
+ probably contains a &lt;body&gt; tag of the form
+ &lt;body&nbsp;bgcolor="#ffffff"&nbsp;text="#000000"&gt;
+ which specifies black text on a pure white background.
+ The background can be grayed down to maybe bgcolor="#e7e7e7",
+ but much darker will begin to show white rings around
+ mimeTeX's anti-aliased characters. This page is displayed
+ using bgcolor="#ffffff". </dd>
+ <dt> <b>-DCENTERWT=<i>n</i> <br>
+ -DADJACENTWT=<i>j</i> <br>
+ -DCORNERWT=<i>k</i></b> </dt>
+ <dd> MimeTeX currently provides a lowpass filtering
+ algorithm for anti-aliasing, which is applied to the
+ existing set of bitmap fonts. This lowpass filter applies
+ weights <img src="../cgi-bin/mimetex.cgi?
+ \tiny\begin{pmatrix}1&2&1\\2&\,8\,&2\\1&2&1\end{pmatrix}"
+ alt="" border=0 align=middle> to neighboring pixels. The defaults
+ weights are CENTERWT=8, ADJACENTWT=2 and CORNERWT=1,
+ which you can adjust to control anti-aliasing. </dd>
+ <dt> <b>-DCACHEPATH=\"<i>path/</i>\"</b> </dt>
+ <dd> This option saves each rendered image to a file in directory
+ <b><i>path/</i></b>, which mimeTeX reads rather than
+ re-rendering the same image every time it's given
+ the same LaTeX expression. Sometimes mimeTeX disables caching,
+ e.g., expressions containing <b>\input{&nbsp;}</b> are
+ re-rendered since the contents of the inputted file may have
+ changed. If compiled without <b>-DCACHEPATH=\"<i>path/</i>\"</b>
+ mimeTeX always re-renders expressions. This usually isn't too
+ cpu intensive, but if you have unusually high hit rates then
+ image caching may be helpful. The <b><i>path/</i></b>
+ is relative to mimetex.cgi, and must be writable by it.
+ Files created under <b><i>path/</i></b> are named
+ <b><i>filename</i>.gif</b>, where <b><i>filename</i></b>
+ is the 32-character MD5 hash of your LaTeX expression. <br>
+ &nbsp; &nbsp; &nbsp; If you're also using mimeTeX's
+ <a href="#valignment">Vertical-Align:</a> feature, prefix your
+ <b><i>path</i>/</b> with a leading&nbsp;<b>&#037;</b> and write
+ &nbsp; <b>-DCACHEPATH=\&quot;&#037;<i>path</i>/\&quot;</b> &nbsp;
+ instead. That leading&nbsp;<b>&#037;</b> won't become part of
+ your cache directory's <b><i>path</i>/</b>, but it will signal
+ mimeTeX to cache headers along with each image.
+ Otherwise, the Vertical-Align: information is lost,
+ and attempts to align cached images will fail. <br>
+ &nbsp; &nbsp; &nbsp; When caching a new image, mimeTeX also
+ updates the file <b><i>path/</i>mimetex.log</b> containing
+ a timestamp, filename and LaTeX expression for each new file
+ created. A sample entry looks like
+<pre>---------------------------------------------------------------------
+2008-09-07:11:29:53am f8ccc8dd93c8eeb1d9c40b353ef781e0.gif
+\LARGE x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
+---------------------------------------------------------------------</pre></dd>
+ <dt><b>-DDEFAULTSIZE=<i>n</i></b> </dt>
+ <dd> MimeTeX currently has eight font sizes numbered 0-7,
+ and always starts out in DEFAULTSIZE, whose default value is 3.
+ Specify -DDEFAULTSIZE=2 on the compile line if you prefer
+ mimeTeX to start in default size 2, etc. </dd>
+ <dt><b>-DDISPLAYSIZE=<i>n</i></b> </dt>
+ <dd> By default, operator limits like <b>\int_a^b</b> are rendered
+ <b>\textstyle</b> <a href="#preview">
+ <img id="displaysize1" onclick="eqntext('displaysize1')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\displaystyle\smashmargin{2}{\int\nolimits_a}^b"
+ alt="" border=0 align=middle></a> at font sizes <b>\normalsize</b>
+ and smaller, and rendered <b>\displaystyle</b> <a href="#preview">
+ <img id="displaysize2" onclick="eqntext('displaysize2')"
+ src="../cgi-bin/mimetex.cgi?\large\int_a^b"
+ alt="" border=0 align=middle></a> at font sizes <b>\large</b> and
+ larger. This default corresponds to <b>-DDISPLAYSIZE=3</b>,
+ which you can adjust; e.g., <b>-DDISPLAYSIZE=0</b> always defaults
+ to <b>\displaystyle</b>, and <b>99</b> (or any large number)
+ always defaults to <b>\textstyle</b>. Note that explicit
+ <b>\textstyle</b>, <b>\displaystyle</b>, <b>\limits</b> or
+ <b>\nolimits</b> directives in an expression always override
+ the <b>DISPLAYSIZE</b> default. </dd>
+ <dt><b>-DGAMMA=<i>gammacorrection</i></b> </dt>
+ <dd> Applies <b><i>gammacorrection</i></b> to antialiased
+ gif images. Default is 1.25 (rather than the standard 2.2).
+ Specify 0.0 to turn off gamma correction (1.0 makes no
+ gamma correction but doesn't actually turn it off). </dd>
+ <dt><b>-DINPUTOK</b> </dt>
+ <dd> To enhance mimeTeX's security, the
+ <a href="#input">\input{&nbsp;}</a> command is disabled
+ by default when you compile mimeTeX. Note that the
+ <a href="#counter">\counter</a> and
+ <a href="#environment">\environment</a> commands are
+ also disabled by default, and <b>-DINPUTOK</b> enables
+ all three commands simultaneously. (Compile mimeTeX with
+ <b>-DCOUNTEROK</b> to enable only \counter, or with
+ <b>-DENVIRONOK</b> to enable only \environment.) <br>
+ &nbsp; &nbsp; &nbsp; Compiling mimeTeX with the
+ <b>-DINPUTOK</b> switch enables \input{&nbsp;} for all users,
+ subject only to your <b>-DPATHPREFIX</b> restrictions,
+ discussed below. And the following two switches give you
+ additional control over \input{&nbsp;}'s usage... </dd>
+ <dt> <b>-DINPUTPATH=\"<i>path</i>\" &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ -DINPUTPATH=\"<i>path1,path2,etc</i>\"</b> </dt>
+ <dd> Permits <b>\input{<i>filename</i>}</b> for specific
+ <i>filename</i>'s, even when the \input{&nbsp;} command
+ is otherwise disabled (for security). <br>
+ &nbsp; &nbsp; &nbsp; If INPUTPATH is defined, mimeTeX
+ performs a case-insensitive test of \input{&nbsp;}'s
+ <i>filename</i> argument, to verify that it contains
+ the authorized 'path' as a substring. <br>
+ &nbsp; &nbsp; &nbsp; If given several 'path's (second form)
+ then <i>filename</i> must contain either 'path1' or
+ 'path2', or etc, as a (case-insensitive) substring. <br>
+ &nbsp; &nbsp; &nbsp; If <i>filename</i> doesn't contain
+ a substring matching any of these path(s), then mimeTeX emits
+ an error message image instead of reading <i>filename</i>. </dd>
+ <dt> <b>-DINPUTREFERER=\"<i>domain</i>\" &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ -DINPUTREFERER=\"<i>domain1,domain2,etc</i>\"</b> </dt>
+ <dd> Permits <b>\input{&nbsp;}</b> for users from specific
+ <i>domain</i>'s, even when the \input{&nbsp;} command
+ is otherwise disabled (for security). <br>
+ &nbsp; &nbsp; &nbsp; If INPUTREFERER is defined
+ but INPUTOK is not defined, then mimeTeX
+ performs a case-insensitive test of the user's
+ HTTP_REFERER environment variable, to verify that it contains
+ the authorized 'domain' as a substring. <br>
+ &nbsp; &nbsp; &nbsp; If given several 'domain's (second form)
+ then HTTP_REFERER must contain either 'domain1' or
+ 'domain2', or etc, as a (case-insensitive) substring. <br>
+ &nbsp; &nbsp; &nbsp; If HTTP_REFERER doesn't contain
+ a substring matching any of these domain(s), then mimeTeX renders
+ an error message image instead of reading <i>filename</i>. <br>
+ &nbsp; &nbsp; &nbsp; Finally, if HTTP_REFERER is not found as
+ an environment variable, then mimeTeX renders the
+ same error message image. </dd>
+ <dt><b><a id="newcommands">-DNEWCOMMANDS=\"<i>newcommands.h</i>\"</a>
+ </b> </dt>
+ <dd> LaTeX-like <b>\newcommand</b>'s are available in mimeTeX,
+ via the following facility to help you define your
+ own "new&nbsp;commands" during compilation. Edit a file named
+ newcommands.h (or any filename you specify between
+ <b>\"...\"</b>'s with the <b>-DNEWCOMMANDS=\"<i>filename</i>\"</b>
+ switch). For newcommands _without_
+ arguments, your file should contain one or more lines
+ like the following examples:
+<pre>{ "\\iint", NULL, "{\\int\\int}" },
+{ "\\rightleftharpoons",NULL,"{\\rightharpoonup\\atop\\leftharpoondown}" },
+{ "\\ldots", NULL, "{\\Large.\\hspace1.\\hspace1.}" },
+{ "\\cr", NULL, "\\\\" },
+{ "\\neq", NULL, "{\\not=}" },</pre>
+ For newcommands _without_ arguments, as illustrated above,
+ the general form of each line in your file should be &nbsp;
+<b>{&nbsp;"\\<i>command</i>",&nbsp;NULL,&nbsp;"{<i>replacement</i>}"&nbsp;},</b>
+ &nbsp; &nbsp; Don't forget a comma at the end of every line,
+ and write a double&nbsp;backslash&nbsp;<b>\\</b>
+ between quotes&nbsp;<b>"...\\..."</b> wherever you actually
+ want a single&nbsp;backslash&nbsp;<b>\</b>. The only effect
+ of the above examples (without arguments) is simple string
+ substitution, i.e., every occurrence of <b>\<i>command</i></b>
+ is replaced by <b>{<i>replacement</i>}</b>. Note that the
+ <b>{&nbsp;}</b>'s surrounding <b><i>replacement</i></b>
+ aren't required, but are usually a good idea (the case
+ of <b>\cr</b> illustrated above is one exception, where
+ <b>{&nbsp;}</b>'s would defeat the purpose).
+ <br> &nbsp; &nbsp; To define newcommands _with_ arguments,
+ change the <b>NULL</b> after the <b>\\<i>command</i></b>
+ to define your command's arguments as illustrated by the
+ following example:
+<pre>{ "\\lvec", "2n", "#2_1,\\cdots,#2_{#1}" },</pre>
+ In this case the <b>NULL</b> has been replaced by <b>"2n"</b>
+ (note the mandatory surrounding quotes <b>"..."</b>). This
+ example corresponds to the similar one discussed in TLC2 on
+ page 845. The first character inside the <b>"..."</b>s is
+ &nbsp; <b>2</b> &nbsp; indicating the number of arguments,
+ which may be <b>1</b> thru <b>9</b>. If there are no
+ subsequent characters followng this one, then all arguments are
+ mandatory, enclosed in <b>{&nbsp;}</b>'s as usual. Otherwise,
+ any subsequent characters signal that the first argument
+ is optional, enclosed in <b>[&nbsp;]</b>'s if given. And
+ these subsequent characters comprise the first argument's
+ default value if it's not explicitly given. The illustrated
+ example's first argument is optional with default value &nbsp;
+ <b>n</b> &nbsp; as shown. In this case that's just a single
+ character, but you can write any length default you like.
+ <br> &nbsp; &nbsp; To see many additional examples, search for the
+ uppercase string NEWCOMMANDS in mimetex.c, and look below that.
+ All the above examples are already there. </dd>
+ <dt> <b>-DNOREFMAXLEN=<i>n</i></b> </dt>
+ <dd> The environment variable HTTP_REFERER identifies the
+ domain a request originates from. If HTTP_REFERER is not
+ defined, then NOREFMAXLEN is the maximum length query&nbsp;string
+ permitted from unidentified domains. It defaults to&nbsp;9999,
+ i.e., any query&nbsp;string is permitted, since
+ mail and various other legitimate programs often don't
+ supply an HTTP_REFERER. See -DREFERER and -DREFLEVELS
+ below for further discussion, and also see -DNOREFSAFELEN
+ immediately below. </dd>
+ <dt> <b>-DNOREFSAFELEN=<i>n</i></b> </dt>
+ <dd> If you compile mimeTeX with either the -DREFERER or
+ -DREFLEVELS switch (discussed below), then the default
+ NOREFMAXLEN value&nbsp;9999 is replaced by the (usually much
+ shorter) NOREFSAFELEN value whose default is&nbsp;24. </dd>
+ <dt> <b>-DOPAQUE</b> </dt>
+ <dd> By default, mimeTeX renders gif images with black symbols
+ on a transparent white background. Defining OPAQUE renders
+ images on an opaque background instead. </dd>
+ <dt> <b>-DPATHPREFIX=\"<i>path/</i>\"</b> </dt>
+ <dd> The <a href="#input">\input{&nbsp;}</a> and
+ <a href="#counter">\counter{&nbsp;}</a> commands discussed below
+ require filename arguments which, by default, point to files
+ residing in the same cgi-bin/ directory as your mimetex.cgi.
+ Moreover, for security, absolute paths with leading <b>/</b>'s
+ or <b>\</b>'s, and paths with <b>../</b>'s or <b>..\</b>'s,
+ are not permitted. Instead, compile mimetex with PATHPREFIX
+ defined as <i>path</i><b>/</b> if you want input files in some
+ other directory. And make sure your <i>path</i><b>/</b> ends
+ with <b>/</b> (or with <b>\</b> for Windows). </dd>
+ <dt> <b>-DPLUSBLANK &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ -DPLUSNOTBLANK</b> </dt>
+ <dd> mimeTeX receives your LaTeX math expression as a url
+ query&nbsp;string, in which blank spaces are often encoded
+ as&nbsp;<b>%20</b> or as plus signs&nbsp;<b>+</b>, and
+ where actual plus signs are often encoded as&nbsp;<b>%2B</b>.
+ But these conventions aren't always respected,
+ and even when they are blank spaces may be either
+ <b>%20</b>&nbsp;or&nbsp;<b>+</b>. The only ambiguity for
+ mimeTeX is whether or not to translate plus signs&nbsp;<b>+</b>
+ back to blank spaces. <br>
+ &nbsp; &nbsp; &nbsp; If you know how your applications behave,
+ then define PLUSBLANK to always translate plus signs&nbsp;<b>+</b>
+ to blank spaces, or define PLUSNOTBLANK to never translate. <br>
+ &nbsp; &nbsp; &nbsp; Otherwise, if you define neither,
+ mimeTeX applies some common-sense rules to decide whether or
+ not to translate. These usually work, but can't be guaranteed.
+ If your query&nbsp;string contains actual blank spaces or
+ blanks encoded as <b>%20</b>, then plus signs&nbsp;<b>+</b>
+ aren't translated. Otherwise, if your query&nbsp;string
+ contains <b>%2B</b>, then plus signs&nbsp;<b>+</b> are
+ translated. If neither <b>%20</b> nor <b>%2B</b>, or both
+ <b>%20</b> and <b>%2B</b>, occur in your query&nbsp;string,
+ then the situation is ambiguous. In this case, if mimeTeX
+ finds two or more plus signs&nbsp;<b>++</b> with no intervening
+ space, then they're translated; otherwise they're not. </dd>
+ <dt> <b>-DREFERER=\"<i>domain</i>\" &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ -DREFERER=\"<i>domain1,domain2,etc</i>\"</b> </dt>
+ <dd> Blocks mimeTeX requests from unauthorized domains that
+ are using your mimetex.cgi (hence your server's resources)
+ without permission. <br>
+ &nbsp; &nbsp; &nbsp; If compiled with -DREFERER, then mimeTeX
+ performs a case-insensitive test of the environment variable
+ HTTP_REFERER to verify that it contains the authorized 'domain'
+ as a substring. For example, if -DREFERER=\"\",<br>
+ &nbsp; &nbsp; &nbsp; If given several 'domain's (second form)
+ then HTTP_REFERER must contain either 'domain1' or
+ 'domain2', or etc, as a (case-insensitive) substring. <br>
+ &nbsp; &nbsp; &nbsp; If HTTP_REFERER doesn't contain a substring
+ matching any of these domain(s), then mimeTeX emits the error
+ message image<br>
+ <img src="../cgi-bin/mimetex.cgi?\message{0}"
+ alt="" align="middle" border=0> <br>
+ instead of the requested image. You can manually
+ modify this invalid_referer_msg, which is msgtable[0]
+ defined immediately above function main(),
+ to personalize the error message displayed for your own site. <br>
+ &nbsp; &nbsp; &nbsp; Finally, if you specify <b>-DREFERER</b>
+ (or -DREFLEVELS discussed immediately below) but HTTP_REFERER
+ is not found as an environment variable, then
+ mimeTeX correctly generates images whose QUERY_STRING's
+ contain&nbsp;24 or fewer characters. For&nbsp;25 or more
+ characters, mimeTeX generates an error.
+ See -DNOREFMAXLEN and -DNOREFSAFELEN above to change
+ the&nbsp;24 limit. </dd>
+ <dt><b>-DREFLEVELS=<i>n</i></b> &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ <b>-DNOREFCHECK</b> </dt>
+ <dd> Besides <b>-DREFERER</b> discussed immediately above,
+ mimeTeX can block requests from HTTP_REFERER's that
+ don't match your HTTP_HOST, <i>i.e.</i>, from pages on
+ different servers than your mimetex.cgi image. <br>
+ &nbsp; &nbsp; &nbsp; The default value of REFLEVELS is&nbsp;3,
+ meaning the topmost three levels of HTTP_REFERER and
+ HTTP_HOST must match. For example, phy.cam.ac.uk matches
+ math.cam.ac.uk because they share the same topmost three
+ levels cam.ac.uk. So a page installed at the physics
+ department can use a mimetex.cgi installed at the math
+ department. If you always want a complete match, compile
+ mimeTeX with <b>-DREFLEVELS=99</b> or any large number.
+ If HTTP_REFERER is not found, then the same&nbsp;24
+ character limit discussed immediately above remains in effect. <br>
+ &nbsp; &nbsp; &nbsp; To completely disable the REFLEVELS check,
+ compile mimeTeX with <b>-DNOREFCHECK</b> (or with
+ <b>-DREFLEVELS=0</b>). Or, if you supply a specific
+ <b>-DREFERER</b> list of authorized domains, as discussed
+ immediately above, then the REFLEVELS check is automatically
+ disabled. </dd>
+ <dt><b>-DSECURITY=<i>n</i></b> </dt>
+ <dd> This is essentially a "paranoid" setting that defaults
+ to a high value 999, which inhibits some optional logging
+ activity. <b>-DCACHEPATH=<i>path</i>/</b> isn't affected,
+ since you're explicitly supplying a <b><i>path</i>/</b>
+ you want files written to. But, for example, you must set
+ <b>-DSECURITY=5</b> (or less) to permit the <b>\counter</b>
+ command to create a new counter file. A malicious user
+ could conceivably flood your file system by submitting
+ zillions of <b>\counter{<i>filename</i>}</b> commands
+ to mimeTeX, each with a different <b><i>filename</i></b>. </dd>
+ <dt><b>-DSMASHMARGIN=<i>n</i> &nbsp; &nbsp; &nbsp; <i>-or-</i><br>
+ -DNOSMASH</b> </dt>
+ <dd> TeX typically renders an expression like
+ <b>\frac12\int_{a+b+c}^{d+e+f}g(x)dx</b> as <a href="#preview">
+ <img id="nosmash1" onclick="eqntext('nosmash1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \nosmash\frac12\int_{a+b+c}^{d+e+f}g(x)dx"
+ alt="" border=0 align=middle></a>. MimeTeX tries to remove extra
+ whitespace, rendering the same expression as <a href="#preview">
+ <img id="nosmash2" onclick="eqntext('nosmash2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \smash\frac12\int_{a+b+c}^{d+e+f}{g(x)}dx"
+ alt="" border=0 align=middle></a> instead.
+ Compile with <b>-DNOSMASH</b> if you prefer the typical TeX
+ behavior as mimeTeX's default. Or, to adjust the minimum
+ number of pixels between smashed symbols (default is 3),
+ compile with <b>-DSMASHMARGIN=<i>n</i></b>.
+ See <a href="#smash">Smash</a> for further discussion. </dd>
+ <dt> <b>-DWARNINGS=<i>n</i> &nbsp; &nbsp; &nbsp; <i>-or-</i> <br>
+ -DNOWARNINGS</b> </dt>
+ <dd> If an expression submitted to mimeTeX contains an
+ unrecognzied escape sequence, e.g., "y=x+\abc+1", then
+ mimeTeX generates a gif image containing an embedded
+ warning in the form "y=x+[\abc?]+1". Or, if an expression
+ contains an unrecognized character, i.e., one for which mimeTeX
+ has no corresponding bitmap, then the embedded warning is [?].
+ If you want these warnings suppressed, either <b>-DWARNINGS=0</b>
+ or <b>-DNOWARNINGS</b> on the compile line tells mimeTeX to treat
+ unrecognized/undisplayable input as white space. </dd>
+ <dt> <b>-DWHITE</b> </dt>
+ <dd> MimeTeX usually renders black symbols on a white
+ background. This option renders white symbols on
+ a transparent black background instead (or on an opaque
+ black background when combined with <b>-DOPAQUE</b>&nbsp;). </dd>
+
+ <dt> <a name="adswitches"> </a> <font color="black" size="5">
+ <br> <b>Advertising switches</b><font size=5>...</font></font>
+ <br> </dt>
+ <dd style="margin-left:0em;"> The next three switches
+ set up a mimeTeX web service that embeds advertising messages
+ along with rendered images.
+ <!-- See <a href="#webservice">mimeTeX&nbsp;web&nbsp;service</a>
+ above for further discussion. --> <br> <br> </dd>
+
+ <dt> <a name="adfrequencyswitch"> </a>
+ <b>&#150;DADFREQUENCY=0</b> </dt>
+ <dd> If ADFREQUENCY is defined as a positive number <b><i>n</i></b>,
+ then one request out of every <b><i>n</i></b> submitted to mimeTeX
+ is randomly selected to be displayed along with a pre-defined
+ "advertisement". For example, if your expression is
+ &nbsp; <b>\large\int_0^xe^{-x^2}dx</b>, &nbsp; then the default
+ advertisement displays <br>
+ &nbsp; &nbsp; &nbsp;
+ <a href="#preview"><img id="adswitch1" onclick="eqntext('adswitch1')"
+ src="../cgi-bin/mimetex.cgi?\large\advertisement
+ \int_0^xe^{-x^2}dx" alt="" align="middle" border=0></a>
+ &nbsp; &nbsp; instead of just &nbsp; &nbsp;
+ <a href="#preview"><img id="adswitch2" onclick="eqntext('adswitch2')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \int_0^xe^{-x^2}dx" alt="" align="middle" border=0></a> <br>
+ See the <b>&#150;DADVERTISEMENT</b> switch <!-- immediately -->
+ below for instructions to define your own advertisement replacing
+ my default. </dd>
+
+ <dt> <a name="adhostswitch"> </a>
+ <b>&#150;DHOST_SHOWAD=\"\\000\"</b> </dt>
+ <dd> Advertisement messages are usually displayed randomly,
+ in one request to mimeTeX out of every <b><i>n</i></b>,
+ as defined by the <b>&#150;DADFREQUENCY</b> switch above.
+ But if a HOST_SHOWAD string is also defined,
+ then advertisements are only displayed when mimeTeX is running
+ on a host whose HTTP_HOST (or SERVER_NAME) environment variable
+ contains that string. For example,
+ <b>&#150;DHOST_SHOWAD=\"mathsite\"</b> displays advertisements
+ on www.mathsite.com but never on www.mathhouse.com&nbsp;.
+ The default HOST_SHOWAD value is an empty string,
+ which displays advertisements on any host. </dd>
+
+ <dt> <a name="advertisementswitch"> </a>
+ <b>&#150;DADVERTISEMENT=\"</b><i>filename</i><b>\"</b> </dt>
+ <dd> To define your own advertisement, replacing my default
+ illustrated immediately above, edit a file containing lines
+ of the form <br>
+ <nobr>&nbsp; &nbsp; &nbsp; <b>"\\</b>begin{gather}{\\small\\text<b>"</b></nobr><br>
+ <nobr>&nbsp; &nbsp; &nbsp; &nbsp; <b>"</b>{\\fbox{\\begin{gather}<b>"</b></nobr><br>
+ <nobr>&nbsp; &nbsp; &nbsp; &nbsp; <b>"</b>mime\\TeX rendering courtesy of\\\\<b>"</b></nobr><br>
+ <nobr>&nbsp; &nbsp; &nbsp; &nbsp; <b>"</b>http://www.forkosh.com/mimetex.html \\end{gather}}}\\\\<b>"</b></nobr><br>
+ <nobr>&nbsp; &nbsp; &nbsp; &nbsp; <b>"</b> %%expression%%<b>"</b></nobr><br>
+ <nobr>&nbsp; &nbsp; &nbsp; <b>"\\</b>end{gather}<b>"</b></nobr><br>
+ Every line in your file must be enclosed in <b>"</b>quotes<b>"</b>,
+ and all backslashes written as double-backslashes <b>\\</b>.
+ Note <b>\\\\</b> at the end of the third and fourth lines,
+ which LaTeX sees as <b>\\</b>. The entire example shows how my
+ default advertisement is defined. <br>
+ &nbsp; &nbsp; &nbsp; Your advertisement may consist of any valid
+ mimeTeX commands you like. But it must somewhere contain the line <br>
+ <nobr>&nbsp; &nbsp; &nbsp; <b>"</b> %%expression%% <b>"</b></nobr><br>
+ which is replaced by the user's expression. <br>
+ &nbsp; &nbsp; &nbsp; Once mimeTeX is compiled with your advertisement,
+ test it by submitting an expression like &nbsp;
+ <b>\advertisement&nbsp;x^2+y^2</b> &nbsp; containing the special
+ mimeTeX &nbsp; \advertisement&nbsp;directive, &nbsp; which forces that
+ expression to be rendered with your advertisement. In this case
+ (and with my default advertisement message) we see <br>
+ &nbsp; &nbsp; &nbsp;
+ <a href="#preview"><img id="adswitch3" onclick="eqntext('adswitch3')"
+ src="../cgi-bin/mimetex.cgi?\advertisement x^2+y^2"
+ alt="" align="middle" border=0></a> &nbsp; &nbsp; instead of
+ just &nbsp; &nbsp;
+ <a href="#preview"><img id="adswitch4" onclick="eqntext('adswitch4')"
+ src="../cgi-bin/mimetex.cgi?x^2+y^2" alt="" border=0></a> <br>
+ regardless of your ADFREQUENCY value. </dd>
+ </dl>
+
+
+<h2> <a name="cmdline"> (IId) Command Line Features &nbsp; </a> </h2>
+
+ <p> MimeTeX usually runs from a browser, obtaining its input expression
+ from a query_string. But you can also run mimeTeX from your Unix
+ shell, supplying all input from the command line. This was briefly
+ illustrated above, where you were advised to test your newly-compiled
+ mimeTeX executable from the command line before installing it. </p>
+
+ <p> In addition to such simple testing, mimeTeX also provides some
+ possibly useful functionality from the command line. In particular,
+ you can store a gif (or xbitmap) image of any expression to a file.
+ No syntax checking is applied to command-line arguments, so enter
+ them carefully. (Likewise, plus signs&nbsp;<b>+</b> are never
+ translated to blank spaces, nor is any other <b>%xx</b> url decoding
+ performed on command-line arguments.) </p>
+
+ <p> The complete command-line syntax for mimeTeX is </p>
+ <pre>
+ ./mimetex [ -d ] dump gif image on stdout,
+ [ -e export_file ] or write gif image to export_file
+ [ expression expression, e.g., "x^2+y^2",
+ | -f input_file ] or read expression from input_file
+ [ -g1 -d ] dump .pbm-formatted image on stdout
+ [ -g1 -e export_file ] or write .pbm image to export_file
+ [ -g2 -d ] dump anti-aliased .pgm image on stdout
+ [ -g2 -e export_file ] or write .pgm image to export_file
+ [ -m msglevel ] verbosity of debugging output
+ [ -o ] render image with opaque background
+ [ -s fontsize ] default fontsize, 0-5
+
+ -d Rather than printing ascii debugging output, mimeTeX
+ dumps the actual gif (or xbitmap) to stdout, e.g.,
+ ./mimetex -d "x^2+y^2" > expression.gif
+ creates expression.gif containing an image of x^2+y^2
+
+ -e export_file Like -d but writes the actual gif
+ (or xbitmap) directly to export_file, e.g.,
+ ./mimetex -e expression.gif "x^2+y^2"
+ creates file expression.gif containing an image of x^2+y^2
+
+ expression Place LaTeX expression directly on command
+ line, with no -switch preceding it, as in the example
+ immediately above, or.....
+
+ -f input_file .....read expression from input_file
+ (and automatically assume -d switch). The input_file
+ may contain the expression on one line or spread out
+ over many lines. MimeTeX will concatanate all lines
+ from input_file to construct one long expression.
+ Blanks, tabs, and newlines are just ignored.
+
+ -g1 -d dumps a .pbm-formatted portable bitmap image to stdout.
+ Note that this is the bitmap image _before_ anti-aliasing.
+
+ -g1 -e export_file Like -g1 -d but writes the .pbm-formatted
+ portable bitmap directly to export_file, e.g.,
+ ./mimetex -g1 -e expression.pbm "x^2+y^2"
+ creates file expression.pbm containing a bitmap image
+ of x^2+y^2 before anti-aliasing.
+
+ -g2 -d dumps a .pgm-formatted portable graphic image to stdout.
+ Note that this is the bytemap image _after_ anti-aliasing.
+
+ -g2 -e export_file Like -g2 -d but writes the .pgm-formatted
+ portable graphic image directly to export_file, e.g.,
+ ./mimetex -g3 -e expression.pgm "x^2+y^2"
+ creates file expression.pgm containing a bytemap image
+ of x^2+y^2 after anti-aliasing.
+
+ -m msglevel 0-99, controls verbosity/message level for
+ debugging output (usually used only while testing code).
+
+ -o Rather than the default transparent gif background,
+ the rendered image will contain black symbols on an
+ opaque white background (or vice versa if compiled
+ with -DWHITE). For example, if you have ImageMagick's
+ display utility,
+ ./mimetex -o -d "x^2+y^2" | display &
+ opens a small window containing the rendered expression.
+ (Note: if you already compiled mimeTeX with -DOPAQUE
+ then -o renders images on a transparent background.)
+
+ -s fontsize 0-7, font size. Font size can also be specified
+ within the expression by a directive, e.g., \Large f(x)=x^2
+ displays f(x)=x^2 at font size 4, overriding -s.
+ Default font size is 3.
+ </pre>
+
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+SECTION III. SYNTAX REFERENCE
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h1> <a name="reference"> (III) Syntax Reference &nbsp; </a> </h1>
+
+<p> Since mimeTeX's syntax is as TeX-like as possible, we'll mostly discuss
+ the occasional differences.
+ <!-- (which exist only to simplify my programming
+ task, not to impose any syntactic aesthetics of mine on you). -->
+ This section contains short paragraphs that each discuss some aspect
+ of mimeTeX where your LaTeX experience might not be precisely
+ duplicated. </p>
+
+<p> Anything not discussed here that still doesn't behave like you expect
+ is probably just not implemented. That includes (La)TeX packages
+ (though a few ams commands like \begin{gather} and \begin{pmatrix}
+ are recognized), non-standard fonts, etc. You can try out any
+ questionable syntax by <a href="#forminput">Submit</a>ting a query
+ to quickly see whether or not it works. And you might want to
+ occasionally re-browse the <a href="#examples">Examples</a> above,
+ which may better illustrate implemented features. </p>
+
+
+<h2> <a name="spaces"> (IIIa) \unitlength{&nbsp;}, Math Spaces and Whitespace
+&nbsp; </a> </h2>
+
+<h3> <a name="unitlength">\unitlength<font size=5>...</font></a> </h3>
+
+ <p> Lengths in mimeTeX are all ultimately expressed in number of pixels.
+ Various commands discussed below require length arguments, including </p>
+ <ul>
+ <li> <a href="#mathspace">\hspace{&nbsp;}</a> </li>
+ <li> <a href="#mathspace">\hfill{&nbsp;}</a> </li>
+ <li> <a href="#raiserotate">\raisebox{&nbsp;}{&nbsp;}</a> </li>
+ <li> <a href="#circleline">\line(&nbsp;,&nbsp;)</a> and
+ <a href="#circleline">\circle(&nbsp;,&nbsp;)</a> </li>
+ <li> <a href="#arrows">\longrightarrow[&nbsp;]</a> </li>
+ </ul> <p class="continue">
+ (the \long<i>xxx</i>arrow [&nbsp;]-arguments are optional mimeTeX
+ extensions to LaTeX) &nbsp; MimeTeX's length-type arguments never
+ take units, e.g., {10pt} and {1cm} are both invalid. Lengths always
+ refer to number of pixels, optionally scaled by a user-specified
+ <b>\unitlength</b>. </p>
+
+ <p> MimeTeX's <b>\unitlength{&nbsp;}</b> command lets you specify
+ the number of pixels per "length&nbsp;unit", e.g.,
+ <b>\unitlength{10}&nbsp;\hspace{2.5}</b> renders a 25-pixel space.
+ Both <b>\unitlength{&nbsp;}</b> and <b>\hspace{&nbsp;}</b>'s
+ length arguments may be integers or may contain decimal points.
+ Ditto for all other mimeTeX commands that take length arguments.
+ The default <b>\unitlength</b> is, you guessed it, <b>1</b>. </p>
+
+ <p> A specified <b>\unitlength</b> applies to all subsequent terms,
+ i.e., everything to its right. And several <b>\unitlength</b>'s
+ may be specified in the same expression, each one overriding
+ those to its left. But if one or more <b>\unitlength</b>'s
+ appear within a <b>{&nbsp;}</b>-enclosed subexpression, then terms
+ following its closing right <b>}</b> revert to the <b>\unitlength</b>
+ in effect before its opening left <b>{</b>. For example, </p> <center>
+ <b>A\hspace{10}&nbsp;{\unitlength{2.5}B\hspace{10}C}&nbsp;\hspace{10}D</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="unitlength1" onclick="eqntext('unitlength1')"
+ src="../cgi-bin/mimetex.cgi?\large A\hspace{10}
+ {\unitlength{2.5}B\hspace{10}C}\hspace{10}D"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ which has a 10-pixel space between <b>A</b>&nbsp;and&nbsp;<b>B</b>, then
+ 25&nbsp;pixels between <b>B</b>&nbsp;and&nbsp;<b>C</b>, and finally
+ another 10&nbsp;pixels between <b>C</b>&nbsp;and&nbsp;<b>D</b>. </p>
+
+<h3> <a name="mathspace">Math Spaces<font size=5>...</font></a> </h3>
+
+ <p> Except inside <a href="#textboxes">text&nbsp;boxes</a>,
+ unescaped blanks, tildes (a&nbsp;<b>~</b>), and all other usual
+ <a href="#whitespace">whitespace</a> characters are completely
+ ignored by mimeTeX, just like they are in LaTeX math mode.
+ As usual, you must explicitly write one of the recognized math
+ spaces to put extra visible space in your rendered expressions. </p>
+
+ <p> MimeTeX recognizes math spaces <b>\/&nbsp;\,&nbsp;\:&nbsp;\;</b>
+ as well as <b>\quad</b> and <b>\qquad</b>&nbsp;,
+ and also a backslashed blank &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?1$\backsl\raise{-5}{\rotate{-90}]}"
+ alt="" border=0 align=middle> &nbsp;
+ (i.e.,&nbsp;a&nbsp;<b>\</b>&nbsp;followed by a blank).
+ For example, &nbsp;
+ <b>(a\/b\,c\:d\;e\&nbsp;&nbsp;f\quad&nbsp;&nbsp;g\qquad&nbsp;&nbsp;h)</b>
+ &nbsp renders &nbsp;
+ <a href="#preview"><img id="spacing2" onclick="eqntext('spacing2')"
+ src="../cgi-bin/mimetex.cgi?(a\/b\,c\:d\;e\ f\quad g\qquad h)"
+ alt="" border=0 align="middle"></a>.
+ In mimeTeX, you may also write &nbsp; <b>\hspace{10}</b> &nbsp;
+ to insert a 10-pixel (or any other number) space, scaled by any
+ preceding <a href="#unitlength">\unitlength</a>, as illustrated
+ just above. </p>
+
+ <p> For negative spaces, &nbsp; <b>\!</b> &nbsp; produces a small (two
+ pixel) negative space, e.g., &nbsp; <b>a=b</b> &nbsp; renders &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?a=b"alt="" border=0 align="bottom">
+ &nbsp; whereas &nbsp; <b>a\!=b</b> &nbsp; renders &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?a\!=b"alt="" border=0 align="bottom">
+ &nbsp; and &nbsp; <b>a\!\!=b</b> &nbsp; renders &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?a\!\!=b"alt="" border=0 align="bottom">.
+ For large negative space, &nbsp; <b>\hspace{-10}</b> &nbsp; permits
+ a negative argument. But it stops at the first pixel to its left
+ rather than "erasing" pixels. If you don't want to stop, use
+ &nbsp; <b>\hspace*{-10}</b> &nbsp; instead. For example,
+ &nbsp; <b>ABC\hspace*{-20}-DEF</b> &nbsp; renders &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?ABC\hspace*{-20}-DEF"
+ alt="" border=0 align="bottom">, &nbsp; erasing all of the <b>C</b>
+ and the right half of the <b>B</b>. </p>
+
+<!--
+ <p> Although some browsers occasionally misinterpret typed blank spaces
+ inside html query_string's, mimeTeX also recognizes escaped blanks
+ <img src="../cgi-bin/mimetex.cgi?\small\backsl\raise{-5}{\rotate{-90}]}"
+ alt="" border=0 align=middle> (a <b>\</b> followed by a blank) as math
+ spaces, just in case you can safely use them. </p>
+-->
+
+ <p> MimeTeX also supports <b>\hfill{<i>textwidth</i>}</b>, where
+ <b><i>textwidth</i></b> is roughly equivalent to LaTeX's
+ <b>\textwidth</b>, i.e., it's the total number of pixels, scaled by
+ <a href="#unitlength">\unitlength</a>, that your entire rendered
+ expression will span. However, if <b>\hfill{&nbsp;}</b> appears
+ within a <b>{&nbsp;}</b>-enclosed subexpression, then it applies
+ only to that subexpression. For example, </p> <center>
+ <b>{abc \hfill{75} def} \hfill{150} ghi</b>
+ &nbsp; &nbsp; produces &nbsp; &nbsp;
+ <a href="#preview"><img id="mathspace1" onclick="eqntext('mathspace1')"
+ src="../cgi-bin/mimetex.cgi?\large{abc\hfill{75}def}\hfill{150}ghi"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ The first/inner <b>\hfill{75}</b> inserts exactly enough whitespace so
+ that subexpression "<b><i>abc&nbsp;&nbsp;def</i></b>" spans 75 pixels.
+ Then the second/outer <b>\hfill{150}</b> inserts exactly enough
+ whitespace so that the entire expression spans 150 pixels.
+ Without explicit <b>{&nbsp;}</b>-nesting, mimeTeX evaluates expressions
+ left-to-right (sinistrally), e.g., <b>...\hfill{150}...\hfill{75}...</b>
+ is exactly equivalent to <b>...\hfill{150}{...\hfill{75}...}</b>.
+ Notice that, this time, the second/right <b><i>textwidth</i></b>
+ argument is necessarily smaller than the first/left. </p>
+
+ <p> Finally, mimeTeX begins a new line whenever you write <b>\\</b>&nbsp;.
+ And you may optionally write <b>\\[10]</b> to put a 10-pixel (or any
+ other number) vertical space, scaled by
+ <a href="#unitlength">\unitlength</a>, between lines.
+ <a href="#array">\begin{eqnarray}</a> also splits long
+ equations over several lines, as illustrated by
+ <a href="#example10">Example&nbsp;10</a> above.
+ But when that's not the best solution, you can also write,
+ for example, </p> <center>
+ <b>y=a+b+c+d\\\hspace{50}+e+f+g+h</b>
+ &nbsp; &nbsp; to produce &nbsp; &nbsp;
+ <a href="#preview"><img id="mathspace2" onclick="eqntext('mathspace2')"
+ src="../cgi-bin/mimetex.cgi?\large y=a+b+c+d\\\hspace{50}+e+f+g+h"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> However, mimeTeX can't correctly handle automatically-sized delimiters
+ across linebreaks, e.g., </p> <center>
+ <b>y=\left\{a+b+c+d\\\hspace{50}+e+f+g+h\right\}</b>
+ &nbsp; &nbsp; produces &nbsp; &nbsp;
+ <a href="#preview"><img id="mathspace3" onclick="eqntext('mathspace3')"
+ src="../cgi-bin/mimetex.cgi?\large y=\{a+b+c+d\\
+ \hspace{50}+e+f+g+h\}" alt="" border=0 align=middle></a> <br>
+ whereas you probably wanted &nbsp; &nbsp; &nbsp; &nbsp;
+ <a href="#preview"><img id="mathspace4" onclick="eqntext('mathspace4')"
+ src="../cgi-bin/mimetex.cgi?\large y=\big{a+b+c+d\\
+ \hspace{50}+e+f+g+h\big}" alt="" border=0 align=middle></a>
+ </center> <p class="continue">
+ which I produced using <b>\big{...\\...\big}</b> instead
+ of <b>\left\{...\\...\right\}</b>. Expressions of the
+ form <b>\left...\right&nbsp;\\&nbsp;\left...\right</b> should all be
+ rendered properly. It's only <b>\left...\\...\right</b> that will
+ look odd. </p>
+
+<h3> <a name="whitespace">Whitespace, Comments,
+and some other characters<font size=5>...</font></a> </h3>
+
+ <p> Some browsers occasionally misinterpret typed blank spaces
+ inside html query_string's. In that case, you can write
+ tildes (a&nbsp;<b>~</b>) wherever blanks are required or desired,
+ e.g., <b>\alpha~w</b> instead of <b>\alpha&nbsp;w</b>, or
+ <b>\frac~xy</b> or <b>\sqrt~z</b>, etc. MimeTeX correctly
+ interprets both blanks and <b>~</b>'s, and all
+ other usual whitespace characters. So use whatever's convenient
+ as long as it's correctly interpreted inside query_string's by your
+ browser. </p>
+
+ <p> Similarly, some browsers occasionally misinterpret linebreaks/newlines
+ inside the middle of long html query_string's.
+ For example, </p>
+<pre>&lt;img src="../cgi-bin/mimetex.cgi?f(x)=\frac1{\sigma\sqrt{2\pi}}
+ \int\limits_{-\infty}^xe^{-\frac{(t-\mu)^2}{2\sig^2}}dt"
+ alt="" border=0 align=middle&gt; </pre><p class="continue">
+ breaks a long query_string over two lines. If your browser interprets
+ this correctly, then mimeTeX will render it correctly, too. Otherwise,
+ you'll have to enter long expressions on one big long line. </p>
+
+ <p> If you can break long query_string's over several lines, then you may
+ find mimeTeX's <b>%%comments%%</b> feature useful, too. Note that
+ comments must be preceded <i>and&nbsp;followed</i> by two <b>%</b>'s
+ rather than LaTeX's usual one. The above example could be written </p>
+<pre>&lt;img src="../cgi-bin/mimetex.cgi?f(x)=\frac1{\sigma\sqrt{2\pi}} %%normalization%%
+ \int\limits_{-\infty}^xe^{-\frac{(t-\mu)^2}{2\sig^2}}dt %%integral%%"
+ alt="" border=0 align=middle&gt; </pre>
+
+ <p> Besides whitespace, browsers may misinterpret embedded apostrophes,
+ and especially quotes, within query strings. The <b>a's</b> and
+ <b>b's</b> in <a href="#example7">Example&nbsp;7</a> above actually use
+ superscripted commas for apostrophes, i.e., <b>a^,s</b> and <b>b^,s</b>,
+ and you can also use LaTeX <b>\prime</b>'s, as in <b>a^\prime&nbsp;s</b>.
+ For quotes, you can use <b>^{,,}</b> since <b>"</b> almost certainly
+ won't work. To help make things easier, in addition to the usual
+ LaTeX <b>\prime</b>, mimeTeX also recognizes <b>\apostrophe</b> and
+ <b>\quote</b> and <b>\percent</b>, all with the obvious meanings. </p>
+
+
+<h2> <a name="symbols"> (IIIb) Math Symbols, Sizes, and Modes &nbsp; </a></h2>
+
+<h3> <a name="characters">Character Sets<font size=5>...</font></a> </h3>
+
+ <p> The <a href="http://www.ctan.org/tex-archive/info/symbols/comprehensive/"
+ target="_top"> Comprehensive&nbsp;LaTeX&nbsp;Symbol&nbsp;List </a>
+ illustrates some 6,000 symbols supported by LaTeX. For complete
+ information about the subset of these characters and math symbols
+ available in mimeTeX, you'll need to browse through the bottom
+ 1500-or-so lines of <b>mimetex.h</b>. And several additional
+ symbols like <b>\ldots</b> and <b>\AA</b> and <b>\hbar</b> are
+ defined by the mimeTeX preprocessor, function <b>mimeprep(&nbsp;)</b>
+ in <b>mimetex.c</b> <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ I haven't exhaustively checked all the name-number matchings for
+ the thousand-or-so symbols in mimetex.h. You can eaily correct
+ any minor mistake you find in what I hope is an obvious manner.
+ The fonts <a href="#fonts">Appendix&nbsp;IVa</a> below provides
+ additional information. </p>
+
+ <p> Generally speaking, I've tried to
+ encode the cmr10, cmmi10, cmmib10, cmsy10, cmex10, bbold10, rsfs10,
+ stmary10 and wncyr10 families with "names", e.g., <b>\alpha \beta
+ \forall \sqcup</b>, etc, identical to your LaTeX expectations.
+ For example, the calligraphic symbols in cmsy10 are accessed by
+ writing <b>\mathcal{A} \mathcal{B} \mathcal{XYZ}</b>. Similarly,
+ write <b>\mathbf{A}</b> for the cmmib fonts, write <b>\mathscr{A}</b>
+ for rsfs10, write <b>\mathbb{R}</b> for bbold10, and write
+ <b>{\cyr&nbsp;Khrushchev}</b> or <b>\cyr{Khrushchev}</b> to see
+ <a href="#preview"><img id="cyrillic1" onclick="eqntext('cyrillic1')"
+ src="../cgi-bin/mimetex.cgi?\large\cyr Khrushchev"
+ alt="" border=0 align="middle"></a>.
+ Most LaTeX distributions supply stmaryrd.dvi and stmaryrd.sty
+ that both document the names of the stmary10 symbols.
+ Similarly, amsfndoc.dvi documents the names of the wncyr10
+ cyrillic symbols and ligatures. </p>
+
+ <!-- But there are various additions and omissions and exceptions
+ vis-a-vis LaTeX. For example, </p>
+ <ul>
+ <li> "Large" operators like \int are often also available as
+ \Bigint, and similarly for \sum \prod \cup \cap, etc.
+ If you find a \Bigxxx in mimetex.h then you'll also find the
+ corresponding \xxx. \Bigxxx operators are somewhat larger
+ than their \xxx counterparts, and they automatically render
+ super/subscripts in <a href="#modes">displaystyle</a>. </li>
+ </ul> -->
+
+
+ <p> In addition to extra LaTeX symbols like <b>\ldots</b>, <b>\AA</b>
+ and <b>\hbar</b>, mentioned above, the mimeTeX preprocessor
+ <b>mimeprep(&nbsp;)</b> also recognizes various html special
+ characters like <b>&amp;lt;</b>, <b>&amp;gt;</b>, <b>&amp;nbsp;</b>,
+ <b>&amp;quot;</b>, <b>&amp;amp;</b>, etc. Some web tools apparently
+ translate characters like, e.g., <b>&gt;</b> to <b>&amp;gt;</b>,
+ even inside quoted query_string's, so mimeTeX's preprocessor
+ translates them back to LaTeX symbols for you. Moreover, html
+ misinterprets quotes &nbsp;<b>&quot;</b>&nbsp; inside a quoted
+ query string as the end of the query string. So, for example,
+ the cyrillic ligature <b>\&quot;E</b> has to be written in the
+ even more cumbersome form <b>\&amp;quot;E</b> inside a query
+ string. </p>
+
+ <p> Illustrated below are some of the character sets and math symbols
+ supported by mimeTeX, starting with several roman character fonts.
+ The blackboard bold font contains many characters besides
+ &nbsp; <b>a-z,A-Z</b>. &nbsp; Calligraphic and script fonts contain
+ uppercase &nbsp; <b>A-Z</b> &nbsp; only. </p>
+
+ <center><a href="#preview"><img id="roman8" onclick="eqntext('roman8')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \begin{array}{|c+57|c|c|c0|c|c|c|c|c| C25 C+15} \hline
+ \large \textrm{a-z} & \small \backslash\textrm{text} &
+ \small \backslash\textrm{mathbb} & &
+ \large \textrm{A-Z} & \small \backslash\textrm{text} &
+ \small \backslash\textrm{mathbb} & \small \backslash\textrm{mathcal} &
+ \small \backslash\textrm{mathscr} \\ \hline
+ a&\text{a}&\mathbb{a}& &A&\text{A}&\mathbb{A}&\mathcal{A}&\mathscr{A}\\
+ b&\text{b}&\mathbb{b}& &B&\text{B}&\mathbb{B}&\mathcal{B}&\mathscr{B}\\
+ c&\text{c}&\mathbb{c}& &C&\text{C}&\mathbb{C}&\mathcal{C}&\mathscr{C}\\
+ d&\text{d}&\mathbb{d}& &D&\text{D}&\mathbb{D}&\mathcal{D}&\mathscr{D}\\
+ e&\text{e}&\mathbb{e}& &E&\text{E}&\mathbb{E}&\mathcal{E}&\mathscr{E}\\
+ f&\text{f}&\mathbb{f}& &F&\text{F}&\mathbb{F}&\mathcal{F}&\mathscr{F}\\
+ g&\text{g}&\mathbb{g}& &G&\text{G}&\mathbb{G}&\mathcal{G}&\mathscr{G}\\
+ h&\text{h}&\mathbb{h}& &H&\text{H}&\mathbb{H}&\mathcal{H}&\mathscr{H}\\
+ i&\text{i}&\mathbb{i}& &I&\text{I}&\mathbb{I}&\mathcal{I}&\mathscr{I}\\
+ j&\text{j}&\mathbb{j}& &J&\text{J}&\mathbb{J}&\mathcal{J}&\mathscr{J}\\
+ k&\text{k}&\mathbb{k}& &K&\text{K}&\mathbb{K}&\mathcal{K}&\mathscr{K}\\
+ l&\text{l}&\mathbb{l}& &L&\text{L}&\mathbb{L}&\mathcal{L}&\mathscr{L}\\
+ m&\text{m}&\mathbb{m}& &M&\text{M}&\mathbb{M}&\mathcal{M}&\mathscr{M}\\
+ n&\text{n}&\mathbb{n}& &N&\text{N}&\mathbb{N}&\mathcal{N}&\mathscr{N}\\
+ o&\text{o}&\mathbb{o}& &O&\text{O}&\mathbb{O}&\mathcal{O}&\mathscr{O}\\
+ p&\text{p}&\mathbb{p}& &P&\text{P}&\mathbb{P}&\mathcal{P}&\mathscr{P}\\
+ q&\text{q}&\mathbb{q}& &Q&\text{Q}&\mathbb{Q}&\mathcal{Q}&\mathscr{Q}\\
+ r&\text{r}&\mathbb{r}& &R&\text{R}&\mathbb{R}&\mathcal{R}&\mathscr{R}\\
+ s&\text{s}&\mathbb{s}& &S&\text{S}&\mathbb{S}&\mathcal{S}&\mathscr{S}\\
+ t&\text{t}&\mathbb{t}& &T&\text{T}&\mathbb{T}&\mathcal{T}&\mathscr{T}\\
+ u&\text{u}&\mathbb{u}& &U&\text{U}&\mathbb{U}&\mathcal{U}&\mathscr{U}\\
+ v&\text{v}&\mathbb{v}& &V&\text{V}&\mathbb{V}&\mathcal{V}&\mathscr{V}\\
+ w&\text{w}&\mathbb{w}& &W&\text{W}&\mathbb{W}&\mathcal{W}&\mathscr{W}\\
+ x&\text{x}&\mathbb{x}& &X&\text{X}&\mathbb{X}&\mathcal{X}&\mathscr{X}\\
+ y&\text{y}&\mathbb{y}& &Y&\text{Y}&\mathbb{Y}&\mathcal{Y}&\mathscr{Y}\\
+ z&\text{z}&\mathbb{z}& &Z&\text{Z}&\mathbb{Z}&\mathcal{Z}&\mathscr{Z}\\
+ \hline \end{array}"
+ alt="" border=0 align="middle"></a></center>
+
+ <p> Characters from the Greek alphabet supported by mimeTeX,
+ along with &nbsp; <b>\mathbb{&nbsp;}</b> &nbsp; versions, are
+ illustrated next. For example, &nbsp; <b>\mathbb{\lambda}</b>
+ &nbsp; renders &nbsp;
+ <a href="#preview"><img id="bblambda" onclick="eqntext('bblambda')"
+ src="../cgi-bin/mimetex.cgi?\large\mathbb{\lambda}"
+ alt="" border=0 align="bottom"></a>. </p>
+
+ <center><a href="#preview"><img id="greek2" onclick="eqntext('greek2')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \begin{array}{|l98c28c28|l98c28c28|l98c28c28|}
+ \hline \; \\
+ \hspace{10}\backslash\textrm{Gamma} & \Gamma & \mathbb{\Gamma} &
+ \hspace{10}\backslash\textrm{Delta} & \Delta & \mathbb{\Delta} &
+ \hspace{10}\backslash\textrm{Theta} & \Theta & \mathbb{\Theta} \\
+ \hspace{10}\backslash\textrm{Lambda} & \Lambda & \mathbb{\Lambda} &
+ \hspace{10}\backslash\textrm{Xi} & \Xi & \mathbb{\Xi} &
+ \hspace{10}\backslash\textrm{Pi} & \Pi & \mathbb{\Pi} \\
+ \hspace{10}\backslash\textrm{Sigma} & \Sigma & \mathbb{\Sigma} &
+ \hspace{10}\backslash\textrm{Upsilon} & \Upsilon & \mathbb{\Upsilon}&
+ \hspace{10}\backslash\textrm{Phi} & \Phi & \mathbb{\Phi} \\
+ \hspace{10}\backslash\textrm{Psi} & \Psi & \mathbb{\Psi} &
+ \hspace{10}\backslash\textrm{Omega} & \Omega & \mathbb{\Omega} \\
+ \; \\ \hline \; \\
+ \hspace{10}\backslash\textrm{alpha} & \alpha & \mathbb{\alpha} &
+ \hspace{10}\backslash\textrm{beta} & \beta & \mathbb{\beta} &
+ \hspace{10}\backslash\textrm{gamma} & \gamma & \mathbb{\gamma} \\
+ \hspace{10}\backslash\textrm{delta} & \delta & \mathbb{\delta} &
+ \hspace{10}\backslash\textrm{epsilon} & \epsilon & \mathbb{\epsilon}&
+ \hspace{10}\backslash\textrm{zeta} & \zeta & \mathbb{\zeta} \\
+ \hspace{10}\backslash\textrm{eta} & \eta & \mathbb{\eta} &
+ \hspace{10}\backslash\textrm{theta} & \theta & \mathbb{\theta} &
+ \hspace{10}\backslash\textrm{iota} & \iota & \mathbb{\iota} \\
+ \hspace{10}\backslash\textrm{kappa} & \kappa & \mathbb{\kappa} &
+ \hspace{10}\backslash\textrm{lambda} & \lambda & \mathbb{\lambda} &
+ \hspace{10}\backslash\textrm{mu} & \mu & \mathbb{\mu} \\
+ \hspace{10}\backslash\textrm{nu} & \nu & \mathbb{\nu} &
+ \hspace{10}\backslash\textrm{xi} & \xi & \mathbb{\xi} &
+ \hspace{10}\backslash\textrm{pi} & \pi & \mathbb{\pi} \\
+ \hspace{10}\backslash\textrm{rho} & \rho & \mathbb{\rho} &
+ \hspace{10}\backslash\textrm{sigma} & \sigma & \mathbb{\sigma} &
+ \hspace{10}\backslash\textrm{tau} & \tau & \mathbb{\tau} \\
+ \hspace{10}\backslash\textrm{upsilon} & \upsilon & \mathbb{\upsilon}&
+ \hspace{10}\backslash\textrm{phi} & \phi & \mathbb{\phi} &
+ \hspace{10}\backslash\textrm{chi} & \chi & \mathbb{\chi} \\
+ \hspace{10}\backslash\textrm{psi} & \psi & \mathbb{\psi} &
+ \hspace{10}\backslash\textrm{omega} & \omega & \mathbb{\omega} \\
+ \; \\ \hline \; \\
+ \hspace{10}\backslash\textrm{varepsilon} & \varepsilon & &
+ \hspace{10}\backslash\textrm{vartheta} & \vartheta & &
+ \hspace{10}\backslash\textrm{varpi} & \varpi & \\
+ \hspace{10}\backslash\textrm{varrho} & \varrho & &
+ \hspace{10}\backslash\textrm{varsigma} & \varsigma & &
+ \hspace{10}\backslash\textrm{varphi} & \varphi & \\
+ \; \\ \hline
+ \end{array}"
+ alt="" border=0 align="middle"></a></center>
+
+ <p> Finally, some of the math symbols supported by mimeTeX are illustrated
+ below. Operators shown in two sizes are automatically
+ "promoted" to the larger size in &nbsp <b>\displaystyle</b>
+ &nbsp; mode. For example, &nbsp;
+ <b>f(x)=\int_{-\infty}^x&nbsp;e^{-t^2}dt</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="mathsy1" onclick="eqntext('mathsy1')"
+ src="../cgi-bin/mimetex.cgi?\textstyle f(x)=\int_{-\infty}^x e^{-t^2}dt"
+ alt="" border=0 align="middle"></a>
+ &nbsp; whereas &nbsp;
+ <b>\displaystyle&nbsp;f(x)=\int_{-\infty}^x&nbsp;e^{-t^2}dt</b>
+ &nbsp; renders &nbsp;
+ <a href="#preview"><img id="mathsy2" onclick="eqntext('mathsy2')"
+ src="../cgi-bin/mimetex.cgi?\displaystyle
+ f(x)=\int_{-\infty}^x e^{-t^2}dt" alt="" border=0 align="middle"></a>
+ </p>
+
+ <center><a href="#preview"><img id="mthtbl1" onclick="eqntext('mthtbl1')"
+ src="../cgi-bin/mimetex.cgi?\large\textstyle
+ \begin{array}{|l98c28c28|l98c28c28|l98c28c28|}
+ \hline \; \\
+ \hspace{10}\backslash\textrm{cdot} & \cdot & &
+ \hspace{10}\backslash\textrm{times} & \times & &
+ \hspace{10}\backslash\textrm{ast} & \ast & \\
+ \hspace{10}\backslash\textrm{div} & \div & &
+ \hspace{10}\backslash\textrm{diamond} & \diamond & &
+ \hspace{10}\backslash\textrm{pm} & \pm & \\
+ \hspace{10}\backslash\textrm{mp} & \mp & &
+ \hspace{10}\backslash\textrm{oplus} & \oplus & \Bigoplus &
+ \hspace{10}\backslash\textrm{ominus} & \ominus & \\
+ \hspace{10}\backslash\textrm{otimes} & \otimes & \Bigotimes &
+ \hspace{10}\backslash\textrm{oslash} & \oslash & &
+ \hspace{10}\backslash\textrm{odot} & \odot & \Bigodot \\
+ \hspace{10}\backslash\textrm{bigcirc} & \bigcirc & &
+ \hspace{10}\backslash\textrm{circ} & \circ & &
+ \hspace{10}\backslash\textrm{bullet} & \bullet & \\
+ \hspace{10}\backslash\textrm{asymp} & \asymp & &
+ \hspace{10}\backslash\textrm{equiv} & \equiv & &
+ \hspace{10}\backslash\textrm{subseteq} & \subseteq & \\
+ \hspace{10}\backslash\textrm{supseteq} & \supseteq & &
+ \hspace{10}\backslash\textrm{leq} & \leq & &
+ \hspace{10}\backslash\textrm{geq} & \geq & \\
+ \hspace{10}\backslash\textrm{preceq} & \preceq & &
+ \hspace{10}\backslash\textrm{succeq} & \succeq & &
+ \hspace{10}\backslash\textrm{sim} & \sim & \\
+ \hspace{10}\backslash\textrm{approx} & \approx & &
+ \hspace{10}\backslash\textrm{subset} & \subset & &
+ \hspace{10}\backslash\textrm{supset} & \supset & \\
+ \hspace{10}\backslash\textrm{ll} & \ll & &
+ \hspace{10}\backslash\textrm{gg} & \gg & &
+ \hspace{10}\backslash\textrm{prec} & \prec & \\
+ \hspace{10}\backslash\textrm{succ} & \succ & &
+ \hspace{10}\normalsize\backslash\textrm{leftarrow} & \leftarrow & &
+ \hspace{10}\normalsize\backslash\textrm{rightarrow} & \rightarrow & \\
+ \hspace{10}\normalsize\backslash\textrm{uparrow} & \uparrow & &
+ \hspace{10}\normalsize\backslash\textrm{downarrow} & \downarrow & &
+ \hspace{10}\normalsize\backslash\textrm{leftrightarrow}&&\leftrightarrow\\
+ \hspace{10}\backslash\textrm{nearrow} & \nearrow & &
+ \hspace{10}\backslash\textrm{searrow} & \searrow & &
+ \hspace{10}\backslash\textrm{simeq} & \simeq & \\
+ \hspace{10}\normalsize\backslash\textrm{Leftarrow} & \Leftarrow & &
+ \hspace{10}\normalsize\backslash\textrm{Rightarrow} & \Rightarrow & &
+ \hspace{10}\normalsize\backslash\textrm{Uparrow} & \Uparrow & \\
+ \hspace{10}\normalsize\backslash\textrm{Downarrow} & \Downarrow & &
+ \hspace{10}\normalsize\backslash\textrm{Leftrightarrow}&&\Leftrightarrow&
+ \hspace{10}\backslash\textrm{nwarrow} & \nwarrow & \\
+ \hspace{10}\backslash\textrm{swarrow} & \swarrow & &
+ \hspace{10}\backslash\textrm{propto} & \propto & &
+ \hspace{10}\backslash\textrm{prime} & \prime & \\
+ \hspace{10}\backslash\textrm{infty} & \infty & &
+ \hspace{10}\backslash\textrm{in} & \in & &
+ \hspace{10}\backslash\textrm{ni} & \ni & \\
+ \hspace{10}\backslash\textrm{triangle} & \triangle & &
+ \hspace{10}\normalsize\backslash\textrm{bigtriangledown}&&\bigtriangledown&
+ \hspace{10}\backslash^\prime & \' & \\
+ \hspace{10}\textrm{/} & / & &
+ \hspace{10}\backslash\textrm{forall} & \forall & &
+ \hspace{10}\backslash\textrm{exists} & \exists & \\
+ \hspace{10}\backslash\textrm{neg} & \neg & &
+ \hspace{10}\backslash\textrm{emptyset} & \emptyset & &
+ \hspace{10}\backslash\textrm{Re} & \Re & \\
+ \hspace{10}\backslash\textrm{Im} & \Im & &
+ \hspace{10}\backslash\textrm{top} & \top & &
+ \hspace{10}\backslash\textrm{bot} & \bot & \\
+ \hspace{10}\backslash\textrm{aleph} & \aleph & &
+ \hspace{10}\normalsize\backslash\textrm{mathcal\lbrace A\rbrace}&\;\mathcal{A}&....&
+ .... \normalsize\backslash\textrm{mathcal\lbrace Z\rbrace}&\;\mathcal{Z}&\\
+ \; \\ \hline
+ \end{array}"
+ alt="" border=0 align="middle"></a><br>
+ <a href="#preview"><img id="mthtbl2" onclick="eqntext('mthtbl2')"
+ src="../cgi-bin/mimetex.cgi?\large\textstyle
+ \begin{array}{|l98c28c28|l98c28c28|l98c28c28|}
+ \hline \; \\
+ \hspace{10}\backslash\textrm{cup} & \cup & \Bigcup &
+ \hspace{10}\backslash\textrm{cap} & \cap & \Bigcap &
+ \hspace{10}\backslash\textrm{uplus} & \uplus & \Biguplus \\
+ \hspace{10}\backslash\textrm{wedge} & \wedge & \Bigwedge &
+ \hspace{10}\backslash\textrm{vee} & \vee & \Bigvee &
+ \hspace{10}\backslash\textrm{vdash} & \vdash & \\
+ \hspace{10}\backslash\textrm{dashv} & \dashv & &
+ \hspace{10}\backslash\textrm{lfloor} & \lfloor & &
+ \hspace{10}\backslash\textrm{rfloor} & \rfloor & \\
+ \hspace{10}\backslash\textrm{lceil} & \lceil & &
+ \hspace{10}\backslash\textrm{rceil} & \rceil & &
+ \hspace{10}\backslash\textrm{lbrace} & \lbrace & \\
+ \hspace{10}\backslash\textrm{rbrace} & \rbrace & &
+ \hspace{10}\backslash\textrm{langle} & \langle & &
+ \hspace{10}\backslash\textrm{rangle} & \rangle & \\
+ \hspace{10}\backslash\textrm{mid} & \mid & &
+ \hspace{10}\backslash\textrm{parallel} & \parallel & &
+ \hspace{10}\normalsize\backslash\textrm{updownarrow}& & \updownarrow \\
+ \hspace{10}\normalsize\backslash\textrm{Updownarrow}& & \Updownarrow &
+ \hspace{10}\backslash\textrm{setminus} & \setminus & &
+ \hspace{10}\backslash\textrm{wr} & \wr & \\
+ \hspace{10}\backslash\textrm{surd} & \raisebox{15}\surd & &
+ \hspace{10}\backslash\textrm{amalg} & \amalg & &
+ \hspace{10}\backslash\textrm{nabla} & \nabla & \\
+ \hspace{10}\backslash\textrm{int} & \int & \Bigint &
+ \hspace{10}\backslash\textrm{sqcup} & \sqcup & \Bigsqcup &
+ \hspace{10}\backslash\textrm{sqcap} & \sqcap & \\
+ \hspace{10}\normalsize\backslash\textrm{sqsubseteq} & \sqsubseteq & &
+ \hspace{10}\normalsize\backslash\textrm{sqsupseteq} & \sqsupseteq & &
+ \hspace{10}\backslash\textrm{S} & \S & \\
+ \hspace{10}\backslash\textrm{dag} & \dag & &
+ \hspace{10}\backslash\textrm{ddag} & \ddag & &
+ \hspace{10}\backslash\textrm{P} & \P & \\
+ \hspace{10}\backslash\textrm{clubsuit} & \clubsuit & &
+ \hspace{10}\backslash\textrm{Diamond} & \Diamond & &
+ \hspace{10}\backslash\textrm{Heart} & \Heart & \\
+ \hspace{10}\backslash\textrm{spadesuit} & \spadesuit & \\
+ \; \\ \hline
+ \end{array}"
+ alt="" border=0 align="middle"></a><br>
+ <a href="#preview"><img id="mthtbl3" onclick="eqntext('mthtbl3')"
+ src="../cgi-bin/mimetex.cgi?\large\textstyle
+ \begin{array}{|l98c28c28|l98c28c28|l98c28c28|}
+ \hline \; \\
+ \hspace{10}\backslash\textrm{oint} & \oint & \Bigoint &
+ \hspace{10}\backslash\textrm{sum} & \sum & \Bigsum &
+ \hspace{10}\backslash\textrm{prod} & \prod & \Bigprod \\
+ \hspace{10}\backslash\textrm{coprod} & \coprod & \Bigcoprod \\
+ \; \\ \hline \; \\
+ \hspace{10}\normalsize\backslash\textrm{leftharpoonup} &&\leftharpoonup&
+ \normalsize\backslash\textrm{leftharpoondown} &&\;\leftharpoondown&
+ \hspace{10}\normalsize\backslash\textrm{rightharpoonup}&&\rightharpoonup\\
+ \normalsize\backslash\textrm{rightharpoondown}&&\;\rightharpoondown&
+ \hspace{10}\normalsize\backslash\textrm{triangleright} &&\triangleright&
+ \hspace{10}\normalsize\backslash\textrm{triangleleft} &&\triangleleft\\
+ \normalsize\backslash\textrm{rightleftharpoons}&&\;\rightleftharpoons&
+ \hspace{10}\backslash\textrm{star} & \LARGE{\star} & &
+ \hspace{10}\backslash\textrm{partial} & \partial & \\
+ \hspace{10}\backslash\textrm{flat} & \flat & &
+ \hspace{10}\backslash\textrm{natural} & \natural & &
+ \hspace{10}\backslash\textrm{sharp} & \sharp & \\
+ \hspace{10}\backslash\textrm{smile} & \smile & &
+ \hspace{10}\backslash\textrm{frown} & \frown & &
+ \hspace{10}\backslash\textrm{ell} & \ell & \\
+ \hspace{10}\backslash\textrm{imath} & \imath & &
+ \hspace{10}\backslash\textrm{jmath} & \jmath & &
+ \hspace{10}\backslash\textrm{wp} & \wp & \\
+ \; \\ \hline \; \\
+ \hspace{10}\backslash\textrm{ss} & \ss & &
+ \hspace{10}\backslash\textrm{ae} & \ae & &
+ \hspace{10}\backslash\textrm{oe} & \oe & \\
+ \hspace{10}\backslash\textrm{AE} & \AE & &
+ \hspace{10}\backslash\textrm{OE} & \OE & \\
+ \; \\ \hline \; \\
+ \hspace{10}\backslash\textrm{AA} & \AA & &
+ \hspace{10}\backslash\textrm{aa} & \aa & &
+ \hspace{10}\backslash\textrm{hbar} & \hbar & \\
+ \hspace{10}\backslash\textrm{ldots} & \ldots & &
+ \hspace{10}\backslash\textrm{cdots} & \cdots & &
+ \hspace{10}\backslash\textrm{vdots} & \vdots & \\
+ \hspace{10}\backslash\textrm{ddots} & \ddots & &
+ \hspace{10}\backslash\textrm{angle} & \angle & &
+ \hspace{10}\backslash\textrm{iint} & \iint & \Bigiint \\
+ \; \\ \hline
+ \end{array}"
+ alt="" border=0 align="middle"></a></center>
+
+<h3> <a name="sizes">Font Sizes<font size=5>...</font></a> </h3>
+
+ <p> MimeTeX currently has eight font sizes, numbered 0-7, with default 3.
+ This font size numbering corresponds to the usual LaTeX directives
+ &nbsp; <b>\tiny</b>, &nbsp; <b>\small</b>, &nbsp; <b>\normalsize</b>,
+ &nbsp; <b>\large</b> (default), &nbsp; <b>\Large</b>, &nbsp;
+ <b>\LARGE</b>, &nbsp; <b>\huge</b> and <b>\Huge</b>.
+ These directives can be placed anywhere in a mimeTeX expression,
+ and they change font size from that point forwards. However, as usual,
+ a font size change inside a <b>{&nbsp;}</b>-subexpression remains
+ in effect only within that subexpression. </p>
+
+ <p> In mimeTeX you may also write <b>\fontsize{0}...\fontsize{7}</b> or
+ the shorter <b>\fs{0},...,\fs{7}</b> for <b>\tiny,...,\Huge</b>.
+ And since these arguments are all single digits, the even shorter
+ form <b>\fs0,...,\fs7</b> works equally well. For example, </p>
+ <center> <table cellpadding=0>
+ <tr align=center>
+ <td align="left"> <b>0</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\tiny</b> f(x)=x^2"&gt;
+ &nbsp; produces... </td>
+ <td> <a href="#preview"><img id="sizes0" onclick="eqntext('sizes0')"
+ src="../cgi-bin/mimetex.cgi?\tiny f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>1</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\fs1</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes1" onclick="eqntext('sizes1')"
+ src="../cgi-bin/mimetex.cgi?\fs1 f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>2</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\normalsize</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes1" onclick="eqntext('sizes1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>3</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b></b>f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes3" onclick="eqntext('sizes3')"
+ src="../cgi-bin/mimetex.cgi?f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>4</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\Large</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes4" onclick="eqntext('sizes4')"
+ src="../cgi-bin/mimetex.cgi?\Large f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>5</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\fs5</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes5" onclick="eqntext('sizes5')"
+ src="../cgi-bin/mimetex.cgi?\fs5f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>6</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\huge</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes6" onclick="eqntext('sizes6')"
+ src="../cgi-bin/mimetex.cgi?\huge f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ <tr align=center>
+ <td align="left"> <b>7</b>: &nbsp;
+ &lt;img src="../cgi-bin/mimetex.cgi?<b>\fs7</b> f(x)=x^2"&gt; </td>
+ <td> <a href="#preview"><img id="sizes7" onclick="eqntext('sizes7')"
+ src="../cgi-bin/mimetex.cgi?\fs7 f(x)=x^2"
+ alt="" border=0 align=middle></a> </td> </tr>
+ </table> </center> <p class="continue">
+ rendering <b>f(x)=x^2</b> in mimeTeX font sizes &nbsp;
+ <b>0</b> (\tiny or \fs0), &nbsp; <b>1</b> (\small or \fs1), &nbsp;
+ <b>2</b> (\normalsize or \fs2), &nbsp; <b>3</b> (default \large), &nbsp;
+ <b>4</b> (\Large or \fs4), &nbsp; <b>5</b> (\LARGE or \fs5), &nbsp;
+ <b>6</b> (\huge or \fs6) &nbsp; and &nbsp; <b>7</b> (\Huge or \fs7). </p>
+
+ <p> You'll soon notice that exponents and \frac's and \atop's
+ are automatically rendered one size smaller than their base
+ expressions. For example, </p> <center>
+ <b>\Large y=e^{x^2}</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="sizes4" onclick="eqntext('sizes4')"
+ src="../cgi-bin/mimetex.cgi?\Large y=e^{x^2}"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ rendering the <b>"y=e"</b> in font size 4 (\Large), the <b>"x"</b> in
+ font size 3 (\large), and the <b>"2"</b> in font size 2 (\normalsize).
+ If you get below font size 0, the font size remains&nbsp;0. </p>
+
+ <p> Explicit size declarations override mimeTeX's default sizing behavior.
+ You can rewrite the preceding example as, say, </p> <center>
+ <b>\Large y=e^{\normalsize x^{\tiny2}}</b> &nbsp; which now produces
+ &nbsp; <a href="#preview"><img id="sizes5" onclick="eqntext('sizes5')"
+ src="../cgi-bin/mimetex.cgi?\Large y=e^{\normalsize x^{\tiny2}}"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ rendering the <b>"y=e"</b> in font size 4 (\Large unchanged),
+ the <b>"x"</b> in font size 2 (\normalsize), and the <b>"2"</b>
+ in font size&nbsp;0 (\tiny). </p>
+
+ <p> Preceding an <b>\fs{&nbsp;}</b> size argument with <b>+</b> or
+ <b>-</b> specifies "relative" sizing. For example,
+ <b>\large\text{abc{\fs{-2}def}ghi}</b> produces
+ <a href="#preview"><img id="sizes6" onclick="eqntext('sizes6')"
+ src="../cgi-bin/mimetex.cgi?\large\text{abc{\fs{-2}def}ghi}"
+ alt="" border=0 align=middle></a>, rendering the <b>"def"</b>
+ in font size 1 (two sizes smaller than \large). Note that
+ <b>\fs{-2}</b> affects only the subexpression in which it appears,
+ and that its braces are no longer optional since <b>-2</b> contains
+ two characters. For exponents (or any other size-changing commands
+ like \frac), </p> <center>
+ <b>\Large y=e^{\fs{-1}x^2}</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="sizes7" onclick="eqntext('sizes7')"
+ src="../cgi-bin/mimetex.cgi?\Large y=e^{\fs{-1}x^2}"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ rendering the <b>"y=e"</b> in font size 4 (\Large), as usual.
+ The <b>"x"</b> would usually be rendered one size smaller,
+ in font size 3, and your <b>\fs{-1}</b> is applied to that,
+ resulting in font size 2. And the final <b>"2"</b> is rendered,
+ by the usual rules, one size smaller than the <b>"x"</b>,
+ in font size&nbsp;1. </p>
+
+ <p> Finally, illustrated below are some examples of fonts and symbols
+ at several mimeTeX sizes. All symbols and sizes from cmr, cmmi,
+ cmmib (use <b>\mathbf{&nbsp;}</b>), cmsy, cmex, bbold (use
+ <b>\mathbb{&nbsp;}</b>), rsfs (use <b>\mathscr{&nbsp;}</b>),
+ stmary and cyrillic wncyr (use <b>{\cyr&nbsp;&nbsp;}</b> or
+ <b>\cyr{&nbsp;}</b>) should be available, but they're not all shown.
+ <!-- And also not shown are various "constructed symbols" like \sqrt,
+ accents, etc. --> The illustrated font sizes are numbered 4=\Large,
+ 3=\large and 2=\normalsize (not shown are 7=\Huge, 6=\huge,
+ 5=\LARGE, 1=\small and 0=\tiny). </p>
+
+ <center> <table cellspacing="7">
+ <tr> <td align="left">
+<font size="4">cmmi latin uppercase, and lowercase</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$A&4$B&4$C&4$D,&4$a&4$b&4$c&4$d\\
+2$\rm~3:~&3$E&3$F&3$G&3$H&3$I&3$J&3$K&3$L,&3$e&3$f&3$g&3$h&3$i&3$j&3$k&3$l\\
+2$\rm~2:~&2$M&2$N&2$O&2$P&2$Q&2$R&2$S&2$T&2$U&2$V&2$W&2$X&2$Y&2$Z,&
+2$m&2$n&2$o&2$p&2$q&2$r&2$s&2$t&2$u&2$v&2$w&2$x&2$y&2$z}"
+alt="" border=0 align=middle>
+ </td> <tr>
+ <tr> <td align="left">
+<font size="4">calligraphic, and rsfs (<b>\cal{A}, \scr{B}, etc</b>)</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\calA&4$\calB&4$\calC&4$\calD&4$\calE&4$\calF&4$\calG,&
+4$\scrA&4$\scrB&4$\scrC&4$\scrD&4$\scrE&4$\scrF&4$\scrG\\
+2$\rm~3:~&3$\calH&3$\calI&3$\calJ&3$\calK&3$\calL&3$\calM&3$\calN&3$\calO&
+3$\calP,&
+3$\scrH&3$\scrI&3$\scrJ&3$\scrK&3$\scrL&3$\scrM&3$\scrN&3$\scrO&3$\scrP\\
+2$\rm~2:~&2$\calQ&2$\calR&2$\calS&2$\calT&2$\calU&
+2$\calV&2$\calW&2$\calX&2$\calY&2$\calZ,&
+2$\scrQ&2$\scrR&2$\scrS&2$\scrT&2$\scrU&2$\scrV&2$\scrW&
+2$\scrX&2$\scrY&2$\scrZ}"
+alt="" border=0 align=middle>
+ </td> <tr>
+ <tr> <td align="left">
+<font size="4">cmmi greek uppercase, and \var lowercase</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\Gamma&4$\Delta&4$\Theta&4$\Lambda&4$\Xi&4$\Pi&4$\Sigma&
+4$\Upsilon&4$\Phi&4$\Psi&4$\Omega,&4$\rm~~&4$\varepsilon&4$\vartheta&4$\varpi&
+4$\varrho&4$\varsigma&4$\varphi\\
+2$\rm~3:~&3$\Gamma&3$\Delta&3$\Theta&3$\Lambda&3$\Xi&3$\Pi&3$\Sigma&
+3$\Upsilon&3$\Phi&3$\Psi&3$\Omega,&~&3$\varepsilon&3$\vartheta&3$\varpi&
+3$\varrho&3$\varsigma&3$\varphi\\
+2$\rm~2:~&2$\Gamma&2$\Delta&2$\Theta&2$\Lambda&2$\Xi&2$\Pi&2$\Sigma&
+2$\Upsilon&2$\Phi&2$\Psi&2$\Omega,&~&2$\varepsilon&2$\vartheta&2$\varpi&
+2$\varrho&2$\varsigma&2$\varphi}"
+alt="" border=0 align=middle>
+ </td> <tr>
+ <tr> <td align="left">
+<font size="4">cmmi greek lowercase</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{r$
+2$\rm~size~4:~&4$\alpha&4$\beta&4$\gamma&4$\delta&4$\epsilon&4$\zeta&
+4$\eta&4$\theta&4$\iota&4$\kappa&4$\lambda&4$\mu&4$\nu&4$\xi&4$%%\omicron%%&
+4$\pi&4$\rho&4$\sigma&4$\tau&4$\upsilon&4$\phi&4$\chi&4$\psi&4$\omega\\
+2$\rm~3:~&3$\alpha&3$\beta&3$\gamma&3$\delta&3$\epsilon&3$\zeta&
+3$\eta&3$\theta&3$\iota&3$\kappa&3$\lambda&3$\mu&3$\nu&3$\xi&3$%%\omicron%%&
+3$\pi&3$\rho&3$\sigma&3$\tau&3$\upsilon&3$\phi&3$\chi&3$\psi&3$\omega\\
+2$\rm~2:~&2$\alpha&2$\beta&2$\gamma&2$\delta&2$\epsilon&2$\zeta&
+2$\eta&2$\theta&2$\iota&2$\kappa&2$\lambda&2$\mu&2$\nu&2$\xi&2$%%\omicron%%&
+2$\pi&2$\rho&2$\sigma&2$\tau&2$\upsilon&2$\phi&2$\chi&2$\psi&2$\omega}"
+alt="" border=0 align=middle>
+ </td> <tr>
+ <tr> <td align="left">
+<font size="4">cmsy symbols at mimeTeX font size 3</font><br>
+<font size="3">(operators shown large are automatically "promoted"<br>
+to the larger size in \displaystyle mode)</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{3,r$1$\rm~chars~\\
+1$\rm~0-15:~&-&\cdot&\times&\ast&\div&\diamond&\pm&\mp&
+\oplus&\ominus&\otimes&\oslash&\odot&\bigcirc&\circ&\bullet\\
+1$\rm~16-31:~&\asymp&\equiv&\subseteq&\supseteq&\leq&\geq&\preceq&\succeq&
+\sim&\approx&\subset&\supset&\ll&\gg&\prec&\succ\\
+1$\rm~32-47:~&\leftar&\rightar&\uparr&\downar&\leftrightar&\near&\sear&
+\simeq&\Leftar&\Rightar&\Upar&\Downar&\Leftrightar&\nwar&\swar&\propto\\
+1$\rm~48-63:~&\prime&\infty&\in&\ni&\triangle&\bigtriangledo&/&\'&
+\forall&\exists&\neg&\emptyset&\Re&\Im&\top&\bot\\
+1$\rm~64-100:~&\aleph&&\calA&4$.\,.\,.&\calZ&&\cup&\cap&
+\uplus&\wedge&\vee&\vdash&\dashv&\lfloor&\rfloor&\lceil\\
+1$\rm~101-116:~&\rceil&\lbrace&\rbrace&\langle&\rangle&\mid&\parallel&
+\updownar&\Updownar&\setminus&\wr&\surd&\amalg&\nabla&\int&\sqcup\\
+1$\rm~117-127:~&\sqcap&\sqsubseteq&\sqsupseteq&\S&\dag&\ddag&\P&\clubsuit&
+\Diamond&\Heart&\spadesuit}" alt="" border=0 align=middle>
+ </td> <tr>
+ <tr> <td align="left">
+<font size="4">a few other cmmi, cmr, stmary and wncyr symbols
+at mimeTeX font size 4</font>
+<br><img src="../cgi-bin/mimetex.cgi?\array{4,r$
+1$\rm~cmmi:~&\leftharpoonup&\leftharpoondo&\rightharpoonup&\rightharpoondo&
+\triangleright&\triangleleft&\star&\partial&
+\flat&\natural&\sharp&\smile&\frown&\ell&\imath&\jmath&\wp&\vec\\
+1$\rm~cmr:~&\ss&\ae&\oe&\AE&\OE \\
+1$\rm~stmary:~&\moo&\Lbag&\Rbag&\lightning&\llbracket&\rrbracket&
+\subsetpluseq&\supsetpluseq&\Yup&\Ydown\\
+1$\rm~wncyr:~&\cyr A&\cyr a&\cyr B&\cyr b&\cyr V&\cyr v&\cyr G&\cyr g&
+\cyr D&\cyr d&\cyr Dj&\cyr dj&\cyr\=E&\cyr\=e&\cyr Zh&\cyr zh}"
+alt="" border=0 align=middle>
+ </td> <tr>
+ </table> </center>
+
+<h3> <a name="modes">Modes<font size=5>...</font></a> </h3>
+
+ <p> MimeTeX is always in a math-like mode, so you needn't surround
+ expressions with <b>$...$</b>'s for <b>\textstyle</b>,
+ or <b>$$...$$</b>'s for <b>\displaystyle</b>.
+ <!-- or <b>\[...\]</b>'s, etc. In fact, mimeTeX interprets <b>$</b>
+ as a "preamble" terminator (e.g., see <a href="#array">\array</a>
+ below), and interprets <b>\[...\]</b> as an abbreviation for
+ <b>\left[...\right]</b>. -->
+ By default, operator limits like <b>\int_a^b</b> are rendered
+ <b>\textstyle</b> <a href="#preview">
+ <img id="modes99a" onclick="eqntext('modes99a')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\int_a^b"
+ alt="" border=0 align=middle></a> at font sizes <b>\normalsize</b>
+ and smaller, and rendered <b>\displaystyle</b> <a href="#preview">
+ <img id="modes99b" onclick="eqntext('modes99b')"
+ src="../cgi-bin/mimetex.cgi?\large\int_a^b"
+ alt="" border=0 align=middle></a> at font sizes <b>\large</b> and
+ larger (see the <b>-DDISPLAYSIZE</b>
+ <a href="#options">compile&nbsp;option</a> to change this default).
+ And when <b>\displaystyle</b> is invoked (either implicitly at font size
+ <b>\large</b> or larger, or if you explicitly write <b>\displaystyle</b>
+ at any font size), then operators <b>\int</b>, <b>\sum</b>,
+ <b>\prod</b>, etc, are automatically promoted to larger sizes.
+ <!-- their <a href="#characters">\Bigxxx</a> counterparts. -->
+ <!-- Conversely, <b>\displaystyle</b> is applied to all
+ <a href="#characters">\Bigxxx</a> operators regardless of font size. -->
+ <!-- i.e., super/subscripts are placed directly above/below
+ <b>\Bigsum</b>, but "alongside" <b>\sum</b>. -->
+ For example, </p> <center>
+ <!-- <b>\Bigsum_{i=1}^ni=\frac{n(n+1)}2</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes1a" onclick="eqntext('modes1a')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\Bigsum_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a>, <br> -->
+ <b>\normalsize \sum_{i=1}^ni=\frac{n(n+1)}2</b>
+ &nbsp; &nbsp; produces &nbsp; &nbsp;
+ <a href="#preview"><img id="modes2a" onclick="eqntext('modes2a')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\sum_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a>, &nbsp; whereas <br>
+ <b>\displaystyle \normalsize \sum_{i=1}^ni=\frac{n(n+1)}2</b>
+ &nbsp;produces&nbsp;
+ <a href="#preview"><img id="modes1b" onclick="eqntext('modes1b')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a>, </center>
+ <p class=continue> and <!-- replacing <b>\Bigsum</b> with the smaller
+ <b>\sum</b> symbol, --> </p> <center>
+ <b>\large \sum_{i=1}^ni=\frac{n(n+1)}2</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes1b" onclick="eqntext('modes1b')"
+ src="../cgi-bin/mimetex.cgi?\large\sum_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a>, &nbsp; whereas <br>
+ <b>\textstyle \large \sum_{i=1}^ni=\frac{n(n+1)}2</b>
+ &nbsp; &nbsp; produces &nbsp; &nbsp;
+ <a href="#preview"><img id="modes2b" onclick="eqntext('modes2b')"
+ src="../cgi-bin/mimetex.cgi?\textstyle\large
+ \sum_{i=1}^ni=\frac{n(n+1)}2" alt="" border=0 align=middle></a>.
+ <!-- &nbsp; instead. --> </center>
+
+ <p> As usual, <b>\nolimits</b> turns displaystyle off (or textstyle on)
+ for the operator immediately preceding it. For example, </p> <center>
+ <b>\large \sum\nolimits_{i=1}^ni=\frac{n(n+1)}2</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes3" onclick="eqntext('modes3')"
+ src="../cgi-bin/mimetex.cgi?
+ \large\sum\nolimits_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a></center> <p class="continue">
+ and likewise, <b>\limits</b> turns displaystyle on for the operator
+ immediately preceding it. For example, </p> <center>
+ <b>\normalsize \sum\limits_{i=1}^ni=\frac{n(n+1)}2</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes4" onclick="eqntext('modes4')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize\sum\limits_{i=1}^ni=\frac{n(n+1)}2"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> By the way, <b>\limits</b> affects <i><b>_any_</b></i> character
+ or subexpression immediately preceding it. For example, </p> <center>
+ <b>A^i_j</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes5" onclick="eqntext('modes5')"
+ src="../cgi-bin/mimetex.cgi?\large A^i_j"
+ alt="" border=0 align=middle></a> &nbsp; &nbsp; as usual, whereas <br>
+ <b>A\limits^i_j</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes6" onclick="eqntext('modes6')"
+ src="../cgi-bin/mimetex.cgi?\large A\limits^i_j"
+ alt="" border=0 align=middle></a> &nbsp; instead. </center>
+ <p class="continue">Likewise, for subexpressions, </p> <center>
+ <b>\widehat{xyz}\limits^a</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes7" onclick="eqntext('modes7')"
+ src="../cgi-bin/mimetex.cgi?\large\widehat{xyz}\limits^a"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ This side effect may occasionally be useful. For example, </p> <center>
+ <b>x\rightarrow\limits^gy</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes8" onclick="eqntext('modes8')"
+ src="../cgi-bin/mimetex.cgi?\large x\rightarrow\limits^gy"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ (mimeTeX automatically centers super/subscripts above/below
+ the long and Long <a href="#arrows">arrow</a> forms) </p>
+
+ <p> The <b>\displaystyle</b> command turns on displaystyle math mode for
+ the entire expression (or <b>{&nbsp;}</b>-enclosed subexpression),
+ affecting <b><i>_all_</i></b> super/subscripts to the right
+ of the \displaystyle, except for character classes Ordinary and
+ Variable (TeXbook page 154). Similarly, <b>\textstyle</b> turns
+ off displaystyle math mode. For example, </p> <center>
+ <b>\sum_1^n {\displaystyle\sum_1^k\sum_1^lx_i^j} \sum_1^m</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="modes9" onclick="eqntext('modes9')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\sum_1^n
+ {\displaystyle\sum_1^k\sum_1^lx_i^j}\sum_1^m"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ Note that <b>\sum</b>'s within the subexpression are all affected by
+ the beginning <b>\displaystyle</b>, but not the Variable <b>x_i^j</b>.
+ An explicit <b>x\limits_i^j</b> always affects any preceding term. </p>
+
+<h3> <a name="textboxes">text boxes<font size=5>...</font></a> </h3>
+
+ <p> Finally, mimeTeX also has a text-like/roman mode
+ entered by writing either <b>\text{anything&nbsp;at&nbsp;all}</b>
+ or the equivalent LaTeX-2.09-like command
+ <b>{\rm&nbsp;anything&nbsp;at&nbsp;all}</b>, both of which render
+ <b>anything&nbsp;at&nbsp;all</b> in roman (font family cmr10).
+ <b>\mbox{&nbsp;}</b> and several similar LaTeX commands are
+ recognized by mimeTeX as synonyms for <b>\text{&nbsp;}</b>.
+ For italic, write <b>\textit{anything&nbsp;at&nbsp;all}</b> or
+ <b>{\it&nbsp;anything&nbsp;at&nbsp;all}</b>, both of which render
+ <b>anything&nbsp;at&nbsp;all</b> in italic (font family cmmi10).
+ All four forms respect spaces between words, except that the
+ first/required space after <b>{\rm&nbsp;etc}</b> and
+ <b>{\it&nbsp;etc}</b> is still ignored. <!-- Math <b>$...$</b>
+ subexpressions inside <b>\mbox{&nbsp;}</b> or <b>\text{&nbsp;}</b>
+ are treated in the usual way. --> For example, </p> <center>
+ <b>anything&nbsp;at&nbsp;all</b> &nbsp; just produces &nbsp;
+ <a href="#preview"><img id="textboxes1" onclick="eqntext('textboxes1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize anything at all"
+ alt="" border=0 align=middle></a> &nbsp; &nbsp; whereas <br> <br>
+ <b>\text{anything&nbsp;at&nbsp;all}</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="textboxes2" onclick="eqntext('textboxes2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\text{anything at all}"
+ alt="" border=0 align=middle></a> &nbsp; &nbsp; and <br> <br>
+ <b>\textit{anything&nbsp;at&nbsp;all}</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="textboxes3" onclick="eqntext('textboxes3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\textit{anything at all}"
+ alt="" border=0 align=middle></a> &nbsp; &nbsp; instead. </center>
+
+ <p> You don't usually surround mimeTeX expressions with <b>$</b>'s,
+ but that works in the usual way for <b>\text{&nbsp;}</b> and
+ <b>\mbox{&nbsp;}</b>, rendering the <b>$...$</b>-enclosed
+ subexpression in mathmode. For example, </p> <center>
+ <b>n=\left\{m/2\text{&nbsp; &nbsp; if $m$ even}
+ \\(m+1)/2\text{&nbsp; if $m$ odd}\right.</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="textboxes9" onclick="eqntext('textboxes9')"
+ src="../cgi-bin/mimetex.cgi?
+ n=\left\{m/2\text{ if $m$ even}\\(m+1)/2\text{ if $m$ odd}\right."
+ alt="" border=0 align=middle></a> </center>
+
+
+<h2> <a name="delimiters"> (IIIc) Delimiters &nbsp; </a> </h2>
+
+<h3> <a name="parens">Parentheses and Braces
+(delimiters)<font size=5>...</font></a> </h3>
+
+ <p> LaTeX's <b>\left(&nbsp;...&nbsp;\right)</b> and the other 21
+ standard LaTeX delimiters are also recognized by mimeTeX.
+ And mimeTeX also recognizes an etex-like <b>\middle</b>. &nbsp;
+ <!-- may be written exactly
+ like that, or may be abbreviated <b>\(</b> and <b>\)</b> in mimeTeX.
+ Not all <b>\left</b> and <b>\right</b> LaTeX delimiters are currently
+ available in mimeTeX, but those that are can be written in the usual
+ way, or can be abbreviated as described above. One exception is
+ that <b>\left\|...\right\|</b> must instead be abbreviated
+ <b>\=...\=</b> or can be written in full <b>\left\|...\right\|</b>
+ as usual. Also, <b>\left\langle...\right\rangle</b> is abbreviated
+ <b>\&lt;...\&gt;</b>&nbsp;. </p> -->
+ <!-- <p> Mixing abbreviated and unabbreviated delimiters within
+ a matching pair is not allowed, e.g., \left(...\) <b>_won't_</b> work.
+ But you can mix nested pairs, e.g., <b>\left(...\(...\)...\right)</b>
+ will work as long as the matching delimiters comprising each pair are
+ either both abbreviated or both unabbreviated. </p>
+ <p> --> Several of the most common automatically sized delimiters
+ are illustrated below... </p> <center>
+ <!-- <table cellpadding=3 cellspacing=0 border=1> -->
+ <table cellspacing=0 cellpadding=2 border=1>
+ <tr align=center>
+ <!-- <td> <b>LaTeX or <br> mimeTeX</b> </td> -->
+ <td> <b>Delimiter</b> </td>
+ <!-- <td> <b>or mimeTeX <br> abbreviation</b> </td> -->
+ <td> <b>example...</b> </td>
+ <td> <b>...renders</b> </td>
+ </tr>
+ <tr align=center>
+ <td> \left(&nbsp;...&nbsp;\right) </td>
+ <!-- <td> \(&nbsp;...&nbsp;\) </td> -->
+ <td> \left( \frac1{1-x^2} \right)^2 </td>
+ <td> <a href="#preview"><img id="parens1" onclick="eqntext('parens1')"
+ src="../cgi-bin/mimetex.cgi?\Large\left(\frac1{1-x^2}\right)^2"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left[&nbsp;...&nbsp;\right] </td>
+ <!-- <td> \[&nbsp;...&nbsp;\] </td> -->
+ <td> \left[ \frac1{\sqrt2}x - y \right]^n </td>
+ <td> <a href="#preview"><img id="parens2" onclick="eqntext('parens2')"
+ src="../cgi-bin/mimetex.cgi?\Large
+ \left[ \frac1{\sqrt2}x - y \right]^n"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left\{&nbsp;...&nbsp;\right\} </td>
+ <!-- <td> \{&nbsp;...&nbsp;\} </td> -->
+ <td> \left\{ 1^2,2^2,3^2,\ldots \right\} </td>
+ <td> <a href="#preview"><img id="parens3" onclick="eqntext('parens3')"
+ src="../cgi-bin/mimetex.cgi?
+ \large\left\{1^2,2^2,3^2,\ldots\right\}"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left\langle &nbsp; ...<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; ... &nbsp;\right\rangle </td>
+ <!-- <td> \<&nbsp;...&nbsp;\> </td> -->
+ <td> \left\langle \varphi \middle| \hat H <br>
+ &nbsp; &nbsp; &nbsp; &nbsp; \middle| \phi \right\rangle </td>
+ <td> <a href="#preview"><img id="parens4" onclick="eqntext('parens4')"
+ src="../cgi-bin/mimetex.cgi?\Large
+ \left\langle\varphi\middle|\hat H\middle|\phi\right\rangle"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left|&nbsp;...&nbsp;\right| </td>
+ <!-- <td> \|&nbsp;...&nbsp;\| </td> -->
+ <td> \left| \begin{matrix} a_1 & a_2 \\<br>
+ &nbsp; &nbsp; &nbsp; a_3 & a_4 \end{matrix} \right|</td>
+ <td> <a href="#preview"><img id="parens5" onclick="eqntext('parens5')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \left|\begin{matrix}a_1&a_2\\a_3&a_4\end{matrix}\right|"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left\|&nbsp;...&nbsp;\right\| </td>
+ <!-- <td> \=&nbsp;...&nbsp;\= </td> -->
+ <td> \left\|x^2-y^2\right\| </td>
+ <td> <a href="#preview"><img id="parens6" onclick="eqntext('parens6')"
+ src="../cgi-bin/mimetex.cgi?\large\left\|x^2-y^2\right\|"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left\{&nbsp;...&nbsp;
+ \right<font size="5"><b>.</b></font> </td>
+ <!-- <td> \{&nbsp;...&nbsp;\<b>.</b> </td> -->
+ <td> y=\left\{ \text{this\\that}
+ \right<font size="5"><b>.</b></font> </td>
+ <td> <a href="#preview"><img id="parens7" onclick="eqntext('parens7')"
+ src="../cgi-bin/mimetex.cgi?
+ \large y=\left\{\text{this\\that}\right."
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ <tr align=center>
+ <td> \left<font size="5"><b>.</b></font>
+ &nbsp;...&nbsp;\right\} </td>
+ <!-- <td> \<b>.</b>&nbsp;...&nbsp;\} </td> -->
+ <td> \left<font size="5"><b>.</b></font>
+ \text{this\\that} \right\}=y </td>
+ <td> <a href="#preview"><img id="parens8" onclick="eqntext('parens8')"
+ src="../cgi-bin/mimetex.cgi?
+ \large\left.\text{this\\that}\right\}=y"
+ alt="" border=0 align=middle></a> </td>
+ </tr>
+ </table> </center>
+ <p> <b><u>Notes...&nbsp;</u></b> </p>
+ <ol compact type=1>
+ <!-- <li> The other LaTeX delimiters, i.e., floor's, ceil's,
+ arrows, etc, can't yet be sized to fit. </li> -->
+ <li> <a href="#sizes">Size&nbsp;declarations</a> inside any of the
+ above delimiter pairs affect only the enclosed subexpression,
+ e.g., <b>\Large w=\left(\small x+y\right)+z</b> produces
+ <a href="#preview"><img id="parens9" onclick="eqntext('parens9')"
+ src="../cgi-bin/mimetex.cgi?\Large w=\left(\small x+y\right)+z"
+ alt="" border=0 align=middle></a> </li>
+ <li> An expression may contain as many etex-like <b>\middle</b>'s as
+ you like, and in mimeTeX the surrounding <b>\left...\right</b>
+ isn't required. When omitted, the scope of <b>\middle</b> is
+ either the entire expression or the &nbsp; <b>{&nbsp;}</b>-enclosed
+ subexpression in which the <b>\middle</b>'s occur. For example, &nbsp;
+ <b>\frac{a+1}b&nbsp;\middle/&nbsp;\middle(\frac{c+1}d&nbsp;\middle/&nbsp;\frac{e+1}f\middle)</b>
+ &nbsp; renders &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?\large
+ \frac{a+1}b\middle/\middle(\frac{c+1}d\middle/\frac{e+1}f\middle)"
+ border=0 align=middle>. </li>
+ <li> In the last two examples, note that mimeTeX recognizes the
+ &nbsp; <b>\\</b> &nbsp; in &nbsp; <b>\text{this\\that}</b> &nbsp;
+ as a linebreak. For example, <b>x=1\\y=2\\z=3</b> renders &nbsp;
+ <a href="#preview"><img id="parens9b" onclick="eqntext('parens9b')"
+ src="../cgi-bin/mimetex.cgi?\small x=1\\y=2\\z=3"
+ alt="" border=0 align=middle></a> </li>
+ <!-- <li> An abbreviated left delimiter must be paired with the same
+ "type" of matching right delimiter, e.g., <b>\[...\]</b> works
+ whereas <b>\[...\)</b> doesn't work. To render an "unmatched"
+ pair of delimiters you must use the unabbreviated form, e.g.,
+ <b>\left[...\right)</b> works fine. </li> -->
+ <!-- <li> Similarly, "unusual" delimiter abbreviations like
+ <b>\)...\(</b> also don't work in mimeTeX. That is, &nbsp;
+ <b>(,&nbsp;[,&nbsp;&lt;,&nbsp;{,</b> etc, must always be "left"
+ in mimeTeX, and &nbsp; <b>),&nbsp;],&nbsp;&gt;,&nbsp;},</b> etc,
+ must always be "right". To render "unusual" delimiter pairs you
+ must use the unabbreviated form, e.g., <b>\left)...\right[</b>
+ works fine. </li> -->
+ <!-- <li> <b>\right.</b> may be paired with any of the automatically
+ sized delimiters, and may optionally be abbreviated as <b>\.</b>
+ &nbsp;&nbsp; The same <b>\.</b> also serves as an abbreviation
+ for <b>\left.</b> &nbsp;&nbsp; MimeTeX correctly interprets your
+ intention if you correctly balance delimiters. For example,
+ either <b>y=\left\{{this\atop&nbsp;that}\right.</b> or
+ <b>y=\{{this\atop&nbsp;that}\.</b> renders the usual useful
+ construction
+ <a href="#preview"><img id="parens10" onclick="eqntext('parens10')"
+ src="../cgi-bin/mimetex.cgi?
+ \normalsize y=\{\text{this\atop that}\."
+ alt="" border=0 align=middle></a> illustrated above. </li> -->
+ <!-- <li> However, abbreviated <b>\.</b>'s cannot be nested in mimeTeX,
+ e.g., <b>\[\(...\.\.</b> doesn't work. Instead, unabbreviated
+ <b>\left.</b> and <b>\right.</b> may be nested, e.g.,
+ <b>\left[\left(...\right.\right.</b> works fine. </li> -->
+ <!-- <li> Simply nested abbreviations like <b>\[\(...\)\]</b> work
+ fine in mimeTeX. But abbreviated delimiters like <b>\|...\|</b>
+ and <b>\=...\=</b>, whose left and right forms are
+ identical, cannot be nested. To nest these delimiters you
+ must use the corresponding unabbreviated <b>\left|..\right|</b>
+ and <b>\left\|...\right\|</b>. </li> -->
+ <!-- <li> All <b>\left(...\right)</b>'s (and abbreviated
+ <b>\(...\)</b>'s), etc, must be correctly balanced,
+ which may include being matched with <b>\left.</b>
+ or <b>\right.</b> (or abbreviated <b>\.</b>).
+ &nbsp;&nbsp; And, to repeat, you may <b>_not_</b> mix
+ abbreviated and unabbreviated \(...\right), etc, within a
+ matching pair. </li> -->
+ </ol>
+
+ <p> Besides the <b>\left...\right</b> delimiters discussed above,
+ mimeTeX also supports constructions like
+ <b>\left\int_a^b...\right<b>.</b></b>&nbsp;, which automatically
+ sizes the <b>\left\int</b> to accommodate everything between it
+ and its matching <b>\right<b>.</b></b> &nbsp; delimiter.
+ The <b>\right</b> delimiter needn't necessarily be
+ the <b>\right<b>.</b></b> &nbsp; illustrated, e.g.,
+ <b>\left\int_a^b&nbsp;x^2dx&nbsp;=\frac{x^3}3\right|_a^b</b>
+ produces
+ <a href="#preview"><img id="parens11" onclick="eqntext('parens11')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \left\int_a^bx^2dx=\frac{x^3}3\right|_a^b" border=0 alt=""
+ align=middle></a>. <!-- Except for Opening (TeX class 4) and
+ Closing (class 5) delimiter characters like <b>(&nbsp;)</b> and
+ <b>[&nbsp;]</b> and <b>\{&nbsp;\}</b>, limits are default-rendered
+ \displaystyle, which is why <b>\right|\nolimits_a^b</b> was required. -->
+ You can also write <b>\left\sum</b>, <b>\left\prod</b>,
+ <b>\left\cup</b>, etc, for many of the symbols in CMEX10 and STMARY10.
+ And any symbol that works with <b>\left</b> will also work
+ with <b>\right</b>&nbsp;. <!-- But mimeTeX abbreviations like &nbsp;
+ <b>\(...\)</b> &nbsp; for &nbsp; <b>\left(...\right)</b> &nbsp;
+ won't work with any of these CMEX10 symbols. You'll have to write
+ the usual unabbreviated <b>\left...\right</b> form. --> </p>
+
+ <p> Unescaped <b>(&nbsp;)</b>'s and <b>[&nbsp;]</b>'s and <b>|&nbsp;|</b>'s
+ and <b>&lt;&nbsp;&gt;</b>'s don't need to be balanced since mimeTeX just
+ displays them like ordinary characters without any special significance.
+ Ditto for the usual four <b>\big(</b> and <b>\Big(</b> and <b>\bigg(</b>
+ and <b>\Bigg(</b>, and for their four right <b>)</b> counterparts, which
+ just display <b>(...)</b>'s at fixed larger sizes, and also have no
+ special significance. All four big <b>[&nbsp;]</b>'s and
+ <b>&lt;&nbsp;&gt;</b>'s and <b>{&nbsp;}</b>'s are also available
+ as ordinary characters. </p>
+
+ <p> As usual, unescaped <b>{...}</b>'s aren't displayed at all,
+ must be balanced, and have the usual special LaTeX significance.
+ MimeTeX interprets escaped <b>\{...\}</b>'s as abbreviations
+ for <b>\left\{...\right\}</b> and therefore always sizes them to fit.
+ If you need displayed but unsized <b>{...}</b>'s, write
+ <b>\lbrace...\rbrace</b> or any of the four <b>\big{...\big}</b>'s. </p>
+
+
+<h2> <a name="accents"> (IIId) Accents, Functions, Arrows,
+Raise&nbsp;and&nbsp;rotate, Compose, Abbreviations, etc. &nbsp; </a> </h2>
+
+<h3> Accents<font size=5>...</font> </h3>
+
+ <p class="continue">
+ <b>\vec{&nbsp;} \hat{&nbsp;} \bar{&nbsp;} \tilde{&nbsp;} \dot{&nbsp;}
+ \ddot{&nbsp}</b> &nbsp; and &nbsp; <b>\acute{&nbsp;} \grave{&nbsp;}
+ \breve{&nbsp;} \check{&nbsp}</b> are the only accents currently
+ supported. The first four are all "wide". For example, you can write
+ <b>\widehat{&nbsp;}</b> if you like, but there's absolutely no
+ difference either way (and <b>\bar{&nbsp;}</b> and
+ <b>\overline{&nbsp;}</b> are identical). The last four accents
+ only take a single character argument. <p>
+
+ <p> Other accent-like directives available in mimeTeX are &nbsp;
+ <b>\underline{&nbsp;} \cancel{&nbsp;} \sout{&nbsp;}</b>, &nbsp;
+ as well as &nbsp;
+ <b>\overset{&nbsp;}{&nbsp;} &nbsp; \underset{&nbsp;}{&nbsp;}</b> &nbsp;
+ and the more ususal &nbsp;
+ <b>\overbrace{&nbsp;}^{&nbsp;} &nbsp; \underbrace{&nbsp;}_{&nbsp;}</b>.
+ &nbsp; And <b>\not</b> also works on the single character immediately
+ following it. Some of these directives are discussed in more detail
+ below. </p>
+
+<h3> <a name="functions">Function names<font size=5>...</font></a> </h3>
+
+ <p> All 32 usual LaTeX function names <b>\arccos</b>,...,<b>\tanh</b>
+ are recognized by mimeTeX and treated in the usual way. MimeTeX
+ also recognizes <b>\tr</b> for the trace, and also <b>\bmod</b>
+ and <b>\pmod</b>. And those functions that normally take "limits"
+ also behave as expected, e.g., </p> <center>
+ <b>\lim_{n\to\infty}S_n=S</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="functions1" onclick="eqntext('functions1')"
+ src="../cgi-bin/mimetex.cgi?\large\lim_{n\to\infty}S_n=S"
+ alt="" border=0 align=middle></a> </center>
+
+<h3> <a name="arrows">long Arrows<font size=5>...</font></a> </h3>
+
+ <p> All mimeTeX \long and \Long arrows take an optional [width] argument
+ that explicitly sets the arrow's width in pixels, scaled by
+ <a href="#unitlength">\unitlength</a>. For example,
+ <b>\longrightarrow[50]</b> draws a 50-pixel wide arrow
+ <a href="#preview"><img id="arrows1" onclick="eqntext('arrows1')"
+ src="../cgi-bin/mimetex.cgi?\longrightarrow[50]" alt="" border=0
+ align=middle></a>, whereas just <b>\longrightarrow</b> calculates
+ a default width
+ <a href="#preview"><img id="arrows2" onclick="eqntext('arrows2')"
+ src="../cgi-bin/mimetex.cgi?\longrightarrow" alt="" border=0
+ align=middle></a>, as usual. And, in addition to the usual
+ right, left and leftright arrows, there are also \long (and \Long) up,
+ down and updown arrows that take an optional [height] argument, also
+ scaled by any preceding <a href="#unitlength">\unitlength</a>. </p>
+
+ <p> In the event that you actually want to place an []-enclosed expression
+ immediately following an "unsized" long arrow, just place a <b>~</b> or
+ any white space after the arrow, e.g., <b>f:x\longrightarrow~[0,1]</b>
+ produces
+ <a href="#preview"><img id="arrows3" onclick="eqntext('arrows3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize f:x\longrightarrow~[0,1]"
+ alt="" border=0 align=middle></a>. Without any intervening white space,
+ mimeTeX would have "eaten" the [0,1]. </p>
+
+ <p> Super/subscripts immediately following all long/Long left/right arrows
+ are displayed the same way <a href="#modes">\limits</a> displays them,
+ e.g., </p> <center>
+ <b>x\longrightarrow^gy</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="arrows4" onclick="eqntext('arrows4')"
+ src="../cgi-bin/mimetex.cgi?\large x\longrightarrow^gy"
+ alt="" border=0 align=middle></a> <br>
+ <b>x\longrightarrow[50]^gy</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="arrows5" onclick="eqntext('arrows5')"
+ src="../cgi-bin/mimetex.cgi?\large x\longrightarrow[50]^gy"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ Subscripted long arrows can occasionally be useful, too, as in
+ <a href="#example11">Example&nbsp;11</a> above, e.g., </p> <center>
+ <b>u\longrightarrow[50]_\beta v</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="arrows6" onclick="eqntext('arrows6')"
+ src="../cgi-bin/mimetex.cgi?\large u\longrightarrow[50]_\beta^{\,}v"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ To defeat this default behavior, e.g., <b>\longrightarrow\nolimits^g</b>
+ displays super/subscripts in the usual way. </p>
+
+ <p> Super/subscripts immediately following all long/Long up/down arrows
+ are treated correspondingly, i.e., superscripts are vertically
+ centered to the arrow's left, and subscripts to its right.
+ For example, </p> <center>
+ <b>\longuparrow[30]^\gamma</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="arrows7" onclick="eqntext('arrows7')"
+ src="../cgi-bin/mimetex.cgi?\large\longuparrow[30]^\gamma"
+ alt="" border=0 align=middle></a> <br>
+ <b>\longdownarrow[30]_\gamma</b> &nbsp; produces &nbsp; &nbsp; &nbsp;
+ <a href="#preview"><img id="arrows8" onclick="eqntext('arrows8')"
+ src="../cgi-bin/mimetex.cgi?\large\longdownarrow[30]_\gamma"
+ alt="" border=0 align=middle></a> </center> <p class="continue">
+ whose occasional usefulness is also illustrated by
+ <a href="#example11">Example&nbsp;11</a>. And as before, to defeat
+ this default behavior, e.g., <b>\longuparrow\nolimits^\gamma</b>
+ displays super/subscripts in the usual way. </p>
+
+<h3> <a name="raiserotate">\raisebox{&nbsp;}{&nbsp;} and
+\rotatebox{&nbsp;}{&nbsp;} and \reflectbox[&nbsp;]{&nbsp;}
+<font size=5>...</font></a> </h3>
+
+ <p> The <b>\raisebox{<i>height</i>}{<i>expression</i>}</b>
+ and <b>\rotatebox{<i>angle</i>}{<i>expression</i>}</b>
+ and <b>\reflectbox[<i>axis</i>]{<i>expression</i>}</b>
+ commands help you fine-tune and manipulate mimeTeX renderings: </p>
+ <ul>
+ <li> <b>\raisebox</b>'s <b><i>height</i></b> argument is number
+ of pixels, scaled by <a href="#unitlength">\unitlength</a>,
+ and can be positive or negative. </li>
+ <li> <b>\rotatebox</b>'s <b><i>angle</i></b> argument is number
+ of degrees, and can also be positive (for clockwise) or
+ negative, but must be a multiple of 90. </li>
+ <li> <b>\reflectbox</b>'s optional <b><i>axis</i></b> argument
+ defaults to 1 if not given, which reflects horizontally
+ (the usual LaTeX behavior), or reflects vertically if
+ specified as 2. </li>
+ <li> For all three commands, the <b><i>expression</i></b>
+ can be any valid LaTeX/mimeTeX expression. </li>
+ </ul>
+ <p> For example, mimeTeX's preprocessor
+ defines the LaTeX <b>?`</b> symbol, an upside-down question
+ mark, like </p> <center>
+ <b>abc\raisebox{-2}{\rotatebox{180}?}def</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="raiserot1" onclick="eqntext('raiserot1')"
+ src="../cgi-bin/mimetex.cgi?
+ \large\rm abc\raiseb{-2}{\rotateb{180}{\LARGE?}}def"
+ alt="" border=0 align=middle></a> </center>
+ <p> Using <b>\reflectbox[2]{&nbsp;}</b> instead of
+ <b>\rotatebox{180}{&nbsp;}</b> would result in the slightly
+ different </p> <center>
+ <b>abc\raisebox{-2}{\reflectbox[2]?}def</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="raiserot2" onclick="eqntext('raiserot2')"
+ src="../cgi-bin/mimetex.cgi?
+ \large\rm abc\raiseb{-2}{\reflectb[2]{\LARGE?}}def"
+ alt="" border=0 align="bottom"></a> </center>
+
+<h3> <a name="compose">\compose{&nbsp;}{&nbsp;}<font size=5>...</font></a></h3>
+
+ <p class="continue">
+ <b>\compose[<i>offset</i>]{<i>base</i>}{<i>overlay</i>}</b>
+ superimposes the <b><i>overlay</i></b> expression on top of the
+ <b><i>base</i></b> expression, displaying the result.
+ The superimposed <b><i>overlay</i></b> is centered, both
+ horizontally and vertically, on the <b><i>base</i></b> image,
+ with the composite image baseline
+ <!-- the same as the <b><i>base</i></b>. -->
+ completely ignored.
+ That means the <b><i>base</i></b> remains positioned in your expression
+ just as if it had been rendered alone, while the <b><i>overlay</i></b>
+ is moved around, vertically as well as horizontally, to accommodate it.
+ For example, </p> <center>
+ <b>\compose{\LARGE O}{\normalsize c}</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="compose1" onclick="eqntext('compose1')"
+ src="../cgi-bin/mimetex.cgi?\compose{\LARGE O}{\normalsize c}"
+ alt="" border=0 align="bottom"></a> </center>
+
+ <p> Optionally, the <b><i>overlay</i></b> is horizontally
+ <b><i>offset</i></b> by the specified number of pixels
+ (positive offsets to the right, negative to the left).
+ For example, </p> <center>
+ <b>\compose[-4]{\LARGE O}{\normalsize c}</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="compose2" onclick="eqntext('compose2')"
+ src="../cgi-bin/mimetex.cgi?\compose[-4]{\LARGE O}{\normalsize c}"
+ alt="" border=0 align="bottom"></a> </center>
+
+ <p> Vertical offset can be obtained using a <b>\raisebox</b>
+ in either the <b><i>base</i></b> or <b><i>overlay</i></b>
+ expression, or in both. (Although, note that
+ <b>\compose{\raisebox{10}{<i>base</i>}}{<i>overlay</i>}</b>
+ renders identically to
+ <b>\raisebox{10}{\compose{<i>base</i>}{<i>overlay</i>}}</b>,
+ so applying <b>\raisebox</b> to the <b><i>base</i></b>
+ expression is typically unnecessary.)
+ Vertical <b><i>overlay</i></b> offset is relative to the
+ centered image, as discussed immediately above,
+ i.e.,&nbsp;<b>\compose{<i>base</i>}{\raisebox{0}{<i>overlay</i>}}</b>
+ has no effect at all, and the <b><i>overlay</i></b> image
+ remains centered on the <b><i>base</i></b>.
+ For example, </p> <center>
+ <b>abc\compose{\LARGE O}{\raisebox{5}{\normalsize c}}def</b>
+ &nbsp; renders &nbsp;
+ <a href="#preview"><img id="compose3" onclick="eqntext('compose3')"
+ src="../cgi-bin/mimetex.cgi?
+ abc\compose{\LARGE O}{\raisebox{5}{\normalsize c}}def"
+ alt="" border=0 align="bottom"></a>, and <br>
+ <b>abc\compose{\raisebox{10}{\LARGE O}}{\raisebox{-20}{\normalsize c}}def</b>
+ &nbsp; renders &nbsp;
+ <a href="#preview"><img id="compose3" onclick="eqntext('compose3')"
+ src="../cgi-bin/mimetex.cgi?abc
+ \compose{\raisebox{10}{\LARGE O}}{\raisebox{-20}{\normalsize c}}def"
+ alt="" border=0 align="bottom"></a></center>
+
+ <p> Separately or in some judicious combination, <b>\compose</b> and
+ <b>\raisebox</b> and <b>\rotatebox</b> and <b>\reflectbox</b>,
+ discussed above, perhaps along with <b>\rule</b> and <b>\eval</b>
+ discussed immediately below, may help you construct special symbols
+ not "natively" available with mimeTeX's limited set of built-in font
+ families. This can be especially useful in conjunction with the
+ <a href="#newcommands">&#150;DNEWCOMMANDS</a> compile-time
+ <a href="#options">option</a> discussed above. </p>
+
+<h3> <a name="rule">\rule{&nbsp;}{&nbsp;}<font size=5>...</font></a></h3>
+
+ <p class="continue">
+ <b>\rule{<i>width</i>}{<i>height</i>}</b> behaves in the usual way,
+ rendering a black rectangle <b><i>width</i></b> pixels wide and
+ <b><i>height</i></b> pixels high, with its base on the established
+ baseline. For example, </p> <center>
+ <b>\frac12xyz\rule{10}{20}ghi</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="rule1" onclick="eqntext('rule1')"
+ src="../cgi-bin/mimetex.cgi?\frac12xyz\rule{10}{20}ghi"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> The mimeTeX version of <b>\rule</b> has an optional
+ <b>[<i>lift</i>]</b> argument, so that its full form is
+ <b>\rule[<i>lift</i>]{<i>width</i>}{<i>height</i>}</b>.
+ <b><i>lift</i></b> moves the rule's baseline by the specified
+ number of pixels, up if positive or down if negative.
+ For example, </p> <center>
+ <b>\frac12xyz\rule[5]{10}{20}ghi</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="rule2" onclick="eqntext('rule2')"
+ src="../cgi-bin/mimetex.cgi?\frac12xyz\rule[5]{10}{20}ghi"
+ alt="" border=0 align=middle></a> &nbsp; and <br>
+ <b>\frac12xyz\rule[-15]{10}{20}ghi</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="rule3" onclick="eqntext('rule3')"
+ src="../cgi-bin/mimetex.cgi?\frac12xyz\rule[-15]{10}{20}ghi"
+ alt="" border=0 align=middle></a> </center>
+
+<h3> <a name="evaluate">\eval{&nbsp;}<font size=5>...</font></a> </h3>
+
+ <p class="continue"> mimeTeX can evaluate arithmetic expressions,
+ which is a feature intended primarily for use in
+ <a href="#newcommands">\newcommand's</a> discussed above.
+ Expressions can be built up from the following elements </p>
+ <ul>
+ <li> digits &nbsp; <b>0</b>-<b>9</b>
+ &nbsp; and numbers composed of uninterrupted (no whitespace)
+ sequences of digits, </li>
+ <li> binary operators &nbsp;
+ <b>+</b>,&nbsp;<b>-</b>,&nbsp;<b>*</b>,&nbsp;<b>/</b>,&nbsp;<b>%</b>
+ &nbsp; (<b>+</b>&nbsp;and&nbsp;<b>-</b> can be unary, preceding
+ the first number in an expression, and&nbsp;<b>%</b>&nbsp;is
+ the modulo operator), </li>
+ <li> balanced &nbsp; <b>(</b>&nbsp;...&nbsp;<b>)</b>
+ &nbsp; parentheses nested to any level (see below), </li>
+ <li> whitespace anywhere
+ (except between digits comprising a number), </li>
+ <li> One additional construction interpreted by <b>\eval{&nbsp;}</b>
+ is similar to (but not identical to) the
+ <a href="http://wikipedia.org/wiki/Conditional_(programming)#As_a_ternary_operator"
+ target="_top">?:&nbsp;conditional</a>, as follows.
+ The expression <b>(i?v0:v1:v2:<i>etc</i>)</b>, usually
+ parenthesized as illustrated, evaluates to <b>v0</b>
+ if <b>i</b> evaluates to <b>0</b>, or evaluates to <b>v1</b>
+ if <b>i</b> evaluates to <b>1</b>, etc. If <b>i&nbsp;&lt;&nbsp;0</b>
+ then <b>v0</b> is used, and if <b>i</b> is too large, the last
+ <b>v</b> is used. All components, <b>i</b> and all <b>v</b>'s,
+ can themselves be expressions, even another
+ <b>(i?v0:v1:v2:<i>etc</i>)</b>, which in this case must be
+ parenthesized. The only situation where parentheses aren't
+ required is when <b>i?v0:v1:v2:<i>etc</i></b> comprises
+ your entire expression.
+ For example, <br> <nobr>&nbsp; &nbsp; &nbsp;
+ <b>\eval{1+2?10:11:12:13:14:15}</b> renders
+ <a href="#preview"><img id="eval1" onclick="eqntext('eval1')"
+ src="../cgi-bin/mimetex.cgi?\large\eval{1+2?10:11:12:13:14:15}"
+ alt="" border=0 align=bottom></a></nobr></li>
+ <li> and <u>&nbsp;most&nbsp;importantly,&nbsp;</u>
+ the built-in variables<br>
+ &nbsp; &nbsp; &nbsp; <b>fs</b> for current fontsize and<br>
+ &nbsp; &nbsp; &nbsp; <b>unitlength</b> for unitlength<br>
+ which provide the capability for useful constructions,
+ as follows... </li>
+ </ul>
+
+ <p> All optional <b>[</b>&nbsp;<b>]</b> and mandatory
+ <b>{</b>&nbsp;<b>}</b> numeric arguments for &nbsp;
+ <a href="#rule">\rule[lift]{width}{height}</a>, &nbsp;
+ <a href="#compose">\compose[offset]{&nbsp;}{&nbsp;}</a>, &nbsp;
+ <a href="#raiserotate">\raisebox{height}{&nbsp;}</a>, &nbsp;
+ <a href="#raiserotate">\rotatebox{angle}{&nbsp;}</a>, &nbsp; and &nbsp;
+ <a href="#arrows">\longarrow[width]</a> &nbsp;
+ can be expressions as described above, rather than just
+ numeric constants. By using the <b>fs</b> variable, you can
+ construct <a href="#newcommands">\newcommand</a>
+ expressions that properly scale with font&nbsp;size.
+ For example, the <b>\mapsto</b> symbol is not explicitly provided
+ in any mimeTeX font, but is instead constructed by the
+ embedded <a href="#newcommands">\newcommand</a><br>
+ <nobr>&nbsp; &nbsp; &nbsp;<b>
+ { "\\mapsto", NULL, "{\\rule[fs/2]{1}{5+fs}\\hspace{-99}\\to}" },</b>
+ </nobr><br>
+ where \rule's [lift]=fs/2 and {height}=5+fs are scaled by
+ font&nbsp;size to render symbols<br>
+ &nbsp;
+ <a href="#preview"><img id="eval2" onclick="eqntext('eval2')"
+ src="../cgi-bin/mimetex.cgi?\small\text\begin{array}{rrl}
+ \backslash tiny & fs=\tiny\eval{fs} & \tiny\mapsto \\
+ \backslash small & fs=\small\eval{fs} & \small\mapsto \\
+ \backslash normalsize & fs=\normal\eval{fs} & \normal\mapsto\\
+ \backslash large & fs=\large\eval{fs} & \large\mapsto \\
+ etc. & &
+ \end{array}" alt="" border=0 align=middle></a><br>
+ whose rendering automatically varies appropriately with font&nbsp;size.
+ This kind of <a href="#newcommands">\newcommand</a> construction
+ is the primary use intended for mimeTeX's expression evaluation feature.
+ </p>
+
+ <p> But mimeTeX also provides the <b>\eval{<i>expression</i>}</b>
+ command to make the expression evaluation feature render
+ &quot;visible&quot; results. It's not particularly useful,
+ but an expression like &nbsp; <b>1+2+3+4+5=\eval{1+2+3+4+5}</b> &nbsp;
+ renders &nbsp;
+ <a href="#preview"><img id="eval2" onclick="eqntext('eval2')"
+ src="../cgi-bin/mimetex.cgi?\small 1+2+3+4+5=\eval{1+2+3+4+5}"
+ alt="" border=0 align="bottom"></a>. </p>
+
+ <p> Finally, one little &quot;gotcha&quot; is mimeTeX's
+ order&nbsp;of&nbsp;evaluation when interpreting expressions.
+ Parentheses are respected as you'd expect. But within
+ &nbsp; <b>(</b>...<b>)</b> &nbsp; parentheses, or in an
+ unparenthesized expression, mimeTeX finds the first (reading
+ from the left) operator, then iteratively evaluates the
+ separate subexpressions to that operator's left and to its right,
+ and then finally combines those two separate results.
+ So an expression like <b>2*3+4</b>&nbsp;renders&nbsp;<b>14</b>,
+ and you need to write <b>(2*3)+4</b>&nbsp;to&nbsp;get&nbsp;<b>10</b>.
+ </p>
+
+
+<h3> <a name="magstep"> \magstep{&nbsp;} &nbsp; and &nbsp;
+ \magbox{&nbsp;}{&nbsp;}<font size=5>...</font></a> </h3>
+
+ <p class="continue">
+ &nbsp;<b>\magstep{<i>magnification</i>}</b>, placed anywhere
+ within an expression, magnifies the entire expression
+ by an integer factor <b>1&lt;=<i>magnification</i>&lt;=10</b>
+ in both width and height.
+ Each single pixel thus becomes a square box, <i>e.g.</i>,
+ for <b><i>magnification</i>=2</b> each single pixel becomes
+ a four-pixel square box with dimensions&nbsp;<b>2</b>-by-<b>2</b>.
+ This compromises mimeTeX's anti-aliasing algorithm,
+ and the resulting image is both hazy/blurry and jagged/staircased
+ compared to an unmagnified image of the same expression.
+ For example, at <b>\LARGE</b> size,<br>
+ <nobr> &nbsp; &nbsp; &nbsp &nbsp;
+ <b>f(x)=x^2</b> &nbsp;
+ renders &nbsp;
+ <a href="#preview"><img id="magbox1" onclick="eqntext('magbox1')"
+ src="../cgi-bin/mimetex.cgi?\LARGE f(x)=x^2"
+ alt="" border=0 align="absmiddle"></a> &nbsp; and </nobr><br>
+ <nobr> &nbsp; &nbsp; &nbsp &nbsp;
+ <b>\magstep{2} f(x)=x^2</b> &nbsp;
+ renders &nbsp;
+ <a href="#preview"><img id="magbox2" onclick="eqntext('magbox2')"
+ src="../cgi-bin/mimetex.cgi?\LARGE\magstep{2} f(x)=x^2"
+ alt="" border=0 align="absmiddle"></a>&nbsp;, &nbsp; whereas </nobr><br>
+ at mimeTeX's largest &quot;native&quot; font&nbsp;size, <br>
+ <nobr> &nbsp; &nbsp; &nbsp &nbsp;
+ <b>\Huge f(x)=x^2</b> &nbsp;
+ renders &nbsp;
+ <a href="#preview"><img id="magbox3" onclick="eqntext('magbox3')"
+ src="../cgi-bin/mimetex.cgi?\HUGE f(x)=x^2"
+ alt="" border=0 align="absmiddle"></a>&nbsp;. </nobr><br>
+ Nevertheless, if you still want to render images larger than
+ mimeTeX's <b>\Huge</b> size, then <b>\magstep{<i>magnification</i>}</b>
+ may render almost-acceptable results. </p>
+
+ <p> To magnify just part of an expression,
+ you can use <b>\magbox{<i>magnification</i>}{<i>expression</i>}</b>,
+ which only magnifies each pixel within the enclosed
+ <b>{<i>expression</i>}</b>, again
+ by an integer factor <b>1&lt;=<i>magnification</i>&lt;=10</b>
+ in both width and height, and also adjusts the baseline accordingly.
+ But <b>\magbox</b> is applied directly to mimeTeX's black-and-white
+ bitmap <u><b><i>&nbsp;before&nbsp;anti-aliasing&nbsp;</i></b></u>.
+ At the present time, this virtually completely defeats
+ mimeTeX's anti-aliasing algorithm, and the resulting image
+ exhibits even more pronounced jagged-line/staircase effects.
+ For example, <br>
+ <nobr> &nbsp; &nbsp; &nbsp &nbsp;
+ <b>\LARGE f(x)={\magbox{2}{x}}^2</b> &nbsp;
+ renders &nbsp;
+ <a href="#preview"><img id="magbox5" onclick="eqntext('magbox5')"
+ src="../cgi-bin/mimetex.cgi?\LARGE f(x)={\magbox{2}{x}}^2"
+ alt="" border=0 align="absmiddle"></a>.</nobr><br>
+ </p>
+
+<h3> <a name="abbreviations">Abbreviations<font size=5>...</font></a> </h3>
+
+ <p class="continue">
+ <b>\ga</b> displays <b>\gamma</b>, but just <b>\g</b> displays
+ <b>\gg</b> (<b>&gt;&gt;</b>). That is, mimeTeX selects the
+ shortest symbol or command which begins with whatever you type.
+ This feature can help shorten an otherwise very long line,
+ but it may be a bit dangerous. </p>
+
+ <p> The mimeTeX <a href="#symbols">preprocessor</a>, briefly mentioned
+ above, is responsible for recognizing several LaTeX symbols like
+ <b>\ldots</b> and several commands like <b>\atop</b>&nbsp;.
+ These symbols and commands cannot be abbreviated. The special
+ html characters like <b>&amp;nbsp;</b> are also recognized by
+ the preprocessor and cannot be abbreviated. </p>
+
+<h3> <a name="colors">Colors<font size=5>...</font></a> </h3>
+
+ <p> Rudimentary color commands are provided by mimeTeX. You can write
+ <b>\color{red}</b> or <b>\color{green}</b> or<b>\color{blue}</b>
+ (which may be abbreviated <b>\red</b> or <b>\green</b> or
+ <b>\blue</b>) anywhere in an expression to render the entire
+ expression in the specified color. That is,
+ <b>abc{\red&nbsp;def}ghi</b> renders the entire expression red,
+ not just the <b>def</b> part. Also, note that mimeTeX's "green"
+ is actually color <b>#00FF00</b>, which the html standard more
+ accurately calls "lime". For example, </p> <center>
+ <b>\blue e^x=\sum_{n=0}^\infty\frac{x^n}{n!}</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="colors1" onclick="eqntext('colors1')"
+ src="../cgi-bin/mimetex.cgi?
+ \Large\color{blue} e^x=\sum_{n=0}^\infty\frac{x^n}{n!}"
+ alt="" border=0 align=middle></a> </center>
+
+<h3> <a name="smash">&quot;Smash&quot;<font size=5>...</font></a> </h3>
+
+ <p> TeX represents characters by boxes, with no idea how ink will be
+ distributed inside. So an expression like
+ <b>\frac12\int_{a+b+c}^{d+e+f}g(x)dx</b> is typically rendered as &nbsp;
+ <a href="#preview"><img id="smash1" onclick="eqntext('smash1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \nosmash\frac12\int_{a+b+c}^{d+e+f}{g(x)dx}"
+ alt="" border=0 align=middle></a>.
+ But mimeTeX knows the character shapes of its fonts, and therefore tries
+ to remove extra whitespace, rendering the same expression as &nbsp;
+ <a href="#preview"><img id="smash2" onclick="eqntext('smash2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \smash\frac12\int_{a+b+c}^{d+e+f}{g(x)}dx"
+ alt="" border=0 align=middle></a> &nbsp; instead. </p>
+
+ <p> Precede any expression with the mimeTeX directive <b>\nosmash</b>
+ to render it without "smashing". Or compile mimetex.c with the
+ <b>-DNOSMASH</b> <a href="#options">option</a> if you prefer
+ the typical TeX behavior as mimeTeX's default. In this case,
+ precede any expression with <b>\smash</b> to render it "smashed".
+ And note that explicit space like <b>\hspace{10}</b>
+ or <b>\;</b>&nbsp;, etc, is never smashed. </p>
+
+ <p> The scope of <b>\smash</b> and <b>\nosmash</b> is the
+ <b>{&nbsp;}</b>-enclosed subexpression in which the directive occurs.
+ For example, if you want the <b><i>g(x)</i></b>&nbsp;part of the
+ preceding example smashed, but not the <b>1/2</b>&nbsp;part,
+ then the expression
+ <b>\nosmash\frac12{\smash\int_{a+b+c}^{d+e+f}g(x)dx}</b>
+ renders as &nbsp;
+ <a href="#preview"><img id="smash3" onclick="eqntext('smash3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \nosmash\frac12{\smash\int_{a+b+c}^{d+e+f}{g(x)dx}}"
+ alt="" border=0 align=middle></a>.
+ <!-- Moreover, explicit space like
+ <b>\hspace{10}</b> or <b>\;</b>, etc, is never smashed.
+ So <b>{\frac12\;\;}\int_{a+b+c}^{d+e+f}g(x)dx</b> renders as &nbsp;
+ <a href="#preview"><img id="smash4" onclick="eqntext('smash4')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ {\frac12\;\;}\int_{a+b+c}^{d+e+f}{g(x)dx}"
+ alt="" border=0 align=middle></a>. --> </p>
+
+ <p> For finer-grained control, note that <b>\smash</b> is shorthand
+ for the default <b>\smashmargin{+3}</b> (and <b>\nosmash</b> is
+ shorthand for <b>\smashmargin{0}</b>). <b>\smashmargin</b>'s value
+ is the minimum number of pixels between smashed symbols. The leading
+ <b>+</b> is optional. If present, the font size (\tiny=0,...,\Huge=7)
+ is added to the specified minimum. Compile mimetex.c with the
+ <b>-DSMASHMARGIN=<i>n</i></b> <a href="#options">option</a> to change
+ the default from <b>3</b> to <b><i>n</i></b>. Compare the preceding
+ example with the over-smashed <b>\smashmargin{1}</b> &nbsp;
+ <a href="#preview"><img id="smash5" onclick="eqntext('smash5')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\displaystyle
+ \smashmargin1\frac12\int_{a+b+c}^{d+e+f}{g(x)}dx"
+ alt="" border=0 align=middle></a> &nbsp; instead. </p>
+
+ <p> Smashing is in "beta testing" and some expressions still don't look
+ quite right when smashed, e.g., <b>1^2,2^2,3^2,\ldots</b> renders as
+ <a href="#preview"><img id="smash6" onclick="eqntext('smash6')"
+ src="../cgi-bin/mimetex.cgi?\Large1^2,2^2,3^2,\ldots"
+ alt="" border=0 align=middle></a>. Just compile with <b>-DNOSMASH</b>
+ if you come across numerous annoying situations. </p>
+
+<h3> <a name="not">\not and \cancel and \sout<font size=5>...</font></a> </h3>
+
+ <p> The usual LaTeX &nbsp; <b>\not</b> &nbsp; "slashes" the single symbol
+ following it, e.g., &nbsp; <b>i\not\partial\equiv&nbsp;i\not\nabla</b>
+ &nbsp; produces <a href="#preview">
+ <img id="not1" onclick="eqntext('not1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize i\not\partial\equiv i\not\nabla"
+ alt="" border=0 align=middle></a>. </p>
+
+ <p> For arbitrary expressions, mimeTeX provides &nbsp; <b>\cancel</b> &nbsp;
+ which draws a line from the upper-right to lower-left corner of its
+ argument, e.g., &nbsp; <b>a\cancel{x^2}=bx^{\not3}</b> &nbsp; produces
+ &nbsp; <a href="#preview"><img id="not2" onclick="eqntext('not2')"
+ src="../cgi-bin/mimetex.cgi?\large a\cancel{x^2}=bx^{\not3}"
+ alt="" border=0 align=bottom></a>. </p>
+
+ <p> Finally, similar to the <b>ulem.sty</b> package, &nbsp; <b>\sout</b>
+ &nbsp; draws a horizontal strikeout line through its argument,
+ e.g., &nbsp; <b>\sout{abcdefg}</b> &nbsp; produces <a href="#preview">
+ <img id="not3" onclick="eqntext('not3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\sout{abcdefg}"
+ alt="" border=0 align=middle></a>. MimeTeX's <b>\sout</b> also
+ takes an optional argument that adjusts the vertical position of its
+ strikeout line by the specified number of pixels, e.g., &nbsp;
+ <b>\sout[+2]{abcdefg}</b> produces <a href="#preview">
+ <img id="not4" onclick="eqntext('not4')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\sout[+2]{abcdefg}"
+ alt="" border=0 align=middle></a> &nbsp; and &nbsp;
+ <b>\sout[-2]{abcdefg}</b> produces
+ <a href="#preview"><img id="not5" onclick="eqntext('not5')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\sout[-2]{abcdefg}"
+ alt="" border=0 align=middle></a>. </p>
+
+
+<h2> <a name="array"> (IIIe) \begin{array}{lcr}...\end{array} Environment
+&nbsp; </a> </h2>
+
+ <p> Rendering vectors and matrices, aligning equations, etc, is all done
+ using the customary LaTeX environment &nbsp;
+ <b>\begin{array}{lcr}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{array}</b>
+ &nbsp; which you can write in exactly that form. MimeTeX also
+ recognizes the following array-like environments </p>
+ <center> <table cellpadding="1" cellspacing="1">
+ <tr> <td align="left"> <b>\begin{array}{lcr}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{array}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{matrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{matrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{tabular}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{tabular}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{pmatrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{pmatrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{bmatrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{bmatrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{Bmatrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{Bmatrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{vmatrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{vmatrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{Vmatrix}</b> </td>
+ <td align="center"> <b>a&b&c \\ d&e&f \\ etc</b> </td>
+ <td align="left"> <b>\end{Vmatrix}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{eqnarray}</b> </td>
+ <td align="center"> <b>a&=&b \\ c&=&d \\ etc</b> </td>
+ <td align="left"> <b>\end{eqnarray}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{align}</b> </td>
+ <td align="center"> <b>a&=b \\ c&=d \\ etc</b> </td>
+ <td align="left"> <b>\end{align}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{cases}</b> </td>
+ <td align="center"> <b>a&b \\ c&d \\ etc</b> </td>
+ <td align="left"> <b>\end{cases}</b> </td> </tr>
+ <tr> <td align="left"> <b>\begin{gather}</b> </td>
+ <td align="center"> <b>a \\ b \\ etc</b> </td>
+ <td align="left"> <b>\end{gather}</b> </td> </tr>
+ </table> </center> <p class="continue">
+ There's a built-in maximum of 64 columns and 64 rows. Nested
+ array environments, e.g.,
+ <b>\begin{pmatrix}a&\begin{matrix}1&2\\3&4\end{matrix}\\c&d\end{pmatrix}</b>,
+ are permitted. </p>
+
+ <p> MimeTeX also provides the abbreviation &nbsp;
+ <b>\array{lcr$a&b&c\\d&e&f\\etc}</b> &nbsp;
+ which has exactly the same effect as &nbsp;
+ <b>\begin{array}{lcr}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{array}</b>.
+ And the <b>lcr$</b> "preamble" in <b>\array{lcr$etc}</b> is optional.
+ In that case, &nbsp; <b>\array{a&b&c\\d&e&f\\etc}</b> &nbsp;
+ has exactly the same effect as &nbsp;
+ <b>\begin{matrix}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{matrix}</b>.
+ You can also write <b>\(\array{etc}\)</b> to "manually abbreviate"
+ the pmatrix environment, or <b>\array{rcl$etc}</b> to abbreviate
+ eqnarray, but mimeTeX has no explicit abbreviations for these
+ other environments. For example, </p> <center>
+ <b>\begin{matrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{matrix}</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="array1" onclick="eqntext('array1')"
+ src="../cgi-bin/mimetex.cgi?\large\begin{matrix}a_1&a_2&a_3\\
+ b_1&b_2&b_3\\c_1&c_2&c_3\end{matrix}"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> Solid <b>\hline</b>'s (but not \cline's) and vertical <b>l|c|r</b> bars
+ are available, as usual. For dashed lines and bars,
+ <b>\begin{array}</b> provides the additional features <b>\hdash</b>
+ and <b>l.c.r</b>&nbsp;. <b>\hline</b> and <b>\hdash</b> may not be
+ abbreviated. For example, </p> <center>
+ <b>\begin{array}{c.c|c} a_1&a_2&a_3 \\\hdash b_1&b_2&b_3 <br>
+ \\\hline c_1&c_2&c_3 \end{array}</b> &nbsp; produces <br>
+ <a href="#preview"> <img id="array22" onclick="eqntext('array22')"
+ src="../cgi-bin/mimetex.cgi?\large\begin{array}{c.c|c}
+ a_1&a_2&a_3\\\hdash b_1&b_2&b_3\\\hline c_1&c_2&c_3\end{array}"
+ alt="" border="0" align="middle"> </a> </center>
+
+ <p> The default font size is unchanged by <b>\array{&nbsp;}</b>, but you
+ can explicitly control it in the usual way, e.g.,
+ <b>{\Large\begin{matrix}...\end{matrix}}</b> renders the entire array
+ in font size 4. In addition, any <b>&...&</b> cell may contain font
+ size declarations which are always local to that cell,
+ e.g., <b>&\fs{-1}...&</b> renders that one cell one font size smaller
+ than current. </p>
+
+ <p> The <b>{lcr}</b> in <b>\begin{array}{lcr}</b> sets left,center,right
+ <i>"horizontal&nbsp;justification"</i> down columns of an array,
+ as usual. And "vertical&nbsp;justification" across rows defaults
+ to what we'll call <b><i>baseline</i></b>, i.e., aligned equations,
+ as in <a href="#example10">Example&nbsp;10</a> above, display properly.
+ But the down arrows (for &nbsp;
+ <a href="#preview"><img id="array3" onclick="eqntext('array3')"
+ src="../cgi-bin/mimetex.cgi?\small\array{C$\gamma&\Large\downarr}"
+ alt="" border=0 align=middle></a> &nbsp; and for &nbsp;
+ <a href="#preview"><img id="array4" onclick="eqntext('array4')"
+ src="../cgi-bin/mimetex.cgi?\small\array{C$\Large\downarr&\beta}"
+ alt="" border=0 align=middle></a>)
+ in <a href="#example11">Example&nbsp;11</a> require
+ <i>"vertical&nbsp;centering"</i> across the middle row of that
+ array. So, in addition to lowercase <b>lcr</b>, mimeTeX's <b>{lcr}</b>
+ in <b>\begin{array}{lcr}</b> may also contain uppercase <b>BC</b> to
+ set "<b>B</b>"aseline or "<b>C</b>"enter vertical justification across
+ the corresponding rows. For example, <b>\begin{array}{rccclBCB}</b>
+ sets baseline justification for the first and third rows, and center
+ justification for the second row. Without any <b>BC</b>'s,
+ all rows default to the usual <b>B</b> baseline justification. </p>
+
+ <p> MimeTeX has no <b>\arraycolsep</b> or <b>\arraystretch</b> parameters.
+ Instead, <b>\begin{array}{lc25rB35C}</b> sets the absolute width
+ of the second column to 25&nbsp;pixels, and the absolute height of the
+ first row to 35&nbsp;pixels, as illustrated by
+ <a href="#example9">Example&nbsp;9</a>. Any number following
+ an <b>lcrBC</b> specification sets the width of that one column
+ (for <b>lcr</b>), or the height of that one row (for <b>BC</b>). <br>
+ <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
+ You can optionally precede the number with a <b>+</b> sign,
+ which "propagates" that value forward to all subsequent columns for
+ <b>lcr</b>, or all subsequent rows for <b>BC</b>. For example,
+ <b>\begin{array}{lc+25rB+35C}</b> sets the absolute width of
+ column&nbsp;2 and all subsequent columns to 25&nbsp;pixels,
+ and the absolute height of row&nbsp;1 and all subsequent rows
+ to 35&nbsp;pixels. After absolute sizing has been set, the special
+ value <b>0</b> reverts to automatic sizing for that one row or
+ column, and <b>+0</b> reverts to automatic sizing for all subsequent
+ rows or columns. For example, <b>\begin{array}{c+25ccc+35ccc+0}</b>
+ sets the absolute widths of columns&nbsp;1-3 to 25&nbsp;pixels,
+ columns&nbsp;4-6 to 35&nbsp;pixels, and then reverts to automatic
+ sizing for columns&nbsp;7 and all subsequent columns. <br>
+ <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
+ The "propagation" introduced by <b>+</b> is local to the
+ <b>\begin{array}</b> in which it occurs. So you have to repeat
+ the same specifications if you want rows aligned across several
+ arrays on the same line (or columns aligned on several lines
+ separated by <b>\\</b>). Instead, a lowercase <b>g</b> globally
+ copies your column specifications to all subsequent arrays,
+ and an uppercase <b>G</b> globally copies your row specifications.
+ And <b>gG</b> copies both column and row specifications. For example,
+ <b>\begin{array}{GC+25}</b> sets the height of all rows in this
+ array to 25 pixels, and ditto for all subsequent arrays to its right.
+ Explicit specifications in subsequent arrays override previous global
+ values. <br>
+ <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
+ Click one of the following examples to see illustrations
+ of the above discussion: </p> <center>
+ <a href="#preview"> <img id="array31" onclick="eqntext('array31')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \left( \begin{array}{GC+30}
+ \cos\frac\theta2 & i\,\sin\frac\theta2\\
+ i\,\sin\frac\theta2 & \cos\frac\theta2 \end{array} \right)
+ \left( \begin{array}
+ z & x_{\tiny-} \\ x_{\tiny+} & -z \end{array} \right)
+ \hfill{300}\text{\normalsize Example 1}"
+ alt="" border="0" align="middle"> </a> <br>
+ <a href="#preview"> <img id="array32" onclick="eqntext('array32')"
+ src="../cgi-bin/mimetex.cgi?\large
+ \left( \begin{array}{GC+30gc+40}
+ \cos\frac\theta2 & i\,\sin\frac\theta2 \\
+ i\,\sin\frac\theta2 & \cos\frac\theta2 \end{array} \right)
+ \left( \begin{array}
+ z & x_{\tiny-} \\ x_{\tiny+} & -z \end{array} \right)
+ \hfill{300}\text{\normalsize Example 2}"
+ alt="" border="0" align="middle"> </a> </center>
+
+ <p> See <a href="#example8">Examples&nbsp;8-11</a> above for several
+ additional <b>\begin{array}{lcr}</b> applications. </p>
+
+
+<h2> <a name="picture"> (IIIf) \picture(&nbsp;){&nbsp;} "Environment",
+ including \line(&nbsp;){&nbsp;} and \circle(&nbsp;) &nbsp; </a> </h2>
+
+ <p> Besides <b>\begin{array}{lcr}</b>, mimeTeX also tries to emulate the
+ familiar LaTeX picture environment with the somewhat similar<br>
+ <b>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \picture(width[,height])&nbsp;
+ {&nbsp;(loc1){pic_elem1}&nbsp;(loc2){pic_elem2}&nbsp;...&nbsp;}</b><br>
+ as illustrated by <a href="#example12">Examples&nbsp;12-13</a> above.
+ Arguments surrounded by <b>[&nbsp;]</b>'s are optional.
+ If the optional <b>[,height]</b> is omitted, then <b>height=width</b>
+ is assumed. Locations <b>(loc1)</b> and <b>(loc2)&nbsp;...</b> each
+ denote either a <b>\put(loc)</b> or a <b>\multiput(loc)</b>,
+ and each location is of the form <b>([c]x,y[;xinc,yinc[;num]])</b>. </p>
+
+ <p> A <b>\put(loc)</b> is denoted by a location of the form <b>([c]x,y)</b>
+ where <b>x,y</b> denotes the coordinate where the lower-left corner
+ of the subsequent picture_element will be placed, unless the letter
+ <b>c</b> precedes the <b>x</b>-number, in which case <b>cx,y</b>
+ denotes the center point instead. The very lower-left corner of the
+ entire picture is always <b>0,0</b>, and the upper-right corner is
+ <b>width-1,height-1</b>. Note, for example, that you'd never want
+ to specify location <b>c0,0</b> since the picture_element would be
+ mostly out-of-bounds (only its upper-right quadrant would be
+ in-bounds). </p>
+
+ <p> A <b>\multiput(loc)</b> starts like a <b>\put(loc)</b>, but location
+ <b>[c]x,y</b> is followed by <b>;xinc,yinc[;num]</b> indicating the
+ <b>x,y-inc</b>rements applied to each of <b>num</b> repetitions
+ of picture_element. If <b>;num</b> is omitted, repetitions continue
+ until the picture_element goes out-of-bounds of the specified
+ <b>width[,height]</b>. Note that <b>x,y</b> are always positive or
+ zero, but <b>xinc,yinc</b> may be postive, zero or negative. </p>
+
+ <p> The <b>\picture(,){...}</b> parameters <b>width, height, x, y, xinc,
+ yinc</b> may be either integer or may contain a decimal point,
+ and they're all scaled by <a href="#unitlength">\unitlength</a>.
+ The <b>num</b> parameter must be integer. </p>
+
+ <p> Picture_element's <b>{pic_elem1}</b> and <b>{pic_elem2} ...</b>
+ may be any expressions recognized by mimeTeX, even including other
+ <b>\picture</b>'s nested to any level. </p>
+
+<h3> <a name="circleline">\line(&nbsp;){&nbsp;} and
+\circle(&nbsp;)<font size=5>...</font></a> </h3>
+
+ <p> To help draw useful picture_element's, mimeTeX provides several
+ drawing commands, <b>\line(xinc,yinc)[{xlen}]</b> and
+ <b>\circle(xdiam[,ydiam][;arc])</b>. Although primarily intended
+ for use in <b>\picture</b>'s, you can use them in any mimeTeX
+ expression, e.g., &nbsp; <b>abc\circle(20)def</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="circleline1" onclick="eqntext('circleline1')"
+ src="../cgi-bin/mimetex.cgi?\large abc\circle(20)def"
+ alt="" border="0" align="middle"></a>. </p>
+
+ <p> Without its optional <b>{xlen}</b> parameter, the expression
+ <b>(x,y){\line(xinc,yinc)}</b> draws a straight line from point
+ <b>x,y</b> to point <b>x+xinc,y+yinc</b>. The <b>inc</b>'s
+ can be positive, zero or negative. Don't prefix location <b>x,y</b>
+ with a leading <b>c</b> for <b>\line</b>'s; the intended "corner"
+ is determined by the signs of <b>xinc</b> and <b>yinc</b>.
+ If given, the optional <b>{xlen}</b> parameter rescales the length
+ of the line so its x-projection is <b>xlen</b> and its slope is
+ unchanged. </p>
+
+ <p> Without optional <b>,ydiam</b> and <b>;arc</b>, the expression
+ <b>(x,y){\circle(xdiam)}</b> draws a circle of diameter <b>xdiam</b>
+ centered at <b>x,y</b>. Don't prefix location <b>x,y</b> with a
+ leading <b>c</b> for <b>\circle</b>'s; centering is assumed.
+ If <b>,ydiam</b> is also given, then <b>(x,y){\circle(xdiam,ydiam)}</b>
+ draws the ellipse inscribed in a rectangle of width <b>xdiam</b>
+ and height <b>ydiam</b> centered at <b>x,y</b>. <br>
+ &nbsp; &nbsp; &nbsp; Finally, <b>;arc</b> specifies the arc to be
+ drawn, in one of two ways. An <b>;arc</b> argument given in the
+ form <b>;1234</b> interprets each digit as a quadrant to be drawn,
+ with <b>1</b> the upper-right quadrant and then proceeding
+ counterclockwise, e.g., <b>\circle(12;34)</b> specifies the
+ lower half of a circle whose diameter is twelve. <br>
+ &nbsp; &nbsp; &nbsp; Alternatively, an <b>;arc</b> argument given in
+ the form <b>45,180</b> or <b>-60,120</b> specifies the endpoints of
+ the desired arc in degrees, with <b>0</b> the positive x-axis and
+ then proceeding counterclockwise. The first number must always
+ be smaller than the second (negative numbers are allowed), and the
+ arc is drawn counterclockwise starting from the smaller number. </p>
+
+ <p> Besides <a href="#example12">Examples 12-13</a> above,
+ it's hard to resist illustrating<br>
+ <font size=4><b>&nbsp; &nbsp; &nbsp;
+ \unitlength{.6} &nbsp; \picture(100) {<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ (50,50){\circle(99)} %%head%%<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ (20,55;50,0;2){\fs{+1}\hat\bullet} %%eyes%%<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ (50,40){\bullet} %%nose%%<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ (50,35){\circle(50,25;34)} %%upper lip%%<br>
+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ (50,35){\circle(50,45;34)} %%lower lip%% &nbsp; }</b></font></p>
+ <center>
+ <a href="#preview"><img id="circleline2" onclick="eqntext('circleline2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\unitlength{.6}\picture(100){
+ (50,50){\circle(99)} (20,55;50,0;2){\fs{+1}\hat\bullet} (50,40){\bullet}
+ (50,35){\circle(50,25;34)} (50,35){\circle(50,45;34)}}"
+ alt="" border=0 align=middle></a><br>Have a nice day!</center>
+
+
+<h2> <a name="commands"> (IIIg) Other mimeTeX Commands &nbsp; </a> </h2>
+
+ <p> Various and sundry other LaTeX-like commands are also provided
+ by mimeTeX. In addition to features explicitly discussed below,
+ mimeTeX supports the usual sub<b>_</b>scripts and super<b>^</b>scripts,
+ and most of the typical LaTeX commands, many already discussed
+ above, including </p>
+ <ul>
+ <li> <b>\frac{&nbsp;}{&nbsp;}</b> and <b>{&nbsp;\over&nbsp;}</b> </li>
+ <li> <b>{&nbsp;\atop&nbsp;}</b> and <b>{&nbsp;\choose&nbsp;}</b> </li>
+ <li> <b>\sqrt{&nbsp;}</b> </li>
+ <li> <b>\lim_{&nbsp;}</b> and all the usual LaTeX function names </li>
+ <li> <b>\hat{&nbsp;}</b> and <b>\widehat{&nbsp;}</b>
+ and many of the usual LaTeX accents </li>
+ <li> <b>\overbrace{&nbsp;}^{&nbsp;}</b> and
+ <b>\underbrace{&nbsp;}_{&nbsp;}</b> </li>
+ <li> <b>\overline{&nbsp;}</b> and <b>\underline{&nbsp;}</b> </li>
+ </ul> <p class="continue">
+ All these typical commands should behave as they usually do
+ in LaTeX, and won't be discussed further. Short discussions
+ of some other commands follow. </p>
+
+<h3> <a name="stackrel">\overset{&nbsp;}{&nbsp;} or
+\stackrel{&nbsp;}{&nbsp;} &nbsp; and &nbsp;
+\underset{&nbsp;}{&nbsp;} or \relstack{&nbsp;}{&nbsp;}
+<font size=5>...</font></a> </h3>
+
+ <p class="continue">
+ <b>\stackrel{&nbsp;}{&nbsp;}</b> behaves as usual in LaTeX,
+ rendering its first argument one font size smaller and centered above
+ its second. And the amsmath-style <b>\overset{&nbsp;}{&nbsp;}</b> is
+ identical. For example, </p> <center>
+ <b>"\vec x\overset{\rm def}=(x_1\ldots x_n)"</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="stackrel1" onclick="eqntext('stackrel1')"
+ src="../cgi-bin/mimetex.cgi?
+ \Large\vec x\,\overset{\small\rm def}=
+ \,(x_1\ldots x_n)" alt="" border=0 align=middle></a> </center>
+
+ <p> "Conversely" to <b>\stackrel{&nbsp;}{&nbsp;}</b>, mimeTeX provides
+ <b>\relstack{&nbsp;}{&nbsp;}</b>, which renders its second argument
+ one font size smaller and centered below its first.
+ And the amsmath-style <b>\underset{&nbsp;}{&nbsp;}</b> renders its
+ first argument one font size smaller and centered below its second.
+ For example, the <b>\log</b> function name doesn't treat
+ limits like <b>\lim_</b>, but you can write, for example, </p> <center>
+ <b>"\underset{\rm base 2}\log32=5"</b> &nbsp; to render &nbsp;
+ <a href="#preview"><img id="stackrel2" onclick="eqntext('stackrel2')"
+ src="../cgi-bin/mimetex.cgi?
+ \Large\underset{\small\rm base 2}\log32\,=\,5"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> MimeTeX's <b>\limits</b> provides an easier but non-standard
+ alternative to achieve the same effect. For example, </p> <center>
+ <b>"\vec x =\limits^{\rm def} (x_1\ldots x_n)"</b>
+ &nbsp; produces &nbsp;
+ <a href="#preview"><img id="stackrel3" onclick="eqntext('stackrel3')"
+ src="../cgi-bin/mimetex.cgi?\Large\vec x\,=\limits^{\small\rm def}
+ \,(x_1\ldots x_n)" alt="" border=0 align=middle></a> <br><br>
+ and &nbsp; <b>"\log\limits_{\rm base 2}32=5"</b> &nbsp;
+ produces &nbsp;
+ <a href="#preview"><img id="stackrel4" onclick="eqntext('stackrel4')"
+ src="../cgi-bin/mimetex.cgi?
+ \Large\log\limits_{\small\rm base 2}32\,=\,5"
+ alt="" border=0 align=middle></a> </center>
+
+<h3> <a name="fbox">\fbox{&nbsp;}<font size=5>...</font></a> </h3>
+
+ <p> In case html border attributes aren't suitable, mimeTeX provides
+ the usual <b>\fbox{<i>expression</i>}</b> command, e.g., </p> <center>
+ <b>"\fbox{x=\frac12}"</b> &nbsp; produces &nbsp;
+ <a href="#preview"><img id="fbox1" onclick="eqntext('fbox1')"
+ src="../cgi-bin/mimetex.cgi?\Large\fbox{x=\frac12}"
+ alt="" border=0 align=middle></a> </center>
+
+ <p> You can also write <b>\fbox[<i>width</i>]{<i>expression</i>}</b>
+ to explicitly set the box's width, or you can write
+ <b>\fbox[<i>width</i>][<i>height</i>]{<i>expression</i>}</b>
+ to explicitly set both width and height. </p>
+
+<h3> <a name="today">\today and \calendar<font size=5>...</font></a> </h3>
+
+ <p class="continue"> <b>\today</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="today1" onclick="eqntext('today1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\today"
+ border=0 align=middle></a> &nbsp;
+ in the usual LaTeX text&nbsp;mode way.
+ That's <b>\today</b>'s default format#1. MimeTeX has
+ an optional format argument so that, for example, &nbsp;
+ <b>\blue\today[2]</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="today2" onclick="eqntext('today2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\blue\today[2]"
+ border=0 align=middle></a>, &nbsp;
+ showing both date and time. And &nbsp;
+ <b>\red\today[3]</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="today3" onclick="eqntext('today3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\red\today[3]"
+ border=0 align=bottom></a>,
+ &nbsp; showing time only. </p>
+
+ <p> To accommodate time zones, you may also write, for example, &nbsp;
+ <b>\small\blue\today[2,+3]</b>, &nbsp; which renders &nbsp;
+ <a href="#preview"><img id="today4" onclick="eqntext('today4')"
+ src="../cgi-bin/mimetex.cgi?\small\blue\today[2,+3]"
+ border=0 align=middle></a>, &nbsp;
+ adding three hours to format#2.
+ The arguments may be in either order. The time zone increment
+ must always be preceded by either <b>+</b>&nbsp;or&nbsp;<b>-</b>,
+ and must be in the range <b>-</b>23&nbsp;to&nbsp;<b>+</b>23. </p>
+
+ <p class="continue"> <b>\calendar</b> &nbsp; renders a calendar for
+ the current month, as illustrated by the left-hand image below.
+ For a different month, the optional argument &nbsp
+ <b>\small\blue\calendar[2001,9]</b> &nbsp; renders the right-hand
+ image, for the requested year and month. Years must be
+ 1973<b>...</b>2099 and months must be 1<b>...</b>12. </p>
+ <center>
+ <a href="#preview"><img id="today5" onclick="eqntext('today5')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\calendar"
+ border=0 align=middle> </a> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
+ <a href="#preview"><img id="today6" onclick="eqntext('today6')"
+ src="../cgi-bin/mimetex.cgi?\small\blue\calendar[2001,9]"
+ border=0 align=middle> </a> </center>
+
+ <p> The default calendar emphasizes the current day of the current month,
+ while any other month emphasizes no day. Day emphasis is controlled
+ by an optional third argument. &nbsp; <b>\calendar[0,0,1]</b> &nbsp;
+ emphasizes the first day of the current month, and
+ &nbsp; <b>\calendar[2001,9,11]</b> &nbsp; emphasizes the eleventh
+ day of that month. &nbsp; <b>\calendar[0,0,99]</b> &nbsp;
+ renders the current month with no day emphasized. </p>
+
+<h3> <a name="input">\input{&nbsp;}<font size=5>...</font></a> </h3>
+
+ <p class="continue">
+ <b>\input{<i>filename</i>}</b> behaves just like the corresponding
+ LaTeX command, reading the entire contents of <b><i>filename</i></b>
+ into your expression at the point where the <b>\input</b> command
+ occurs. By default, <b><i>filename</i></b> resides in the same
+ directory as mimetex.cgi. Moreover, for security, absolute paths
+ with leading <b>/</b>'s or <b>\</b>'s, and paths with <b>../</b>'s
+ or <b>..\</b>'s, are not permitted. See the <b>-DPATHPREFIX</b>
+ <a href="#options">compile&nbsp;option</a>, discussed above,
+ if you want <b>\input</b> files in some other directory.
+ In any case, if <b><i>filename</i></b> isn't found, then
+ <b>\input</b> tries to read <b><i>filename</i>.tex</b> instead.</p>
+
+ <p> And for further security, <b>\input{&nbsp;}</b> is disabled by default
+ unless mimeTeX is compiled with either the <b>-DINPUTOK</b> or
+ <b>-DINPUTPATH</b> or <b>-DINPUTREFERER</b>
+ <a href="#options">compile&nbsp;option</a> discussed above.
+ When it's disabled, the command <b>\input{<i>filename</i>}</b>
+ renders the error message
+ <b>[\input{<i>filename</i>}&nbsp;not&nbsp;permitted]</b>&nbsp;. </p>
+
+ <p> MimeTeX also supports the optional form
+ <b>\input{<i>filename:tag</i>}</b>. In this case,
+ <b><i>filename</i></b> is read as before, but only those characters
+ between <b>&lt;<i>tag</i>&gt;...&lt;/<i>tag</i>&gt;</b> are placed
+ into your expression. This permits you to have one file containing
+ many different <b>&lt;<i>tag</i>&gt;</b>'s, e.g., one file containing
+ all the questions and/or answers to a homework assignment or a quiz,
+ etc. </p>
+
+<h3> <a name="counter">\counter[&nbsp;]{&nbsp;}
+<font size=5>...</font></a> </h3>
+
+ <p> The bottom-right corner of this page contains a page hit counter
+ that's maintained using mimeTeX's
+ <b>\counter[<i>logfile</i>]{<i>counterfile</i>:<i>tag</i>}</b>
+ command. As with <b>\input</b>, described immediately above,
+ both the required <b><i>counterfile</i></b> and the optional
+ <b><i>logfile</i></b> are the names of files that reside in the
+ same directory as your mimetex.cgi executable, unless you compiled
+ mimetex with the <b>-DPATHPREFIX</b>
+ <a href="#options">compile&nbsp;option</a>. Before using
+ the <b>\counter</b> command, Unix "touch" and "chmod" those files
+ so they're mimeTeX readable and writable. </p>
+
+ <p> Also as with <b>\input</b>, for security <b>\counter</b> is
+ disabled by default unless mimeTeX is compiled with either
+ the <b>-DINPUTOK</b> or the <b>-DCOUNTEROK</b>
+ <a href="#options">compile&nbsp;option</a>
+ (notice that <b>-DINPUTOK</b> also enables <b>\counter</b>).
+ If you've compiled mimeTeX with <b>\counter</b> enabled,
+ then it behaves as <nobr>follows...</nobr> </p>
+
+ <p> If <b><i>counterfile</i></b> isn't readable and writable,
+ then the <b>\counter</b> command always displays
+ <b>1<sup><u>st</u></sup></b>. Otherwise, it maintains a
+ line in <b><i>counterfile</i></b> of the form
+ <b>&lt;<i>tag</i>&gt;&nbsp;<i>value</i>&nbsp;&lt;/<i>tag</i>&gt;</b>
+ where <b><i>value</i></b> is initialized as <b>1_</b> if the
+ specified <b>&lt;<i>tag</i>&gt;</b> line doesn't already exist,
+ and then incremented on each subsequent call. That trailing
+ underscore on the value in the file, e.g., <b>99_</b>, tells
+ mimeTeX to display <b>99<sup><u>th</u></sup></b> with an
+ ordinal suffix. Edit the value in the file and remove the
+ underscore if you don't want the ordinal suffix displayed.
+ Finally, mimeTeX makes no effort to lock files or
+ records&nbsp;(tags), so be careful using <b>\counter</b>
+ if your hit rates are high enough so that frequent collisions
+ are likely. </p>
+
+ <p> The same <b><i>counterfile</i></b> can contain as many different
+ <b>&lt;<i>tag</i>&gt;</b> lines as you like, so counters for
+ all the pages on your site can be maintained in one file.
+ MimeTeX also maintains a special <b>&lt;timestamp&gt;</b> tag
+ in <b><i>counterfile</i></b> that logs the the date/time and
+ name of the most recently updated tag. </p>
+
+ <p> Somewhat more detailed log information can be accumulated in
+ the optional <b><i>logfile</i></b>. If you provide that
+ filename, mimeTeX writes a line to it of the form
+ <b>2008-09-07:12:59:33pm&nbsp;&lt;<i>tag</i>&gt;=99&nbsp;192.168.1.1&nbsp;<i>http_referer</i></b>
+ containing a timestamp, the counter tag and its current value,
+ and the user's IP address and http_referer page if they're
+ available. </p>
+
+ <p> The page hit counter displayed at the bottom-right corner
+ of this page is maintained by the command
+ <b>\counter[counters.log]{counters.txt:mimetex.html}</b>.
+ After compiling and installing your
+ own mimetex.cgi and your own copy of this page, that counter will
+ continually show <b>1<sup><u>st</u></sup></b>'s
+ unless/until you "touch" and "chmod" counters.txt (and, optionally,
+ counters.log) in your mimetex.cgi directory. </p>
+
+<h3> <a name="environment">\environment
+<font size=5>...</font></a> </h3>
+ <p> Submitting the expression &nbsp; <b>\environment</b> &nbsp;
+ to mimeTeX renders </p> <center>
+ <img id="environ1"
+ src="../cgi-bin/mimetex.cgi?\nocaching\environment"
+ align="middle" border=0> </center>
+ <p class="continue"> displaying the http environment variables
+ known to mimeTeX. This is primarily a programming aid,
+ showing information available to mimeTeX that might facilitate
+ future enhancements. </p>
+
+ <p> As with <b>\input</b> and <b>\counter</b> above,
+ for security <b>\environment</b> is
+ disabled by default unless mimeTeX is compiled with either
+ the <b>-DINPUTOK</b> or the <b>-DENVIRONOK</b>
+ <a href="#options">compile&nbsp;option</a>
+ (notice that <b>-DINPUTOK</b> also enables <b>\environment</b>). </p>
+
+
+<h2> <a name="exceptions"> (IIIh) Other Exceptions
+to LaTeX Syntax &nbsp; </a> </h2>
+
+<h3> Binding Exceptions<font size=5>...</font> </h3>
+
+ <p> MimeTeX's bindings are pretty much left-to-right. For example,
+ although mimeTeX correctly interprets <b>\frac12</b> as well as
+ <b>\frac{1}{2}</b>, etc, the legal LaTeX expression <b>x^\frac12</b>
+ must be written <b>x^{\frac12}</b>. Otherwise, mimeTeX interprets
+ it as <b>{x^\frac}12</b>, i.e., the same way <b>x^\alpha12</b>
+ would be interpreted, which is entirely wrong for <b>\frac</b>.
+ The same requirement also applies to other combinations of commands,
+ e.g., you must write <b>\sqrt{\frac\alpha\beta}</b>, etc. </p>
+
+
+<h2> <a name="messages"> (IIIi) mimeTeX Errors
+and Messages &nbsp; </a> </h2>
+
+<h3> mimeTeX Errors<font size=5>...</font> </h3>
+
+ <p> Any (La)TeX error is typically also a mimeTeX error.
+ However, mimeTeX has no command line interface or
+ <b>.</b>log file for reporting errors. Its only
+ communication with you is through the mimeTeX image
+ rendered by your browser. So error messages are embedded
+ in that image whenever feasible. For example,
+ suppose you want to see
+ <a href="#preview"><img id="messages1" onclick="eqntext('messages1')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\alpha\beta\gamma\delta"
+ border=0 align=bottom></a>, but you mistakenly type
+ &nbsp; <b>\alpha\bethe\gamma\delta</b> &nbsp; instead.
+ Then the image rendered is
+ <a href="#preview"><img id="messages2" onclick="eqntext('messages2')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\alpha\bethe\gamma\delta"
+ border=0 align=bottom></a>, indicating the unrecognized
+ <b>[\bethe?]</b> where you wanted to type &nbsp; <b>\beta</b> &nbsp;
+ and hoped to see
+ <a href="#preview"><img id="messages3" onclick="eqntext('messages3')"
+ src="../cgi-bin/mimetex.cgi?\normalsize\bf\beta"
+ border=0 align=bottom></a>.
+ If your expression contains some unprintable character
+ (meaning any character mimeTeX has no bitmap for),
+ then just &nbsp;
+ <a href="#preview"><img id="messages4" onclick="eqntext('messages4')"
+ src="../cgi-bin/mimetex.cgi?\small\bf[?]"
+ border=0 align=bottom></a> &nbsp; is displayed in the
+ corresponding position. </p>
+
+ <p> The preceding example illustrates a pretty trivial error.
+ Any non-trivial errors in your expression are likely to
+ go unrecognized and unreported by mimeTeX, and to render
+ unexpected images. While checking your input expression
+ for syntax errors, keep in mind the following points
+ about mimeTeX's behavior: </p>
+ <ul>
+ <li> An unmatched left brace &nbsp; <b>{</b> &nbsp; is matched
+ by mimeTeX with a "phantom" right brace &nbsp; <b>}</b> &nbsp;
+ that's imagined to be at the end of your expression. </li>
+ <li> Likewise, an unmatched &nbsp; <b>\left(</b>, &nbsp;
+ or <b>\left\{</b> &nbsp; or <b>\left\</b><i>anything</i>, &nbsp;
+ is matched by mimeTeX with a "phantom" &nbsp; <b>\right.</b>
+ &nbsp; at the end of your expression. </li>
+ <li> On the other hand, an unmatched right brace &nbsp; <b>}</b>
+ &nbsp; is displayed in place, as if you had typed \rbrace. </li>
+ <li> But an unmatched &nbsp; <b>\right\</b><i>anything</i> &nbsp;
+ is interpreted as an abbreviation for <b>\</b>rightarrow
+ followed by <b>\</b><i>anything</i>. For example, &nbsp;
+ <b>\leff(&nbsp;abc&nbsp;\right)&nbsp;def</b> &nbsp; renders &nbsp;
+ <a href="#preview"><img id="messages5"
+ onclick="eqntext('messages5')"
+ src="../cgi-bin/mimetex.cgi?\small\leff(abc\right)def"
+ border=0 align=bottom></a>. </li>
+ </ul> <!-- p class="continue">
+ </p -->
+
+<h3> mimeTeX Messages<font size=5>...</font> </h3>
+
+<!--
+ <p> The special mimeTeX directive &nbsp; <b>\version</b> &nbsp;
+ displays the following information </p>
+ <center>
+ <a href="#preview"><img id="messages6" onclick="eqntext('messages6')"
+ src="../cgi-bin/mimetex.cgi?\version"
+ border=0 align=middle> </a> </center>
+-->
+ <p> The latest release of mimeTeX is version
+ <a href="#preview"><img id="messages11" onclick="eqntext('messages11')"
+ src="../cgi-bin/mimetex.cgi?\small\versionnumber"
+ alt="" border=0 align="bottom"></a>
+ which was last revised
+ <a href="#preview"><img id="messages12" onclick="eqntext('messages12')"
+ src="../cgi-bin/mimetex.cgi?\small\revisiondate"
+ alt="" border=0 align="bottom"></a>.
+ The special mimeTeX directive &nbsp; <b>\version</b> &nbsp;
+ displays that same information, </p>
+ <center>
+ <a href="#preview"><img id="messages13" onclick="eqntext('messages13')"
+ src="../cgi-bin/mimetex.cgi?\version"
+ alt="" border=0 align=middle></a> </center>
+ <p> To check that your own release of mimeTeX is current,
+ type a url into your browser's locator window something like <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ <b>http://www.<i>yourdomain</i>.com/cgi-bin/mimetex.cgi?\version</b> <br>
+ which will display the version and revision date of
+ mimeTeX installed on your server. </p>
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+SECTION IV. APPENDICES
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h1> <a name="appendices"> (IV) Appendices &nbsp; </a> </h1>
+
+<p> Programming information to help you modify mimeTeX's behavior,
+ and to use its functionality in your own programs, is provided
+ by these appendices. The currently available appendices discuss
+ (a)how to modify or extend mimeTeX's fonts, (b)how to use
+ mimeTeX's principal function, make_raster(), and (c)how to use
+ <a href="http://shh.thathost.com" target="_top">Sverre Huseby's</a>
+ gifsave.c library. </p>
+
+
+<h2> <a name="fonts"> (IVa) &nbsp; mimeTeX Fonts &nbsp; </a> </h2>
+
+<p> The font information mimeTeX uses to render characters is
+ derived from .gf font files (usually generated by <b>metafont</b>
+ running against .mf files), which are then run through
+ <b>gftype -i</b> and finally through my <b>gfuntype</b> program
+ (supplied with your mimeTeX distribution). </p>
+
+<p> The final output from each such sequence of three runs
+ (metafont &gt; gftype -i &gt; gfuntype) gives mimeTeX the
+ bitmap information it needs to render one particular font
+ family at one particular size. The file <b>texfonts.h</b>
+ supplied with your mimeTeX distribution collects the output
+ from 72 such (sequences of) runs, representing nine font
+ families at eight sizes each. </p>
+
+<p> This collection of information in &nbsp; texfonts.h &nbsp; is
+ "wired" into mimeTeX through tables maintained in <b>mimetex.h</b>.
+ To change mimeTeX's fonts, you'll have to first modify (or totally
+ replace) texfonts.h using your own gfuntype output, and then
+ change mimetex.h to reflect your texfonts.h modifications. </p>
+
+<p> This appendix provides a brief description of the above
+ process, though you'll probably need at least some previous
+ C programming experience to confidently accomplish it.
+ Your motivation might be to add more fonts to mimeTeX,
+ to change the font sizes I chose, or to add more
+ font sizes, etc. MimeTeX's design permits all this to be
+ easily done once you understand the process. </p>
+
+<p> Running <b>metafont</b> to generate a <b>.gf</b> file from <b>.mf</b>
+ source will usually be your very first step. A typical such run
+ might be </p>
+ <!-- <b>mf '\mode=onetz; mag=magstep(.5); input cmmi10'</b> --> <center>
+ <b>mf '\mode=preview; mag=magstep(-16.393225); input cmmi10'</b></center>
+<p class="continue"> which in this case generates output file
+ <b>cmmi10.131gf</b> (which is mimeTeX's font size 3 for the
+ cmmi family). </p>
+
+<p> Given the cmmi10.131gf file from this metafont run
+ (or substitute any other .gf file you like), next run </p>
+ <center><b>gftype -i cmmi10.131gf &gt; typeout</b></center>
+<p class="continue"> where <b>typeout</b> can be any temporary
+ filename you like. </p>
+
+<p> Finally, run <b>gfuntype</b> against the typeout file
+ you just generated with the command </p>
+ <center><b>gfuntype -n cmmi131 typeout cmmi131.h</b></center>
+ <p class="continue"> to generate the final output file <b>cmmi131.h</b>
+ (or any filename you supply as the last arg). This
+ contains the cmmi data in an array whose name is taken
+ from the <b>-n</b> arg you supplied to gfuntype. </p>
+
+<p> The above sequence of three runs resulted in output file
+ <b>cmmi131.h</b>, containing the font information mimeTeX needs
+ for one font family (cmmi) at one font size (3). Repeat this
+ sequence of three runs for each font size and each font family.
+ Then pull all the output files into one big <b>texfonts.h</b> file
+ (or write a small texfonts.h which just #include's them all). </p>
+
+<p> For your information, the 72 sequences of runs represented
+ in the texfonts.h file supplied with your mimeTeX distribution
+ correspond to the following eight inital metafont runs for cmr10 </p>
+<!--
+ 1 (.100gf) mf '\mode=nextscrn; input cmr10'
+ 2 (.118gf) mf '\mode=lview; input cmr10'
+ 3 (.131gf) mf '\mode=onetz; mag=magstep(.5); input cmr10'
+ 4 (.160gf) mf '\mode=itoh; input cmr10'
+ 5 (.180gf) mf '\mode=lqlores; input cmr10'
+-->
+ <pre> size=0 (.83gf) mf '\mode=eighthre; input cmr10'
+ 1 (.100gf) mf '\mode=preview; mag=magstep(-17.874274); input cmr10'
+ 2 (.118gf) mf '\mode=preview; mag=magstep(-16.966458); input cmr10'
+ 3 (.131gf) mf '\mode=preview; mag=magstep(-16.393225); input cmr10'
+ 4 (.160gf) mf '\mode=preview; mag=magstep(-15.296391); input cmr10'
+ 5 (.180gf) mf '\mode=preview; mag=magstep(-14.650373); input cmr10'
+ 6 (.210gf) mf '\mode=preview; mag=magstep(-13.804885); input cmr10'
+ 7 (.250gf) mf '\mode=preview; mag=magstep(-12.848589); input cmr10'</pre>
+ <p class="continue">
+ Then ditto for the eight other font families cmmi10, cmmib10, cmsy10,
+ cmex10, bbold10, rsfs10, stmary10 and wncyr10. And to generate other
+ <b>.</b><i>dpi</i><b>gf</b> font sizes, calculate magsteps &nbsp;
+ <img src="../cgi-bin/mimetex.cgi?\normalsize\frac{\log(dpi/2602)}{\log1.2}"
+ alt="" align=middle border=0>. &nbsp; All the subsequent gftype and
+ gfuntype runs just follow the standard format described above. </p>
+
+<p> To incorporate all this font information you just generated into
+ mimeTeX, edit your <b>mimetex.h</b> file and find the table that looks
+ something like </p><pre>static fontfamily aafonttable[] = {
+ /* ----------------------------------------------------------------------------------------
+ family size=0, 1, 2, 3, 4, 5, 6, 7
+ ----------------------------------------------------------------------------------------- */
+ { CMR10,{ cmr83, cmr100, cmr118, cmr131, cmr160, cmr180, cmr210, cmr250}},
+ { CMMI10,{ cmmi83, cmmi100, cmmi118, cmmi131, cmmi160, cmmi180, cmmi210, cmmi250}},
+ { CMMIB10,{ cmmib83, cmmib100, cmmib118, cmmib131, cmmib160, cmmib180, cmmib210, cmmib250}},
+ { CMSY10,{ cmsy83, cmsy100, cmsy118, cmsy131, cmsy160, cmsy180, cmsy210, cmsy250}},
+ { CMEX10,{ cmex83, cmex100, cmex118, cmex131, cmex160, cmex180, cmex210, cmex250}},
+ { RSFS10,{ rsfs83, rsfs100, rsfs118, rsfs131, rsfs160, rsfs180, rsfs210, rsfs250}},
+ { BBOLD10,{ bbold83, bbold100, bbold118, bbold131, bbold160, bbold180, bbold210, bbold250}},
+ {STMARY10,{stmary83,stmary100,stmary118,stmary131,stmary160,stmary180,stmary210,stmary250}},
+ { CYR10,{ wncyr83, wncyr100, wncyr118, wncyr131, wncyr160, wncyr180, wncyr210, wncyr250}},
+ { -999,{ NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL}}
+} ; /* --- end-of-fonttable[] --- */</pre><p class="continue">
+ Note the 72 names <b>cmr83...wncyr250</b> in the table. These must
+ correspond to (or must be changed to) the names following the <b>-n</b>
+ switch you specified for your &nbsp; gfuntype &nbsp; runs. </p>
+
+<p> If you want more than eight font sizes, first build up texfonts.h
+ with all the necessary information. Then change LARGESTSIZE (and
+ probably NORMALSIZE) in mimetex.h, and finally edit the above aafonttable[]
+ by extending the columns in each row up to your largest size. </p>
+
+<p> You can also add new rows by #define'ing a new family,
+ and then adding a whole lot of character definitions at the bottom
+ of mimetex.h, all in the obvious way (i.e., it should become obvious
+ after reviewing mimetex.h). A new row would be required,
+ for example, to make another font available in mimeTeX. </p>
+
+<p> One small problem with the above procedure is that the default
+ &nbsp; gftype &nbsp; program supplied with most TeX distributions
+ can't emit the long lines needed to display mimeTeX's larger font sizes.
+ <a href="http://www.forkosh.com/gftype.zip"
+ target="_top">gftype.zip</a>&nbsp;contains a statically linked linux
+ executable modified to emit the necessary long lines.
+ It may or may not run on your intel linux machine.
+ If not, you'll need to compile your own version from source.
+ The following instructions are for Unix/Linux: <br> &nbsp; &nbsp;
+ &nbsp; &nbsp; First, download both
+ <!-- http://www.ctan.org/tex-archive/systems/web2c/web-7.5.3.tar.gz -->
+ <a href="http://www.forkosh.com/web-7.5.3.tar.gz"
+ target="_top">web-7.5.3.tar.gz</a> and
+ <!-- http://www.ctan.org/tex-archive/systems/web2c/web2c-7.5.3.tar.gz -->
+ <a href="http://www.forkosh.com/web2c-7.5.3.tar.gz"
+ target="_top">web2c-7.5.3.tar.gz</a>
+ <!-- or more recent versions. --> (note: these files are no longer
+ explicitly archived by&nbsp;<a href="http://www.ctan.org/"
+ target="_top">ctan</a>, having been superceded
+ by&nbsp;<a href="http://www.ctan.org/tex-archive/systems/texlive"
+ target="_top">texlive</a>&nbsp;sources, so the preceding two links
+ point to copies kept on my site, www.forkosh.com).
+ Then &nbsp; untar &nbsp; both gzipped tar files,
+ &nbsp; cd&nbsp;web2c-7.5.3/ &nbsp; and run &nbsp; ./configure &nbsp;
+ and &nbsp; make &nbsp; in the usual way (make may fail before
+ completion if you don't have all needed fonts installed,
+ but it will create and compile gftype.c before failing). Now edit
+ &nbsp; texk/web2c/gftype.c&nbsp; and notice three lines very near the top
+ that &nbsp; #define&nbsp;maxrow&nbsp;(79) &nbsp and similarly for
+ maxcol and linelength. Change all three 79's to 1024, and
+ then re-run make. The new &nbsp; texk/web2c/gftype &nbsp; executable
+ image can emit the long lines needed for mimeTeX's larger font sizes. </p>
+
+<p> Finally, the Unix/Linux bash shell script
+ <a href="http://www.forkosh.com/texfonts.sh"
+ target="_top">texfonts.sh</a> generates file &nbsp; texfonts.h &nbsp;
+ containing the information for all 72 mimeTeX fonts discussed above
+ (and, optionally, an extra 1200dpi cmr font used to test mimeTeX's
+ supersampling algorithm). You'll need to understand and edit this
+ script to use it meaningfully. But it helps automate mimeTeX's font
+ generation procedure in case you want to experiment with different
+ fonts. (Note that metafont emits a complaint while generating the
+ 83dpi rsfs font. Just press &lt;CR&gt; and it completes
+ successfully.) </p>
+
+
+<h2> <a name="makeraster"> (IVb) mimeTeX's make_raster()
+function &nbsp; </a> </h2>
+
+<p> MimeTeX converts an input LaTeX math expression to a corresponding GIF
+ image in two steps. First, it converts the input LaTeX expression to a
+ corresponding bitmap raster. Then <a href="http://shh.thathost.com"
+ target="_top">Sverre Huseby's</a> gifsave library, discussed
+ <a href="#gifsave">below</a>, converts that bitmap to the emitted gif.
+ Though you never explicitly see that bitmap, it's mimeTeX's principal
+ result. MimeTeX is written so any program can easily use its
+ expression-to-bitmap conversion capability with just a single line of code.
+ The following complete program demonstrates the simplest such use. </p>
+
+<pre> #include &lt;stdio.h&gt;
+ #include "mimetex.h"
+ int main ( int argc, char *argv[] )
+ {
+ raster *rp = make_raster(argv[1],NORMALSIZE);
+ type_raster(rp,stdout); /* display ascii image of raster */
+ }</pre>
+
+<p> Cut-and-paste the above sample code from this file to, say,
+ mimedemo.c (and fix the brackets around stdio.h). Then compile <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ cc -DTEXFONTS mimedemo.c mimetex.c -lm -o mimedemo <br>
+ and run it from your unix shell command line like <br>
+ &nbsp; &nbsp; &nbsp; &nbsp; ./mimedemo &nbsp; &quot;x^2+y^2&quot; </p>
+
+<p> MimeTeX's expression-to-bitmap conversion is accomplished by the
+ make_raster() call, whose first argument is just a pointer to a
+ (null-terminated) string containing any mimeTeX-compliant LaTeX
+ expression, and whose second argument is the mimeTeX font size
+ to use (overridden if your expression contains a preamble).
+ The ascii display of the bitmap raster returned by make_raster()
+ results from the subsequent call to type_raster(). That's all
+ this program does, but you could use make_raster()'s returned bitmap
+ for any other purpose you have in mind. </p>
+
+<p> MimeTeX's primary purpose is to emit either xbitmaps or gif images
+ rather than ascii displays. And mimeTeX has anti-aliasing and various
+ other options that further complicate its main() function compared to
+ the simple example above. The example below demonstrates mimeTeX
+ usage in the slightly more realistic situation where an input expression
+ is converted to a gif, without anti-aliasing, and emitted on stdout. </p>
+
+<pre> #include &lt;stdio.h&gt;
+ #include &lt;stdlib.h&gt;
+ #include "mimetex.h"
+
+ /* --- global needed by callback function, below, for gifsave.c --- */
+ static raster *rp = NULL; /* 0/1 bitmap raster image */
+
+ /* --- callback function to return pixel value at col x, row y --- */
+ int GetPixel ( int x, int y ) /* pixel value will be 0 or 1 */
+ { return (int)getpixel(rp,y,x); } /* just use getpixel() macro */
+
+ /* --- main() entry point --- */
+ int main ( int argc, char *argv[] )
+ {
+ /* --- get LaTeX expression from either browser query or command-line --- */
+ char *query = getenv("QUERY_STRING"), /* check for query string */
+ *expression = (query!=NULL? query : /* input either from query */
+ (argc>1? argv[1] : "f(x)=x^2")); /* or from command line */
+ /* ---- mimeTeX converts expression to bitmap raster ---- */
+ rp = make_raster(expression,NORMALSIZE); /* mimeTeX rasterizes expression */
+ /* ---- convert returned bitmap raster to gif, and emit it on stdout ---- */
+ if ( query != NULL ) /* Content-type line for browser */
+ fprintf( stdout, "Content-type: image/gif\n\n" );
+ /* --- initialize gifsave library and colors, and set transparent bg --- */
+ GIF_Create(NULL, rp->width, rp->height, 2, 8); /* init for black/white */
+ GIF_SetColor(0, 255, 255, 255); /* always set background white */
+ GIF_SetColor(1, 0, 0, 0); /* and foreground black */
+ GIF_SetTransparent(0); /* and set transparent background */
+ /* --- finally, emit compressed gif image (to stdout) --- */
+ GIF_CompressImage(0, 0, -1, -1, GetPixel);
+ GIF_Close();
+ }</pre>
+
+<p> Cut-and-paste as before, compile like <br>
+ &nbsp; &nbsp; &nbsp; &nbsp;
+ cc -DTEXFONTS mimedemo.c mimetex.c gifsave.c -lm -o mimedemo <br>
+ and run it like the first example, but this time you may want to redirect
+ stdout <br>
+ &nbsp; &nbsp; &nbsp; &nbsp; ./mimedemo &nbsp; &quot;x^2+y^2&quot;
+ &nbsp; <b>&gt;</b> &nbsp; mimedemo.gif <br>
+ since output is now a gif image consisting of mostly unprintable bytes.
+ Input is typically from the command line as illustrated, but this example
+ checks for a browser query string too. That means you could actually
+ replace mimetex.cgi with this executable, though anti-aliasing wouldn't
+ be available. </p>
+
+<p> Of course, this example's intent isn't to replace the mimetex.cgi
+ executable, but rather to illustrate GIFSAVE library usage, documented
+ in detail below. And this example also illustrates usage of several
+ mimeTeX raster structure elements, like rp-&gt;width and rp-&gt;height.
+ So you'll probably also want to refer to mimetex.h, which contains those
+ raster structures and other relevant definitions. For instance, the
+ example's GetPixel() callback function illustrates usage of the getpixel()
+ macro in mimetex.h, to retrieve individual pixels by their x,y-coordinates.
+ And there's a similar setpixel() macro in mimetex.h to store pixels.
+ After completing all this reading, you'll be prepared to begin using
+ mimeTeX functions in your own code. </p>
+
+
+
+<h2> <a name="gifsave">
+(IVc)</a> <a href="http://shh.thathost.com" target="_top">Sverre Huseby's</a>
+gifsave.c library &nbsp; </h2>
+
+<p> The information below is taken from the README file accompanying
+ <a href="http://shh.thathost.com" target="_top">Sverre Huseby's</a>
+ distribution of GIFSAVE. I've made a few small editorial modifications,
+ including descriptions of the several minor changes necessary
+ to support mimeTeX. And the mimeTeX example program immediately above
+ uses GIFSAVE in a very straightforward way that should help clarify
+ any questions which may remain after reading the documentation below. </p>
+
+<pre>
+ INTRODUCTION
+ ============
+
+ The GIFSAVE functions make it possible to save GIF images from
+ your own C programs.
+
+ GIFSAVE creates simple GIF files following the GIF87a standard.
+ Interlaced images cannot be created. There should only be
+ one image per file.
+
+ GIFSAVE consists of five functions, all returning type int,
+ and no separate header file is required.
+
+ The functions should be called in the order listed below
+ for each GIF-file. One file must be closed before a new one
+ can be created.
+
+ GIF_Create() creates new GIF-files. It takes parameters
+ specifying filename, screen size, number of colors,
+ and color resolution.
+
+ GIF_SetColor() sets up red, green, blue color components.
+ It should be called once for each possible color.
+
+ GIF_SetTransparent() is optional. If called, it sets the
+ color number of the color that should be transparent,
+ i.e., the background color shows through this one.
+
+ GIF_CompressImage() performs the compression of the image.
+ It accepts parameters describing the position and size
+ of the image on screen, and a user defined callback
+ function that is supposed to fetch the pixel values.
+
+ GIF_Close() terminates and closes the file.
+
+ To use these functions, you must also write a callback
+ function that returns the pixel values for each point
+ in the image.
+
+
+ THE FUNCTIONS
+ =============
+
+ GIF_Create()
+ ------------
+ Function Creates a new GIF-file, and stores info on
+ the screen.
+
+ Syntax int GIF_Create(
+ char *filename,
+ int width, int height,
+ int numcolors, int colorres
+ );
+
+ Remarks Creates a new (or overwrites an existing)
+ GIF-file with the given filename. No
+ .GIF-extension is added.
+
+ If filename is passed as a NULL pointer,
+ output is directed to stdout.
+
+ The width- and height- parameters specify
+ the size of the image in pixels.
+
+ numcolors is the number of colors used in
+ the image.
+
+ colorres is number of bits used to encode a
+ primary color (red, green or blue).
+ In GIF-files, colors are built by combining
+ given amounts of each primary color.
+ On VGA-cards, each color is built by
+ combining red, green and blue values in
+ the range [0, 63]. Encoding the number 63
+ would require 6 bits, so colorres would be
+ set to 6.
+
+ Return value GIF_OK - OK
+ GIF_ERRCREATE - Error creating file
+ GIF_ERRWRITE - Error writing to file
+ GIF_OUTMEM - Out of memory
+
+
+ GIF_SetColor()
+ --------------
+ Function Specifies the primary color component of a
+ color used in the image.
+
+ Syntax void GIF_SetColor(
+ int colornum,
+ int red, int green, int blue
+ );
+
+ Remarks This function updates the colortable-values
+ for color number colornum in the image.
+
+ Should be called for each color in the range
+ [0, numcolors]
+
+ with red, green and blue components in the
+ range [0, (2^colorres)-1]
+
+ colorres and colornum are values previousely
+ given to the function GIF_Create().
+
+ Return value None
+
+
+ GIF_SetTransparent()
+ --------------------
+ Function Specifies the color number of the color
+ that should be considered transparent.
+
+ Syntax void GIF_SetTransparent(
+ int colornum
+ );
+
+ Remarks Need not be called at all. But if called,
+ should be called only once with colornum in
+ the range [0, numcolors] i.e., colornum
+ must be one of the values previously
+ given to GIF_SetColor().
+
+ Return value None
+
+
+ GIF_CompressImage()
+ -------------------
+ Function Compresses an image and stores it in the
+ current file.
+
+ Syntax int GIF_CompressImage(
+ int left, int top,
+ int width, int height,
+ int (*getpixel)(int x, int y)
+ );
+
+ Remarks The left- and top- parameters indicate the
+ image offset from the upper left corner of
+ the screen. They also give the start values
+ for calls to the userdefined callback
+ function.
+
+ width and height give the size of the image.
+ A value of -1 indicates the equivalent screen
+ size given in the call to GIF_Create().
+
+ If the image is supposed to cover the entire
+ screen, values 0, 0, -1, -1 should be given.
+
+ GIF_CompressImage() obtains the pixel values
+ by calling a user specified function. This
+ function is passed in the parameter getpixel.
+ See "callback()" further down for a
+ description of this function.
+
+ Return value GIF_OK - OK
+ GIF_ERRWRITE - Error writing to file
+ GIF_OUTMEM - Out of memory
+
+
+ GIF_Close()
+ -----------
+ Function Closes the GIF-file.
+
+ Syntax int GIF_Close(void);
+
+ Remarks This function writes a terminating descriptor
+ to the file, and then closes it. Also frees
+ memory used by the other functions of GIFSAVE.
+
+ Return value GIF_OK - OK
+ GIF_ERRWRITE - Error writing to file
+
+
+ THE CALLBACK FUNCTION
+ =====================
+
+ callback()
+ ----------
+ Function Obtains pixel-values for the
+ GIF_CompressImage() -function.
+
+ Syntax int callback(int x, int y);
+
+ Remarks This function must be written by the
+ programmer. It should accept two integer
+ parameters specifying a point in the image,
+ and return the pixel value at this point.
+
+ The ranges for these parameters are as
+ follows
+ x : [img_left, img_left + img_width - 1]
+ y : [img_top, img_top + img_height - 1]
+
+ where img_left, img_top, img_width and
+ img_height are the values left, top, width
+ and height passed to GIF_CompressImage().
+
+ An example; if the screen has width 640 and
+ height 350, and the image covers the entire
+ screen, x will be in the range [0, 639]
+ and y in the range [0, 349].
+
+ callback() need not get its values from the
+ screen. The values can be fetched from a
+ memory array, they can be calculated for
+ each point requested, etc.
+
+ The function is passed as a parameter to
+ GIF_CompressImage(), and can thus have any
+ name, not only callback().
+
+ Return value Pixel value at the point requested. Should
+ be in the range [0, numcolors-1] where
+ numcolors is as specified to GIF_Create().
+</pre>
+
+
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+CONCLUDING REMARKS
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<h1 id="remarks"> Concluding Remarks &nbsp; </h1>
+
+<p> I hope you find mimeTeX useful. If so, a contribution to your
+ country's <a href="http://www.tug.org" target="_top">TeX Users Group</a>,
+ or to the <a href="http://www.gnu.org" target="_top">GNU</a> project, is
+ suggested, especially if you're a company that's currently profitable. </p>
+
+<!--
+<p> If you also like mimeTeX's source, I'm an independent contractor
+ incorporated in the US as John Forkosh Associates, Inc.
+ A <a href="http://www.forkosh.com/resume.html" target="_top">resume</a>
+ is at <a href="http://www.forkosh.com" target="_top">www.forkosh.com</a>
+ or email
+ <a href="mailto:john&#64;forkosh&#46;com">john&#64;forkosh&#46;com</a> </p>
+-->
+
+<!-- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Footer across bottom of page
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ -->
+<hr size=4>
+<table> <tr>
+ <td> <font size=3 color="maroon"> <b>
+ <nobr>Copyright <font size=5>&copy;</font> 2002-2012,
+ <a href="http://www.forkosh.com">John Forkosh Associates, Inc.</a>
+ </nobr><br>
+ email: <a href="mailto:john&#64;forkosh&#46;com">john&#64;forkosh&#46;com</a>
+ </b> </font> </td>
+ <td> <img src="../cgi-bin/mimetex.cgi?\hspace{100}" alt="" border=0> </td>
+ <td> <img src="../cgi-bin/mimetex.cgi?\blue{\small\rm You're the }
+ \Large\counter[counters.log]{counters.txt:mimetex.html}\\[0]
+ {\small\rm visitor to this page." alt="" border=0 align=bottom> </td>
+</tr> </table>
+</body>
+</html>
+<!-- end-of-file mimetex.html -->