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Edit File: mimetex.html

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<script type="text/javascript"
 src="http://www.mathtran.org/js/mathtran_img.js"></script>
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<body>

<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> 
 m i m e T e X &nbsp; m a n u a l 
 ( 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> ) 
 Click for:&nbsp;
 
 <a href="http://www.forkosh.com/mimetextutorial.html" target="_top">
 LaTeX tutorial</a> 
 <a href="http://www.forkosh.com/mimetex.html" target="_top">
 mimeTeX QuickStart</a> 
 <a href="http://www.forkosh.com/mimetex.zip">
 
 download&nbsp;mimeTeX</a>
 </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> 
 <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. 
 (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.)
 </td> </tr>
 </table>
</center>
<hr size=4>
<center>
Copyright &copy; 2002-2010,
<a href="http://www.forkosh.com">John Forkosh Associates, Inc.</a> 
email: <a href="mailto:john&#64;forkosh&#46;com">john&#64;forkosh&#46;com</a>
 
<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>

<center>
 &nbsp; &nbsp; &nbsp; &nbsp; C o n t e n t s &nbsp; &nbsp; &nbsp; &nbsp;
 
<table cellspacing=0 class="medium">
 <tr>
 <td valign="top" align="center" width=150>
 - - - T u t o r i a l - - - </td>
 <td valign="top" align="center" colspan=3 width=450>
 - - - - - - - - - - - - - - R e f e r e n c e - - - - - - - - - - - - - -
 </td>
 </tr>
 <tr>
 <td valign="top" align="center" width=150> 
 <a href="#introduction">&nbsp; (I) Introduction &nbsp;</a> 
 <a href="#quickstart"> a. Quick Start </a> 
 <a href="#examples"> b. Examples </a> 
 <a href="#gpl"> c. GPL License </a> </td>
 <td valign="top" align="center" width=150> 
 <a href="#build">&nbsp; (II) Building mimeTeX &nbsp;</a> 
 <a href="#compile"> a. Compile </a> 
 <a href="#install"> b. Install </a> 
 <a href="#options"> c. Compile Options </a> 
 <a href="#cmdline"> d. Command Line </a> </td>
 <td valign="top" align="center" width=150> 
 <a href="#reference">&nbsp; (III) Syntax Reference &nbsp;</a> 
 <a href="#spaces"> a. Math & White Space </a> 
 <a href="#symbols"> b. Symbols, Sizes, Modes </a> 
 <a href="#delimiters"> c. Delimiters </a> 
 <a href="#accents"> d. Accents, Arrows, etc. </a> 
 <a href="#array"> e. \begin{array} </a> 
 <a href="#picture"> f. \picture(&nbsp;){&nbsp;} </a> 
 <a href="#commands"> g. Other Commands </a> 
 <a href="#exceptions"> h. Other Exceptions </a> 
 <a href="#messages"> i. Errors and Messages </a> </td>
 <td valign="top" align="center" width=150> 
 <a href="#appendices">&nbsp; &nbsp; (IV) Appendices &nbsp; &nbsp;</a> 
 <a href="#fonts"> a. Fonts </a> 
 <a href="#makeraster"> b. make_raster() </a> 
 <a href="#gifsave"> c. gifsave.c </a>
 <a href="#remarks"> &nbsp; Remarks &nbsp; </a> </td>
 </tr>
</table>
</center>

This page contains more information
 than you'll probably need to read. If you follow the
 Installation&nbsp;and&nbsp;Usage&nbsp;Summary
 below, try installing mimeTeX immediately.  Or continue reading until you feel comfortable
 trying to install mimeTeX. 
 Prerequisites are: some knowledge of your OS's shell,
 of installing cgi's, of LaTeX. 
 
 &nbsp; &nbsp; &nbsp; &nbsp;
 &quotComputers are like Old Testament gods:
 lots of rules and no mercy.&quot 
 &nbsp; &nbsp; &nbsp; &nbsp;
 &#150;&#150; Joseph Campbell, The Power of Myth &nbsp;
 (Doubleday 1988, page 18)

<center>
<table border="0">
<tr> 
 <td align="left">
 
 - - - - - - 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 - - - - - -
 </td> </tr>
<tr>
 <td valign="top"> 
 <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> Download <a href="http://www.forkosh.com/mimetex.zip">
 mimetex.zip</a> and then type 
 &nbsp; &nbsp; unzip mimetex.zip 
 &nbsp; &nbsp; cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi
 Now just mv mimetex.cgi to your cgi-bin/
 directory, set permissions as necessary, and you're all done.
 </td></tr>
 <tr><td colspan="2"> &nbsp; </td></tr>
 <tr><td align="right" valign="top">
 <a href="#introduction">Usage</a>: &nbsp; &nbsp; </td>
 <td> To see the image &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> 
 just write the tag 
 &nbsp; &nbsp; &lt;img&nbsp;src="/cgi-bin/mimetex.cgi? 
 &nbsp; &nbsp; x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}"&gt;
 </td></tr>
 </table>
 </td>
</tr>
</table>
</center>

<h1> <a name="introduction">(I) Introduction</a> &nbsp; </h1>

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.
 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="#quickbuild">install</a>. And it's equally
 easy to use. Just place an html &lt;img&gt; tag in your document
 wherever you want to see the corresponding LaTeX expression.
 For example, 
<pre> &lt;img&nbsp;src="../cgi-bin/mimetex.cgi?f(x)=\int_{-\infty}^xe^{-t^2}dt"
 alt="" border=0 align=middle&gt;</pre> immediately
 generates the corresponding gif image on-the-fly, displaying
 <a href="#preview"><img id="imageI1" onclick="eqntext('imageI1')"
 src="../cgi-bin/mimetex.cgi?\normalsize
 f(x)=\int\limits_{-\infty}^xe^{-t^2}dt"
 alt="" border=0 style="Vertical-Align:-11px"></a>
 wherever you put that &lt;img&gt tag.
 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; -DCACHEPATH=\&quot;path/\&quot; &nbsp;
 <a href="#options">compile&nbsp;option</a>.)

<h3> <a name="plugins">
mimeTeX plugins...</a> </h3>
 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.

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;
 &lt;img&nbsp;alt="mimetex:c=\sqrt{a^2+b^2}"&gt; &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; 
 <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.yourdomain.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>

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
 [tex]&nbsp;c=\sqrt{a^2+b^2}&nbsp;[/tex] 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; 
 <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>
 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;[tex]{TEXT}[/tex] &nbsp;
 with the HTML replacement
 &lt;img&nbsp;src="/cgi-bin/mimetex.cgi?{TEXT}"&nbsp;align=middle&gt;

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
 {$&nbsp;f(x)=\int_{-\infty}^xe^{-t^2}dt&nbsp;$}
 to obtain that same image. &nbsp; Several other packages
 also have similar mimeTeX plugins: 
 <center><table>
 <tr> <td align=center> &nbsp;Package&nbsp; </td>
 <td> &nbsp; </td>
 <td align=center> &nbsp;&nbsp;Plugin&nbsp;&nbsp; </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.mediawiki.org/wiki/MediaWiki"
 target="_top">MediaWiki</a> </td>
	 <td align=center> &nbsp; </td>
	 <td align=center>
	 
	 <a href="http://www.mediawiki.org/wiki/Mimetex_alternative"
	 target="_top">&quot;mimeTeX&nbsp;alternative&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.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">
 
	 mimeTeX&nbsp;plugin</a>  </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>
 
 
 
 </table></center>

Please note: If you're writing your own plugin for mimeTeX,
 please don't write php code using system(&nbsp;), or any other
 shell escape mechanism, just to cache images. Use mimeTeX's
 &nbsp; -DCACHEPATH=\&quot;path/\&quot; &nbsp;
 <a href="#options">compile&nbsp;option</a> instead.
 system(&nbsp;) 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 system(&nbsp;)
 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.

<h3> <a name="valignment">
Vertical alignment...</a> </h3>
 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:-11px"></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; Vertical-Align:&nbsp;&#150;nn &nbsp;
 header, where &#150;nn is the number of pixels
 (usually negative as illustrated) needed for a
 &nbsp; style="Vertical-Align:&nbsp;&#150;nn&nbsp;px"
 &nbsp; attribute in the &lt;img&gt;&nbsp;tag used to
 render your expression.

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 
 <pre class="medium" style="margin-top:.5em;margin-bottom:.5em"
> &lt;?php
 $mimetexurl = "http://www.yourdomain.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 . $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 . $expression;
 echo ' &lt;img src="',$url,'" ';
 echo ' style="Vertical-Align:',$valign,'px" ';
 echo ' alt="" border=0&gt;', "\n";
 }
 ?&gt;</pre>

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:-5px"></a>
 correctly aligned. 
 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.

If you're using mimeTeX's
 &nbsp; -DCACHEPATH=\&quot;path/\&quot; &nbsp;
 <a href="#options">compile&nbsp;option</a>, prefix your
 path/ with a leading&nbsp;&#037; and write &nbsp;
 -DCACHEPATH=\&quot;&#037;path/\&quot; &nbsp; instead.
 That leading&nbsp;&#037; won't become part of your cache
 directory's path/, 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.

<h3> <a name="alternatives">
Alternative solutions...</a> </h3>
 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,
 <a href="#preview"><img id="imageI2" onclick="eqntext('imageI2')"
 src="../cgi-bin/mimetex.cgi?\normalsize
 f(x)=\int\limits_{-\infty}^xe^{-t^2}dt"
 alt="" border=0 style="Vertical-Align:-11px"></a>,
 with arbitrary mean
 <a href="#preview"><img id="imageI3" onclick="eqntext('imageI3')"
 src="../cgi-bin/mimetex.cgi?\large\mu" alt="" border=0
 style="Vertical-Align:-5px"></a> and standard deviation
 <a href="#preview"><img id="imageI4" onclick="eqntext('imageI4')"
 src="../cgi-bin/mimetex.cgi?\large\sigma" alt="" border=0
 style="Vertical-Align:0px"></a>,
 and at mimeTeX's next larger font size, looks like 
 <center>
 <table>
 <tr align="center">
	<td> latexrender </td>
	<td> <img src="../cgi-bin/mimetex.cgi?\hspace{30}"
 alt="" border=0> </td>
	<td> mimeTeX </td>
 </tr>
 <tr align="center">
	<td> <img src="http://www.forkosh.com/lrender.gif"
	 alt="" border=0 align=middle> </td>
 <td> &nbsp; </td>
 	<td>
	 <a href="#preview"><img id="imageI5" onclick="eqntext('imageI5')"
	 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>
 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>.

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 
 &nbsp; &nbsp;
 &lt;script type="text/javascript" 
 &nbsp; &nbsp; &nbsp; &nbsp;
 src="http://www.mathtran.org/js/mathtran_img.js"&gt;&lt;/script&gt; 
 and in the &lt;body&gt;, wherever you want to see latex images,
 place tags like 
 &nbsp; &nbsp;
 &lt;img alt="tex:any latex math expression"&gt; 
 For comparison, 
 &nbsp; &nbsp;
 &lt;img alt="tex: f(x) = \frac1{\sigma\sqrt{2\pi}} 
 &nbsp; &nbsp;
 \int_{-\infty}^x e^{-\frac{(t-\mu)^2}{2\sigma^2}}dt"&gt; 
 looks like 
 <center>
 <table>
 <tr align="center">
	<td> mathtran </td>
	<td> <img src="../cgi-bin/mimetex.cgi?\hspace{30}"
 alt="" border=0> </td>
	<td> mimeTeX </td>
 </tr>
 <tr align="center">
	<td> <img alt="tex:\displaystyle f(x) = \frac1{\sigma\sqrt{2\pi}}
 \int_{-\infty}^x e^{-\frac{(t-\mu)^2}{2\sigma^2}}dt"> </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>

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.

<h2> <a name="quickstart"> (Ia) Quick Start &nbsp; </a> </h2>

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  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 
 you can Click any of the <a href="#examples">Examples</a> below
 to place that corresponding expression in the Query Box.

Meanwhile, here are just a few quickstart tips for Submitting
 your own mimeTeX expressions in the Query Box below: 
 <ul>
 <li> MimeTeX currently has eight font sizes selected by
 one of the usual directives &nbsp; \tiny
 or \small or \normalsize&nbsp;,
 or \large&nbsp;(default) or \Large
 or \LARGE&nbsp;, or \huge or \Huge&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
 {&nbsp;}-enclosed subexpression in which they occur.
 For example, &nbsp; "a+\small&nbsp;b+c"
 &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; "\small&nbsp;a+{\Large&nbsp;b+}c" &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>  
 
 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 \normalsize 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 \large and larger.
 The LaTeX directives \displaystyle or \textstyle,
 and \limits or \nolimits, override mimeTeX's default
 in the usual way. Or see the -DDISPLAYSIZE=n
 <a href="#options">compile&nbsp;option</a> below to change
 the default. </li>
 </ul>
 <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. 
 <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">
 First enter your own LaTeX expression,
 or Click any example... 
 <textarea name="formdata" rows="5" cols="72"
 >\Large f(x)=\int_{-\infty}^x e^{-t^2}dt</textarea> 
 </td></tr>
 <tr align="center"><td>
 <input type="button" onClick="cleartext()"
 value="Clear Expression"> &nbsp; &nbsp;
 &nbsp; <input type="submit" value="Submit Expression"> 
 </td></tr>
 </table>
 </form> </td></tr> <tr align="left"><td align="center">
 Now click Submit to see it rendered below... 
 <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>
 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.

The &lt;img&gt; tag to embed this same integral anywhere
 in your own document is 
<pre> &lt;img&nbsp;src="../cgi-bin/mimetex.cgi?\large f(x)=\int_{-\infty}^xe^{-t^2}dt"
 alt="" border=0 align=middle&gt;</pre>

And recall that the typical mimeTeX &lt;img&gt; tag has the form 
<pre> &lt;img&nbsp;src="../cgi-bin/mimetex.cgi?any valid LaTeX/mimeTeX expression"
 alt="" border=0 align=middle&gt;</pre> 
 where ../cgi-bin/mimetex.cgi is the relative path from your html
 page containing these tags to your compiled mimetex.cgi program, and
 where any&nbsp;valid&nbsp;LaTeX/mimeTeX&nbsp;expression
 is pretty much any valid LaTeX math expression: <ul>
 
 <li>  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 \frac12 as well as
 \frac1{x^2}, etc, the legal LaTeX expression
 x^\frac12 must be written x^{\frac12}.
 Otherwise, mimeTeX interprets it as {x^\frac}12, i.e.,
 the same way x^\alpha12 would be interpreted, which is
 nonsense for \frac. The same "gotcha" also applies to
 other combinations of commands, e.g., you must write
 \sqrt{\frac\alpha\beta}, or
 \frac\alpha{\sqrt\beta}, etc.
 The <a href="#reference">Syntax&nbsp;Reference</a> section
 contains much additional information.  </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 \int\nolimits_a^b renders
 <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
 <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>.
 To render the latter image you have to write the somewhat
 cumbersome expression {\smashmargin2{\int\nolimits_a}^b}
 instead (see <a href="#smash">smash</a> below). </li>
 <li> Besides such exceptions, mimeTeX
 also provides various LaTeX extensions.  For example, font size
 directives like \Large are permitted within mimeTeX
 math&nbsp;mode expressions, but flagged as errors by LaTeX.
  </li> </ul>

<h2> <a name="examples"> (Ib) Examples &nbsp; </a> </h2>

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.

<tr>
 <td>
 (2) </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>

<tr>
 <td>
 (3) </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>

<tr>
 <td>
 (4) </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> </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>

<tr>
 <td>
 (5) </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 \frac{}{} for continued fraction </td>
 </tr>

<tr>
 <td>
 (6) </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 \left\{...\right.
  
 and note the accents </td>
 </tr>

<tr>
 <td>
 (7) </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}
 \large\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>
 \overbrace{}^{} and \underbrace{}_{} 
 (TeXbook page 181, Exercise 18.41) </td>
 </tr>

<tr>
 <td>
 (8) </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> </td> </tr>
 <tr>
 <td align="left">
 <a href="#preview">
 <img id="example8b" onclick="eqntext('example8b')"
 src="../cgi-bin/mimetex.cgi?\Large A\ =\ \large\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>

<tr>
 <td>
 <a name="example9">(9)</a> </td>
 <td align="left" colspan="2">
 <a href="#preview">
 <img id="example9c" onclick="eqntext('example9c')"
 src="../cgi-bin/mimetex.cgi?\normalsize
 \left(\large\begin{array}{GC+23}
 \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 \begin{array}'s. 
 Also, note rows aligned across all three arrays.
 </td>
 </tr>

<tr>
 <td>
 (10) </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>

<tr>
 <td>
 (11) </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>

<tr>
 <td>
 (12) </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)}^{4$\;\;a}}
 (52,50){\line(125)} (50,52;115;2){\mid} (52,55){\longleftar[60]}
 (130,56){\longrightar[35]} (116,58){r} (c85,50;80;2){\bullet}
 (c85,36){\large-q} (c165,36){\large q}
 (42,29){\underbrace{\line(32)}_{\small 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 - q
 for a grounded conducting sphere of radius a with
 a charge q at distance r &gt; a outside it. </td>
 </tr>

<tr>
 <td>
 (13) </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. 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>

<h3> Some font examples ...</a> </h3>
 Finally, illustrated below are some examples of fonts and symbols
 available with mimeTeX. All symbols and sizes from cmr, cmmi,
 cmmib (use \mathbf{&nbsp;}), cmsy, cmex, bbold (use
 \mathbb{&nbsp;}), rsfs (use \mathscr{&nbsp;}),
 stmary and cyrillic wncyr (use {\cyr&nbsp;&nbsp;} or
 \cyr{&nbsp;}) 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).

<h3>cmmi latin uppercase, and lowercase</h3>
 <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>

<h3>calligraphic, and rsfs (\cal{A}, \scr{B}, etc)</h3>
 <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>

<h3>cmmi greek uppercase, and \var lowercase</h3>
 <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>

<h3>cmmi greek lowercase</h3>
 <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>

<h3>cmsy symbols at mimeTeX font size 3 
(operators shown large are automatically "promoted" 
to the larger size in \displaystyle mode) </h3>
 <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>

<h3>a few other cmmi, cmr, stmary and wncyr symbols
at mimeTeX font size 4</h3>
 <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>

<h2> <a name="gpl"> (Ic) GPL License &nbsp; </a> </h2>

&quotMy grandfather once told me there are two kinds of people: 
&nbsp &nbsp Those who do the work and those who take the credit. 
&nbsp &nbsp He told me to try to be in the first group; there was much
less competition.&quot 
Indira Gandhi, the late Prime Minister of India

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.

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.

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.

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.
 
 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.

<h1> <a name="build"> (II) Building mimeTeX &nbsp; </a> </h1>

<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">
 
 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>unzip mimetex.zip 
 cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi</td>
 </tr></table>
 &nbsp; &nbsp; &nbsp; Now mv mimetex.cgi to your cgi-bin/
 directory, and you're all done. &nbsp; &nbsp; &nbsp; 
 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>

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).

<h2> <a name="compile"> (IIa) Download and Compile &nbsp; </a> </h2>

The steps needed to download and compile mimeTeX are 
 <ul>
 <li> Download and unzip 
 <a href="http://www.forkosh.com/mimetex.zip">
 
 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 gftype -i
 and writes bitmap data</td></tr>
 <tr><td>texfonts.h</td> <td>output from several gfuntype 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
 </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 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc -DAA mimetex.c gifsave.c -lm -o mimetex.cgi </li>
 <li> Or, to compile an executable that emit gif images
 without anti-aliasing 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc -DGIF mimetex.c gifsave.c -lm -o mimetex.cgi </li>
 <li> Alternatively, to compile an executable that emits mime xbitmaps 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc -DXBITMAP mimetex.c -lm -o mimetex.cgi </li>
 <li> Compile Notes: <ul>
 <li> If (and only if) you're compiling a Windows executable with
 the -DAA or -DGIF option (but not -DXBITMAP), then
 add -DWINDOWS&nbsp;. For example, 
 &nbsp; &nbsp; &nbsp; &nbsp; gcc -DAA -DWINDOWS
 mimetex.c gifsave.c -lm -o mimetex.exe 
 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". 
 &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 
 <img src="../cgi-bin/mimetex.cgi?\message{3}"
 alt="" align="middle" border=0> 
 In this case, compile mimetex.cgi with the -DNOREFCHECK switch,
 e.g., 
 &nbsp; &nbsp; &nbsp; &nbsp; cc -DAA -DNOREFCHECK
 mimetex.c gifsave.c -lm -o mimetex.cgi 
 and read the -DREFLEVELS=n discussion under
 <a href="#options">compile&nbsp;options</a> below. </li>
 
 </ul> </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 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc gfuntype.c mimetex.c -lm -o gfuntype </li>
 </ul>
 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.

Immediately after compiling mimeTeX, test your new executable
 by typing &nbsp; ./mimetex.cgi&nbsp;"x^2+y^2" &nbsp;
 from the Unix shell (or &nbsp; mimetex&nbsp;"x^2+y^2"
 &nbsp; from the Windows Command Prompt), which should emit
 two "ascii&nbsp;rasters" something like the following <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>
 (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.) Just typing ./mimetex.cgi
 without an argument should produce ascii rasters for the default
 expression f(x)=x^2. If you see these two ascii rasters then
 your binary's good. Otherwise, you must find and fix the problem
 before proceeding.

<h2> <a name="install"> (IIb) Install &nbsp; </a> </h2>

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 
 <ul>
 <li> mv mimetex.cgi &nbsp; (or move mimetex.exe) &nbsp;
 to your server's cgi-bin/ directory, wherever cgi
 programs are expected. </li>
 <li> Now you may need to chmod&nbsp;755&nbsp;mimetex.cgi &nbsp;
 and/or chown 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 cgi-bin/
 directory, with permissions and owner set as necessary,
 you're all done. </li>
 </ul>

Immediately after installing mimeTeX, test your new mimetex.cgi
 by typing a url into your browser's locator window something like 
 &nbsp; &nbsp; &nbsp; &nbsp;
 http://www.yourdomain.com/cgi-bin/mimetex.cgi?x^2+y^2 
 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, 
 &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> 
 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 yourdomain link, then you've completed
 a successful mimeTeX installation.

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 cgi-bin/ directory, set the correct chmod
 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.

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: 
 <ul>
 <li> mv mimetex.html (this file) to your server's
 htdocs/ directory </li>
 <li> Paths to cgi-bin/ and htdocs/ directories
 are typically path/www/cgi-bin/ and
 path/www/htdocs/, so I set up mimtex.html
 to access mimetex.cgi from the relative path ../cgi-bin/.
 If your directories are non-conforming, you may have to edit
 the few dozen occurrences of ../cgi-bin/mimetex.cgi
 in your mimetex.html page. Sometimes a suitable symlink works;
 if not, you'll have to edit. Globally changing
 ../cgi-bin/mimetex.cgi usually works. </li>
 <li> Now visit your page &nbsp;
 http://www.yourdomain.com/mimetex.html </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>

That's all there is to installing mimeTeX. .

<h2> <a name="options"> (IIc) Additional Compile-Line Options &nbsp; </a></h2>

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. 
 <dl>
 <dt> -DAA </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. 
 &nbsp; &nbsp; &nbsp; Anti-aliasing can't be applied to mime
 xbitmaps, so don't specify -DAA if you also specify -DXBITMAP. 
 &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> -DCENTERWT=n 
 -DADJACENTWT=j 
 -DCORNERWT=k </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> -DCACHEPATH=\"path/\" </dt>
 <dd> This option saves each rendered image to a file in directory
 path/, 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 \input{&nbsp;} are
 re-rendered since the contents of the inputted file may have
 changed. If compiled without -DCACHEPATH=\"path/\"
 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 path/
 is relative to mimetex.cgi, and must be writable by it.
 Files created under path/ are named
 filename.gif, where filename
 is the 32-character MD5 hash of your LaTeX expression. 
 &nbsp; &nbsp; &nbsp; If you're also using mimeTeX's
 <a href="#valignment">Vertical-Align:</a> feature, prefix your
 path/ with a leading&nbsp;&#037; and write
 &nbsp; -DCACHEPATH=\&quot;&#037;path/\&quot; &nbsp;
 instead. That leading&nbsp;&#037; won't become part of
 your cache directory's path/, 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. 
 &nbsp; &nbsp; &nbsp; When caching a new image, mimeTeX also
 updates the file path/mimetex.log 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>-DDEFAULTSIZE=n </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>-DDISPLAYSIZE=n </dt>
 <dd> By default, operator limits like \int_a^b are rendered
 \textstyle <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 \normalsize
 and smaller, and rendered \displaystyle <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 \large and
 larger. This default corresponds to -DDISPLAYSIZE=3,
 which you can adjust; e.g., -DDISPLAYSIZE=0 always defaults
 to \displaystyle, and 99 (or any large number)
 always defaults to \textstyle. Note that explicit
 \textstyle, \displaystyle, \limits or
 \nolimits directives in an expression always override
 the DISPLAYSIZE default. </dd>
 <dt>-DGAMMA=gammacorrection </dt>
 <dd> Applies gammacorrection 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>-DINPUTOK </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 -DINPUTOK enables
 all three commands simultaneously. (Compile mimeTeX with
 -DCOUNTEROK to enable only \counter, or with
 -DENVIRONOK to enable only \environment.) 
 &nbsp; &nbsp; &nbsp; Compiling mimeTeX with the
 -DINPUTOK switch enables \input{&nbsp;} for all users,
 subject only to your -DPATHPREFIX restrictions,
 discussed below. And the following two switches give you
 additional control over \input{&nbsp;}'s usage... </dd>
 <dt> -DINPUTPATH=\"path\" &nbsp; &nbsp; &nbsp; -or- 
 -DINPUTPATH=\"path1,path2,etc\" </dt>
 <dd> Permits \input{filename} for specific
 filename's, even when the \input{&nbsp;} command
 is otherwise disabled (for security). 
 &nbsp; &nbsp; &nbsp; If INPUTPATH is defined, mimeTeX
 performs a case-insensitive test of \input{&nbsp;}'s
 filename argument, to verify that it contains
 the authorized 'path' as a substring. 
 &nbsp; &nbsp; &nbsp; If given several 'path's (second form)
 then filename must contain either 'path1' or
 'path2', or etc, as a (case-insensitive) substring. 
 &nbsp; &nbsp; &nbsp; If filename doesn't contain
 a substring matching any of these path(s), then mimeTeX emits
 an error message image instead of reading filename. </dd>
 <dt> -DINPUTREFERER=\"domain\" &nbsp; &nbsp; &nbsp; -or- 
 -DINPUTREFERER=\"domain1,domain2,etc\" </dt>
 <dd> Permits \input{&nbsp;} for users from specific
 domain's, even when the \input{&nbsp;} command
 is otherwise disabled (for security). 
 &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. 
 &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. 
 &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 filename. 
 &nbsp; &nbsp; &nbsp; Finally, if HTTP_REFERER is not found as
 an environment variable, then mimeTeX renders the
 same error message image. </dd>
 <dt>-DNEWCOMMANDS=\"newcommands.h\" </dt>
 <dd> LaTeX-like \newcommand'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 
 \"...\"'s with the -DNEWCOMMANDS=\"filename\"
 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;
{&nbsp;"\\command",&nbsp;NULL,&nbsp;"{replacement}"&nbsp;},
 &nbsp; &nbsp; Don't forget a comma at the end of every line,
 and write a double&nbsp;backslash&nbsp;\\
 between quotes&nbsp;"...\\..." wherever you actually
 want a single&nbsp;backslash&nbsp;\. The only effect
 of the above examples (without arguments) is simple string
 substitution, i.e., every occurrence of \command
 is replaced by {replacement}. Note that the
 {&nbsp;}'s surrounding replacement
 aren't required, but are usually a good idea (the case
 of \cr illustrated above is one exception, where
 {&nbsp;}'s would defeat the purpose).
 &nbsp; &nbsp; To define newcommands _with_ arguments,
 change the NULL after the \\command
 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 NULL has been replaced by "2n"
 (note the mandatory surrounding quotes "..."). This
 example corresponds to the similar one discussed in TLC2 on
 page 845. The first character inside the "..."s is
 &nbsp; 2 &nbsp; indicating the number of arguments,
 which may be 1 thru 9. If there are no
 subsequent characters followng this one, then all arguments are
 mandatory, enclosed in {&nbsp;}'s as usual. Otherwise,
 any subsequent characters signal that the first argument
 is optional, enclosed in [&nbsp;]'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;
 n &nbsp; as shown. In this case that's just a single
 character, but you can write any length default you like.
 &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> -DNOREFMAXLEN=n </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> -DNOREFSAFELEN=n </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> -DOPAQUE </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> -DPATHPREFIX=\"path/\" </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 /'s
 or \'s, and paths with ../'s or ..\'s,
 are not permitted. Instead, compile mimetex with PATHPREFIX
 defined as path/ if you want input files in some
 other directory. And make sure your path/ ends
 with / (or with \ for Windows). </dd>
 <dt> -DPLUSBLANK &nbsp; &nbsp; &nbsp; -or- 
 -DPLUSNOTBLANK </dt>
 <dd> mimeTeX receives your LaTeX math expression as a url
 query&nbsp;string, in which blank spaces are often encoded
 as&nbsp;%20 or as plus signs&nbsp;+, and
 where actual plus signs are often encoded as&nbsp;%2B.
 But these conventions aren't always respected,
 and even when they are blank spaces may be either
 %20&nbsp;or&nbsp;+. The only ambiguity for
 mimeTeX is whether or not to translate plus signs&nbsp;+
 back to blank spaces. 
 &nbsp; &nbsp; &nbsp; If you know how your applications behave,
 then define PLUSBLANK to always translate plus signs&nbsp;+
 to blank spaces, or define PLUSNOTBLANK to never translate. 
 &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 %20, then plus signs&nbsp;+
 aren't translated. Otherwise, if your query&nbsp;string
 contains %2B, then plus signs&nbsp;+ are
 translated. If neither %20 nor %2B, or both
 %20 and %2B, occur in your query&nbsp;string,
 then the situation is ambiguous. In this case, if mimeTeX
 finds two or more plus signs&nbsp;++ with no intervening
 space, then they're translated; otherwise they're not. </dd>
 <dt> -DREFERER=\"domain\" &nbsp; &nbsp; &nbsp; -or- 
 -DREFERER=\"domain1,domain2,etc\" </dt>
 <dd> Blocks mimeTeX requests from unauthorized domains that
 are using your mimetex.cgi (hence your server's resources)
 without permission. 
 &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=\"\", 
 &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. 
 &nbsp; &nbsp; &nbsp; If HTTP_REFERER doesn't contain a substring
 matching any of these domain(s), then mimeTeX emits the error
 message image 
 <img src="../cgi-bin/mimetex.cgi?\message{0}"
 alt="" align="middle" border=0> 
 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. 
 &nbsp; &nbsp; &nbsp; Finally, if you specify -DREFERER
 (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>-DREFLEVELS=n &nbsp; &nbsp; &nbsp; -or- 
 -DNOREFCHECK </dt>
 <dd> Besides -DREFERER discussed immediately above,
 mimeTeX can block requests from HTTP_REFERER's that
 don't match your HTTP_HOST, i.e., from pages on
 different servers than your mimetex.cgi image. 
 &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 -DREFLEVELS=99 or any large number.
 If HTTP_REFERER is not found, then the same&nbsp;24
 character limit discussed immediately above remains in effect. 
 &nbsp; &nbsp; &nbsp; To completely disable the REFLEVELS check,
 compile mimeTeX with -DNOREFCHECK (or with
 -DREFLEVELS=0). Or, if you supply a specific
 -DREFERER list of authorized domains, as discussed
 immediately above, then the REFLEVELS check is automatically
 disabled. </dd>
 <dt>-DSECURITY=n </dt>
 <dd> This is essentially a "paranoid" setting that defaults
 to a high value 999, which inhibits some optional logging
 activity. -DCACHEPATH=path/ isn't affected,
 since you're explicitly supplying a path/
 you want files written to. But, for example, you must set
 -DSECURITY=5 (or less) to permit the \counter
 command to create a new counter file. A malicious user
 could conceivably flood your file system by submitting
 zillions of \counter{filename} commands
 to mimeTeX, each with a different filename. </dd>
 <dt>-DSMASHMARGIN=n &nbsp; &nbsp; &nbsp; -or- 
 -DNOSMASH </dt>
 <dd> TeX typically renders an expression like
 \frac12\int_{a+b+c}^{d+e+f}g(x)dx 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 -DNOSMASH 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 -DSMASHMARGIN=n.
 See <a href="#smash">Smash</a> for further discussion. </dd>
 <dt> -DWARNINGS=n &nbsp; &nbsp; &nbsp; -or- 
 -DNOWARNINGS </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 -DWARNINGS=0
 or -DNOWARNINGS on the compile line tells mimeTeX to treat
 unrecognized/undisplayable input as white space. </dd>
 <dt> -DWHITE </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 -DOPAQUE&nbsp;). </dd>
 </dl>

<h2> <a name="cmdline"> (IId) Command Line Features &nbsp; </a> </h2>

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.

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;+ are never
 translated to blank spaces, nor is any other %xx url decoding
 performed on command-line arguments.) 
 
 The complete command-line syntax for mimeTeX is 
 <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>

<h1> <a name="reference"> (III) Syntax Reference &nbsp; </a> </h1>

Since mimeTeX's syntax is as TeX-like as possible, we'll mostly discuss
 the occasional differences.
 
 This section contains short paragraphs that each discuss some aspect
 of mimeTeX where your LaTeX experience might not be precisely
 duplicated.

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.

<h2> <a name="spaces"> (IIIa) \unitlength{&nbsp;}, Math Spaces and Whitespace
&nbsp; </a> </h2>

<h3> <a name="unitlength">\unitlength...</a> </h3>

Lengths in mimeTeX are all ultimately expressed in number of pixels.
 Various commands discussed below require length arguments, including 
 <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> 
 (the \longxxxarrow [&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
 \unitlength.

MimeTeX's \unitlength{&nbsp;} command lets you specify
 the number of pixels per "length&nbsp;unit", e.g.,
 \unitlength{10}&nbsp;\hspace{2.5} renders a 25-pixel space.
 Both \unitlength{&nbsp;} and \hspace{&nbsp;}'s
 length arguments may be integers or may contain decimal points.
 Ditto for all other mimeTeX commands that take length arguments.
 The default \unitlength is, you guessed it, 1.

A specified \unitlength applies to all subsequent terms,
 i.e., everything to its right. And several \unitlength's
 may be specified in the same expression, each one overriding
 those to its left. But if one or more \unitlength's
 appear within a {&nbsp;}-enclosed subexpression, then terms
 following its closing right } revert to the \unitlength
 in effect before its opening left {. For example, <center>
 A\hspace{10}&nbsp;{\unitlength{2.5}B\hspace{10}C}&nbsp;\hspace{10}D
 &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> 
 which has a 10-pixel space between A&nbsp;and&nbsp;B, then
 25&nbsp;pixels between B&nbsp;and&nbsp;C, and finally
 another 10&nbsp;pixels between C&nbsp;and&nbsp;D.

<h3> <a name="mathspace">Math Spaces...</a> </h3>

Except inside <a href="#textboxes">text&nbsp;boxes</a>,
 unescaped blanks, tildes (a&nbsp;~), 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.

MimeTeX recognizes math spaces \/&nbsp;\,&nbsp;\:&nbsp;\;
 as well as \quad and \qquad&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;\&nbsp;followed by a blank).
 For example, &nbsp;
 (a\/b\,c\:d\;e\&nbsp;&nbsp;f\quad&nbsp;&nbsp;g\qquad&nbsp;&nbsp;h)
 &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; \hspace{10} &nbsp;
 to insert a 10-pixel (or any other number) space, scaled by any
 preceding <a href="#unitlength">\unitlength</a>, as illustrated
 just above.

For negative spaces, &nbsp; \! &nbsp; produces a small (two
 pixel) negative space, e.g., &nbsp; a=b &nbsp; renders &nbsp;
 <img src="../cgi-bin/mimetex.cgi?a=b"alt="" border=0 align="bottom">
 &nbsp; whereas &nbsp; a\!=b &nbsp; renders &nbsp;
 <img src="../cgi-bin/mimetex.cgi?a\!=b"alt="" border=0 align="bottom">
 &nbsp; and &nbsp; a\!\!=b &nbsp; renders &nbsp;
 <img src="../cgi-bin/mimetex.cgi?a\!\!=b"alt="" border=0 align="bottom">.
 For large negative space, &nbsp; \hspace{-10} &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; \hspace*{-10} &nbsp; instead. For example,
 &nbsp; ABC\hspace*{-20}-DEF &nbsp; renders &nbsp;
 <img src="../cgi-bin/mimetex.cgi?ABC\hspace*{-20}-DEF"
 alt="" border=0 align="bottom">, &nbsp; erasing all of the C
 and the right half of the B.

MimeTeX also supports \hfill{textwidth}, where
 textwidth is roughly equivalent to LaTeX's
 \textwidth, 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 \hfill{&nbsp;} appears
 within a {&nbsp;}-enclosed subexpression, then it applies
 only to that subexpression. For example, <center>
 {abc \hfill{75} def} \hfill{150} ghi
 &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> 
 The first/inner \hfill{75} inserts exactly enough whitespace so
 that subexpression "abc&nbsp;&nbsp;def" spans 75 pixels.
 Then the second/outer \hfill{150} inserts exactly enough
 whitespace so that the entire expression spans 150 pixels.
 Without explicit {&nbsp;}-nesting, mimeTeX evaluates expressions
 left-to-right (sinistrally), e.g., ...\hfill{150}...\hfill{75}...
 is exactly equivalent to ...\hfill{150}{...\hfill{75}...}.
 Notice that, this time, the second/right textwidth
 argument is necessarily smaller than the first/left.

Finally, mimeTeX begins a new line whenever you write \\&nbsp;.
 And you may optionally write \\[10] 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, <center>
 y=a+b+c+d\\\hspace{50}+e+f+g+h
 &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>

However, mimeTeX can't correctly handle automatically-sized delimiters
 across linebreaks, e.g., <center>
 y=\left\{a+b+c+d\\\hspace{50}+e+f+g+h\right\}
 &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> 
	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> 
 which I produced using \big{...\\...\big} instead
 of \left\{...\\...\right\}. Expressions of the
 form \left...\right&nbsp;\\&nbsp;\left...\right should all be
 rendered properly. It's only \left...\\...\right that will
 look odd.

<h3> <a name="whitespace">Whitespace, Comments,
and some other characters...</a> </h3>

Some browsers occasionally misinterpret typed blank spaces
 inside html query_string's. In that case, you can write
 tildes (a&nbsp;~) wherever blanks are required or desired,
 e.g., \alpha~w instead of \alpha&nbsp;w, or
 \frac~xy or \sqrt~z, etc. MimeTeX correctly
 interprets both blanks and ~'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.

Similarly, some browsers occasionally misinterpret linebreaks/newlines
 inside the middle of long html query_string's.
 For example, 
<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>
 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.

If you can break long query_string's over several lines, then you may
 find mimeTeX's %%comments%% feature useful, too. Note that
 comments must be preceded and&nbsp;followed by two %'s
 rather than LaTeX's usual one. The above example could be written 
<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>

Besides whitespace, browsers may misinterpret embedded apostrophes,
 and especially quotes, within query strings. The a's and
 b's in <a href="#example7">Example&nbsp;7</a> above actually use
 superscripted commas for apostrophes, i.e., a^,s and b^,s,
 and you can also use LaTeX \prime's, as in a^\prime&nbsp;s.
 For quotes, you can use ^{,,} since " almost certainly
 won't work. To help make things easier, in addition to the usual
 LaTeX \prime, mimeTeX also recognizes \apostrophe and
 \quote and \percent, all with the obvious meanings.

<h2> <a name="symbols"> (IIIb) Math Symbols, Sizes, and Modes &nbsp; </a></h2>

<h3> <a name="characters">Character Sets...</a> </h3>

For complete information about the characters and math symbols
 available in mimeTeX, you'll need to browse through the bottom
 500-or-so lines of mimetex.h. And several additional
 symbols like \ldots and \AA and \hbar are
 defined by the mimeTeX preprocessor, function mimeprep(&nbsp;)
 in mimetex.c &nbsp; &nbsp; Generally speaking, I've tried to
 encode the cmr10, cmmi10, cmmib10, cmsy10, cmex10, bbold10, rsfs10,
 stmary10 and wncyr10 families with "names", e.g., \alpha \beta
 \forall \sqcup, etc, identical to your LaTeX expectations.
 For example, the calligraphic symbols in cmsy10 are accessed by
 writing \mathcal{A} \mathcal{B} \mathcal{XYZ}. Similarly,
 write \mathbf{A} for the cmmib fonts, write \mathscr{A}
 for rsfs10, write \mathbb{R} for bbold10, and write
 {\cyr&nbsp;Khrushchev} or \cyr{Khrushchev} 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. 
 
 I haven't exhaustively checked all the name-number matchings for
 the hundreds of 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.

In addition to extra LaTeX symbols like \ldots, \AA
 and \hbar, mentioned above, the mimeTeX preprocessor
 mimeprep(&nbsp;) also recognizes various html special
 characters like &amp;lt;, &amp;gt;, &amp;nbsp;,
 &amp;quot;, &amp;amp;, etc. Some web tools apparently
 translate characters like, e.g., &gt; to &amp;gt;,
 even inside quoted query_string's, so mimeTeX's preprocessor
 translates them back to LaTeX symbols for you. Moreover, html
 misinterprets quotes &nbsp;&quot;&nbsp; inside a quoted
 query string as the end of the query string. So, for example,
 the cyrillic ligature \&quot;E has to be written in the
 even more cumbersome form \&amp;quot;E inside a query
 string.

<h3> <a name="sizes">Font Sizes...</a> </h3>

MimeTeX currently has eight font sizes, numbered 0-7, with default 3.
 This font size numbering corresponds to the usual LaTeX directives
 &nbsp; \tiny, &nbsp; \small, &nbsp; \normalsize,
 &nbsp; \large (default), &nbsp; \Large, &nbsp;
 \LARGE, &nbsp; \huge and \Huge.
 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 {&nbsp;}-subexpression remains
 in effect only within that subexpression.

In mimeTeX you may also write \fontsize{0}...\fontsize{7} or
 the shorter \fs{0},...,\fs{7} for \tiny,...,\Huge.
 And since these arguments are all single digits, the even shorter
 form \fs0,...,\fs7 works equally well. For example, 
 <center> <table cellpadding=0>
 <tr align=center>
 <td align="left"> 0: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\tiny 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"> 1: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\fs1 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"> 2: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\normalsize 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"> 3: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?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"> 4: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\Large 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"> 5: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\fs5 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"> 6: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\huge 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"> 7: &nbsp;
 &lt;img src="../cgi-bin/mimetex.cgi?\fs7 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> 
 rendering f(x)=x^2 in mimeTeX font sizes &nbsp;
 0 (\tiny or \fs0), &nbsp; 1 (\small or \fs1), &nbsp;
 2 (\normalsize or \fs2), &nbsp; 3 (default \large), &nbsp;
 4 (\Large or \fs4), &nbsp; 5 (\LARGE or \fs5), &nbsp;
 6 (\huge or \fs6) &nbsp; and &nbsp; 7 (\Huge or \fs7).

You'll soon notice that exponents and \frac's and \atop's
 are automatically rendered one size smaller than their base
 expressions. For example, <center>
 \Large y=e^{x^2} &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> 
 rendering the "y=e" in font size 4 (\Large), the "x" in
 font size 3 (\large), and the "2" in font size 2 (\normalsize).
 If you get below font size 0, the font size remains&nbsp;0.

Explicit size declarations override mimeTeX's default sizing behavior.
 You can rewrite the preceding example as, say, <center>
 \Large y=e^{\normalsize x^{\tiny2}} &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> 
 rendering the "y=e" in font size 4 (\Large unchanged),
 the "x" in font size 2 (\normalsize), and the "2"
 in font size&nbsp;0 (\tiny).

Preceding an \fs{&nbsp;} size argument with + or
 - specifies "relative" sizing. For example,
 \large\text{abc{\fs{-2}def}ghi} 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 "def"
 in font size 1 (two sizes smaller than \large). Note that
 \fs{-2} affects only the subexpression in which it appears,
 and that its braces are no longer optional since -2 contains
 two characters. For exponents (or any other size-changing commands
 like \frac), <center>
 \Large y=e^{\fs{-1}x^2} &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> 
 rendering the "y=e" in font size 4 (\Large), as usual.
 The "x" would usually be rendered one size smaller,
 in font size 3, and your \fs{-1} is applied to that,
 resulting in font size 2. And the final "2" is rendered,
 by the usual rules, one size smaller than the "x",
 in font size&nbsp;1.

<h3> <a name="modes">Modes...</a> </h3>

MimeTeX is always in a math-like mode, so you needn't surround
 expressions with $...$'s for \textstyle,
 or $$...$$'s for \displaystyle.
 
 By default, operator limits like \int_a^b are rendered
 \textstyle <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 \normalsize
 and smaller, and rendered \displaystyle <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 \large and
 larger (see the -DDISPLAYSIZE
 <a href="#options">compile&nbsp;option</a> to change this default).
 And when \displaystyle is invoked (either implicitly at font size
 \large or larger, or if you explicitly write \displaystyle
 at any font size), then operators \int, \sum,
 \prod, etc, are automatically promoted to larger sizes.
 
 
 
 For example, <center>
 
 \normalsize \sum_{i=1}^ni=\frac{n(n+1)}2
 &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 
 \displaystyle \normalsize \sum_{i=1}^ni=\frac{n(n+1)}2
 &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>
 and  <center>
 \large \sum_{i=1}^ni=\frac{n(n+1)}2 &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 
 \textstyle \large \sum_{i=1}^ni=\frac{n(n+1)}2
 &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>.
  </center>

As usual, \nolimits turns displaystyle off (or textstyle on)
 for the operator immediately preceding it. For example, <center>
 \large \sum\nolimits_{i=1}^ni=\frac{n(n+1)}2
 &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> 
 and likewise, \limits turns displaystyle on for the operator
 immediately preceding it. For example, <center>
 \normalsize \sum\limits_{i=1}^ni=\frac{n(n+1)}2
 &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>

By the way, \limits affects _any_ character
 or subexpression immediately preceding it. For example, <center>
 A^i_j &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 
 A\limits^i_j &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>
 Likewise, for subexpressions, <center>
 \widehat{xyz}\limits^a &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> 
 This side effect may occasionally be useful. For example, <center>
 x\rightarrow\limits^gy &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> 
 (mimeTeX automatically centers super/subscripts above/below
 the long and Long <a href="#arrows">arrow</a> forms)

The \displaystyle command turns on displaystyle math mode for
 the entire expression (or {&nbsp;}-enclosed subexpression),
 affecting _all_ super/subscripts to the right
 of the \displaystyle, except for character classes Ordinary and
 Variable (TeXbook page 154). Similarly, \textstyle turns
 off displaystyle math mode. For example, <center>
 \sum_1^n {\displaystyle\sum_1^k\sum_1^lx_i^j} \sum_1^m
 &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> 
 Note that \sum's within the subexpression are all affected by
 the beginning \displaystyle, but not the Variable x_i^j.
 An explicit x\limits_i^j always affects any preceding term.

<h3> <a name="textboxes">text boxes...</a> </h3>

Finally, mimeTeX also has a text-like/roman mode
 entered by writing either \text{anything&nbsp;at&nbsp;all}
 or the equivalent LaTeX-2.09-like command
 {\rm&nbsp;anything&nbsp;at&nbsp;all}, both of which render
 anything&nbsp;at&nbsp;all in roman (font family cmr10).
 \mbox{&nbsp;} and several similar LaTeX commands are
 recognized by mimeTeX as synonyms for \text{&nbsp;}.
 For italic, write \textit{anything&nbsp;at&nbsp;all} or
 {\it&nbsp;anything&nbsp;at&nbsp;all}, both of which render
 anything&nbsp;at&nbsp;all in italic (font family cmmi10).
 All four forms respect spaces between words, except that the
 first/required space after {\rm&nbsp;etc} and
 {\it&nbsp;etc} is still ignored.  For example, <center>
 anything&nbsp;at&nbsp;all &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 
 \text{anything&nbsp;at&nbsp;all} &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 
 \textit{anything&nbsp;at&nbsp;all} &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>

You don't usually surround mimeTeX expressions with $'s,
 but that works in the usual way for \text{&nbsp;} and
 \mbox{&nbsp;}, rendering the $...$-enclosed
 subexpression in mathmode. For example, <center>
 n=\left\{m/2\text{&nbsp; &nbsp; if $m$ even}
 \\(m+1)/2\text{&nbsp; if $m$ odd}\right.
 &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)...</a> </h3>

LaTeX's \left(&nbsp;...&nbsp;\right) and the other 21
 standard LaTeX delimiters are also recognized by mimeTeX.
 And mimeTeX also recognizes an etex-like \middle. &nbsp;
 
  Several of the most common automatically sized delimiters
 are illustrated below... <center>
 
 <table cellspacing=0 cellpadding=2 border=1>
 <tr align=center>
 
 <td> Delimiter </td>
 
 <td> example... </td>
 <td> ...renders </td>
 </tr>
 <tr align=center>
 <td> \left(&nbsp;...&nbsp;\right) </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> \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> \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; ... 
 &nbsp; &nbsp; &nbsp; &nbsp; ... &nbsp;\right\rangle </td>
 
 <td> \left\langle \varphi \middle| \hat H 
 &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> \left| \begin{matrix} a_1 & a_2 \\ 
 &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> \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. </td>
 
 <td> y=\left\{ \text{this\\that}
 \right. </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.
 &nbsp;...&nbsp;\right\} </td>
 
 <td> \left.
 \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>
 Notes...&nbsp; 
 <ol compact type=1>
 
 <li> <a href="#sizes">Size&nbsp;declarations</a> inside any of the
 above delimiter pairs affect only the enclosed subexpression,
 e.g., \Large w=\left(\small x+y\right)+z 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 \middle's as
 you like, and in mimeTeX the surrounding \left...\right
 isn't required. When omitted, the scope of \middle is
 either the entire expression or the &nbsp; {&nbsp;}-enclosed
 subexpression in which the \middle's occur. For example, &nbsp;
 \frac{a+1}b&nbsp;\middle/&nbsp;\middle(\frac{c+1}d&nbsp;\middle/&nbsp;\frac{e+1}f\middle)
 &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; \\ &nbsp; in &nbsp; \text{this\\that} &nbsp;
 as a linebreak. For example, x=1\\y=2\\z=3 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>
 
 
 
 
 
 
 </ol>

Besides the \left...\right delimiters discussed above,
 mimeTeX also supports constructions like
 \left\int_a^b...\right.&nbsp;, which automatically
 sizes the \left\int to accommodate everything between it
 and its matching \right. &nbsp; delimiter.
 The \right delimiter needn't necessarily be
 the \right. &nbsp; illustrated, e.g.,
 \left\int_a^b&nbsp;x^2dx&nbsp;=\frac{x^3}3\right|_a^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>. 
 You can also write \left\sum, \left\prod,
 \left\cup, etc, for many of the symbols in CMEX10 and STMARY10.
 And any symbol that works with \left will also work
 with \right&nbsp;.

Unescaped (&nbsp;)'s and [&nbsp;]'s and |&nbsp;|'s
 and &lt;&nbsp;&gt;'s don't need to be balanced since mimeTeX just
 displays them like ordinary characters without any special significance.
 Ditto for the usual four \big( and \Big( and \bigg(
 and \Bigg(, and for their four right ) counterparts, which
 just display (...)'s at fixed larger sizes, and also have no
 special significance. All four big [&nbsp;]'s and
 &lt;&nbsp;&gt;'s and {&nbsp;}'s are also available
 as ordinary characters.

As usual, unescaped {...}'s aren't displayed at all,
 must be balanced, and have the usual special LaTeX significance.
 MimeTeX interprets escaped \{...\}'s as abbreviations
 for \left\{...\right\} and therefore always sizes them to fit.
 If you need displayed but unsized {...}'s, write
 \lbrace...\rbrace or any of the four \big{...\big}'s.

<h2> <a name="accents"> (IIId) Accents, Functions, Arrows,
Raise&nbsp;and&nbsp;rotate, Compose, Abbreviations, etc. &nbsp; </a> </h2>

<h3> Accents... </h3>
 
 
 \vec{&nbsp;} \hat{&nbsp;} \bar{&nbsp;} \tilde{&nbsp;} \dot{&nbsp;}
 \ddot{&nbsp} &nbsp; and &nbsp; \acute{&nbsp;} \grave{&nbsp;}
 \breve{&nbsp;} \check{&nbsp} are the only accents currently
 supported. The first four are all "wide". For example, you can write
 \widehat{&nbsp;} if you like, but there's absolutely no
 difference either way (and \bar{&nbsp;} and
 \overline{&nbsp;} are identical). The last four accents
 only take a single character argument.

Other accent-like directives available in mimeTeX are &nbsp;
 \underline{&nbsp;} \cancel{&nbsp;} \sout{&nbsp;}, &nbsp;
 as well as &nbsp;
 \overset{&nbsp;}{&nbsp;} &nbsp; \underset{&nbsp;}{&nbsp;} &nbsp;
 and the more ususal &nbsp;
 \overbrace{&nbsp;}^{&nbsp;} &nbsp; \underbrace{&nbsp;}_{&nbsp;}.
 &nbsp; And \not also works on the single character immediately
 following it. Some of these directives are discussed in more detail
 below.

<h3> <a name="functions">Function names...</a> </h3>

All 32 usual LaTeX function names \arccos,...,\tanh
 are recognized by mimeTeX and treated in the usual way. MimeTeX
 also recognizes \tr for the trace, and also \bmod
 and \pmod. And those functions that normally take "limits"
 also behave as expected, e.g., <center>
 \lim_{n\to\infty}S_n=S &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...</a> </h3>

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,
 \longrightarrow[50] 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 \longrightarrow 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>.

In the event that you actually want to place an []-enclosed expression
 immediately following an "unsized" long arrow, just place a ~ or
 any white space after the arrow, e.g., f:x\longrightarrow~[0,1]
 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].

Super/subscripts immediately following all long/Long left/right arrows
 are displayed the same way <a href="#modes">\limits</a> displays them,
 e.g., <center>
 x\longrightarrow^gy &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> 
 x\longrightarrow[50]^gy &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> 
 Subscripted long arrows can occasionally be useful, too, as in
 <a href="#example11">Example&nbsp;11</a> above, e.g., <center>
 u\longrightarrow[50]_\beta v &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> 
 To defeat this default behavior, e.g., \longrightarrow\nolimits^g
 displays super/subscripts in the usual way.

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, <center>
 \longuparrow[30]^\gamma &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> 
 \longdownarrow[30]_\gamma &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> 
 whose occasional usefulness is also illustrated by
 <a href="#example11">Example&nbsp;11</a>. And as before, to defeat
 this default behavior, e.g., \longuparrow\nolimits^\gamma
 displays super/subscripts in the usual way.

<h3> <a name="raiserotate">\raisebox{&nbsp;}{&nbsp;} and
\rotatebox{&nbsp;}{&nbsp;} and \reflectbox[&nbsp;]{&nbsp;}
...</a> </h3>

The \raisebox{height}{expression}
 and \rotatebox{angle}{expression}
 and \reflectbox[axis]{expression}
 commands help you fine-tune and manipulate mimeTeX renderings: 
 <ul>
 <li> \raisebox's height argument is number
 of pixels, scaled by <a href="#unitlength">\unitlength</a>,
 and can be positive or negative. </li>
 <li> \rotatebox's angle argument is number
 of degrees, and can also be positive (for clockwise) or
 negative, but must be a multiple of 90. </li>
 <li> \reflectbox's optional axis 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 expression
 can be any valid LaTeX/mimeTeX expression. </li>
 </ul>
 For example, mimeTeX's preprocessor
 defines the LaTeX ?` symbol, an upside-down question
 mark, like <center>
 abc\raisebox{-2}{\rotatebox{180}?}def &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>
 Using \reflectbox[2]{&nbsp;} instead of
 \rotatebox{180}{&nbsp;} would result in the slightly
 different <center>
 abc\raisebox{-2}{\reflectbox[2]?}def &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=middle></a> </center>

<h3> <a name="compose">\compose{&nbsp;}{&nbsp;}...</a></h3>

\compose[offset]{base}{overlay}
 superimposes the overlay expression on top of the
 base expression, displaying the result.
 Optionally, the overlay is horizontally offset
 by the specified number of pixels (positive offsets to the right,
 negative to the left). For example, <center>
 \compose{\LARGE O}{\normalsize c} &nbsp; produces &nbsp;
 <a href="#preview"><img id="compose1" onclick="eqntext('compose1')"
 src="../cgi-bin/mimetex.cgi?\compose{\LARGE O}{\normalsize c}"
 alt="" border=0 align=middle></a> </center>

Separately or in some judicious combination, \compose and
 \raisebox and \rotatebox and \reflectbox
 should 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
 -DNEWCOMMANDS compile-time
 <a href="#options">option</a> discussed above.

\rule{width}{height} behaves in the usual way,
 rendering a black rectangle width pixels wide and
 height pixels high, with its base on the established
 baseline. For example, <center>
 \frac12xyz\rule{10}{20}ghi &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>

The mimeTeX version of \rule has an optional
 [lift] argument, so that its full form is
 \rule[lift]{width}{height}.
 lift moves the rule's baseline by the specified
 number of pixels, up if positive or down if negative.
 For example, <center>
 \frac12xyz\rule[5]{10}{20}ghi &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 
 \frac12xyz\rule[-15]{10}{20}ghi &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="abbreviations">Abbreviations...</a> </h3>

\ga displays \gamma, but just \g displays
 \gg (&gt;&gt;). 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.

The mimeTeX <a href="#symbols">preprocessor</a>, briefly mentioned
 above, is responsible for recognizing several LaTeX symbols like
 \ldots and several commands like \atop&nbsp;.
 These symbols and commands cannot be abbreviated. The special
 html characters like &amp;nbsp; are also recognized by
 the preprocessor and cannot be abbreviated.

<h3> <a name="colors">Colors...</a> </h3>

Rudimentary color commands are provided by mimeTeX. You can write
 \color{red} or \color{green} or\color{blue}
 (which may be abbreviated \red or \green or
 \blue) anywhere in an expression to render the entire
 expression in the specified color. That is,
 abc{\red&nbsp;def}ghi renders the entire expression red,
 not just the def part. Also, note that mimeTeX's "green"
 is actually color #00FF00, which the html standard more
 accurately calls "lime". For example, <center>
 \blue e^x=\sum_{n=0}^\infty\frac{x^n}{n!} &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;...</a> </h3>

TeX represents characters by boxes, with no idea how ink will be
 distributed inside. So an expression like
 \frac12\int_{a+b+c}^{d+e+f}g(x)dx 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.

Precede any expression with the mimeTeX directive \nosmash
 to render it without "smashing". Or compile mimetex.c with the
 -DNOSMASH <a href="#options">option</a> if you prefer
 the typical TeX behavior as mimeTeX's default. In this case,
 precede any expression with \smash to render it "smashed".
 And note that explicit space like \hspace{10}
 or \;&nbsp;, etc, is never smashed.

The scope of \smash and \nosmash is the
 {&nbsp;}-enclosed subexpression in which the directive occurs.
 For example, if you want the g(x)&nbsp;part of the
 preceding example smashed, but not the 1/2&nbsp;part,
 then the expression
 \nosmash\frac12{\smash\int_{a+b+c}^{d+e+f}g(x)dx}
 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>.

For finer-grained control, note that \smash is shorthand
 for the default \smashmargin{+3} (and \nosmash is
 shorthand for \smashmargin{0}). \smashmargin's value
 is the minimum number of pixels between smashed symbols. The leading
 + is optional. If present, the font size (\tiny=0,...,\Huge=7)
 is added to the specified minimum. Compile mimetex.c with the
 -DSMASHMARGIN=n <a href="#options">option</a> to change
 the default from 3 to n. Compare the preceding
 example with the over-smashed \smashmargin{1} &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.

Smashing is in "beta testing" and some expressions still don't look
 quite right when smashed, e.g., 1^2,2^2,3^2,\ldots 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 -DNOSMASH
 if you come across numerous annoying situations.

<h3> <a name="not">\not and \cancel and \sout...</a> </h3>

The usual LaTeX &nbsp; \not &nbsp; "slashes" the single symbol
 following it, e.g., &nbsp; i\not\partial\equiv&nbsp;i\not\nabla
 &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>.

For arbitrary expressions, mimeTeX provides &nbsp; \cancel &nbsp;
 which draws a line from the upper-right to lower-left corner of its
 argument, e.g., &nbsp; a\cancel{x^2}=bx^{\not3} &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>.

Finally, similar to the ulem.sty package, &nbsp; \sout
 &nbsp; draws a horizontal strikeout line through its argument,
 e.g., &nbsp; \sout{abcdefg} &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 \sout also
 takes an optional argument that adjusts the vertical position of its
 strikeout line by the specified number of pixels, e.g., &nbsp;
 \sout[+2]{abcdefg} 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;
 \sout[-2]{abcdefg} 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>.

<h2> <a name="array"> (IIIe) \begin{array}{lcr}...\end{array} Environment
&nbsp; </a> </h2>

Rendering vectors and matrices, aligning equations, etc, is all done
 using the customary LaTeX environment &nbsp;
 \begin{array}{lcr}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{array}
 &nbsp; which you can write in exactly that form. MimeTeX also
 recognizes the following array-like environments 
 <center> <table cellpadding="1" cellspacing="1">
 <tr> <td align="left"> \begin{array}{lcr} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{array} </td> </tr>
 <tr> <td align="left"> \begin{matrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{matrix} </td> </tr>
 <tr> <td align="left"> \begin{pmatrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{pmatrix} </td> </tr>
 <tr> <td align="left"> \begin{bmatrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{bmatrix} </td> </tr>
 <tr> <td align="left"> \begin{Bmatrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{Bmatrix} </td> </tr>
 <tr> <td align="left"> \begin{vmatrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{vmatrix} </td> </tr>
 <tr> <td align="left"> \begin{Vmatrix} </td>
 <td align="center"> a&b&c \\ d&e&f \\ etc </td>
 <td align="left"> \end{Vmatrix} </td> </tr>
 <tr> <td align="left"> \begin{eqnarray} </td>
 <td align="center"> a&=&b \\ c&=&d \\ etc </td>
 <td align="left"> \end{eqnarray} </td> </tr>
 <tr> <td align="left"> \begin{align} </td>
 <td align="center"> a&=b \\ c&=d \\ etc </td>
 <td align="left"> \end{align} </td> </tr>
 <tr> <td align="left"> \begin{cases} </td>
 <td align="center"> a&b \\ c&d \\ etc </td>
 <td align="left"> \end{cases} </td> </tr>
 <tr> <td align="left"> \begin{gather} </td>
 <td align="center"> a \\ b \\ etc </td>
 <td align="left"> \end{gather} </td> </tr>
 </table> </center> 
 There's a built-in maximum of 64 columns and 64 rows. Nested
 array environments, e.g.,
 \begin{pmatrix}a&\begin{matrix}1&2\\3&4\end{matrix}\\c&d\end{pmatrix},
 are permitted.

MimeTeX also provides the abbreviation &nbsp;
 \array{lcr$a&b&c\\d&e&f\\etc} &nbsp;
 which has exactly the same effect as &nbsp;
 \begin{array}{lcr}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{array}.
 And the lcr$ "preamble" in \array{lcr$etc} is optional.
 In that case, &nbsp; \array{a&b&c\\d&e&f\\etc} &nbsp;
 has exactly the same effect as &nbsp;
 \begin{matrix}&nbsp;a&b&c\\d&e&f\\etc&nbsp;\end{matrix}.
 You can also write $\array{etc}$ to "manually abbreviate"
 the pmatrix environment, or \array{rcl$etc} to abbreviate
 eqnarray, but mimeTeX has no explicit abbreviations for these
 other environments. For example, <center>
 \begin{matrix}a_1&a_2&a_3\\b_1&b_2&b_3\\c_1&c_2&c_3\end{matrix}
 &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>

Solid \hline's (but not \cline's) and vertical l|c|r bars
 are available, as usual. For dashed lines and bars,
 \begin{array} provides the additional features \hdash
 and l.c.r&nbsp;. \hline and \hdash may not be
 abbreviated. For example, <center>
 \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} &nbsp; produces 
 <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>

The default font size is unchanged by \array{&nbsp;}, but you
 can explicitly control it in the usual way, e.g.,
 {\Large\begin{matrix}...\end{matrix}} renders the entire array
 in font size 4. In addition, any &...& cell may contain font
 size declarations which are always local to that cell,
 e.g., &\fs{-1}...& renders that one cell one font size smaller
 than current.

The {lcr} in \begin{array}{lcr} sets left,center,right
 "horizontal&nbsp;justification" down columns of an array,
 as usual. And "vertical&nbsp;justification" across rows defaults
 to what we'll call baseline, 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
 "vertical&nbsp;centering" across the middle row of that
 array. So, in addition to lowercase lcr, mimeTeX's {lcr}
 in \begin{array}{lcr} may also contain uppercase BC to
 set "B"aseline or "C"enter vertical justification across
 the corresponding rows. For example, \begin{array}{rccclBCB}
 sets baseline justification for the first and third rows, and center
 justification for the second row. Without any BC's,
 all rows default to the usual B baseline justification.

MimeTeX has no \arraycolsep or \arraystretch parameters.
 Instead, \begin{array}{lc25rB35C} 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 lcrBC specification sets the width of that one column
 (for lcr), or the height of that one row (for BC). 
 <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
 You can optionally precede the number with a + sign,
 which "propagates" that value forward to all subsequent columns for
 lcr, or all subsequent rows for BC. For example,
 \begin{array}{lc+25rB+35C} 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 0 reverts to automatic sizing for that one row or
 column, and +0 reverts to automatic sizing for all subsequent
 rows or columns. For example, \begin{array}{c+25ccc+35ccc+0}
 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. 
 <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
 The "propagation" introduced by + is local to the
 \begin{array} 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 \\). Instead, a lowercase g globally
 copies your column specifications to all subsequent arrays,
 and an uppercase G globally copies your row specifications.
 And gG copies both column and row specifications. For example,
 \begin{array}{GC+25} 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. 
 <img src="../cgi-bin/mimetex.cgi?\hspace{35}" alt="" border=0>
 Click one of the following examples to see illustrations
 of the above discussion: <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> 
 <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>

See <a href="#example8">Examples&nbsp;8-11</a> above for several
 additional \begin{array}{lcr} applications.

<h2> <a name="picture"> (IIIf) \picture(&nbsp;){&nbsp;} "Environment",
 including \line(&nbsp;){&nbsp;} and \circle(&nbsp;) &nbsp; </a> </h2>

Besides \begin{array}{lcr}, mimeTeX also tries to emulate the
 familiar LaTeX picture environment with the somewhat similar 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \picture(width[,height])&nbsp;
 {&nbsp;(loc1){pic_elem1}&nbsp;(loc2){pic_elem2}&nbsp;...&nbsp;} 
 as illustrated by <a href="#example12">Examples&nbsp;12-13</a> above.
 Arguments surrounded by [&nbsp;]'s are optional.
 If the optional [,height] is omitted, then height=width
 is assumed. Locations (loc1) and (loc2)&nbsp;... each
 denote either a \put(loc) or a \multiput(loc),
 and each location is of the form ([c]x,y[;xinc,yinc[;num]]).

A \put(loc) is denoted by a location of the form ([c]x,y)
 where x,y denotes the coordinate where the lower-left corner
 of the subsequent picture_element will be placed, unless the letter
 c precedes the x-number, in which case cx,y
 denotes the center point instead. The very lower-left corner of the
 entire picture is always 0,0, and the upper-right corner is
 width-1,height-1. Note, for example, that you'd never want
 to specify location c0,0 since the picture_element would be
 mostly out-of-bounds (only its upper-right quadrant would be
 in-bounds).

A \multiput(loc) starts like a \put(loc), but location
 [c]x,y is followed by ;xinc,yinc[;num] indicating the
 x,y-increments applied to each of num repetitions
 of picture_element. If ;num is omitted, repetitions continue
 until the picture_element goes out-of-bounds of the specified
 width[,height]. Note that x,y are always positive or
 zero, but xinc,yinc may be postive, zero or negative.

The \picture(,){...} parameters width, height, x, y, xinc,
 yinc may be either integer or may contain a decimal point,
 and they're all scaled by <a href="#unitlength">\unitlength</a>.
 The num parameter must be integer.

Picture_element's {pic_elem1} and {pic_elem2} ...
 may be any expressions recognized by mimeTeX, even including other
 \picture's nested to any level.

<h3> <a name="circleline">\line(&nbsp;){&nbsp;} and
\circle(&nbsp;)...</a> </h3>

To help draw useful picture_element's, mimeTeX provides several
 drawing commands, \line(xinc,yinc)[{xlen}] and
 \circle(xdiam[,ydiam][;arc]). Although primarily intended
 for use in \picture's, you can use them in any mimeTeX
 expression, e.g., &nbsp; abc\circle(20)def &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>.

Without its optional {xlen} parameter, the expression
 (x,y){\line(xinc,yinc)} draws a straight line from point
 x,y to point x+xinc,y+yinc. The inc's
 can be positive, zero or negative. Don't prefix location x,y
 with a leading c for \line's; the intended "corner"
 is determined by the signs of xinc and yinc.
 If given, the optional {xlen} parameter rescales the length
 of the line so its x-projection is xlen and its slope is
 unchanged.

Without optional ,ydiam and ;arc, the expression
 (x,y){\circle(xdiam)} draws a circle of diameter xdiam
 centered at x,y. Don't prefix location x,y with a
 leading c for \circle's; centering is assumed.
 If ,ydiam is also given, then (x,y){\circle(xdiam,ydiam)}
 draws the ellipse inscribed in a rectangle of width xdiam
 and height ydiam centered at x,y. 
 &nbsp; &nbsp; &nbsp; Finally, ;arc specifies the arc to be
 drawn, in one of two ways. An ;arc argument given in the
 form ;1234 interprets each digit as a quadrant to be drawn,
 with 1 the upper-right quadrant and then proceeding
 counterclockwise, e.g., \circle(12;34) specifies the
 lower half of a circle whose diameter is twelve. 
 &nbsp; &nbsp; &nbsp; Alternatively, an ;arc argument given in
 the form 45,180 or -60,120 specifies the endpoints of
 the desired arc in degrees, with 0 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.

Besides <a href="#example12">Examples 12-13</a> above,
 it's hard to resist illustrating 
 &nbsp; &nbsp; &nbsp;
 \unitlength{.6} &nbsp; \picture(100) { 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 (50,50){\circle(99)} %%head%% 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 (20,55;50,0;2){\fs{+1}\hat\bullet} %%eyes%% 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 (50,40){\bullet} %%nose%% 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 (50,35){\circle(50,25;34)} %%upper lip%% 
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 (50,35){\circle(50,45;34)} %%lower lip%% &nbsp; }
 <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> Have a nice day!</center>

<h2> <a name="commands"> (IIIg) Other mimeTeX Commands &nbsp; </a> </h2>

Various and sundry other LaTeX-like commands are also provided
 by mimeTeX. In addition to features explicitly discussed below,
 mimeTeX supports the usual sub_scripts and super^scripts,
 and most of the typical LaTeX commands, many already discussed
 above, including 
 <ul>
 <li> \frac{&nbsp;}{&nbsp;} and {&nbsp;\over&nbsp;} </li>
 <li> {&nbsp;\atop&nbsp;} and {&nbsp;\choose&nbsp;} </li>
 <li> \sqrt{&nbsp;} </li>
 <li> \lim_{&nbsp;} and all the usual LaTeX function names </li>
 <li> \hat{&nbsp;} and \widehat{&nbsp;}
 and many of the usual LaTeX accents </li>
 <li> \overbrace{&nbsp;}^{&nbsp;} and
 \underbrace{&nbsp;}_{&nbsp;} </li>
 <li> \overline{&nbsp;} and \underline{&nbsp;} </li>
 </ul> 
 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.

<h3> <a name="stackrel">\overset{&nbsp;}{&nbsp;} or 
\stackrel{&nbsp;}{&nbsp;} &nbsp; and &nbsp;
\underset{&nbsp;}{&nbsp;} or \relstack{&nbsp;}{&nbsp;}
...</a> </h3>

\stackrel{&nbsp;}{&nbsp;} behaves as usual in LaTeX,
 rendering its first argument one font size smaller and centered above
 its second. And the amsmath-style \overset{&nbsp;}{&nbsp;} is
 identical. For example, <center>
 "\vec x\overset{\rm def}=(x_1\ldots x_n)"
 &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>

"Conversely" to \stackrel{&nbsp;}{&nbsp;}, mimeTeX provides
 \relstack{&nbsp;}{&nbsp;}, which renders its second argument
 one font size smaller and centered below its first.
 And the amsmath-style \underset{&nbsp;}{&nbsp;} renders its
 first argument one font size smaller and centered below its second.
 For example, the \log function name doesn't treat
 limits like \lim_, but you can write, for example, <center>
 "\underset{\rm base 2}\log32=5" &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>

MimeTeX's \limits provides an easier but non-standard
 alternative to achieve the same effect. For example, <center>
 "\vec x =\limits^{\rm def} (x_1\ldots x_n)"
 &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> 
 and &nbsp; "\log\limits_{\rm base 2}32=5" &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>

In case html border attributes aren't suitable, mimeTeX provides
 the usual \fbox{expression} command, e.g., <center>
 "\fbox{x=\frac12}" &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>

You can also write \fbox[width]{expression}
 to explicitly set the box's width, or you can write
 \fbox[width][height]{expression}
 to explicitly set both width and height.

<h3> <a name="today">\today and \calendar...</a> </h3>

\today &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 \today's default format#1. MimeTeX has
 an optional format argument so that, for example, &nbsp;
 \blue\today[2] &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;
 \red\today[3] &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.

To accommodate time zones, you may also write, for example, &nbsp;
 \small\blue\today[2,+3], &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 +&nbsp;or&nbsp;-,
 and must be in the range -23&nbsp;to&nbsp;+23.

\calendar &nbsp; renders a calendar for
 the current month, as illustrated by the left-hand image below.
 For a different month, the optional argument &nbsp
 \small\blue\calendar[2001,9] &nbsp; renders the right-hand
 image, for the requested year and month. Years must be
 1973...2099 and months must be 1...12. 
 <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>

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; \calendar[0,0,1] &nbsp;
 emphasizes the first day of the current month, and
 &nbsp; \calendar[2001,9,11] &nbsp; emphasizes the eleventh
 day of that month. &nbsp; \calendar[0,0,99] &nbsp;
 renders the current month with no day emphasized.

<h3> <a name="input">\input{&nbsp;}...</a> </h3>

\input{filename} behaves just like the corresponding
 LaTeX command, reading the entire contents of filename
 into your expression at the point where the \input command
 occurs. By default, filename resides in the same
 directory as mimetex.cgi. Moreover, for security, absolute paths
 with leading /'s or \'s, and paths with ../'s
 or ..\'s, are not permitted. See the -DPATHPREFIX
 <a href="#options">compile&nbsp;option</a>, discussed above,
 if you want \input files in some other directory.
 In any case, if filename isn't found, then
 \input tries to read filename.tex instead.

And for further security, \input{&nbsp;} is disabled by default
 unless mimeTeX is compiled with either the -DINPUTOK or
 -DINPUTPATH or -DINPUTREFERER
 <a href="#options">compile&nbsp;option</a> discussed above.
 When it's disabled, the command \input{filename}
 renders the error message
 [\input{filename}&nbsp;not&nbsp;permitted]&nbsp;.

MimeTeX also supports the optional form
 \input{filename:tag}. In this case,
 filename is read as before, but only those characters
 between &lt;tag&gt;...&lt;/tag&gt; are placed
 into your expression. This permits you to have one file containing
 many different &lt;tag&gt;'s, e.g., one file containing
 all the questions and/or answers to a homework assignment or a quiz,
 etc.

<h3> <a name="counter">\counter[&nbsp;]{&nbsp;}
...</a> </h3>

The bottom-right corner of this page contains a page hit counter
 that's maintained using mimeTeX's
 \counter[logfile]{counterfile:tag}
 command. As with \input, described immediately above,
 both the required counterfile and the optional
 logfile are the names of files that reside in the
 same directory as your mimetex.cgi executable, unless you compiled
 mimetex with the -DPATHPREFIX
 <a href="#options">compile&nbsp;option</a>. Before using
 the \counter command, Unix "touch" and "chmod" those files
 so they're mimeTeX readable and writable.

Also as with \input, for security \counter is
 disabled by default unless mimeTeX is compiled with either
 the -DINPUTOK or the -DCOUNTEROK
 <a href="#options">compile&nbsp;option</a>
 (notice that -DINPUTOK also enables \counter).
 If you've compiled mimeTeX with \counter enabled,
 then it behaves as follows...

If counterfile isn't readable and writable,
 then the \counter command always displays
 1st. Otherwise, it maintains a
 line in counterfile of the form
 &lt;tag&gt;&nbsp;value&nbsp;&lt;/tag&gt;
 where value is initialized as 1_ if the
 specified &lt;tag&gt; line doesn't already exist,
 and then incremented on each subsequent call. That trailing
 underscore on the value in the file, e.g., 99_, tells
 mimeTeX to display 99th 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 \counter
 if your hit rates are high enough so that frequent collisions
 are likely. 
 
 The same counterfile can contain as many different
 &lt;tag&gt; lines as you like, so counters for
 all the pages on your site can be maintained in one file.
 MimeTeX also maintains a special &lt;timestamp&gt; tag
 in counterfile that logs the the date/time and
 name of the most recently updated tag.

Somewhat more detailed log information can be accumulated in
 the optional logfile. If you provide that
 filename, mimeTeX writes a line to it of the form
 2008-09-07:12:59:33pm&nbsp;&lt;tag&gt;=99&nbsp;192.168.1.1&nbsp;http_referer
 containing a timestamp, the counter tag and its current value,
 and the user's IP address and http_referer page if they're
 available.

The page hit counter displayed at the bottom-right corner
 of this page is maintained by the command
 \counter[counters.log]{counters.txt:mimetex.html}.
 After compiling and installing your
 own mimetex.cgi and your own copy of this page, that counter will
 continually show 1st's
 unless/until you "touch" and "chmod" counters.txt (and, optionally,
 counters.log) in your mimetex.cgi directory.

<h3> <a name="environment">\environment
...</a> </h3>
 Submitting the expression &nbsp; \environment &nbsp;
 to mimeTeX renders <center>
 <img id="environ1"
 src="../cgi-bin/mimetex.cgi?\nocaching\environment"
 align="middle" border=0> </center>
 displaying the http environment variables
 known to mimeTeX. This is primarily a programming aid,
 showing information available to mimeTeX that might facilitate
 future enhancements.

As with \input and \counter above,
 for security \environment is
 disabled by default unless mimeTeX is compiled with either
 the -DINPUTOK or the -DENVIRONOK
 <a href="#options">compile&nbsp;option</a>
 (notice that -DINPUTOK also enables \environment).

<h2> <a name="exceptions"> (IIIh) Other Exceptions
to LaTeX Syntax &nbsp; </a> </h2>

<h3> Binding Exceptions... </h3>

MimeTeX's bindings are pretty much left-to-right. For example,
 although mimeTeX correctly interprets \frac12 as well as
 \frac{1}{2}, etc, the legal LaTeX expression x^\frac12
 must be written x^{\frac12}. Otherwise, mimeTeX interprets
 it as {x^\frac}12, i.e., the same way x^\alpha12
 would be interpreted, which is entirely wrong for \frac.
 The same requirement also applies to other combinations of commands,
 e.g., you must write \sqrt{\frac\alpha\beta}, etc.

<h2> <a name="messages"> (IIIi) mimeTeX Errors
and Messages &nbsp; </a> </h2>

<h3> mimeTeX Errors... </h3>

Any (La)TeX error is typically also a mimeTeX error.
 However, mimeTeX has no command line interface or
 .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; \alpha\bethe\gamma\delta &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
 [\bethe?] where you wanted to type &nbsp; \beta &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.

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: 
 <ul>
 <li> An unmatched left brace &nbsp; { &nbsp; is matched
 by mimeTeX with a "phantom" right brace &nbsp; } &nbsp;
 that's imagined to be at the end of your expression. </li>
 <li> Likewise, an unmatched &nbsp; \left(, &nbsp;
 or \left\{ &nbsp; or \left\anything, &nbsp;
 is matched by mimeTeX with a "phantom" &nbsp; \right.
 &nbsp; at the end of your expression. </li>
 <li> On the other hand, an unmatched right brace &nbsp; }
 &nbsp; is displayed in place, as if you had typed \rbrace. </li>
 <li> But an unmatched &nbsp; \right\anything &nbsp;
 is interpreted as an abbreviation for \rightarrow
 followed by \anything. For example, &nbsp;
 \leff(&nbsp;abc&nbsp;\right)&nbsp;def &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">

<h3> mimeTeX Messages... </h3>

The special mimeTeX directive &nbsp; \version &nbsp;
 displays the following information 
 <center>
 <a href="#preview"><img id="messages6" onclick="eqntext('messages6')"
 src="../cgi-bin/mimetex.cgi?\version"
 border=0 align=middle> </a> </center>

<h1> <a name="appendices"> (IV) Appendices &nbsp; </a> </h1>

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.

<h2> <a name="fonts"> (IVa) &nbsp; mimeTeX Fonts &nbsp; </a> </h2>

The font information mimeTeX uses to render characters is
 derived from .gf font files (usually generated by metafont
 running against .mf files), which are then run through
 gftype -i and finally through my gfuntype program
 (supplied with your mimeTeX distribution).

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 texfonts.h
 supplied with your mimeTeX distribution collects the output
 from 72 such (sequences of) runs, representing nine font
 families at eight sizes each.

This collection of information in &nbsp; texfonts.h &nbsp; is
 "wired" into mimeTeX through tables maintained in mimetex.h.
 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.

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.

Running metafont to generate a .gf file from .mf
 source will usually be your very first step. A typical such run
 might be 
  <center>
 mf '\mode=preview; mag=magstep(-16.393225); input cmmi10'</center>
 which in this case generates output file
 cmmi10.131gf (which is mimeTeX's font size 3 for the
 cmmi family).

Given the cmmi10.131gf file from this metafont run
 (or substitute any other .gf file you like), next run 
 <center>gftype -i cmmi10.131gf &gt; typeout</center>
 where typeout can be any temporary
 filename you like.

Finally, run gfuntype against the typeout file
 you just generated with the command 
 <center>gfuntype -n cmmi131 typeout cmmi131.h</center>
 to generate the final output file cmmi131.h
 (or any filename you supply as the last arg). This
 contains the cmmi data in an array whose name is taken
 from the -n arg you supplied to gfuntype.

The above sequence of three runs resulted in output file
 cmmi131.h, 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 texfonts.h file
 (or write a small texfonts.h which just #include's them all).

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 

 <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>
 
 Then ditto for the eight other font families cmmi10, cmmib10, cmsy10,
 cmex10, bbold10, rsfs10, stmary10 and wncyr10. And to generate other
 .dpigf 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.

To incorporate all this font information you just generated into
 mimeTeX, edit your mimetex.h file and find the table that looks
 something like <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>
 Note the 72 names cmr83...wncyr250 in the table. These must
 correspond to (or must be changed to) the names following the -n
 switch you specified for your &nbsp; gfuntype &nbsp; runs.

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.

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.

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. You'll need to compile your own version from source.
 The following instructions are for Unix/Linux: &nbsp; &nbsp;
 &nbsp; &nbsp; First, download both 
 <a href="http://www.ctan.org/tex-archive/systems/web2c/web-7.5.3.tar.gz"
 target="_top">web-7.5.3.tar.gz</a> and
 <a href="http://www.ctan.org/tex-archive/systems/web2c/web2c-7.5.3.tar.gz"
 target="_top">web2c-7.5.3.tar.gz</a>,
 or more recent versions. Then &nbsp; untar &nbsp; them both,
 &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 two lines very near the top
 that &nbsp; #define&nbsp;maxrow&nbsp;(79) &nbsp and similarly for maxcol.
 Change both 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.

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.)

<h2> <a name="makeraster"> (IVb) mimeTeX's make_raster()
function &nbsp; </a> </h2>

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.

<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>

Cut-and-paste the above sample code from this file to, say,
 mimedemo.c (and fix the brackets around stdio.h). Then compile 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc -DTEXFONTS mimedemo.c mimetex.c -lm -o mimedemo 
 and run it from your unix shell command line like 
 &nbsp; &nbsp; &nbsp; &nbsp; ./mimedemo &nbsp; &quot;x^2+y^2&quot; 
 
 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.

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.

<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>

Cut-and-paste as before, compile like 
 &nbsp; &nbsp; &nbsp; &nbsp;
 cc -DTEXFONTS mimedemo.c mimetex.c gifsave.c -lm -o mimedemo 
 and run it like the first example, but this time you may want to redirect
 stdout 
 &nbsp; &nbsp; &nbsp; &nbsp; ./mimedemo &nbsp; &quot;x^2+y^2&quot;
 &nbsp; &gt; &nbsp; mimedemo.gif 
 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.

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.

<h2> <a name="gifsave">
(IVc)</a> <a href="http://shh.thathost.com" target="_top">Sverre Huseby's</a>
gifsave.c library &nbsp; </h2>

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.

<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>

<h1 id="remarks"> Concluding Remarks &nbsp; </h1>

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.

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