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<li><a class="reference internal" href="#">Writing mathematical expressions</a><ul>
<li><a class="reference internal" href="#subscripts-and-superscripts">Subscripts and superscripts</a></li>
<li><a class="reference internal" href="#fractions-binomials-and-stacked-numbers">Fractions, binomials, and stacked numbers</a></li>
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<div class="sphx-glr-download-link-note admonition note">
<p class="first admonition-title">Note</p>
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<div class="sphx-glr-example-title section" id="writing-mathematical-expressions">
<span id="sphx-glr-tutorials-text-mathtext-py"></span><h1>Writing mathematical expressions<a class="headerlink" href="#writing-mathematical-expressions" title="Permalink to this headline">¶</a></h1>
<p>An introduction to writing mathematical expressions in Matplotlib.</p>
<p>You can use a subset TeX markup in any matplotlib text string by placing it
inside a pair of dollar signs ($).</p>
<p>Note that you do not need to have TeX installed, since Matplotlib ships
its own TeX expression parser, layout engine, and fonts. The layout engine
is a fairly direct adaptation of the layout algorithms in Donald Knuth's
TeX, so the quality is quite good (matplotlib also provides a <code class="docutils literal notranslate"><span class="pre">usetex</span></code>
option for those who do want to call out to TeX to generate their text (see
<a class="reference internal" href="usetex.html"><span class="doc">Text rendering With LaTeX</span></a>).</p>
<p>Any text element can use math text. You should use raw strings (precede the
quotes with an <code class="docutils literal notranslate"><span class="pre">'r'</span></code>), and surround the math text with dollar signs ($), as
in TeX. Regular text and mathtext can be interleaved within the same string.
Mathtext can use DejaVu Sans (default), DejaVu Serif, the Computer Modern fonts
(from (La)TeX), <a class="reference external" href="http://www.stixfonts.org/">STIX</a> fonts (with are designed
to blend well with Times), or a Unicode font that you provide. The mathtext
font can be selected with the customization variable <code class="docutils literal notranslate"><span class="pre">mathtext.fontset</span></code> (see
<a class="reference internal" href="../introductory/customizing.html"><span class="doc">Customizing Matplotlib with style sheets and rcParams</span></a>)</p>
<p>Here is a simple example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># plain text</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'alpha > beta'</span><span class="p">)</span>
</pre></div>
</div>
<p>produces "alpha > beta".</p>
<p>Whereas this:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># math text</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">'$\alpha > \beta$'</span><span class="p">)</span>
</pre></div>
</div>
<p>produces "<img src="../../_images/mathmpl/math-9876f47506.png" style="position: relative; bottom: -7px"/>".</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Mathtext should be placed between a pair of dollar signs ($). To make it
easy to display monetary values, e.g., "$100.00", if a single dollar sign
is present in the entire string, it will be displayed verbatim as a dollar
sign. This is a small change from regular TeX, where the dollar sign in
non-math text would have to be escaped ('\$').</p>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p>While the syntax inside the pair of dollar signs ($) aims to be TeX-like,
the text outside does not. In particular, characters such as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># $ % & ~ _ ^ \ { } \( \) \[ \]</span>
</pre></div>
</div>
<p class="last">have special meaning outside of math mode in TeX. Therefore, these
characters will behave differently depending on <code class="docutils literal notranslate"><a class="reference external" href="../../tutorials/introductory/customizing.html?highlight=text.usetex#a-sample-matplotlibrc-file"><span class="pre">rcParams["text.usetex"]</span></a></code> (default: <code class="docutils literal notranslate"><span class="pre">False</span></code>). See the
<a class="reference internal" href="usetex.html"><span class="doc">usetex tutorial</span></a> for more information.</p>
</div>
<div class="section" id="subscripts-and-superscripts">
<h2>Subscripts and superscripts<a class="headerlink" href="#subscripts-and-superscripts" title="Permalink to this headline">¶</a></h2>
<p>To make subscripts and superscripts, use the <code class="docutils literal notranslate"><span class="pre">'_'</span></code> and <code class="docutils literal notranslate"><span class="pre">'^'</span></code> symbols:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\alpha_i > \beta_i$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\alpha_i > \beta_i\]</div>
<p>To display multi-letter subscripts or superscripts correctly,
you should put them in curly braces <code class="docutils literal notranslate"><span class="pre">{...}</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\alpha^</span><span class="si">{ic}</span><span class="s1"> > \beta_</span><span class="si">{ic}</span><span class="s1">$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\alpha^{ic} > \beta_{ic}\]</div>
<p>Some symbols automatically put their sub/superscripts under and over the
operator. For example, to write the sum of <img src="../../_images/mathmpl/math-3842b45874.png" style="position: relative; bottom: -6px"/> from <img src="../../_images/mathmpl/math-e5cadf28b9.png" style="position: relative; bottom: -3px"/> to
<img src="../../_images/mathmpl/math-a761b7733e.png" style="position: relative; bottom: -3px"/>, you could do:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\sum_{i=0}^\infty x_i$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\sum_{i=0}^\infty x_i\]</div>
</div>
<div class="section" id="fractions-binomials-and-stacked-numbers">
<h2>Fractions, binomials, and stacked numbers<a class="headerlink" href="#fractions-binomials-and-stacked-numbers" title="Permalink to this headline">¶</a></h2>
<p>Fractions, binomials, and stacked numbers can be created with the
<code class="docutils literal notranslate"><span class="pre">\frac{}{}</span></code>, <code class="docutils literal notranslate"><span class="pre">\binom{}{}</span></code> and <code class="docutils literal notranslate"><span class="pre">\genfrac{}{}{}{}{}{}</span></code> commands,
respectively:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\frac</span><span class="si">{3}{4}</span><span class="s1"> \binom</span><span class="si">{3}{4}</span><span class="s1"> \genfrac</span><span class="si">{}{}{0}{}{3}{4}</span><span class="s1">$'</span>
</pre></div>
</div>
<p>produces</p>
<div class="math notranslate nohighlight">
\[\frac{3}{4} \binom{3}{4} \genfrac{}{}{0pt}{}{3}{4}\]</div>
<p>Fractions can be arbitrarily nested:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\frac{5 - \frac</span><span class="si">{1}{x}</span><span class="s1">}</span><span class="si">{4}</span><span class="s1">$'</span>
</pre></div>
</div>
<p>produces</p>
<div class="math notranslate nohighlight">
\[\frac{5 - \frac{1}{x}}{4}\]</div>
<p>Note that special care needs to be taken to place parentheses and brackets
around fractions. Doing things the obvious way produces brackets that are too
small:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$(\frac{5 - \frac</span><span class="si">{1}{x}</span><span class="s1">}</span><span class="si">{4}</span><span class="s1">)$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[(\frac{5 - \frac{1}{x}}{4})\]</div>
<p>The solution is to precede the bracket with <code class="docutils literal notranslate"><span class="pre">\left</span></code> and <code class="docutils literal notranslate"><span class="pre">\right</span></code> to inform
the parser that those brackets encompass the entire object.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\left(\frac{5 - \frac</span><span class="si">{1}{x}</span><span class="s1">}</span><span class="si">{4}</span><span class="s1">\right)$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\left(\frac{5 - \frac{1}{x}}{4}\right)\]</div>
</div>
<div class="section" id="radicals">
<h2>Radicals<a class="headerlink" href="#radicals" title="Permalink to this headline">¶</a></h2>
<p>Radicals can be produced with the <code class="docutils literal notranslate"><span class="pre">\sqrt[]{}</span></code> command. For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\sqrt</span><span class="si">{2}</span><span class="s1">$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\sqrt{2}\]</div>
<p>Any base can (optionally) be provided inside square brackets. Note that the
base must be a simple expression, and can not contain layout commands such as
fractions or sub/superscripts:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$\sqrt[3]</span><span class="si">{x}</span><span class="s1">$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\sqrt[3]{x}\]</div>
</div>
<div class="section" id="fonts">
<span id="mathtext-fonts"></span><h2>Fonts<a class="headerlink" href="#fonts" title="Permalink to this headline">¶</a></h2>
<p>The default font is <em>italics</em> for mathematical symbols.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This default can be changed using <code class="docutils literal notranslate"><a class="reference external" href="../../tutorials/introductory/customizing.html?highlight=mathtext.default#a-sample-matplotlibrc-file"><span class="pre">rcParams["mathtext.default"]</span></a></code> (default: <code class="docutils literal notranslate"><span class="pre">'it'</span></code>). This is
useful, for example, to use the same font as regular non-math text for math
text, by setting it to <code class="docutils literal notranslate"><span class="pre">regular</span></code>.</p>
</div>
<p>To change fonts, e.g., to write "sin" in a Roman font, enclose the text in a
font command:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$s(t) = \mathcal</span><span class="si">{A}</span><span class="s1">\mathrm</span><span class="si">{sin}</span><span class="s1">(2 \omega t)$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[s(t) = \mathcal{A}\mathrm{sin}(2 \omega t)\]</div>
<p>More conveniently, many commonly used function names that are typeset in
a Roman font have shortcuts. So the expression above could be written as
follows:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'$s(t) = \mathcal</span><span class="si">{A}</span><span class="s1">\sin(2 \omega t)$'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[s(t) = \mathcal{A}\sin(2 \omega t)\]</div>
<p>Here "s" and "t" are variable in italics font (default), "sin" is in Roman
font, and the amplitude "A" is in calligraphy font. Note in the example above
the calligraphy <code class="docutils literal notranslate"><span class="pre">A</span></code> is squished into the <code class="docutils literal notranslate"><span class="pre">sin</span></code>. You can use a spacing
command to add a little whitespace between them:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s1">'s(t) = \mathcal</span><span class="si">{A}</span><span class="s1">\/\sin(2 \omega t)'</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[s(t) = \mathcal{A}\,\sin(2 \omega t)\]</div>
<p>The choices available with all fonts are:</p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="44%" />
<col width="56%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Command</th>
<th class="head">Result</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\mathrm{Roman}</span></code></td>
<td><img src="../../_images/mathmpl/math-19194d54c3.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\mathit{Italic}</span></code></td>
<td><img src="../../_images/mathmpl/math-00022ae738.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\mathtt{Typewriter}</span></code></td>
<td><img src="../../_images/mathmpl/math-9e5a913e0a.png" style="position: relative; bottom: -8px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\mathcal{CALLIGRAPHY}</span></code></td>
<td><img src="../../_images/mathmpl/math-f614988806.png" style="position: relative; bottom: -5px"/></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>When using the <a class="reference external" href="http://www.stixfonts.org/">STIX</a> fonts, you also have the
choice of:</p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="44%" />
<col width="56%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Command</th>
<th class="head">Result</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\mathbb{blackboard}</span></code></td>
<td><img src="../../_images/mathmpl/math-340c66cf40.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\mathrm{\mathbb{blackboard}}</span></code></td>
<td><img src="../../_images/mathmpl/math-4533229649.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\mathfrak{Fraktur}</span></code></td>
<td><img src="../../_images/mathmpl/math-5bc6d49653.png" style="position: relative; bottom: -7px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\mathsf{sansserif}</span></code></td>
<td><img src="../../_images/mathmpl/math-49f3f2784e.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\mathrm{\mathsf{sansserif}}</span></code></td>
<td><img src="../../_images/mathmpl/math-462e2c02f1.png" style="position: relative; bottom: -3px"/></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>There are also five global "font sets" to choose from, which are
selected using the <code class="docutils literal notranslate"><span class="pre">mathtext.fontset</span></code> parameter in <a class="reference internal" href="../introductory/customizing.html#matplotlibrc-sample"><span class="std std-ref">matplotlibrc</span></a>.</p>
<p><code class="docutils literal notranslate"><span class="pre">dejavusans</span></code>: DejaVu Sans</p>
<blockquote>
<div><img src="../../_images/mathmpl/math-0101db15ef.png" class="center" /></div></blockquote>
<p><code class="docutils literal notranslate"><span class="pre">dejavuserif</span></code>: DejaVu Serif</p>
<blockquote>
<div><img src="../../_images/mathmpl/math-050e387807.png" class="center" /></div></blockquote>
<p><code class="docutils literal notranslate"><span class="pre">cm</span></code>: Computer Modern (TeX)</p>
<blockquote>
<div><img src="../../_images/mathmpl/math-3e45c5a9b2.png" class="center" /></div></blockquote>
<p><code class="docutils literal notranslate"><span class="pre">stix</span></code>: STIX (designed to blend well with Times)</p>
<blockquote>
<div><img src="../../_images/mathmpl/math-a049f342a0.png" class="center" /></div></blockquote>
<p><code class="docutils literal notranslate"><span class="pre">stixsans</span></code>: STIX sans-serif</p>
<blockquote>
<div><img src="../../_images/mathmpl/math-4a858610d4.png" class="center" /></div></blockquote>
<p>Additionally, you can use <code class="docutils literal notranslate"><span class="pre">\mathdefault{...}</span></code> or its alias
<code class="docutils literal notranslate"><span class="pre">\mathregular{...}</span></code> to use the font used for regular text outside of
mathtext. There are a number of limitations to this approach, most notably
that far fewer symbols will be available, but it can be useful to make math
expressions blend well with other text in the plot.</p>
<div class="section" id="custom-fonts">
<h3>Custom fonts<a class="headerlink" href="#custom-fonts" title="Permalink to this headline">¶</a></h3>
<p>mathtext also provides a way to use custom fonts for math. This method is
fairly tricky to use, and should be considered an experimental feature for
patient users only. By setting <code class="docutils literal notranslate"><a class="reference external" href="../../tutorials/introductory/customizing.html?highlight=mathtext.fontset#a-sample-matplotlibrc-file"><span class="pre">rcParams["mathtext.fontset"]</span></a></code> (default: <code class="docutils literal notranslate"><span class="pre">'dejavusans'</span></code>) to <code class="docutils literal notranslate"><span class="pre">custom</span></code>,
you can then set the following parameters, which control which font file to use
for a particular set of math characters.</p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="45%" />
<col width="55%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Parameter</th>
<th class="head">Corresponds to</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">mathtext.it</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathit{}</span></code> or default italic</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">mathtext.rm</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathrm{}</span></code> Roman (upright)</td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">mathtext.tt</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathtt{}</span></code> Typewriter (monospace)</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">mathtext.bf</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathbf{}</span></code> bold italic</td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">mathtext.cal</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathcal{}</span></code> calligraphic</td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">mathtext.sf</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\mathsf{}</span></code> sans-serif</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>Each parameter should be set to a fontconfig font descriptor (as defined in the
yet-to-be-written font chapter).</p>
<p>The fonts used should have a Unicode mapping in order to find any
non-Latin characters, such as Greek. If you want to use a math symbol
that is not contained in your custom fonts, you can set
<code class="docutils literal notranslate"><a class="reference external" href="../../tutorials/introductory/customizing.html?highlight=mathtext.fallback#a-sample-matplotlibrc-file"><span class="pre">rcParams["mathtext.fallback"]</span></a></code> (default: <code class="docutils literal notranslate"><span class="pre">'cm'</span></code>) to either <code class="docutils literal notranslate"><span class="pre">'cm'</span></code>, <code class="docutils literal notranslate"><span class="pre">'stix'</span></code> or <code class="docutils literal notranslate"><span class="pre">'stixsans'</span></code>
which will cause the mathtext system to use
characters from an alternative font whenever a particular
character can not be found in the custom font.</p>
<p>Note that the math glyphs specified in Unicode have evolved over time, and many
fonts may not have glyphs in the correct place for mathtext.</p>
</div>
</div>
<div class="section" id="accents">
<h2>Accents<a class="headerlink" href="#accents" title="Permalink to this headline">¶</a></h2>
<p>An accent command may precede any symbol to add an accent above it. There are
long and short forms for some of them.</p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="48%" />
<col width="52%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Command</th>
<th class="head">Result</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\acute</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\'a</span></code></td>
<td><img src="../../_images/mathmpl/math-6f2c9a48e5.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\bar</span> <span class="pre">a</span></code></td>
<td><img src="../../_images/mathmpl/math-dc0a66342e.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\breve</span> <span class="pre">a</span></code></td>
<td><img src="../../_images/mathmpl/math-84e18ecce7.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\ddot</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\''a</span></code></td>
<td><img src="../../_images/mathmpl/math-5ef49195c3.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\dot</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\.a</span></code></td>
<td><img src="../../_images/mathmpl/math-6b66544034.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\grave</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\`a</span></code></td>
<td><img src="../../_images/mathmpl/math-5fe06607a9.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\hat</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\^a</span></code></td>
<td><img src="../../_images/mathmpl/math-76affdfab5.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\tilde</span> <span class="pre">a</span></code> or <code class="docutils literal notranslate"><span class="pre">\~a</span></code></td>
<td><img src="../../_images/mathmpl/math-4c882716a1.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\vec</span> <span class="pre">a</span></code></td>
<td><img src="../../_images/mathmpl/math-58f2478293.png" style="position: relative; bottom: -3px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\overline{abc}</span></code></td>
<td><img src="../../_images/mathmpl/math-f5fb404176.png" style="position: relative; bottom: -3px"/></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>In addition, there are two special accents that automatically adjust to the
width of the symbols below:</p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="48%" />
<col width="52%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Command</th>
<th class="head">Result</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><code class="docutils literal notranslate"><span class="pre">\widehat{xyz}</span></code></td>
<td><img src="../../_images/mathmpl/math-770780107f.png" style="position: relative; bottom: -7px"/></td>
</tr>
<tr class="row-odd"><td><code class="docutils literal notranslate"><span class="pre">\widetilde{xyz}</span></code></td>
<td><img src="../../_images/mathmpl/math-98bb610df5.png" style="position: relative; bottom: -7px"/></td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>Care should be taken when putting accents on lower-case i's and j's. Note that
in the following <code class="docutils literal notranslate"><span class="pre">\imath</span></code> is used to avoid the extra dot over the i:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="sa">r</span><span class="s2">"$\hat i\ \ \hat \imath$"</span>
</pre></div>
</div>
<div class="math notranslate nohighlight">
\[\hat i\ \ \hat \imath\]</div>
</div>
<div class="section" id="symbols">
<h2>Symbols<a class="headerlink" href="#symbols" title="Permalink to this headline">¶</a></h2>
<p>You can also use a large number of the TeX symbols, as in <code class="docutils literal notranslate"><span class="pre">\infty</span></code>,
<code class="docutils literal notranslate"><span class="pre">\leftarrow</span></code>, <code class="docutils literal notranslate"><span class="pre">\sum</span></code>, <code class="docutils literal notranslate"><span class="pre">\int</span></code>.</p>
<p><strong>Lower-case Greek</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>α <code class="docutils literal notranslate"><span class="pre">\alpha</span></code></td>
<td>β <code class="docutils literal notranslate"><span class="pre">\beta</span></code></td>
<td>χ <code class="docutils literal notranslate"><span class="pre">\chi</span></code></td>
<td>δ <code class="docutils literal notranslate"><span class="pre">\delta</span></code></td>
<td>ϝ <code class="docutils literal notranslate"><span class="pre">\digamma</span></code></td>
<td>ε <code class="docutils literal notranslate"><span class="pre">\epsilon</span></code></td>
</tr>
<tr class="row-even"><td>η <code class="docutils literal notranslate"><span class="pre">\eta</span></code></td>
<td>γ <code class="docutils literal notranslate"><span class="pre">\gamma</span></code></td>
<td>ι <code class="docutils literal notranslate"><span class="pre">\iota</span></code></td>
<td>κ <code class="docutils literal notranslate"><span class="pre">\kappa</span></code></td>
<td>λ <code class="docutils literal notranslate"><span class="pre">\lambda</span></code></td>
<td>μ <code class="docutils literal notranslate"><span class="pre">\mu</span></code></td>
</tr>
<tr class="row-odd"><td>ν <code class="docutils literal notranslate"><span class="pre">\nu</span></code></td>
<td>ω <code class="docutils literal notranslate"><span class="pre">\omega</span></code></td>
<td>ϕ <code class="docutils literal notranslate"><span class="pre">\phi</span></code></td>
<td>π <code class="docutils literal notranslate"><span class="pre">\pi</span></code></td>
<td>ψ <code class="docutils literal notranslate"><span class="pre">\psi</span></code></td>
<td>ρ <code class="docutils literal notranslate"><span class="pre">\rho</span></code></td>
</tr>
<tr class="row-even"><td>σ <code class="docutils literal notranslate"><span class="pre">\sigma</span></code></td>
<td>τ <code class="docutils literal notranslate"><span class="pre">\tau</span></code></td>
<td>θ <code class="docutils literal notranslate"><span class="pre">\theta</span></code></td>
<td>υ <code class="docutils literal notranslate"><span class="pre">\upsilon</span></code></td>
<td>ε <code class="docutils literal notranslate"><span class="pre">\varepsilon</span></code></td>
<td>ϰ <code class="docutils literal notranslate"><span class="pre">\varkappa</span></code></td>
</tr>
<tr class="row-odd"><td>φ <code class="docutils literal notranslate"><span class="pre">\varphi</span></code></td>
<td>ϖ <code class="docutils literal notranslate"><span class="pre">\varpi</span></code></td>
<td>ϱ <code class="docutils literal notranslate"><span class="pre">\varrho</span></code></td>
<td>ς <code class="docutils literal notranslate"><span class="pre">\varsigma</span></code></td>
<td>ϑ <code class="docutils literal notranslate"><span class="pre">\vartheta</span></code></td>
<td>ξ <code class="docutils literal notranslate"><span class="pre">\xi</span></code></td>
</tr>
<tr class="row-even"><td>ζ <code class="docutils literal notranslate"><span class="pre">\zeta</span></code></td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Upper-case Greek</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="13%" />
<col width="13%" />
<col width="13%" />
<col width="13%" />
<col width="13%" />
<col width="13%" />
<col width="13%" />
<col width="13%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>Δ <code class="docutils literal notranslate"><span class="pre">\Delta</span></code></td>
<td>Γ <code class="docutils literal notranslate"><span class="pre">\Gamma</span></code></td>
<td>Λ <code class="docutils literal notranslate"><span class="pre">\Lambda</span></code></td>
<td>Ω <code class="docutils literal notranslate"><span class="pre">\Omega</span></code></td>
<td>Φ <code class="docutils literal notranslate"><span class="pre">\Phi</span></code></td>
<td>Π <code class="docutils literal notranslate"><span class="pre">\Pi</span></code></td>
<td>Ψ <code class="docutils literal notranslate"><span class="pre">\Psi</span></code></td>
<td>Σ <code class="docutils literal notranslate"><span class="pre">\Sigma</span></code></td>
</tr>
<tr class="row-even"><td>Θ <code class="docutils literal notranslate"><span class="pre">\Theta</span></code></td>
<td>Υ <code class="docutils literal notranslate"><span class="pre">\Upsilon</span></code></td>
<td>Ξ <code class="docutils literal notranslate"><span class="pre">\Xi</span></code></td>
<td>℧ <code class="docutils literal notranslate"><span class="pre">\mho</span></code></td>
<td>∇ <code class="docutils literal notranslate"><span class="pre">\nabla</span></code></td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Hebrew</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>ℵ <code class="docutils literal notranslate"><span class="pre">\aleph</span></code></td>
<td>ℶ <code class="docutils literal notranslate"><span class="pre">\beth</span></code></td>
<td>ℸ <code class="docutils literal notranslate"><span class="pre">\daleth</span></code></td>
<td>ℷ <code class="docutils literal notranslate"><span class="pre">\gimel</span></code></td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Delimiters</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>/ <code class="docutils literal notranslate"><span class="pre">/</span></code></td>
<td>[ <code class="docutils literal notranslate"><span class="pre">[</span></code></td>
<td>⇓ <code class="docutils literal notranslate"><span class="pre">\Downarrow</span></code></td>
<td>⇑ <code class="docutils literal notranslate"><span class="pre">\Uparrow</span></code></td>
<td>‖ <code class="docutils literal notranslate"><span class="pre">\Vert</span></code></td>
<td><code class="docutils literal notranslate"><span class="pre">\backslash</span></code></td>
</tr>
<tr class="row-even"><td>↓ <code class="docutils literal notranslate"><span class="pre">\downarrow</span></code></td>
<td>⟨ <code class="docutils literal notranslate"><span class="pre">\langle</span></code></td>
<td>⌈ <code class="docutils literal notranslate"><span class="pre">\lceil</span></code></td>
<td>⌊ <code class="docutils literal notranslate"><span class="pre">\lfloor</span></code></td>
<td>⌞ <code class="docutils literal notranslate"><span class="pre">\llcorner</span></code></td>
<td>⌟ <code class="docutils literal notranslate"><span class="pre">\lrcorner</span></code></td>
</tr>
<tr class="row-odd"><td>⟩ <code class="docutils literal notranslate"><span class="pre">\rangle</span></code></td>
<td>⌉ <code class="docutils literal notranslate"><span class="pre">\rceil</span></code></td>
<td>⌋ <code class="docutils literal notranslate"><span class="pre">\rfloor</span></code></td>
<td>⌜ <code class="docutils literal notranslate"><span class="pre">\ulcorner</span></code></td>
<td>↑ <code class="docutils literal notranslate"><span class="pre">\uparrow</span></code></td>
<td>⌝ <code class="docutils literal notranslate"><span class="pre">\urcorner</span></code></td>
</tr>
<tr class="row-even"><td><div class="first last line-block">
<div class="line"><code class="docutils literal notranslate"><span class="pre">\vert</span></code></div>
</div>
</td>
<td>{ <code class="docutils literal notranslate"><span class="pre">\{</span></code></td>
<td><div class="first last line-block">
<div class="line"><code class="docutils literal notranslate"><span class="pre">\|</span></code></div>
</div>
</td>
<td>} <code class="docutils literal notranslate"><span class="pre">\}</span></code></td>
<td>] <code class="docutils literal notranslate"><span class="pre">]</span></code></td>
<td><div class="first last line-block">
<div class="line"><code class="docutils literal notranslate"><span class="pre">|</span></code></div>
</div>
</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Big symbols</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>⋂ <code class="docutils literal notranslate"><span class="pre">\bigcap</span></code></td>
<td>⋃ <code class="docutils literal notranslate"><span class="pre">\bigcup</span></code></td>
<td>⨀ <code class="docutils literal notranslate"><span class="pre">\bigodot</span></code></td>
<td>⨁ <code class="docutils literal notranslate"><span class="pre">\bigoplus</span></code></td>
<td>⨂ <code class="docutils literal notranslate"><span class="pre">\bigotimes</span></code></td>
<td>⨄ <code class="docutils literal notranslate"><span class="pre">\biguplus</span></code></td>
</tr>
<tr class="row-even"><td>⋁ <code class="docutils literal notranslate"><span class="pre">\bigvee</span></code></td>
<td>⋀ <code class="docutils literal notranslate"><span class="pre">\bigwedge</span></code></td>
<td>∐ <code class="docutils literal notranslate"><span class="pre">\coprod</span></code></td>
<td>∫ <code class="docutils literal notranslate"><span class="pre">\int</span></code></td>
<td>∮ <code class="docutils literal notranslate"><span class="pre">\oint</span></code></td>
<td>∏ <code class="docutils literal notranslate"><span class="pre">\prod</span></code></td>
</tr>
<tr class="row-odd"><td>∑ <code class="docutils literal notranslate"><span class="pre">\sum</span></code></td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Standard function names</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
<col width="17%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>Pr <code class="docutils literal notranslate"><span class="pre">\Pr</span></code></td>
<td>arccos <code class="docutils literal notranslate"><span class="pre">\arccos</span></code></td>
<td>arcsin <code class="docutils literal notranslate"><span class="pre">\arcsin</span></code></td>
<td>arctan <code class="docutils literal notranslate"><span class="pre">\arctan</span></code></td>
<td>arg <code class="docutils literal notranslate"><span class="pre">\arg</span></code></td>
<td>cos <code class="docutils literal notranslate"><span class="pre">\cos</span></code></td>
</tr>
<tr class="row-even"><td>cosh <code class="docutils literal notranslate"><span class="pre">\cosh</span></code></td>
<td>cot <code class="docutils literal notranslate"><span class="pre">\cot</span></code></td>
<td>coth <code class="docutils literal notranslate"><span class="pre">\coth</span></code></td>
<td>csc <code class="docutils literal notranslate"><span class="pre">\csc</span></code></td>
<td>deg <code class="docutils literal notranslate"><span class="pre">\deg</span></code></td>
<td>det <code class="docutils literal notranslate"><span class="pre">\det</span></code></td>
</tr>
<tr class="row-odd"><td>dim <code class="docutils literal notranslate"><span class="pre">\dim</span></code></td>
<td>exp <code class="docutils literal notranslate"><span class="pre">\exp</span></code></td>
<td>gcd <code class="docutils literal notranslate"><span class="pre">\gcd</span></code></td>
<td>hom <code class="docutils literal notranslate"><span class="pre">\hom</span></code></td>
<td>inf <code class="docutils literal notranslate"><span class="pre">\inf</span></code></td>
<td>ker <code class="docutils literal notranslate"><span class="pre">\ker</span></code></td>
</tr>
<tr class="row-even"><td>lg <code class="docutils literal notranslate"><span class="pre">\lg</span></code></td>
<td>lim <code class="docutils literal notranslate"><span class="pre">\lim</span></code></td>
<td>liminf <code class="docutils literal notranslate"><span class="pre">\liminf</span></code></td>
<td>limsup <code class="docutils literal notranslate"><span class="pre">\limsup</span></code></td>
<td>ln <code class="docutils literal notranslate"><span class="pre">\ln</span></code></td>
<td>log <code class="docutils literal notranslate"><span class="pre">\log</span></code></td>
</tr>
<tr class="row-odd"><td>max <code class="docutils literal notranslate"><span class="pre">\max</span></code></td>
<td>min <code class="docutils literal notranslate"><span class="pre">\min</span></code></td>
<td>sec <code class="docutils literal notranslate"><span class="pre">\sec</span></code></td>
<td>sin <code class="docutils literal notranslate"><span class="pre">\sin</span></code></td>
<td>sinh <code class="docutils literal notranslate"><span class="pre">\sinh</span></code></td>
<td>sup <code class="docutils literal notranslate"><span class="pre">\sup</span></code></td>
</tr>
<tr class="row-even"><td>tan <code class="docutils literal notranslate"><span class="pre">\tan</span></code></td>
<td>tanh <code class="docutils literal notranslate"><span class="pre">\tanh</span></code></td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div></blockquote>
<p><strong>Binary operation and relation symbols</strong></p>
<blockquote>
<div><table border="1" class="docutils align-default">
<colgroup>
<col width="25%" />
<col width="25%" />
<col width="25%" />
<col width="25%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>≎ <code class="docutils literal notranslate"><span class="pre">\Bumpeq</span></code></td>
<td>⋒ <code class="docutils literal notranslate"><span class="pre">\Cap</span></code></td>
<td>⋓ <code class="docutils literal notranslate"><span class="pre">\Cup</span></code></td>
<td>≑ <code class="docutils literal notranslate"><span class="pre">\Doteq</span></code></td>
</tr>
<tr class="row-even"><td>⨝ <code class="docutils literal notranslate"><span class="pre">\Join</span></code></td>
<td>⋐ <code class="docutils literal notranslate"><span class="pre">\Subset</span></code></td>
<td>⋑ <code class="docutils literal notranslate"><span class="pre">\Supset</span></code></td>
<td>⊩ <code class="docutils literal notranslate"><span class="pre">\Vdash</span></code></td>
</tr>
<tr class="row-odd"><td>⊪ <code class="docutils literal notranslate"><span class="pre">\Vvdash</span></code></td>
<td>≈ <code class="docutils literal notranslate"><span class="pre">\approx</span></code></td>
<td>≊ <code class="docutils literal notranslate"><span class="pre">\approxeq</span></code></td>
<td>∗ <code class="docutils literal notranslate"><span class="pre">\ast</span></code></td>
</tr>
<tr class="row-even"><td>≍ <code class="docutils literal notranslate"><span class="pre">\asymp</span></code></td>
<td>϶ <code class="docutils literal notranslate"><span class="pre">\backepsilon</span></code></td>
<td>∽ <code class="docutils literal notranslate"><span class="pre">\backsim</span></code></td>
<td>⋍ <code class="docutils literal notranslate"><span class="pre">\backsimeq</span></code></td>
</tr>
<tr class="row-odd"><td>⊼ <code class="docutils literal notranslate"><span class="pre">\barwedge</span></code></td>
<td>∵ <code class="docutils literal notranslate"><span class="pre">\because</span></code></td>
<td>≬ <code class="docutils literal notranslate"><span class="pre">\between</span></code></td>
<td>○ <code class="docutils literal notranslate"><span class="pre">\bigcirc</span></code></td>
</tr>
<tr class="row-even"><td>▽ <code class="docutils literal notranslate"><span class="pre">\bigtriangledown</span></code></td>
<td>△ <code class="docutils literal notranslate"><span class="pre">\bigtriangleup</span></code></td>
<td>◀ <code class="docutils literal notranslate"><span class="pre">\blacktriangleleft</span></code></td>
<td>▶ <code class="docutils literal notranslate"><span class="pre">\blacktriangleright</span></code></td>
</tr>
<tr class="row-odd"><td>⊥ <code class="docutils literal notranslate"><span class="pre">\bot</span></code></td>
<td>⋈ <code class="docutils literal notranslate"><span class="pre">\bowtie</span></code></td>
<td>⊡ <code class="docutils literal notranslate"><span class="pre">\boxdot</span></code></td>
<td>⊟ <code class="docutils literal notranslate"><span class="pre">\boxminus</span></code></td>
</tr>
<tr class="row-even"><td>⊞ <code class="docutils literal notranslate"><span class="pre">\boxplus</span></code></td>
<td>⊠ <code class="docutils literal notranslate"><span class="pre">\boxtimes</span></code></td>
<td>∙ <code class="docutils literal notranslate"><span class="pre">\bullet</span></code></td>
<td>≏ <code class="docutils literal notranslate"><span class="pre">\bumpeq</span></code></td>
</tr>
<tr class="row-odd"><td>∩ <code class="docutils literal notranslate"><span class="pre">\cap</span></code></td>
<td>⋅ <code class="docutils literal notranslate"><span class="pre">\cdot</span></code></td>
<td>∘ <code class="docutils literal notranslate"><span class="pre">\circ</span></code></td>
<td>≗ <code class="docutils literal notranslate"><span class="pre">\circeq</span></code></td>
</tr>
<tr class="row-even"><td>≔ <code class="docutils literal notranslate"><span class="pre">\coloneq</span></code></td>
<td>≅ <code class="docutils literal notranslate"><span class="pre">\cong</span></code></td>
<td>∪ <code class="docutils literal notranslate"><span class="pre">\cup</span></code></td>
<td>⋞ <code class="docutils literal notranslate"><span class="pre">\curlyeqprec</span></code></td>
</tr>
<tr class="row-odd"><td>⋟ <code class="docutils literal notranslate"><span class="pre">\curlyeqsucc</span></code></td>
<td>⋎ <code class="docutils literal notranslate"><span class="pre">\curlyvee</span></code></td>
<td>⋏ <code class="docutils literal notranslate"><span class="pre">\curlywedge</span></code></td>
<td>† <code class="docutils literal notranslate"><span class="pre">\dag</span></code></td>
</tr>
<tr class="row-even"><td>⊣ <code class="docutils literal notranslate"><span class="pre">\dashv</span></code></td>
<td>‡ <code class="docutils literal notranslate"><span class="pre">\ddag</span></code></td>
<td>⋄ <code class="docutils literal notranslate"><span class="pre">\diamond</span></code></td>
<td>÷ <code class="docutils literal notranslate"><span class="pre">\div</span></code></td>
</tr>
<tr class="row-odd"><td>⋇ <code class="docutils literal notranslate"><span class="pre">\divideontimes</span></code></td>
<td>≐ <code class="docutils literal notranslate"><span class="pre">\doteq</span></code></td>
<td>≑ <code class="docutils literal notranslate"><span class="pre">\doteqdot</span></code></td>
<td>∔ <code class="docutils literal notranslate"><span class="pre">\dotplus</span></code></td>
</tr>
<tr class="row-even"><td>⌆ <code class="docutils literal notranslate"><span class="pre">\doublebarwedge</span></code></td>
<td>≖ <code class="docutils literal notranslate"><span class="pre">\eqcirc</span></code></td>
<td>≕ <code class="docutils literal notranslate"><span class="pre">\eqcolon</span></code></td>
<td>≂ <code class="docutils literal notranslate"><span class="pre">\eqsim</span></code></td>
</tr>
<tr class="row-odd"><td>⪖ <code class="docutils literal notranslate"><span class="pre">\eqslantgtr</span></code></td>
<td>⪕ <code class="docutils literal notranslate"><span class="pre">\eqslantless</span></code></td>
<td>≡ <code class="docutils literal notranslate"><span class="pre">\equiv</span></code></td>
<td>≒ <code class="docutils literal notranslate"><span class="pre">\fallingdotseq</span></code></td>
</tr>
<tr class="row-even"><td>⌢ <code class="docutils literal notranslate"><span class="pre">\frown</span></code></td>
<td>≥ <code class="docutils literal notranslate"><span class="pre">\geq</span></code></td>
<td>≧ <code class="docutils literal notranslate"><span class="pre">\geqq</span></code></td>
<td>⩾ <code class="docutils literal notranslate"><span class="pre">\geqslant</span></code></td>
</tr>
<tr class="row-odd"><td>≫ <code class="docutils literal notranslate"><span class="pre">\gg</span></code></td>
<td>⋙ <code class="docutils literal notranslate"><span class="pre">\ggg</span></code></td>
<td>⪺ <code class="docutils literal notranslate"><span class="pre">\gnapprox</span></code></td>
<td>≩ <code class="docutils literal notranslate"><span class="pre">\gneqq</span></code></td>
</tr>
<tr class="row-even"><td>⋧ <code class="docutils literal notranslate"><span class="pre">\gnsim</span></code></td>
<td>⪆ <code class="docutils literal notranslate"><span class="pre">\gtrapprox</span></code></td>
<td>⋗ <code class="docutils literal notranslate"><span class="pre">\gtrdot</span></code></td>
<td>⋛ <code class="docutils literal notranslate"><span class="pre">\gtreqless</span></code></td>
</tr>
<tr class="row-odd"><td>⪌ <code class="docutils literal notranslate"><span class="pre">\gtreqqless</span></code></td>
<td>≷ <code class="docutils literal notranslate"><span class="pre">\gtrless</span></code></td>
<td>≳ <code class="docutils literal notranslate"><span class="pre">\gtrsim</span></code></td>
<td>∈ <code class="docutils literal notranslate"><span class="pre">\in</span></code></td>
</tr>
<tr class="row-even"><td>⊺ <code class="docutils literal notranslate"><span class="pre">\intercal</span></code></td>
<td>⋋ <code class="docutils literal notranslate"><span class="pre">\leftthreetimes</span></code></td>
<td>≤ <code class="docutils literal notranslate"><span class="pre">\leq</span></code></td>
<td>≦ <code class="docutils literal notranslate"><span class="pre">\leqq</span></code></td>
</tr>
<tr class="row-odd"><td>⩽ <code class="docutils literal notranslate"><span class="pre">\leqslant</span></code></td>
<td>⪅ <code class="docutils literal notranslate"><span class="pre">\lessapprox</span></code></td>
<td>⋖ <code class="docutils literal notranslate"><span class="pre">\lessdot</span></code></td>
<td>⋚ <code class="docutils literal notranslate"><span class="pre">\lesseqgtr</span></code></td>
</tr>
<tr class="row-even"><td>⪋ <code class="docutils literal notranslate"><span class="pre">\lesseqqgtr</span></code></td>
<td>≶ <code class="docutils literal notranslate"><span class="pre">\lessgtr</span></code></td>
<td>≲ <code class="docutils literal notranslate"><span class="pre">\lesssim</span></code></td>
<td>≪ <code class="docutils literal notranslate"><span class="pre">\ll</span></code></td>
</tr>
<tr class="row-odd"><td>⋘ <code class="docutils literal notranslate"><span class="pre">\lll</span></code></td>
<td>⪹ <code class="docutils literal notranslate"><span class="pre">\lnapprox</span></code></td>
<td>≨ <code class="docutils literal notranslate"><span class="pre">\lneqq</span></code></td>
<td>⋦ <code class="docutils literal notranslate"><span class="pre">\lnsim</span></code></td>
</tr>
<tr class="row-even"><td>⋉ <code class="docutils literal notranslate"><span class="pre">\ltimes</span></code></td>
<td>∣ <code class="docutils literal notranslate"><span class="pre">\mid</span></code></td>
<td>⊧ <code class="docutils literal notranslate"><span class="pre">\models</span></code></td>
<td>∓ <code class="docutils literal notranslate"><span class="pre">\mp</span></code></td>
</tr>
<tr class="row-odd"><td>⊯ <code class="docutils literal notranslate"><span class="pre">\nVDash</span></code></td>
<td>⊮ <code class="docutils literal notranslate"><span class="pre">\nVdash</span></code></td>
<td>≉ <code class="docutils literal notranslate"><span class="pre">\napprox</span></code></td>
<td>≇ <code class="docutils literal notranslate"><span class="pre">\ncong</span></code></td>
</tr>
<tr class="row-even"><td>≠ <code class="docutils literal notranslate"><span class="pre">\ne</span></code></td>
<td>≠ <code class="docutils literal notranslate"><span class="pre">\neq</span></code></td>
<td>≠ <code class="docutils literal notranslate"><span class="pre">\neq</span></code></td>
<td>≢ <code class="docutils literal notranslate"><span class="pre">\nequiv</span></code></td>
</tr>
<tr class="row-odd"><td>≱ <code class="docutils literal notranslate"><span class="pre">\ngeq</span></code></td>
<td>≯ <code class="docutils literal notranslate"><span class="pre">\ngtr</span></code></td>
<td>∋ <code class="docutils literal notranslate"><span class="pre">\ni</span></code></td>
<td>≰ <code class="docutils literal notranslate"><span class="pre">\nleq</span></code></td>
</tr>
<tr class="row-even"><td>≮ <code class="docutils literal notranslate"><span class="pre">\nless</span></code></td>
<td>∤ <code class="docutils literal notranslate"><span class="pre">\nmid</span></code></td>
<td>∉ <code class="docutils literal notranslate"><span class="pre">\notin</span></code></td>
<td>∦ <code class="docutils literal notranslate"><span class="pre">\nparallel</span></code></td>
</tr>
<tr class="row-odd"><td>⊀ <code class="docutils literal notranslate"><span class="pre">\nprec</span></code></td>
<td>≁ <code class="docutils literal notranslate"><span class="pre">\nsim</span></code></td>
<td>⊄ <code class="docutils literal notranslate"><span class="pre">\nsubset</span></code></td>
<td>⊈ <code class="docutils literal notranslate"><span class="pre">\nsubseteq</span></code></td>
</tr>
<tr class="row-even"><td>⊁ <code class="docutils literal notranslate"><span class="pre">\nsucc</span></code></td>
<td>⊅ <code class="docutils literal notranslate"><span class="pre">\nsupset</span></code></td>
<td>⊉ <code class="docutils literal notranslate"><span class="pre">\nsupseteq</span></code></td>
<td>⋪ <code class="docutils literal notranslate"><span class="pre">\ntriangleleft</span></code></td>
</tr>
<tr class="row-odd"><td>⋬ <code class="docutils literal notranslate"><span class="pre">\ntrianglelefteq</span></code></td>
<td>⋫ <code class="docutils literal notranslate"><span class="pre">\ntriangleright</span></code></td>
<td>⋭ <code class="docutils literal notranslate"><span class="pre">\ntrianglerighteq</span></code></td>
<td>⊭ <code class="docutils literal notranslate"><span class="pre">\nvDash</span></code></td>
</tr>
<tr class="row-even"><td>⊬ <code class="docutils literal notranslate"><span class="pre">\nvdash</span></code></td>
<td>⊙ <code class="docutils literal notranslate"><span class="pre">\odot</span></code></td>
<td>⊖ <code class="docutils literal notranslate"><span class="pre">\ominus</span></code></td>
<td>⊕ <code class="docutils literal notranslate"><span class="pre">\oplus</span></code></td>
</tr>
<tr class="row-odd"><td>⊘ <code class="docutils literal notranslate"><span class="pre">\oslash</span></code></td>
<td>⊗ <code class="docutils literal notranslate"><span class="pre">\otimes</span></code></td>
<td>∥ <code class="docutils literal notranslate"><span class="pre">\parallel</span></code></td>
<td>⟂ <code class="docutils literal notranslate"><span class="pre">\perp</span></code></td>
</tr>
<tr class="row-even"><td>⋔ <code class="docutils literal notranslate"><span class="pre">\pitchfork</span></code></td>
<td>± <code class="docutils literal notranslate"><span class="pre">\pm</span></code></td>
<td>≺ <code class="docutils literal notranslate"><span class="pre">\prec</span></code></td>
<td>⪷ <code class="docutils literal notranslate"><span class="pre">\precapprox</span></code></td>
</tr>
<tr class="row-odd"><td>≼ <code class="docutils literal notranslate"><span class="pre">\preccurlyeq</span></code></td>
<td>≼ <code class="docutils literal notranslate"><span class="pre">\preceq</span></code></td>
<td>⪹ <code class="docutils literal notranslate"><span class="pre">\precnapprox</span></code></td>
<td>⋨ <code class="docutils literal notranslate"><span class="pre">\precnsim</span></code></td>
</tr>
<tr class="row-even"><td>≾ <code class="docutils literal notranslate"><span class="pre">\precsim</span></code></td>
<td>∝ <code class="docutils literal notranslate"><span class="pre">\propto</span></code></td>
<td>⋌ <code class="docutils literal notranslate"><span class="pre">\rightthreetimes</span></code></td>
<td>≓ <code class="docutils literal notranslate"><span class="pre">\risingdotseq</span></code></td>
</tr>
<tr class="row-odd"><td>⋊ <code class="docutils literal notranslate"><span class="pre">\rtimes</span></code></td>
<td>∼ <code class="docutils literal notranslate"><span class="pre">\sim</span></code></td>
<td>≃ <code class="docutils literal notranslate"><span class="pre">\simeq</span></code></td>
<td>∕ <code class="docutils literal notranslate"><span class="pre">\slash</span></code></td>
</tr>
<tr class="row-even"><td>⌣ <code class="docutils literal notranslate"><span class="pre">\smile</span></code></td>
<td>⊓ <code class="docutils literal notranslate"><span class="pre">\sqcap</span></code></td>
<td>⊔ <code class="docutils literal notranslate"><span class="pre">\sqcup</span></code></td>
<td>⊏ <code class="docutils literal notranslate"><span class="pre">\sqsubset</span></code></td>
</tr>
<tr class="row-odd"><td>⊏ <code class="docutils literal notranslate"><span class="pre">\sqsubset</span></code></td>
<td>⊑ <code class="docutils literal notranslate"><span class="pre">\sqsubseteq</span></code></td>
<td>⊐ <code class="docutils literal notranslate"><span class="pre">\sqsupset</span></code></td>
<td>⊐ <code class="docutils literal notranslate"><span class="pre">\sqsupset</span></code></td>
</tr>
<tr class="row-even"><td>⊒ <code class="docutils literal notranslate"><span class="pre">\sqsupseteq</span></code></td>
<td>⋆ <code class="docutils literal notranslate"><span class="pre">\star</span></code></td>
<td>⊂ <code class="docutils literal notranslate"><span class="pre">\subset</span></code></td>
<td>⊆ <code class="docutils literal notranslate"><span class="pre">\subseteq</span></code></td>
</tr>
<tr class="row-odd"><td>⫅ <code class="docutils literal notranslate"><span class="pre">\subseteqq</span></code></td>
<td>⊊ <code class="docutils literal notranslate"><span class="pre">\subsetneq</span></code></td>
<td>⫋ <code class="docutils literal notranslate"><span class="pre">\subsetneqq</span></code></td>