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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"

"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<head>

<title>Writing mathematical expressions — Matplotlib 3.5.0 documentation</title>

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Writing mathematical expressions

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<p>Click <a class="reference internal" href="#sphx-glr-download-tutorials-text-mathtext-py"><span class="std std-ref">here</span></a>

to download the full example code</p>

</div>

<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>You can use a subset of 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>

<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-ca525d8410.png" srcset="../../_images/mathmpl/math-ca525d8410.png, ../../_images/mathmpl/math-ca525d8410-2x.png 2x" style="position: relative; bottom: -4px"/>".</p>

<p>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>

<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>

</pre></div>

</div>

<p>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>

<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>

\[\alpha_i > \beta_i\]</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>

\[\alpha^{ic} > \beta_{ic}\]</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-3a2e7f36d3.png" srcset="../../_images/mathmpl/math-3a2e7f36d3.png, ../../_images/mathmpl/math-3a2e7f36d3-2x.png 2x" style="position: relative; bottom: -3px"/> from <img src="../../_images/mathmpl/math-b69eb39e09.png" srcset="../../_images/mathmpl/math-b69eb39e09.png, ../../_images/mathmpl/math-b69eb39e09-2x.png 2x" style="position: relative; bottom: -2px"/> to

<img src="../../_images/mathmpl/math-918327c3a6.png" srcset="../../_images/mathmpl/math-918327c3a6.png, ../../_images/mathmpl/math-918327c3a6-2x.png 2x" style="position: relative; bottom: -2px"/>, 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>

\[\sum_{i=0}^\infty x_i\]</div>

</section>

<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>

\[\frac{3}{4} \binom{3}{4} \genfrac{}{}{0pt}{}{3}{4}\]</div>

<p>Fractions can be arbitrarily nested:</p>

</pre></div>

</div>

<p>produces</p>

\[\frac{5 - \frac{1}{x}}{4}\]</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>

</pre></div>

</div>

\[(\frac{5 - \frac{1}{x}}{4})\]</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>

\[\left(\frac{5 - \frac{1}{x}}{4}\right)\]</div>

</section>

<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>

</pre></div>

</div>

\[\sqrt{2}\]</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>

</pre></div>

</div>

\[\sqrt[3]{x}\]</div>

</section>

<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>

<p>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>

\[s(t) = \mathcal{A}\mathrm{sin}(2 \omega t)\]</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>

</pre></div>

</div>

\[s(t) = \mathcal{A}\sin(2 \omega t)\]</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>

\[s(t) = \mathcal{A}\,\sin(2 \omega t)\]</div>

<p>The choices available with all fonts are:</p>

</colgroup>

<thead>

<tr class="row-odd"><th class="head"><p>Command</p></th>

<th class="head"><p>Result</p></th>

</tr>

</thead>

<tbody>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\mathrm{Roman}</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\mathit{Italic}</span></code></p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\mathtt{Typewriter}</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\mathcal{CALLIGRAPHY}</span></code></p></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>

</colgroup>

<thead>

<tr class="row-odd"><th class="head"><p>Command</p></th>

<th class="head"><p>Result</p></th>

</tr>

</thead>

<tbody>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\mathbb{blackboard}</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\mathrm{\mathbb{blackboard}}</span></code></p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\mathfrak{Fraktur}</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\mathsf{sansserif}</span></code></p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\mathrm{\mathsf{sansserif}}</span></code></p></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>

<p><code class="docutils literal notranslate"><span class="pre">dejavuserif</span></code>: DejaVu Serif</p>

<p><code class="docutils literal notranslate"><span class="pre">cm</span></code>: Computer Modern (TeX)</p>

<p><code class="docutils literal notranslate"><span class="pre">stix</span></code>: STIX (designed to blend well with Times)</p>

<p><code class="docutils literal notranslate"><span class="pre">stixsans</span></code>: STIX sans-serif</p>

<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>

<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>

</colgroup>

<thead>

<tr class="row-odd"><th class="head"><p>Parameter</p></th>

<th class="head"><p>Corresponds to</p></th>

</tr>

</thead>

<tbody>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.it</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathit{}</span></code> or default italic</p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.rm</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathrm{}</span></code> Roman (upright)</p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.tt</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathtt{}</span></code> Typewriter (monospace)</p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.bf</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathbf{}</span></code> bold italic</p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.cal</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathcal{}</span></code> calligraphic</p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">mathtext.sf</span></code></p></td>

<td><p><code class="docutils literal notranslate"><span class="pre">\mathsf{}</span></code> sans-serif</p></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>

</section>

<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>

</colgroup>

<thead>

<tr class="row-odd"><th class="head"><p>Command</p></th>

<th class="head"><p>Result</p></th>

</tr>

</thead>

<tbody>

<tr class="row-even"><td><p><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></p></td>

</tr>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\breve</span> <span class="pre">a</span></code></p></td>

</tr>

</tr>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\dddot</span> <span class="pre">a</span></code></p></td>

</tr>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\ddddot</span> <span class="pre">a</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><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></p></td>

</tr>

</tr>

<tr class="row-odd"><td><p><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></p></td>

</tr>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\overline{abc}</span></code></p></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>

</colgroup>

<thead>

<tr class="row-odd"><th class="head"><p>Command</p></th>

<th class="head"><p>Result</p></th>

</tr>

</thead>

<tbody>

<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">\widehat{xyz}</span></code></p></td>

</tr>

<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">\widetilde{xyz}</span></code></p></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>

\[\hat i\ \ \hat \imath\]</div>

</section>

<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>

</colgroup>

<tbody>

<tr class="row-odd"><td><p>α <code class="docutils literal notranslate"><span class="pre">\alpha</span></code></p></td>

<td><p>δ <code class="docutils literal notranslate"><span class="pre">\delta</span></code></p></td>

<td><p>ϝ <code class="docutils literal notranslate"><span class="pre">\digamma</span></code></p></td>

<td><p>ε <code class="docutils literal notranslate"><span class="pre">\epsilon</span></code></p></td>

</tr>

<td><p>γ <code class="docutils literal notranslate"><span class="pre">\gamma</span></code></p></td>

<td><p>κ <code class="docutils literal notranslate"><span class="pre">\kappa</span></code></p></td>

<td><p>λ <code class="docutils literal notranslate"><span class="pre">\lambda</span></code></p></td>

</tr>

<td><p>ω <code class="docutils literal notranslate"><span class="pre">\omega</span></code></p></td>

</tr>

<tr class="row-even"><td><p>σ <code class="docutils literal notranslate"><span class="pre">\sigma</span></code></p></td>

<td><p>θ <code class="docutils literal notranslate"><span class="pre">\theta</span></code></p></td>

<td><p>υ <code class="docutils literal notranslate"><span class="pre">\upsilon</span></code></p></td>

<td><p>ε <code class="docutils literal notranslate"><span class="pre">\varepsilon</span></code></p></td>

<td><p>ϰ <code class="docutils literal notranslate"><span class="pre">\varkappa</span></code></p></td>

</tr>

<tr class="row-odd"><td><p>φ <code class="docutils literal notranslate"><span class="pre">\varphi</span></code></p></td>

<td><p>ϖ <code class="docutils literal notranslate"><span class="pre">\varpi</span></code></p></td>

<td><p>ϱ <code class="docutils literal notranslate"><span class="pre">\varrho</span></code></p></td>

<td><p>ς <code class="docutils literal notranslate"><span class="pre">\varsigma</span></code></p></td>

<td><p>ϑ <code class="docutils literal notranslate"><span class="pre">\vartheta</span></code></p></td>

</tr>

</tr>

</tbody>

</table>

</div></blockquote>

<p><strong>Upper-case Greek</strong></p>

</colgroup>

<tbody>

<tr class="row-odd"><td><p>Δ <code class="docutils literal notranslate"><span class="pre">\Delta</span></code></p></td>

<td><p>Γ <code class="docutils literal notranslate"><span class="pre">\Gamma</span></code></p></td>

<td><p>Λ <code class="docutils literal notranslate"><span class="pre">\Lambda</span></code></p></td>

<td><p>Ω <code class="docutils literal notranslate"><span class="pre">\Omega</span></code></p></td>

<td><p>Σ <code class="docutils literal notranslate"><span class="pre">\Sigma</span></code></p></td>

</tr>

<tr class="row-even"><td><p>Θ <code class="docutils literal notranslate"><span class="pre">\Theta</span></code></p></td>

<td><p>Υ <code class="docutils literal notranslate"><span class="pre">\Upsilon</span></code></p></td>

<td><p>∇ <code class="docutils literal notranslate"><span class="pre">\nabla</span></code></p></td>

</tr>

</tbody>

</table>

</div></blockquote>

<p><strong>Hebrew</strong></p>

</colgroup>

<tbody>

<tr class="row-odd"><td><p>ℵ <code class="docutils literal notranslate"><span class="pre">\aleph</span></code></p></td>

<td><p>ℸ <code class="docutils literal notranslate"><span class="pre">\daleth</span></code></p></td>

<td><p>ℷ <code class="docutils literal notranslate"><span class="pre">\gimel</span></code></p></td>

</tr>

</tbody>

</table>

</div></blockquote>

<p><strong>Delimiters</strong></p>

</colgroup>

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