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<div class="document" id="latex-syntax-for-mathematics">
<h1 class="title">LaTeX syntax for mathematics</h1>
<div class="abstract topic">
<p class="topic-title">Abstract</p>
<p>Docutils supports mathematical content with a <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/directives.html#math">"math"
directive</a> and <a class="reference external" href="https://docutils.sourceforge.io/docs/ref/rst/roles.html#math">role</a>. The input format is <em>LaTeX math
syntax</em><a class="footnote-reference" href="#math-syntax" id="footnote-reference-1">[1]</a> with support for Unicode symbols.</p>
</div>
<!-- Minimal menu bar for inclusion in documentation sources
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Attention: this is not a standalone document. -->
<div class="contents topic" id="contents">
<p class="topic-title">Contents</p>
<ul class="auto-toc simple">
<li><a class="reference internal" href="#inline-formulas-and-displayed-equations" id="toc-entry-1">1 Inline formulas and displayed equations</a></li>
<li><a class="reference internal" href="#mathematical-symbols" id="toc-entry-2">2 Mathematical symbols</a><ul class="auto-toc">
<li><a class="reference internal" href="#accents-and-embellishments" id="toc-entry-3">2.1 Accents and embellishments</a></li>
<li><a class="reference internal" href="#binary-operators" id="toc-entry-4">2.2 Binary operators</a></li>
<li><a class="reference internal" href="#extensible-delimiters" id="toc-entry-5">2.3 Extensible delimiters</a><ul class="auto-toc">
<li><a class="reference internal" href="#pairing-delimiters" id="toc-entry-6">2.3.1 Pairing delimiters</a></li>
<li><a class="reference internal" href="#nonpairing-delimiters" id="toc-entry-7">2.3.2 Nonpairing delimiters</a></li>
</ul>
</li>
<li><a class="reference internal" href="#extensible-vertical-arrows" id="toc-entry-8">2.4 Extensible vertical arrows</a></li>
<li><a class="reference internal" href="#functions-named-operators" id="toc-entry-9">2.5 Functions (named operators)</a></li>
<li><a class="reference internal" href="#greek-letters" id="toc-entry-10">2.6 Greek letters</a></li>
<li><a class="reference internal" href="#letterlike-symbols" id="toc-entry-11">2.7 Letterlike symbols</a></li>
<li><a class="reference internal" href="#mathematical-alphabets" id="toc-entry-12">2.8 Mathematical Alphabets</a></li>
<li><a class="reference internal" href="#miscellaneous-symbols" id="toc-entry-13">2.9 Miscellaneous symbols</a></li>
<li><a class="reference internal" href="#punctuation" id="toc-entry-14">2.10 Punctuation</a></li>
<li><a class="reference internal" href="#relation-symbols" id="toc-entry-15">2.11 Relation symbols</a><ul class="auto-toc">
<li><a class="reference internal" href="#arrows" id="toc-entry-16">2.11.1 Arrows</a></li>
<li><a class="reference internal" href="#comparison" id="toc-entry-17">2.11.2 Comparison</a></li>
<li><a class="reference internal" href="#miscellaneous-relations" id="toc-entry-18">2.11.3 Miscellaneous relations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#variable-sized-operators" id="toc-entry-19">2.12 Variable-sized operators</a></li>
</ul>
</li>
<li><a class="reference internal" href="#notations" id="toc-entry-20">3 Notations</a><ul class="auto-toc">
<li><a class="reference internal" href="#top-and-bottom-embellishments" id="toc-entry-21">3.1 Top and bottom embellishments</a></li>
<li><a class="reference internal" href="#extensible-arrows" id="toc-entry-22">3.2 Extensible arrows</a></li>
<li><a class="reference internal" href="#affixing-symbols-to-other-symbols" id="toc-entry-23">3.3 Affixing symbols to other symbols</a></li>
<li><a class="reference internal" href="#matrices" id="toc-entry-24">3.4 Matrices</a></li>
<li><a class="reference internal" href="#spacing-commands" id="toc-entry-25">3.5 Spacing commands</a></li>
<li><a class="reference internal" href="#roots" id="toc-entry-26">3.6 Roots</a></li>
<li><a class="reference internal" href="#boxed-formulas" id="toc-entry-27">3.7 Boxed formulas</a></li>
</ul>
</li>
<li><a class="reference internal" href="#fractions-and-related-constructions" id="toc-entry-28">4 Fractions and related constructions</a></li>
<li><a class="reference internal" href="#delimiter-sizes" id="toc-entry-29">5 Delimiter sizes</a></li>
<li><a class="reference internal" href="#text" id="toc-entry-30">6 Text</a></li>
<li><a class="reference internal" href="#integrals-and-sums" id="toc-entry-31">7 Integrals and sums</a><ul class="auto-toc">
<li><a class="reference internal" href="#altering-the-placement-of-limits" id="toc-entry-32">7.1 Altering the placement of limits</a></li>
</ul>
</li>
<li><a class="reference internal" href="#changing-the-size-of-elements-in-a-formula" id="toc-entry-33">8 Changing the size of elements in a formula</a></li>
<li><a class="reference internal" href="#appendix" id="toc-entry-34">9 Appendix</a><ul class="auto-toc">
<li><a class="reference internal" href="#tests" id="toc-entry-35">9.1 Tests</a><ul class="auto-toc">
<li><a class="reference internal" href="#font-changes" id="toc-entry-36">9.1.1 Font changes</a></li>
<li><a class="reference internal" href="#inferred-mrow-s-in-mathml" id="toc-entry-37">9.1.2 Inferred <mrow>s in MathML</a></li>
<li><a class="reference internal" href="#scripts-and-limits" id="toc-entry-38">9.1.3 Scripts and Limits</a></li>
<li><a class="reference internal" href="#nested-groups" id="toc-entry-39">9.1.4 Nested groups</a></li>
<li><a class="reference internal" href="#big-delimiters-and-symbols" id="toc-entry-40">9.1.5 Big delimiters and symbols</a></li>
<li><a class="reference internal" href="#text-1" id="toc-entry-41">9.1.6 Text</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
<div class="section" id="inline-formulas-and-displayed-equations">
<h1><a class="toc-backref" href="#toc-entry-1">1 Inline formulas and displayed equations</a></h1>
<p>The <strong>math role</strong> can be used for inline mathematical expressions:
<tt class="docutils literal"><span class="pre">:math:`\psi(r)</span> = <span class="pre">\exp(-2r)`</span></tt> will produce <span class="m formula"><i>ψ</i>(<i>r</i>) = exp( − 2<i>r</i>)</span>.
Inside the backtics you can write anything you would write between dollar
signs in a LaTeX document. <a class="footnote-reference" href="#math-syntax" id="footnote-reference-2">[1]</a></p>
<div class="admonition tip">
<p class="first admonition-title">Tip</p>
<p class="last">If you put <tt class="docutils literal">.. <span class="pre">default-role::</span> math</tt> at the top of your
document, you can write <tt class="docutils literal">`x^2`</tt> instead of the longer
version: <tt class="docutils literal"><span class="pre">:math:`x^2`</span></tt>. You can also introduce an
abbreviation like this <tt class="docutils literal">.. role:: m(math)</tt>. That will allow
you to write <tt class="docutils literal"><span class="pre">:m:`x^2`</span></tt> or <tt class="docutils literal"><span class="pre">`x^2`:m:</span></tt>.</p>
</div>
<p>The <strong>math directive</strong> is used for displayed equations. It corresponds to
an <tt class="docutils literal">equation*</tt> or <tt class="docutils literal">align*</tt> environment in a LaTeX document. If you
write:</p>
<pre class="literal-block">
.. math:: \psi(r) = e^{-2r}
</pre>
<p>you will get:</p>
<div class="formula">
<i>ψ</i>(<i>r</i>) = <i>e</i><sup> − 2<i>r</i></sup>
</div>
<p>A more complex example is the definition of the <a class="reference internal" href="#fourier-transform">Fourier transform</a>:</p>
<pre class="literal-block">
.. math::
:name: Fourier transform
(\mathcal{F}f)(y)
= \frac{1}{\sqrt{2\pi}^{\ n}}
\int_{\mathbb{R}^n} f(x)\,
e^{-\mathrm{i} y \cdot x} \,\mathrm{d} x.
</pre>
<p>which is rendered as:</p>
<div class="formula" id="fourier-transform">
(ℱ<i>f</i>)(<i>y</i>) = <span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2<i>π</i></span><span class="ignored">)</span></span><sup> <i>n</i></sup></span><span class="ignored">)</span></span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">ℝ<sup><i>n</i></sup></sub></span><i>f</i>(<i>x</i>) <i>e</i><sup> − <span class="mathrm">i</span><i>y</i>⋅<i>x</i></sup> <span class="mathrm">d</span><i>x</i>.
</div>
<p>The <tt class="docutils literal">:name:</tt> option puts a label on the equation that can be
linked to by <a class="reference external" href="../ref/rst/restructuredtext.html#hyperlink-references">hyperlink references</a>.</p>
<p>Displayed equations can use <tt class="docutils literal">\\</tt> and <tt class="docutils literal">&</tt> for line shifts and alignments:</p>
<pre class="literal-block">
.. math::
a &= (x + y)^2 & b &= (x - y)^2 \\
&= x^2 + 2xy + y^2 & &= x^2 - 2xy + y^2
</pre>
<p>LaTeX output will wrap it in an <tt class="docutils literal">align*</tt> environment.
The result is:</p>
<div class="formula">
<span class="environment align"><span class="arrayrow">
<span class="arraycell align-r">
<i>a</i>
</span>
<span class="arraycell align-l">
= (<i>x</i> + <i>y</i>)<sup>2</sup>
</span>
<span class="arraycell align-r">
<i>b</i>
</span>
<span class="arraycell align-l">
= (<i>x</i> − <i>y</i>)<sup>2</sup>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
= <i>x</i><sup>2</sup> + 2<i>xy</i> + <i>y</i><sup>2</sup>
</span>
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
= <i>x</i><sup>2</sup> − 2<i>xy</i> + <i>y</i><sup>2</sup>
</span>
</span>
</span>
</div>
<table class="docutils footnote" frame="void" id="math-syntax" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[1]</td><td><em>(<a class="fn-backref" href="#footnote-reference-1">1</a>, <a class="fn-backref" href="#footnote-reference-2">2</a>)</em> <p>The supported LaTeX commands include AMS extensions
(see, e.g., the <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>). Some of the shown symbols
require the "amssymb" <a class="reference external" href="../../user/latex.html#latex-document-classes-and-packages">LaTeX package</a> (or another package providing
the AMS symbol macros) when exported with the "latex" writer.</p>
<p class="last">The support is limited to a subset of <em>LaTeX math</em> by the conversion
required for many output formats. For HTML, the <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
configuration setting (or the corresponding <tt class="docutils literal"><span class="pre">--math-output</span></tt> command
line option) selects between alternative output formats with different
subsets of supported elements. If a writer does not support math
typesetting, the content is inserted verbatim.</p>
</td></tr>
</tbody>
</table>
</div>
<div class="section" id="mathematical-symbols">
<h1><a class="toc-backref" href="#toc-entry-2">2 Mathematical symbols</a></h1>
<p>The following tables are adapted from the first edition of
"The LaTeX Companion" (Goossens, Mittelbach, Samarin) and the
AMS <a class="reference external" href="https://mirrors.ctan.org/info/short-math-guide/short-math-guide.pdf">Short Math Guide</a>.</p>
<div class="section" id="accents-and-embellishments">
<h2><a class="toc-backref" href="#toc-entry-3">2.1 Accents and embellishments</a></h2>
<p>The "narrow" accents are intended for a single-letter base.</p>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"><i>x́</i></span></td>
<td><tt class="docutils literal">\acute{x}</tt></td>
<td><span class="formula"><i>ṫ</i></span></td>
<td><tt class="docutils literal">\dot{t}</tt></td>
<td><span class="formula"><i>x̂</i></span></td>
<td><tt class="docutils literal">\hat{x}</tt></td>
</tr>
<tr><td><span class="formula"><span class="embellished"><sup>‒</sup><span class="base"><i>v</i></span></span></span></td>
<td><tt class="docutils literal">\bar{v}</tt></td>
<td><span class="formula"><i>ẗ</i></span></td>
<td><tt class="docutils literal">\ddot{t}</tt></td>
<td><span class="formula"><i>x̊</i></span></td>
<td><tt class="docutils literal">\mathring{x}</tt></td>
</tr>
<tr><td><span class="formula"><i>x̆</i></span></td>
<td><tt class="docutils literal">\breve{x}</tt></td>
<td><span class="formula"><span class="embellished"><sup><span class="smallsymbol">⋯</span></sup><span class="base"><i>t</i></span></span></span></td>
<td><tt class="docutils literal">\dddot{t}</tt></td>
<td><span class="formula"><i>ñ</i></span></td>
<td><tt class="docutils literal">\tilde{n}</tt></td>
</tr>
<tr><td><span class="formula"><i>x̌</i></span></td>
<td><tt class="docutils literal">\check{x}</tt></td>
<td><span class="formula"><i>x̀</i></span></td>
<td><tt class="docutils literal">\grave{x}</tt></td>
<td><span class="formula"><span class="embellished"><sup><span class="smallsymbol">→</span></sup><span class="base"><i>x</i></span></span></span></td>
<td><tt class="docutils literal">\vec{x}</tt></td>
</tr>
</tbody>
</table>
<p>When adding an accent to an i or j in math, dotless variants can be
obtained with <tt class="docutils literal">\imath</tt> and <tt class="docutils literal">\jmath</tt>: <span class="formula"><i>ı̂</i></span>, <span class="formula"><span class="embellished"><sup><span class="smallsymbol">→</span></sup><span class="base"><i>ȷ</i></span></span></span>.</p>
<p>For embellishments that span multiple symbols, use:</p>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"><span class="embellished"><sup>～</sup><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\widetilde{gbi}</tt></td>
<td><span class="formula"><span class="embellished"><sup>^</sup><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\widehat{gbi}</tt></td>
</tr>
<tr><td><span class="formula"><span class="overline"><i>gbi</i></span></span></td>
<td><tt class="docutils literal">\overline{gbi}</tt></td>
<td><span class="formula"><i>gbi</i></span></td>
<td><tt class="docutils literal">\underline{gbi}</tt></td>
</tr>
<tr><td><span class="formula"><span class="overbrace"><i>gbi</i></span></span></td>
<td><tt class="docutils literal">\overbrace{gbi}</tt></td>
<td><span class="formula"><span class="underbrace"><i>gbi</i></span></span></td>
<td><tt class="docutils literal">\underbrace{gbi}</tt></td>
</tr>
<tr><td><span class="formula"><span class="embellished"><sup>⟵</sup><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\overleftarrow{gbi}</tt></td>
<td><span class="formula"><span class="embellished"><sub>⟵</sub><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\underleftarrow{gbi}</tt></td>
</tr>
<tr><td><span class="formula"><span class="embellished"><sup>⟶</sup><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\overrightarrow{gbi}</tt></td>
<td><span class="formula"><span class="embellished"><sub>⟶</sub><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\underrightarrow{gbi}</tt></td>
</tr>
<tr><td><span class="formula"><span class="embellished"><sup>⟷</sup><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\overleftrightarrow{gbi}</tt></td>
<td><span class="formula"><span class="embellished"><sub>⟷</sub><span class="base"><i>gbi</i></span></span></span></td>
<td><tt class="docutils literal">\underleftrightarrow{gbi}</tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="binary-operators">
<h2><a class="toc-backref" href="#toc-entry-4">2.2 Binary operators</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">*</span></td>
<td><tt class="docutils literal">*</tt></td>
<td><span class="formula">⊛</span></td>
<td><tt class="docutils literal">\circledast</tt></td>
<td><span class="formula">⊖</span></td>
<td><tt class="docutils literal">\ominus</tt></td>
</tr>
<tr><td><span class="formula"> + </span></td>
<td><tt class="docutils literal">+</tt></td>
<td><span class="formula">⊚</span></td>
<td><tt class="docutils literal">\circledcirc</tt></td>
<td><span class="formula">⊕</span></td>
<td><tt class="docutils literal">\oplus</tt></td>
</tr>
<tr><td><span class="formula"> − </span></td>
<td><tt class="docutils literal">-</tt></td>
<td><span class="formula">⊝</span></td>
<td><tt class="docutils literal">\circleddash</tt></td>
<td><span class="formula">⊘</span></td>
<td><tt class="docutils literal">\oslash</tt></td>
</tr>
<tr><td><span class="formula"> : </span></td>
<td><tt class="docutils literal">:</tt></td>
<td><span class="formula">∪</span></td>
<td><tt class="docutils literal">\cup</tt></td>
<td><span class="formula">⊗</span></td>
<td><tt class="docutils literal">\otimes</tt></td>
</tr>
<tr><td><span class="formula">⋒</span></td>
<td><tt class="docutils literal">\Cap</tt></td>
<td><span class="formula">⋎</span></td>
<td><tt class="docutils literal">\curlyvee</tt></td>
<td><span class="formula">±</span></td>
<td><tt class="docutils literal">\pm</tt></td>
</tr>
<tr><td><span class="formula">⋓</span></td>
<td><tt class="docutils literal">\Cup</tt></td>
<td><span class="formula">⋏</span></td>
<td><tt class="docutils literal">\curlywedge</tt></td>
<td><span class="formula">⋌</span></td>
<td><tt class="docutils literal">\rightthreetimes</tt></td>
</tr>
<tr><td><span class="formula">⨿</span></td>
<td><tt class="docutils literal">\amalg</tt></td>
<td><span class="formula">†</span></td>
<td><tt class="docutils literal">\dagger</tt></td>
<td><span class="formula">⋊</span></td>
<td><tt class="docutils literal">\rtimes</tt></td>
</tr>
<tr><td><span class="formula">∗</span></td>
<td><tt class="docutils literal">\ast</tt></td>
<td><span class="formula">‡</span></td>
<td><tt class="docutils literal">\ddagger</tt></td>
<td><span class="formula">⧵</span></td>
<td><tt class="docutils literal">\setminus</tt></td>
</tr>
<tr><td><span class="formula">◯</span></td>
<td><tt class="docutils literal">\bigcirc</tt></td>
<td><span class="formula">⋄</span></td>
<td><tt class="docutils literal">\diamond</tt></td>
<td><span class="formula">∖</span></td>
<td><tt class="docutils literal">\smallsetminus</tt></td>
</tr>
<tr><td><span class="formula">▽</span></td>
<td><tt class="docutils literal">\bigtriangledown</tt></td>
<td><span class="formula">÷</span></td>
<td><tt class="docutils literal">\div</tt></td>
<td><span class="formula">⊓</span></td>
<td><tt class="docutils literal">\sqcap</tt></td>
</tr>
<tr><td><span class="formula">△</span></td>
<td><tt class="docutils literal">\bigtriangleup</tt></td>
<td><span class="formula">⋇</span></td>
<td><tt class="docutils literal">\divideontimes</tt></td>
<td><span class="formula">⊔</span></td>
<td><tt class="docutils literal">\sqcup</tt></td>
</tr>
<tr><td><span class="formula">⊡</span></td>
<td><tt class="docutils literal">\boxdot</tt></td>
<td><span class="formula">∔</span></td>
<td><tt class="docutils literal">\dotplus</tt></td>
<td><span class="formula">⋆</span></td>
<td><tt class="docutils literal">\star</tt></td>
</tr>
<tr><td><span class="formula">⊟</span></td>
<td><tt class="docutils literal">\boxminus</tt></td>
<td><span class="formula">⩞</span></td>
<td><tt class="docutils literal">\doublebarwedge</tt></td>
<td><span class="formula">×</span></td>
<td><tt class="docutils literal">\times</tt></td>
</tr>
<tr><td><span class="formula">⊞</span></td>
<td><tt class="docutils literal">\boxplus</tt></td>
<td><span class="formula">⋗</span></td>
<td><tt class="docutils literal">\gtrdot</tt></td>
<td><span class="formula">◃</span></td>
<td><tt class="docutils literal">\triangleleft</tt></td>
</tr>
<tr><td><span class="formula">⊠</span></td>
<td><tt class="docutils literal">\boxtimes</tt></td>
<td><span class="formula">⊺</span></td>
<td><tt class="docutils literal">\intercal</tt></td>
<td><span class="formula">▹</span></td>
<td><tt class="docutils literal">\triangleright</tt></td>
</tr>
<tr><td><span class="formula">•</span></td>
<td><tt class="docutils literal">\bullet</tt></td>
<td><span class="formula">⋋</span></td>
<td><tt class="docutils literal">\leftthreetimes</tt></td>
<td><span class="formula">⊎</span></td>
<td><tt class="docutils literal">\uplus</tt></td>
</tr>
<tr><td><span class="formula">∩</span></td>
<td><tt class="docutils literal">\cap</tt></td>
<td><span class="formula">⋖</span></td>
<td><tt class="docutils literal">\lessdot</tt></td>
<td><span class="formula">∨</span></td>
<td><tt class="docutils literal">\vee</tt></td>
</tr>
<tr><td><span class="formula">⋅</span></td>
<td><tt class="docutils literal">\cdot</tt></td>
<td><span class="formula">⋉</span></td>
<td><tt class="docutils literal">\ltimes</tt></td>
<td><span class="formula">⊻</span></td>
<td><tt class="docutils literal">\veebar</tt></td>
</tr>
<tr><td><span class="formula">⬝</span></td>
<td><tt class="docutils literal">\centerdot</tt></td>
<td><span class="formula">∓</span></td>
<td><tt class="docutils literal">\mp</tt></td>
<td><span class="formula">∧</span></td>
<td><tt class="docutils literal">\wedge</tt></td>
</tr>
<tr><td><span class="formula">∘</span></td>
<td><tt class="docutils literal">\circ</tt></td>
<td><span class="formula">⊙</span></td>
<td><tt class="docutils literal">\odot</tt></td>
<td><span class="formula">≀</span></td>
<td><tt class="docutils literal">\wr</tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="extensible-delimiters">
<h2><a class="toc-backref" href="#toc-entry-5">2.3 Extensible delimiters</a></h2>
<p>Unless you indicate otherwise, delimiters in math formulas remain at the
standard size regardless of the height of the enclosed material. To get
adaptable sizes, use <tt class="docutils literal">\left</tt> and <tt class="docutils literal">\right</tt> prefixes, for example
<span class="formula"><i>g</i>(<i>A</i>, <i>B</i>, <i>Y</i>) = <i>f</i><span class="stretchy">(</span><i>A</i>, <i>B</i>, <i>X</i> = <i>h</i><sup>[<i>X</i>]</sup>(<i>Y</i>)<span class="stretchy">)</span></span> or</p>
<div class="formula">
<i>a</i><sub><i>n</i></sub> = <span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><sup><i>n</i></sup>
</div>
<p>Use <tt class="docutils literal">.</tt> for "empty" delimiters:</p>
<div class="formula">
<i>A</i> = <span class="emptydot"></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator">1 − <i>n</i></span><span class="ignored">)</span></span> <span class="array"><span class="arrayrow"><span class="bracket align-right">|</span></span><span class="arrayrow"><span class="bracket align-right">|</span></span></span><span class="scripts"><sup class="script">∞</sup><sub class="script"><i>n</i> = 0</sub></span>
</div>
<p>See also the commands for fixed <a class="reference internal" href="#delimiter-sizes">delimiter sizes</a> below.</p>
<p>The following symbols extend when used with <tt class="docutils literal">\left</tt> and <tt class="docutils literal">\right</tt>:</p>
<div class="section" id="pairing-delimiters">
<h3><a class="toc-backref" href="#toc-entry-6">2.3.1 Pairing delimiters</a></h3>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">()</span></td>
<td><tt class="docutils literal">( )</tt></td>
<td><span class="formula">⟨⟩</span></td>
<td><tt class="docutils literal">\langle \rangle</tt></td>
</tr>
<tr><td><span class="formula">[]</span></td>
<td><tt class="docutils literal">[ ]</tt></td>
<td><span class="formula">⌈⌉</span></td>
<td><tt class="docutils literal">\lceil \rceil</tt></td>
</tr>
<tr><td><span class="formula">{}</span></td>
<td><tt class="docutils literal">\{ \}</tt></td>
<td><span class="formula">⌊⌋</span></td>
<td><tt class="docutils literal">\lfloor \rfloor</tt></td>
</tr>
<tr><td><span class="formula">||</span></td>
<td><tt class="docutils literal">\lvert \rvert</tt></td>
<td><span class="formula">⟮⟯</span></td>
<td><tt class="docutils literal">\lgroup \rgroup</tt></td>
</tr>
<tr><td><span class="formula">‖‖</span></td>
<td><tt class="docutils literal">\lVert \rVert</tt></td>
<td><span class="formula">⎰⎱</span></td>
<td><tt class="docutils literal">\lmoustache \rmoustache</tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="nonpairing-delimiters">
<h3><a class="toc-backref" href="#toc-entry-7">2.3.2 Nonpairing delimiters</a></h3>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">|</span></td>
<td><tt class="docutils literal">|</tt></td>
<td><span class="formula">|</span></td>
<td><tt class="docutils literal">\vert</tt></td>
<td><span class="formula">⏐</span></td>
<td><tt class="docutils literal">\arrowvert</tt></td>
</tr>
<tr><td><span class="formula">‖</span></td>
<td><tt class="docutils literal">\|</tt></td>
<td><span class="formula">‖</span></td>
<td><tt class="docutils literal">\Vert</tt></td>
<td><span class="formula">‖</span></td>
<td><tt class="docutils literal">\Arrowvert</tt></td>
</tr>
<tr><td><span class="formula"> ⁄ </span></td>
<td><tt class="docutils literal">/</tt></td>
<td><span class="formula">\</span></td>
<td><tt class="docutils literal">\backslash</tt></td>
<td><span class="formula">⎪</span></td>
<td><tt class="docutils literal">\bracevert</tt></td>
</tr>
</tbody>
</table>
<p>The use of <tt class="docutils literal">|</tt> and <tt class="docutils literal">\|</tt> for pairs of vertical bars may produce
incorrect spacing, e.g., <tt class="docutils literal"><span class="pre">|k|=|-k|</span></tt> produces <span class="formula">|<i>k</i>| = | − <i>k</i>|</span> and
<tt class="docutils literal">|\sin(x)|</tt> produces <span class="formula">|sin(<i>x</i>)|</span>. The pairing delimiters, e.g.
<span class="formula">| − <i>k</i>|</span> and <span class="formula">|sin(<i>x</i>)|</span>, prevent this problem
(in LaTeX and MathJax).</p>
<!-- TODO: fix spacing before unary minus (see also cases example below). -->
</div>
</div>
<div class="section" id="extensible-vertical-arrows">
<h2><a class="toc-backref" href="#toc-entry-8">2.4 Extensible vertical arrows</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"> ↑ </span> <tt class="docutils literal">\uparrow</tt></td>
<td><span class="formula"> ⇑ </span> <tt class="docutils literal">\Uparrow</tt></td>
</tr>
<tr><td><span class="formula"> ↓ </span> <tt class="docutils literal">\downarrow</tt></td>
<td><span class="formula"> ⇓ </span> <tt class="docutils literal">\Downarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↕ </span> <tt class="docutils literal">\updownarrow</tt></td>
<td><span class="formula"> ⇕ </span> <tt class="docutils literal">\Updownarrow</tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="functions-named-operators">
<h2><a class="toc-backref" href="#toc-entry-9">2.5 Functions (named operators)</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">arccos</span></td>
<td><tt class="docutils literal">\arccos</tt></td>
<td><span class="formula">gcd</span></td>
<td><tt class="docutils literal">\gcd</tt></td>
<td><span class="formula">Pr</span></td>
<td><tt class="docutils literal">\Pr</tt></td>
</tr>
<tr><td><span class="formula">arcsin</span></td>
<td><tt class="docutils literal">\arcsin</tt></td>
<td><span class="formula">hom</span></td>
<td><tt class="docutils literal">\hom</tt></td>
<td><span class="formula">proj lim</span></td>
<td><tt class="docutils literal">\projlim</tt></td>
</tr>
<tr><td><span class="formula">arctan</span></td>
<td><tt class="docutils literal">\arctan</tt></td>
<td><span class="formula"><span class="limits"><span class="limit">inf</span></span></span></td>
<td><tt class="docutils literal">\inf</tt></td>
<td><span class="formula">sec</span></td>
<td><tt class="docutils literal">\sec</tt></td>
</tr>
<tr><td><span class="formula">arg</span></td>
<td><tt class="docutils literal">\arg</tt></td>
<td><span class="formula">inj lim</span></td>
<td><tt class="docutils literal">\injlim</tt></td>
<td><span class="formula">sin</span></td>
<td><tt class="docutils literal">\sin</tt></td>
</tr>
<tr><td><span class="formula">cos</span></td>
<td><tt class="docutils literal">\cos</tt></td>
<td><span class="formula">ker</span></td>
<td><tt class="docutils literal">\ker</tt></td>
<td><span class="formula">sinh</span></td>
<td><tt class="docutils literal">\sinh</tt></td>
</tr>
<tr><td><span class="formula">cosh</span></td>
<td><tt class="docutils literal">\cosh</tt></td>
<td><span class="formula">lg</span></td>
<td><tt class="docutils literal">\lg</tt></td>
<td><span class="formula"><span class="limits"><span class="limit">sup</span></span></span></td>
<td><tt class="docutils literal">\sup</tt></td>
</tr>
<tr><td><span class="formula">cot</span></td>
<td><tt class="docutils literal">\cot</tt></td>
<td><span class="formula"><span class="limits"><span class="limit">lim</span></span></span></td>
<td><tt class="docutils literal">\lim</tt></td>
<td><span class="formula">tan</span></td>
<td><tt class="docutils literal">\tan</tt></td>
</tr>
<tr><td><span class="formula">coth</span></td>
<td><tt class="docutils literal">\coth</tt></td>
<td><span class="formula">lim inf</span></td>
<td><tt class="docutils literal">\liminf</tt></td>
<td><span class="formula">tanh</span></td>
<td><tt class="docutils literal">\tanh</tt></td>
</tr>
<tr><td><span class="formula">csc</span></td>
<td><tt class="docutils literal">\csc</tt></td>
<td><span class="formula">lim sup</span></td>
<td><tt class="docutils literal">\limsup</tt></td>
<td><span class="formula"><span class="unknown">\varlimsup</span></span></td>
<td><tt class="docutils literal">\varlimsup</tt></td>
</tr>
<tr><td><span class="formula">deg</span></td>
<td><tt class="docutils literal">\deg</tt></td>
<td><span class="formula">ln</span></td>
<td><tt class="docutils literal">\ln</tt></td>
<td><span class="formula"><span class="unknown">\varliminf</span></span></td>
<td><tt class="docutils literal">\varliminf</tt></td>
</tr>
<tr><td><span class="formula">det</span></td>
<td><tt class="docutils literal">\det</tt></td>
<td><span class="formula">log</span></td>
<td><tt class="docutils literal">\log</tt></td>
<td><span class="formula"><span class="unknown">\varprojlim</span></span></td>
<td><tt class="docutils literal">\varprojlim</tt></td>
</tr>
<tr><td><span class="formula">dim</span></td>
<td><tt class="docutils literal">\dim</tt></td>
<td><span class="formula"><span class="limits"><span class="limit">max</span></span></span></td>
<td><tt class="docutils literal">\max</tt></td>
<td><span class="formula"><span class="unknown">\varinjlim</span></span></td>
<td><tt class="docutils literal">\varinjlim</tt></td>
</tr>
<tr><td><span class="formula">exp</span></td>
<td><tt class="docutils literal">\exp</tt></td>
<td><span class="formula"><span class="limits"><span class="limit">min</span></span></span></td>
<td><tt class="docutils literal">\min</tt></td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<p>Named operators outside the above list can be typeset with
<tt class="docutils literal">\operatorname{name}</tt>, e.g.</p>
<div class="formula">
<span class="mathrm">sgn</span>( − 3) = − 1.
</div>
<!-- TODO: \operatorname* for function name with limits. -->
<p>The <tt class="docutils literal">\DeclareMathOperator</tt> command can only be used in the
<a class="reference external" href="latex.html#latex-preamble">LaTeX preamble</a>.</p>
</div>
<div class="section" id="greek-letters">
<h2><a class="toc-backref" href="#toc-entry-10">2.6 Greek letters</a></h2>
<p>Greek letters that have Latin look-alikes are rarely used in math
formulas and not supported by LaTeX.</p>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">Γ</span></td>
<td><tt class="docutils literal">\Gamma</tt></td>
<td><span class="formula"><i>α</i></span></td>
<td><tt class="docutils literal">\alpha</tt></td>
<td><span class="formula"><i>μ</i></span></td>
<td><tt class="docutils literal">\mu</tt></td>
<td><span class="formula"><i>ω</i></span></td>
<td><tt class="docutils literal">\omega</tt></td>
</tr>
<tr><td><span class="formula">Δ</span></td>
<td><tt class="docutils literal">\Delta</tt></td>
<td><span class="formula"><i>β</i></span></td>
<td><tt class="docutils literal">\beta</tt></td>
<td><span class="formula"><i>ν</i></span></td>
<td><tt class="docutils literal">\nu</tt></td>
<td><span class="formula"><i>ϝ</i></span></td>
<td><tt class="docutils literal">\digamma</tt></td>
</tr>
<tr><td><span class="formula">Λ</span></td>
<td><tt class="docutils literal">\Lambda</tt></td>
<td><span class="formula"><i>γ</i></span></td>
<td><tt class="docutils literal">\gamma</tt></td>
<td><span class="formula"><i>ξ</i></span></td>
<td><tt class="docutils literal">\xi</tt></td>
<td><span class="formula"><i>ε</i></span></td>
<td><tt class="docutils literal">\varepsilon</tt></td>
</tr>
<tr><td><span class="formula">Φ</span></td>
<td><tt class="docutils literal">\Phi</tt></td>
<td><span class="formula"><i>δ</i></span></td>
<td><tt class="docutils literal">\delta</tt></td>
<td><span class="formula"><i>π</i></span></td>
<td><tt class="docutils literal">\pi</tt></td>
<td><span class="formula"><i>ϰ</i></span></td>
<td><tt class="docutils literal">\varkappa</tt></td>
</tr>
<tr><td><span class="formula">Π</span></td>
<td><tt class="docutils literal">\Pi</tt></td>
<td><span class="formula"><i>ϵ</i></span></td>
<td><tt class="docutils literal">\epsilon</tt></td>
<td><span class="formula"><i>ρ</i></span></td>
<td><tt class="docutils literal">\rho</tt></td>
<td><span class="formula"><i>φ</i></span></td>
<td><tt class="docutils literal">\varphi</tt></td>
</tr>
<tr><td><span class="formula">Ψ</span></td>
<td><tt class="docutils literal">\Psi</tt></td>
<td><span class="formula"><i>ζ</i></span></td>
<td><tt class="docutils literal">\zeta</tt></td>
<td><span class="formula"><i>σ</i></span></td>
<td><tt class="docutils literal">\sigma</tt></td>
<td><span class="formula"><i>ϖ</i></span></td>
<td><tt class="docutils literal">\varpi</tt></td>
</tr>
<tr><td><span class="formula">Σ</span></td>
<td><tt class="docutils literal">\Sigma</tt></td>
<td><span class="formula"><i>η</i></span></td>
<td><tt class="docutils literal">\eta</tt></td>
<td><span class="formula"><i>τ</i></span></td>
<td><tt class="docutils literal">\tau</tt></td>
<td><span class="formula"><i>ϱ</i></span></td>
<td><tt class="docutils literal">\varrho</tt></td>
</tr>
<tr><td><span class="formula">Θ</span></td>
<td><tt class="docutils literal">\Theta</tt></td>
<td><span class="formula"><i>θ</i></span></td>
<td><tt class="docutils literal">\theta</tt></td>
<td><span class="formula"><i>υ</i></span></td>
<td><tt class="docutils literal">\upsilon</tt></td>
<td><span class="formula"><i>ς</i></span></td>
<td><tt class="docutils literal">\varsigma</tt></td>
</tr>
<tr><td><span class="formula">Υ</span></td>
<td><tt class="docutils literal">\Upsilon</tt></td>
<td><span class="formula"><i>ι</i></span></td>
<td><tt class="docutils literal">\iota</tt></td>
<td><span class="formula"><i>ϕ</i></span></td>
<td><tt class="docutils literal">\phi</tt></td>
<td><span class="formula"><i>ϑ</i></span></td>
<td><tt class="docutils literal">\vartheta</tt></td>
</tr>
<tr><td><span class="formula">Ξ</span></td>
<td><tt class="docutils literal">\Xi</tt></td>
<td><span class="formula"><i>κ</i></span></td>
<td><tt class="docutils literal">\kappa</tt></td>
<td><span class="formula"><i>χ</i></span></td>
<td><tt class="docutils literal">\chi</tt></td>
<td> </td>
<td> </td>
</tr>
<tr><td><span class="formula">Ω</span></td>
<td><tt class="docutils literal">\Omega</tt></td>
<td><span class="formula"><i>λ</i></span></td>
<td><tt class="docutils literal">\lambda</tt></td>
<td><span class="formula"><i>ψ</i></span></td>
<td><tt class="docutils literal">\psi</tt></td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<p>In LaTeX, the default font for capital Greek letters is upright/roman.
<em>Italic</em> capital Greek letters can be obtained by loading a <a class="reference external" href="https://mirrors.ctan.org/macros/latex/contrib/isomath/isomath.html#table-2">package
providing the "ISO" math style</a>. They are used by default in MathML.</p>
<p>Individual Greek italic capitals can also be achieved preceding the
letter name with <tt class="docutils literal">var</tt> like <tt class="docutils literal">\varPhi</tt>:
<span class="formula"><i>𝛤</i> <i>𝛥</i> <i>𝛬</i> <i>𝛷</i> <i>𝛱</i> <i>𝛹</i> <i>𝛴</i> <i>𝛩</i> <i>𝛶</i> <i>𝛯</i> <i>𝛺</i></span></p>
</div>
<div class="section" id="letterlike-symbols">
<h2><a class="toc-backref" href="#toc-entry-11">2.7 Letterlike symbols</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">∀</span></td>
<td><tt class="docutils literal">\forall</tt></td>
<td><span class="formula"><i>ℵ</i></span></td>
<td><tt class="docutils literal">\aleph</tt></td>
<td><span class="formula"><i>ħ</i></span></td>
<td><tt class="docutils literal">\hbar</tt></td>
<td><span class="formula"><i>ℓ</i></span></td>
<td><tt class="docutils literal">\ell</tt></td>
</tr>
<tr><td><span class="formula">∁</span></td>
<td><tt class="docutils literal">\complement</tt></td>
<td><span class="formula"><i>ℶ</i></span></td>
<td><tt class="docutils literal">\beth</tt></td>
<td><span class="formula"><i>ℏ</i></span></td>
<td><tt class="docutils literal">\hslash</tt></td>
<td><span class="formula"><i>℘</i></span></td>
<td><tt class="docutils literal">\wp</tt></td>
</tr>
<tr><td><span class="formula">∃</span></td>
<td><tt class="docutils literal">\exists</tt></td>
<td><span class="formula"><i>ℷ</i></span></td>
<td><tt class="docutils literal">\gimel</tt></td>
<td><span class="formula"><i>ℑ</i></span></td>
<td><tt class="docutils literal">\Im</tt></td>
<td><span class="formula"><i>ℜ</i></span></td>
<td><tt class="docutils literal">\Re</tt></td>
</tr>
<tr><td><span class="formula">Ⅎ</span></td>
<td><tt class="docutils literal">\Finv</tt></td>
<td><span class="formula"><i>ℸ</i></span></td>
<td><tt class="docutils literal">\daleth</tt></td>
<td><span class="formula"><i>ı</i></span></td>
<td><tt class="docutils literal">\imath</tt></td>
<td><span class="formula">Ⓡ</span></td>
<td><tt class="docutils literal">\circledR</tt></td>
</tr>
<tr><td><span class="formula">⅁</span></td>
<td><tt class="docutils literal">\Game</tt></td>
<td><span class="formula">∂</span></td>
<td><tt class="docutils literal">\partial</tt></td>
<td><span class="formula"><i>ȷ</i></span></td>
<td><tt class="docutils literal">\jmath</tt></td>
<td><span class="formula">Ⓢ</span></td>
<td><tt class="docutils literal">\circledS</tt></td>
</tr>
<tr><td><span class="formula">℧</span></td>
<td><tt class="docutils literal">\mho</tt></td>
<td><span class="formula"><i>ð</i></span></td>
<td><tt class="docutils literal">\eth</tt></td>
<td><span class="formula"><i>𝕜</i></span></td>
<td><tt class="docutils literal">\Bbbk</tt></td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="mathematical-alphabets">
<h2><a class="toc-backref" href="#toc-entry-12">2.8 Mathematical Alphabets</a></h2>
<p>Mathematical alphabets select a combination of font attributes (shape,
weight, family) <a class="footnote-reference" href="#footnote-1" id="footnote-reference-3">[2]</a>. They are intended for mathematical variables where
style variations are important semantically.</p>
<table border="1" class="docutils">
<thead valign="bottom">
<tr><th class="head">command</th>
<th class="head">example</th>
<th class="head">result</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal">\mathbf</tt></td>
<td><tt class="docutils literal"><span class="pre">\mathbf{r}^2=x^2+y^2+z^2</span></tt></td>
<td><span class="formula"><b>r</b><sup>2</sup> = <i>x</i><sup>2</sup> + <i>y</i><sup>2</sup> + <i>z</i><sup>2</sup></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathbb</tt></td>
<td><tt class="docutils literal">\mathbb{R \subset C}</tt></td>
<td><span class="formula"><span class="blackboard">R ⊂ C</span></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathcal</tt></td>
<td><tt class="docutils literal">\mathcal{F}f(x)</tt></td>
<td><span class="formula">ℱ<i>f</i>(<i>x</i>)</span></td>
</tr>
<tr><td><tt class="docutils literal">\mathfrak</tt></td>
<td><tt class="docutils literal">\mathfrak{a}</tt></td>
<td><span class="formula"><span class="fraktur">a</span></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathit</tt></td>
<td><tt class="docutils literal"><span class="pre">\mathit{\Gamma}</span></tt></td>
<td><span class="formula"><i>Γ</i></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathrm</tt></td>
<td><tt class="docutils literal">s_\mathrm{out}</tt></td>
<td><span class="formula"><i>s</i><sub><span class="mathrm">out</span></sub></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathsf</tt></td>
<td><tt class="docutils literal">\mathsf x</tt></td>
<td><span class="formula"><span class="mathsf">x</span></span></td>
</tr>
<tr><td><tt class="docutils literal">\mathtt</tt></td>
<td><tt class="docutils literal">\mathtt{0.12}</tt></td>
<td><span class="formula"><span class="mathtt">0.12</span></span></td>
</tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="footnote-1" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-3">[2]</a></td><td>TeX’s <em>math alphabets</em> correspond to the <a class="reference external" href="https://en.wikipedia.org/wiki/Mathematical_Alphanumeric_Symbols">mathematical
alphanumeric symbols</a> block in Unicode and the "mathvariant" <a class="reference external" href="https://developer.mozilla.org/en-US/docs/Web/MathML/Attribute">style
attribute</a> in MathML.</td></tr>
</tbody>
</table>
<p>Additional alphabets are defined in LaTeX packages, e.g.</p>
<table border="1" class="docutils">
<thead valign="bottom">
<tr><th class="head">TeX command</th>
<th class="head">LaTeX package</th>
<th class="head">MathML "mathvariant"</th>
</tr>
</thead>
<tbody valign="top">
<tr><td>mathbfit</td>
<td><a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a></td>
<td>bold-italic</td>
</tr>
<tr><td>mathsfit</td>
<td><a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a></td>
<td>sans-serif-italic</td>
</tr>
<tr><td>mathsfbfit</td>
<td><a class="reference external" href="https://www.ctan.org/pkg/isomath">isomath</a></td>
<td>sans-serif-bold-italic</td>
</tr>
<tr><td>mathscr</td>
<td><a class="reference external" href="https://www.ctan.org/pkg/mathrsfs">mathrsfs</a></td>
<td>script</td>
</tr>
</tbody>
</table>
<p>This can be used to typeset vector symbols in bold italic
in line with the International Standard [ISO-80000-2].</p>
<!-- ``\mathbfit{r}^2=x^2+y^2+z^2`` becomes
.. math:: \mathbfit{r}^2=x^2+y^2+z^2. -->
<p>The package <a class="reference external" href="https://www.ctan.org/pkg/mathrsfs">mathrsfs</a> (and some drop-in replacements) define the <tt class="docutils literal">\mathscr</tt>
macro that selects a differently shaped "script" alphabet.
Compare <span class="formula"><span class="mathscr">A, B, …, Z, a, b, …, z</span></span>
with <span class="formula"><span class="scriptfont">A, B, …, Z, a, b, …, z</span></span>.</p>
<p>In contrast to the math alphabet selectors, <tt class="docutils literal">\boldsymbol</tt> only changes
the <em>font weight</em>. In LaTeX, it can be used to get a bold version of any
mathematical symbol (for other output formats, results are mixed):</p>
<div class="formula">
<b>cos(x)±α ≈ 3Γ ∀x ∈ ℝ</b>
</div>
</div>
<div class="section" id="miscellaneous-symbols">
<h2><a class="toc-backref" href="#toc-entry-13">2.9 Miscellaneous symbols</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">#</span></td>
<td><tt class="docutils literal">\#</tt></td>
<td><span class="formula">♣</span></td>
<td><tt class="docutils literal">\clubsuit</tt></td>
<td><span class="formula">¬</span></td>
<td><tt class="docutils literal">\neg</tt></td>
</tr>
<tr><td><span class="formula">&</span></td>
<td><tt class="docutils literal">\&</tt></td>
<td><span class="formula">♢</span></td>
<td><tt class="docutils literal">\diamondsuit</tt></td>
<td><span class="formula">∄</span></td>
<td><tt class="docutils literal">\nexists</tt></td>
</tr>
<tr><td><span class="formula">∠</span></td>
<td><tt class="docutils literal">\angle</tt></td>
<td><span class="formula">∅</span></td>
<td><tt class="docutils literal">\emptyset</tt></td>
<td><span class="formula">′</span></td>
<td><tt class="docutils literal">\prime</tt></td>
</tr>
<tr><td><span class="formula">‵</span></td>
<td><tt class="docutils literal">\backprime</tt></td>
<td><span class="formula">∃</span></td>
<td><tt class="docutils literal">\exists</tt></td>
<td><span class="formula">♯</span></td>
<td><tt class="docutils literal">\sharp</tt></td>
</tr>
<tr><td><span class="formula">★</span></td>
<td><tt class="docutils literal">\bigstar</tt></td>
<td><span class="formula">♭</span></td>
<td><tt class="docutils literal">\flat</tt></td>
<td><span class="formula">♠</span></td>
<td><tt class="docutils literal">\spadesuit</tt></td>
</tr>
<tr><td><span class="formula">⧫</span></td>
<td><tt class="docutils literal">\blacklozenge</tt></td>
<td><span class="formula">∀</span></td>
<td><tt class="docutils literal">\forall</tt></td>
<td><span class="formula">∢</span></td>
<td><tt class="docutils literal">\sphericalangle</tt></td>
</tr>
<tr><td><span class="formula">◼</span></td>
<td><tt class="docutils literal">\blacksquare</tt></td>
<td><span class="formula">♡</span></td>
<td><tt class="docutils literal">\heartsuit</tt></td>
<td><span class="formula">◻</span></td>
<td><tt class="docutils literal">\square</tt></td>
</tr>
<tr><td><span class="formula">▴</span></td>
<td><tt class="docutils literal">\blacktriangle</tt></td>
<td><span class="formula">∞</span></td>
<td><tt class="docutils literal">\infty</tt></td>
<td><span class="formula">√</span></td>
<td><tt class="docutils literal">\surd</tt></td>
</tr>
<tr><td><span class="formula">▾</span></td>
<td><tt class="docutils literal">\blacktriangledown</tt></td>
<td><span class="formula">◊</span></td>
<td><tt class="docutils literal">\lozenge</tt></td>
<td><span class="formula">⊤</span></td>
<td><tt class="docutils literal">\top</tt></td>
</tr>
<tr><td><span class="formula">⊥</span></td>
<td><tt class="docutils literal">\bot</tt></td>
<td><span class="formula">∡</span></td>
<td><tt class="docutils literal">\measuredangle</tt></td>
<td><span class="formula">△</span></td>
<td><tt class="docutils literal">\triangle</tt></td>
</tr>
<tr><td><span class="formula">⟍</span></td>
<td><tt class="docutils literal">\diagdown</tt></td>
<td><span class="formula">∇</span></td>
<td><tt class="docutils literal">\nabla</tt></td>
<td><span class="formula">▽</span></td>
<td><tt class="docutils literal">\triangledown</tt></td>
</tr>
<tr><td><span class="formula">⟋</span></td>
<td><tt class="docutils literal">\diagup</tt></td>
<td><span class="formula">♮</span></td>
<td><tt class="docutils literal">\natural</tt></td>
<td><span class="formula">⌀</span></td>
<td><tt class="docutils literal">\varnothing</tt></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="punctuation">
<h2><a class="toc-backref" href="#toc-entry-14">2.10 Punctuation</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula">.</span></td>
<td><tt class="docutils literal">.</tt></td>
<td><span class="formula">!</span></td>
<td><tt class="docutils literal">!</tt></td>
<td><span class="formula">⋮</span></td>
<td><tt class="docutils literal">\vdots</tt></td>
</tr>
<tr><td><span class="formula"> ⁄ </span></td>
<td><tt class="docutils literal">/</tt></td>
<td><span class="formula">?</span></td>
<td><tt class="docutils literal">?</tt></td>
<td><span class="formula">⋯</span></td>
<td><tt class="docutils literal">\dotsb</tt></td>
</tr>
<tr><td><span class="formula">|</span></td>
<td><tt class="docutils literal">|</tt></td>
<td><span class="formula">: </span></td>
<td><tt class="docutils literal">\colon</tt> <a class="footnote-reference" href="#footnote-2" id="footnote-reference-4">[3]</a></td>
<td><span class="formula">…</span></td>
<td><tt class="docutils literal">\dotsc</tt></td>
</tr>
<tr><td><span class="formula">’</span></td>
<td><tt class="docutils literal">'</tt></td>
<td><span class="formula">⋯</span></td>
<td><tt class="docutils literal">\cdots</tt></td>
<td><span class="formula">⋯</span></td>
<td><tt class="docutils literal">\dotsi</tt></td>
</tr>
<tr><td><span class="formula">;</span></td>
<td><tt class="docutils literal">;</tt></td>
<td><span class="formula">⋱</span></td>
<td><tt class="docutils literal">\ddots</tt></td>
<td><span class="formula">⋯</span></td>
<td><tt class="docutils literal">\dotsm</tt></td>
</tr>
<tr><td><span class="formula"> : </span></td>
<td><tt class="docutils literal">:</tt></td>
<td><span class="formula">…</span></td>
<td><tt class="docutils literal">\ldots</tt></td>
<td><span class="formula">…</span></td>
<td><tt class="docutils literal">\dotso</tt></td>
</tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="footnote-2" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-4">[3]</a></td><td>Punctuation (not ratio):
Compare spacing in <span class="formula"><i>a</i>: <i>b</i> → <i>c</i></span> to <span class="formula"><i>a</i> : <i>b</i> = <i>c</i></span>.</td></tr>
</tbody>
</table>
</div>
<div class="section" id="relation-symbols">
<h2><a class="toc-backref" href="#toc-entry-15">2.11 Relation symbols</a></h2>
<div class="section" id="arrows">
<h3><a class="toc-backref" href="#toc-entry-16">2.11.1 Arrows</a></h3>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"> ↺ </span></td>
<td><tt class="docutils literal">\circlearrowleft</tt></td>
<td><span class="formula"> ↻ </span></td>
<td><tt class="docutils literal">\circlearrowright</tt></td>
</tr>
<tr><td><span class="formula"> ↶ </span></td>
<td><tt class="docutils literal">\curvearrowleft</tt></td>
<td><span class="formula"> ↷ </span></td>
<td><tt class="docutils literal">\curvearrowright</tt></td>
</tr>
<tr><td><span class="formula"> ↩ </span></td>
<td><tt class="docutils literal">\hookleftarrow</tt></td>
<td><span class="formula"> ↪ </span></td>
<td><tt class="docutils literal">\hookrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ← </span></td>
<td><tt class="docutils literal">\leftarrow</tt></td>
<td><span class="formula"> → </span></td>
<td><tt class="docutils literal">\rightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⇐ </span></td>
<td><tt class="docutils literal">\Leftarrow</tt></td>
<td><span class="formula"> ⇒ </span></td>
<td><tt class="docutils literal">\Rightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↢ </span></td>
<td><tt class="docutils literal">\leftarrowtail</tt></td>
<td><span class="formula"> ↣ </span></td>
<td><tt class="docutils literal">\rightarrowtail</tt></td>
</tr>
<tr><td><span class="formula"> ↽ </span></td>
<td><tt class="docutils literal">\leftharpoondown</tt></td>
<td><span class="formula"> ⇁ </span></td>
<td><tt class="docutils literal">\rightharpoondown</tt></td>
</tr>
<tr><td><span class="formula"> ↼ </span></td>
<td><tt class="docutils literal">\leftharpoonup</tt></td>
<td><span class="formula"> ⇀ </span></td>
<td><tt class="docutils literal">\rightharpoonup</tt></td>
</tr>
<tr><td><span class="formula"> ⇇ </span></td>
<td><tt class="docutils literal">\leftleftarrows</tt></td>
<td><span class="formula"> ⇉ </span></td>
<td><tt class="docutils literal">\rightrightarrows</tt></td>
</tr>
<tr><td><span class="formula"> ↔ </span></td>
<td><tt class="docutils literal">\leftrightarrow</tt></td>
<td><span class="formula"> ⇔ </span></td>
<td><tt class="docutils literal">\Leftrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⇆ </span></td>
<td><tt class="docutils literal">\leftrightarrows</tt></td>
<td><span class="formula"> ⇄ </span></td>
<td><tt class="docutils literal">\rightleftarrows</tt></td>
</tr>
<tr><td><span class="formula"> ⇋ </span></td>
<td><tt class="docutils literal">\leftrightharpoons</tt></td>
<td><span class="formula"> ⇌ </span></td>
<td><tt class="docutils literal">\rightleftharpoons</tt></td>
</tr>
<tr><td><span class="formula"> ↭ </span></td>
<td><tt class="docutils literal">\leftrightsquigarrow</tt></td>
<td><span class="formula"> ⇝ </span></td>
<td><tt class="docutils literal">\rightsquigarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⇚ </span></td>
<td><tt class="docutils literal">\Lleftarrow</tt></td>
<td><span class="formula"> ⇛ </span></td>
<td><tt class="docutils literal">\Rrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⟵ </span></td>
<td><tt class="docutils literal">\longleftarrow</tt></td>
<td><span class="formula"> ⟶ </span></td>
<td><tt class="docutils literal">\longrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⟸ </span></td>
<td><tt class="docutils literal">\Longleftarrow</tt></td>
<td><span class="formula"> ⟹ </span></td>
<td><tt class="docutils literal">\Longrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⟷ </span></td>
<td><tt class="docutils literal">\longleftrightarrow</tt></td>
<td><span class="formula"> ⟺ </span></td>
<td><tt class="docutils literal">\Longleftrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↫ </span></td>
<td><tt class="docutils literal">\looparrowleft</tt></td>
<td><span class="formula"> ↬ </span></td>
<td><tt class="docutils literal">\looparrowright</tt></td>
</tr>
<tr><td><span class="formula"> ↰ </span></td>
<td><tt class="docutils literal">\Lsh</tt></td>
<td><span class="formula"> ↱ </span></td>
<td><tt class="docutils literal">\Rsh</tt></td>
</tr>
<tr><td><span class="formula"> ↦ </span></td>
<td><tt class="docutils literal">\mapsto</tt></td>
<td><span class="formula"> ⟼ </span></td>
<td><tt class="docutils literal">\longmapsto</tt></td>
</tr>
<tr><td><span class="formula"> ⊸ </span></td>
<td><tt class="docutils literal">\multimap</tt></td>
<td> </td>
<td> </td>
</tr>
<tr><td><span class="formula"> ↚ </span></td>
<td><tt class="docutils literal">\nleftarrow</tt></td>
<td><span class="formula"> ↛ </span></td>
<td><tt class="docutils literal">\nrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ⇍ </span></td>
<td><tt class="docutils literal">\nLeftarrow</tt></td>
<td><span class="formula"> ⇏ </span></td>
<td><tt class="docutils literal">\nRightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↮ </span></td>
<td><tt class="docutils literal">\nleftrightarrow</tt></td>
<td><span class="formula"> ⇎ </span></td>
<td><tt class="docutils literal">\nLeftrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↖ </span></td>
<td><tt class="docutils literal">\nwarrow</tt></td>
<td><span class="formula"> ↗ </span></td>
<td><tt class="docutils literal">\nearrow</tt></td>
</tr>
<tr><td><span class="formula"> ↙ </span></td>
<td><tt class="docutils literal">\swarrow</tt></td>
<td><span class="formula"> ↘ </span></td>
<td><tt class="docutils literal">\searrow</tt></td>
</tr>
<tr><td><span class="formula"> ↞ </span></td>
<td><tt class="docutils literal">\twoheadleftarrow</tt></td>
<td><span class="formula"> ↠ </span></td>
<td><tt class="docutils literal">\twoheadrightarrow</tt></td>
</tr>
<tr><td><span class="formula"> ↿ </span></td>
<td><tt class="docutils literal">\upharpoonleft</tt></td>
<td><span class="formula"> ↾ </span></td>
<td><tt class="docutils literal">\upharpoonright</tt></td>
</tr>
<tr><td><span class="formula"> ⇃ </span></td>
<td><tt class="docutils literal">\downharpoonleft</tt></td>
<td><span class="formula"> ⇂ </span></td>
<td><tt class="docutils literal">\downharpoonright</tt></td>
</tr>
<tr><td><span class="formula"> ⇈ </span></td>
<td><tt class="docutils literal">\upuparrows</tt></td>
<td><span class="formula"> ⇊ </span></td>
<td><tt class="docutils literal">\downdownarrows</tt></td>
</tr>
</tbody>
</table>
<p>Synonyms: <span class="formula"> ← </span> <tt class="docutils literal">\gets</tt>, <span class="formula"> → </span> <tt class="docutils literal">\to</tt>, <span class="formula"> ↾ </span> <tt class="docutils literal">\restriction</tt>.</p>
</div>
<div class="section" id="comparison">
<h3><a class="toc-backref" href="#toc-entry-17">2.11.2 Comparison</a></h3>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"> < </span></td>
<td><tt class="docutils literal"><</tt></td>
<td><span class="formula"> ≥ </span></td>
<td><tt class="docutils literal">\geq</tt></td>
<td><span class="formula"> ≪ </span></td>
<td><tt class="docutils literal">\ll</tt></td>
<td><span class="formula"> ≺ </span></td>
<td><tt class="docutils literal">\prec</tt></td>
</tr>
<tr><td><span class="formula"> = </span></td>
<td><tt class="docutils literal">=</tt></td>
<td><span class="formula"> ≧ </span></td>
<td><tt class="docutils literal">\geqq</tt></td>
<td><span class="formula"> ⋘ </span></td>
<td><tt class="docutils literal">\lll</tt></td>
<td><span class="formula"> ⪷ </span></td>
<td><tt class="docutils literal">\precapprox</tt></td>
</tr>
<tr><td><span class="formula"> > </span></td>
<td><tt class="docutils literal">></tt></td>
<td><span class="formula"> ⩾ </span></td>
<td><tt class="docutils literal">\geqslant</tt></td>
<td><span class="formula"> ⪉ </span></td>
<td><tt class="docutils literal">\lnapprox</tt></td>
<td><span class="formula"> ≼ </span></td>
<td><tt class="docutils literal">\preccurlyeq</tt></td>
</tr>
<tr><td><span class="formula"> ≈ </span></td>
<td><tt class="docutils literal">\approx</tt></td>
<td><span class="formula"> ≫ </span></td>
<td><tt class="docutils literal">\gg</tt></td>
<td><span class="formula"> ⪇ </span></td>
<td><tt class="docutils literal">\lneq</tt></td>
<td><span class="formula"> ⪯ </span></td>
<td><tt class="docutils literal">\preceq</tt></td>
</tr>
<tr><td><span class="formula"> ≊ </span></td>
<td><tt class="docutils literal">\approxeq</tt></td>
<td><span class="formula"> ⋙ </span></td>
<td><tt class="docutils literal">\ggg</tt></td>
<td><span class="formula"> ≨ </span></td>
<td><tt class="docutils literal">\lneqq</tt></td>
<td><span class="formula"> ⪹ </span></td>
<td><tt class="docutils literal">\precnapprox</tt></td>
</tr>
<tr><td><span class="formula"> ≍ </span></td>
<td><tt class="docutils literal">\asymp</tt></td>
<td><span class="formula"> ⪊ </span></td>
<td><tt class="docutils literal">\gnapprox</tt></td>
<td><span class="formula"> ⋦ </span></td>
<td><tt class="docutils literal">\lnsim</tt></td>
<td><span class="formula"> ⪵ </span></td>
<td><tt class="docutils literal">\precneqq</tt></td>
</tr>
<tr><td><span class="formula"> ∽ </span></td>
<td><tt class="docutils literal">\backsim</tt></td>
<td><span class="formula"> ⪈ </span></td>
<td><tt class="docutils literal">\gneq</tt></td>
<td><span class="formula"> ≇ </span></td>
<td><tt class="docutils literal">\ncong</tt></td>
<td><span class="formula"> ⋨ </span></td>
<td><tt class="docutils literal">\precnsim</tt></td>
</tr>
<tr><td><span class="formula"> ⋍ </span></td>
<td><tt class="docutils literal">\backsimeq</tt></td>
<td><span class="formula"> ≩ </span></td>
<td><tt class="docutils literal">\gneqq</tt></td>
<td><span class="formula"> ≠ </span></td>
<td><tt class="docutils literal">\neq</tt></td>
<td><span class="formula"> ≾ </span></td>
<td><tt class="docutils literal">\precsim</tt></td>
</tr>
<tr><td><span class="formula"> ≏ </span></td>
<td><tt class="docutils literal">\bumpeq</tt></td>
<td><span class="formula"> ⋧ </span></td>
<td><tt class="docutils literal">\gnsim</tt></td>
<td><span class="formula"> ≱ </span></td>
<td><tt class="docutils literal">\ngeq</tt></td>
<td><span class="formula"> ≓ </span></td>
<td><tt class="docutils literal">\risingdotseq</tt></td>
</tr>
<tr><td><span class="formula"> ≎ </span></td>
<td><tt class="docutils literal">\Bumpeq</tt></td>
<td><span class="formula"> ⪆ </span></td>
<td><tt class="docutils literal">\gtrapprox</tt></td>
<td><span class="formula"> ≧̸ </span></td>
<td><tt class="docutils literal">\ngeqq</tt></td>
<td><span class="formula"> ∼ </span></td>
<td><tt class="docutils literal">\sim</tt></td>
</tr>
<tr><td><span class="formula"> ≗ </span></td>
<td><tt class="docutils literal">\circeq</tt></td>
<td><span class="formula"> ⋛ </span></td>
<td><tt class="docutils literal">\gtreqless</tt></td>
<td><span class="formula"> ⩾̸ </span></td>
<td><tt class="docutils literal">\ngeqslant</tt></td>
<td><span class="formula"> ≃ </span></td>
<td><tt class="docutils literal">\simeq</tt></td>
</tr>
<tr><td><span class="formula"> ≅ </span></td>
<td><tt class="docutils literal">\cong</tt></td>
<td><span class="formula"> ⪌ </span></td>
<td><tt class="docutils literal">\gtreqqless</tt></td>
<td><span class="formula"> ≯ </span></td>
<td><tt class="docutils literal">\ngtr</tt></td>
<td><span class="formula"> ≻ </span></td>
<td><tt class="docutils literal">\succ</tt></td>
</tr>
<tr><td><span class="formula"> ⋞ </span></td>
<td><tt class="docutils literal">\curlyeqprec</tt></td>
<td><span class="formula"> ≷ </span></td>
<td><tt class="docutils literal">\gtrless</tt></td>
<td><span class="formula"> ≰ </span></td>
<td><tt class="docutils literal">\nleq</tt></td>
<td><span class="formula"> ⪸ </span></td>
<td><tt class="docutils literal">\succapprox</tt></td>
</tr>
<tr><td><span class="formula"> ⋟ </span></td>
<td><tt class="docutils literal">\curlyeqsucc</tt></td>
<td><span class="formula"> ≳ </span></td>
<td><tt class="docutils literal">\gtrsim</tt></td>
<td><span class="formula"> ≦̸ </span></td>
<td><tt class="docutils literal">\nleqq</tt></td>
<td><span class="formula"> ≽ </span></td>
<td><tt class="docutils literal">\succcurlyeq</tt></td>
</tr>
<tr><td><span class="formula"> ≐ </span></td>
<td><tt class="docutils literal">\doteq</tt></td>
<td><span class="formula"> ≤ </span></td>
<td><tt class="docutils literal">\leq</tt></td>
<td><span class="formula"> ⩽̸ </span></td>
<td><tt class="docutils literal">\nleqslant</tt></td>
<td><span class="formula"> ⪰ </span></td>
<td><tt class="docutils literal">\succeq</tt></td>
</tr>
<tr><td><span class="formula"> ≑ </span></td>
<td><tt class="docutils literal">\doteqdot</tt></td>
<td><span class="formula"> ≦ </span></td>
<td><tt class="docutils literal">\leqq</tt></td>
<td><span class="formula"> ≮ </span></td>
<td><tt class="docutils literal">\nless</tt></td>
<td><span class="formula"> ⪺ </span></td>
<td><tt class="docutils literal">\succnapprox</tt></td>
</tr>
<tr><td><span class="formula"> ≖ </span></td>
<td><tt class="docutils literal">\eqcirc</tt></td>
<td><span class="formula"> ⩽ </span></td>
<td><tt class="docutils literal">\leqslant</tt></td>
<td><span class="formula"> ⊀ </span></td>
<td><tt class="docutils literal">\nprec</tt></td>
<td><span class="formula"> ⪶ </span></td>
<td><tt class="docutils literal">\succneqq</tt></td>
</tr>
<tr><td><span class="formula"> ≂ </span></td>
<td><tt class="docutils literal">\eqsim</tt></td>
<td><span class="formula"> ⪅ </span></td>
<td><tt class="docutils literal">\lessapprox</tt></td>
<td><span class="formula"> ⋠ </span></td>
<td><tt class="docutils literal">\npreceq</tt></td>
<td><span class="formula"> ⋩ </span></td>
<td><tt class="docutils literal">\succnsim</tt></td>
</tr>
<tr><td><span class="formula"> ⪖ </span></td>
<td><tt class="docutils literal">\eqslantgtr</tt></td>
<td><span class="formula"> ⋚ </span></td>
<td><tt class="docutils literal">\lesseqgtr</tt></td>
<td><span class="formula"> ≁ </span></td>
<td><tt class="docutils literal">\nsim</tt></td>
<td><span class="formula"> ≿ </span></td>
<td><tt class="docutils literal">\succsim</tt></td>
</tr>
<tr><td><span class="formula"> ⪕ </span></td>
<td><tt class="docutils literal">\eqslantless</tt></td>
<td><span class="formula"> ⪋ </span></td>
<td><tt class="docutils literal">\lesseqqgtr</tt></td>
<td><span class="formula"> ⊁ </span></td>
<td><tt class="docutils literal">\nsucc</tt></td>
<td><span class="formula"> <span class="boldsymbol">≈</span> </span></td>
<td><tt class="docutils literal">\thickapprox</tt></td>
</tr>
<tr><td><span class="formula"> ≡ </span></td>
<td><tt class="docutils literal">\equiv</tt></td>
<td><span class="formula"> ≶ </span></td>
<td><tt class="docutils literal">\lessgtr</tt></td>
<td><span class="formula"> ⋡ </span></td>
<td><tt class="docutils literal">\nsucceq</tt></td>
<td><span class="formula"> <span class="boldsymbol">∼</span> </span></td>
<td><tt class="docutils literal">\thicksim</tt></td>
</tr>
<tr><td><span class="formula"> ≒ </span></td>
<td><tt class="docutils literal">\fallingdotseq</tt></td>
<td><span class="formula"> ≲ </span></td>
<td><tt class="docutils literal">\lesssim</tt></td>
<td> </td>
<td> </td>
<td><span class="formula"> ≜ </span></td>
<td><tt class="docutils literal">\triangleq</tt></td>
</tr>
</tbody>
</table>
<p>The commands <tt class="docutils literal">\lvertneqq</tt> and <tt class="docutils literal">\gvertneqq</tt> are not supported by
LateX2MathML, as there is no corresponding Unicode character.</p>
<p>Synonyms: <span class="formula"> ≠ </span> <tt class="docutils literal">\ne</tt>, <span class="formula"> ≤ </span> <tt class="docutils literal">\le</tt>, <span class="formula"> ≥ </span> <tt class="docutils literal">\ge</tt>,
<span class="formula"> ≑ </span> <tt class="docutils literal">\Doteq</tt>, <span class="formula"> ⋘ </span> <tt class="docutils literal">\llless</tt>, <span class="formula"> ⋙ </span> <tt class="docutils literal">\gggtr</tt>.</p>
<p>Symbols can be negated prepending <tt class="docutils literal">\not</tt>, e.g.
<span class="formula"> ≠ </span> <tt class="docutils literal">\not=</tt>, <span class="formula"> ≢ </span> <tt class="docutils literal">\not\equiv</tt>,
<span class="formula"> ≹ </span> <tt class="docutils literal">\not\gtrless</tt>, <span class="formula"> ≸ </span> <tt class="docutils literal">\not\lessgtr</tt>.</p>
</div>
<div class="section" id="miscellaneous-relations">
<h3><a class="toc-backref" href="#toc-entry-18">2.11.3 Miscellaneous relations</a></h3>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"> ∍ </span></td>
<td><tt class="docutils literal">\backepsilon</tt></td>
<td><span class="formula"> ⋬ </span></td>
<td><tt class="docutils literal">\ntrianglelefteq</tt></td>
<td><span class="formula"> ⊆ </span></td>
<td><tt class="docutils literal">\subseteq</tt></td>
</tr>
<tr><td><span class="formula"> ∵ </span></td>
<td><tt class="docutils literal">\because</tt></td>
<td><span class="formula"> ⋫ </span></td>
<td><tt class="docutils literal">\ntriangleright</tt></td>
<td><span class="formula"> ⫅ </span></td>
<td><tt class="docutils literal">\subseteqq</tt></td>
</tr>
<tr><td><span class="formula"> ≬ </span></td>
<td><tt class="docutils literal">\between</tt></td>
<td><span class="formula"> ⋭ </span></td>
<td><tt class="docutils literal">\ntrianglerighteq</tt></td>
<td><span class="formula"> ⊊ </span></td>
<td><tt class="docutils literal">\subsetneq</tt></td>
</tr>
<tr><td><span class="formula"> ◂ </span></td>
<td><tt class="docutils literal">\blacktriangleleft</tt></td>
<td><span class="formula"> ⊬ </span></td>
<td><tt class="docutils literal">\nvdash</tt></td>
<td><span class="formula"> ⫋ </span></td>
<td><tt class="docutils literal">\subsetneqq</tt></td>
</tr>
<tr><td><span class="formula"> ▸ </span></td>
<td><tt class="docutils literal">\blacktriangleright</tt></td>
<td><span class="formula"> ⊮ </span></td>
<td><tt class="docutils literal">\nVdash</tt></td>
<td><span class="formula"> ⊃ </span></td>
<td><tt class="docutils literal">\supset</tt></td>
</tr>
<tr><td><span class="formula"> ⋈ </span></td>
<td><tt class="docutils literal">\bowtie</tt></td>
<td><span class="formula"> ⊭ </span></td>
<td><tt class="docutils literal">\nvDash</tt></td>
<td><span class="formula"> ⋑ </span></td>
<td><tt class="docutils literal">\Supset</tt></td>
</tr>
<tr><td><span class="formula"> ⊣ </span></td>
<td><tt class="docutils literal">\dashv</tt></td>
<td><span class="formula"> ⊯ </span></td>
<td><tt class="docutils literal">\nVDash</tt></td>
<td><span class="formula"> ⊇ </span></td>
<td><tt class="docutils literal">\supseteq</tt></td>
</tr>
<tr><td><span class="formula"> ⌢ </span></td>
<td><tt class="docutils literal">\frown</tt></td>
<td><span class="formula"> ∥ </span></td>
<td><tt class="docutils literal">\parallel</tt></td>
<td><span class="formula"> ⫆ </span></td>
<td><tt class="docutils literal">\supseteqq</tt></td>
</tr>
<tr><td><span class="formula"> ∈ </span></td>
<td><tt class="docutils literal">\in</tt></td>
<td><span class="formula"> ⟂ </span></td>
<td><tt class="docutils literal">\perp</tt></td>
<td><span class="formula"> ⊋ </span></td>
<td><tt class="docutils literal">\supsetneq</tt></td>
</tr>
<tr><td><span class="formula"> ∣ </span></td>
<td><tt class="docutils literal">\mid</tt></td>
<td><span class="formula"> ⋔ </span></td>
<td><tt class="docutils literal">\pitchfork</tt></td>
<td><span class="formula"> ⫌ </span></td>
<td><tt class="docutils literal">\supsetneqq</tt></td>
</tr>
<tr><td><span class="formula"> ⊧ </span></td>
<td><tt class="docutils literal">\models</tt></td>
<td><span class="formula"> ∝ </span></td>
<td><tt class="docutils literal">\propto</tt></td>
<td><span class="formula"> ∴ </span></td>
<td><tt class="docutils literal">\therefore</tt></td>
</tr>
<tr><td><span class="formula"> ∋ </span></td>
<td><tt class="docutils literal">\ni</tt></td>
<td><span class="formula"> <span class="smallsymbol">∣</span> </span></td>
<td><tt class="docutils literal">\shortmid</tt></td>
<td><span class="formula"> ⊴ </span></td>
<td><tt class="docutils literal">\trianglelefteq</tt></td>
</tr>
<tr><td><span class="formula"> ∤ </span></td>
<td><tt class="docutils literal">\nmid</tt></td>
<td><span class="formula"> <span class="smallsymbol">∥</span> </span></td>
<td><tt class="docutils literal">\shortparallel</tt></td>
<td><span class="formula"> ⊵ </span></td>
<td><tt class="docutils literal">\trianglerighteq</tt></td>
</tr>
<tr><td><span class="formula"> ∉ </span></td>
<td><tt class="docutils literal">\notin</tt></td>
<td><span class="formula"> <span class="smallsymbol">⌢</span> </span></td>
<td><tt class="docutils literal">\smallfrown</tt></td>
<td><span class="formula"> <span class="mathsf">∝</span> </span></td>
<td><tt class="docutils literal">\varpropto</tt></td>
</tr>
<tr><td><span class="formula"> ∦ </span></td>
<td><tt class="docutils literal">\nparallel</tt></td>
<td><span class="formula"> <span class="smallsymbol">⌣</span> </span></td>
<td><tt class="docutils literal">\smallsmile</tt></td>
<td><span class="formula"> ▵ </span></td>
<td><tt class="docutils literal">\vartriangle</tt></td>
</tr>
<tr><td><span class="formula"> <span class="smallsymbol">∤</span> </span></td>
<td><tt class="docutils literal">\nshortmid</tt></td>
<td><span class="formula"> ⌣ </span></td>
<td><tt class="docutils literal">\smile</tt></td>
<td><span class="formula"> ⊲ </span></td>
<td><tt class="docutils literal">\vartriangleleft</tt></td>
</tr>
<tr><td><span class="formula"> <span class="smallsymbol">∦</span> </span></td>
<td><tt class="docutils literal">\nshortparallel</tt></td>
<td><span class="formula"> ⊏ </span></td>
<td><tt class="docutils literal">\sqsubset</tt></td>
<td><span class="formula"> ⊳ </span></td>
<td><tt class="docutils literal">\vartriangleright</tt></td>
</tr>
<tr><td><span class="formula"> ⊈ </span></td>
<td><tt class="docutils literal">\nsubseteq</tt></td>
<td><span class="formula"> ⊑ </span></td>
<td><tt class="docutils literal">\sqsubseteq</tt></td>
<td><span class="formula"> ⊢ </span></td>
<td><tt class="docutils literal">\vdash</tt></td>
</tr>
<tr><td><span class="formula"> ⫅̸ </span></td>
<td><tt class="docutils literal">\nsubseteqq</tt></td>
<td><span class="formula"> ⊐ </span></td>
<td><tt class="docutils literal">\sqsupset</tt></td>
<td><span class="formula"> ⊩ </span></td>
<td><tt class="docutils literal">\Vdash</tt></td>
</tr>
<tr><td><span class="formula"> ⊉ </span></td>
<td><tt class="docutils literal">\nsupseteq</tt></td>
<td><span class="formula"> ⊒ </span></td>
<td><tt class="docutils literal">\sqsupseteq</tt></td>
<td><span class="formula"> ⊨ </span></td>
<td><tt class="docutils literal">\vDash</tt></td>
</tr>
<tr><td><span class="formula"> ⫆̸ </span></td>
<td><tt class="docutils literal">\nsupseteqq</tt></td>
<td><span class="formula"> ⊂ </span></td>
<td><tt class="docutils literal">\subset</tt></td>
<td><span class="formula"> ⊪ </span></td>
<td><tt class="docutils literal">\Vvdash</tt></td>
</tr>
<tr><td><span class="formula"> ⋪ </span></td>
<td><tt class="docutils literal">\ntriangleleft</tt></td>
<td><span class="formula"> ⋐ </span></td>
<td><tt class="docutils literal">\Subset</tt></td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<p>Synonyms: <span class="formula"> ∋ </span> <tt class="docutils literal">\owns</tt>.</p>
<p>Symbols can be negated prepending <tt class="docutils literal">\not</tt>, e.g.
<span class="formula"> ∉ </span> <tt class="docutils literal">\not\in</tt>, <span class="formula"> ∌ </span> <tt class="docutils literal">\not\ni</tt>.</p>
<p>The commands <tt class="docutils literal">\varsubsetneq</tt>, <tt class="docutils literal">\varsubsetneqq</tt>, <tt class="docutils literal">\varsupsetneq</tt>,
and <tt class="docutils literal">\varsupsetneqq</tt> are not supported by LateX2MathML, as there is no
corresponding Unicode character.</p>
</div>
</div>
<div class="section" id="variable-sized-operators">
<h2><a class="toc-backref" href="#toc-entry-19">2.12 Variable-sized operators</a></h2>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span></span> <tt class="docutils literal">\sum</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span></span> <tt class="docutils literal">\prod</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⋂</span></span></span></span> <tt class="docutils literal">\bigcap</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⨀</span></span></span></span> <tt class="docutils literal">\bigodot</tt></td>
</tr>
<tr><td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span></span> <tt class="docutils literal">\int</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">∐</span></span></span></span> <tt class="docutils literal">\coprod</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⋃</span></span></span></span> <tt class="docutils literal">\bigcup</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⨁</span></span></span></span> <tt class="docutils literal">\bigoplus</tt></td>
</tr>
<tr><td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∮</span></span></span></span> <tt class="docutils literal">\oint</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⋀</span></span></span></span> <tt class="docutils literal">\bigwedge</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⨄</span></span></span></span> <tt class="docutils literal">\biguplus</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⨂</span></span></span></span> <tt class="docutils literal">\bigotimes</tt></td>
</tr>
<tr><td><span class="formula"><span class="limits"><span class="limit"><span class="smallsymbol integral">∫</span></span></span></span> <tt class="docutils literal">\smallint</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⋁</span></span></span></span> <tt class="docutils literal">\bigvee</tt></td>
<td><span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">⨆</span></span></span></span> <tt class="docutils literal">\bigsqcup</tt></td>
<td> </td>
</tr>
</tbody>
</table>
<p>Larger symbols are used in displayed formulas, sum-like symbols have
indices above/below the symbol (see also <a class="reference internal" href="#scripts-and-limits">scripts and limits</a>):</p>
<div class="formula">
<span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>n</i> = 1</sub></span><i>a</i><sub><i>n</i></sub> <span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span><i>f</i>(<i>x</i>) <i>dx</i> <span class="limits"><sup class="limit">10</sup><span class="limit"><span class="bigoperator">∏</span></span><sub class="limit"><i>i</i> = 1</sub></span><i>b</i><sub><i>i</i></sub>…
</div>
</div>
</div>
<div class="section" id="notations">
<h1><a class="toc-backref" href="#toc-entry-20">3 Notations</a></h1>
<div class="section" id="top-and-bottom-embellishments">
<h2><a class="toc-backref" href="#toc-entry-21">3.1 Top and bottom embellishments</a></h2>
<p>See <a class="reference internal" href="#accents-and-embellishments">Accents and embellishments</a>.</p>
</div>
<div class="section" id="extensible-arrows">
<h2><a class="toc-backref" href="#toc-entry-22">3.2 Extensible arrows</a></h2>
<p>xleftarrow and xrightarrow produce arrows that extend automatically to
accommodate unusually wide subscripts or superscripts. These commands
take one optional argument (the subscript) and one mandatory argument
(the superscript, possibly empty):</p>
<pre class="literal-block">
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
</pre>
<p>results in</p>
<div class="formula">
<i>A</i><span class="unknown">\xleftarrow</span><i>n</i> + <i>μ</i> − 1<i>B</i><span class="unknown">\xrightarrow</span>[<i>T</i>]<i>n</i>±<i>i</i> − 1<i>C</i>
</div>
</div>
<div class="section" id="affixing-symbols-to-other-symbols">
<h2><a class="toc-backref" href="#toc-entry-23">3.3 Affixing symbols to other symbols</a></h2>
<p>In addition to the standard <a class="reference internal" href="#accents-and-embellishments">accents and embellishments</a>, other symbols
can be placed above or below a base symbol with the <tt class="docutils literal">\overset</tt> and
<tt class="docutils literal">\underset</tt> commands. The symbol is set in "scriptstyle" (smaller font
size). For example, writing <tt class="docutils literal"><span class="pre">\overset{*}{X}</span></tt> becomes <span class="formula"><span class="unknown">\overset</span>*<i>X</i></span>
and <tt class="docutils literal"><span class="pre">\underset{+}{M}</span></tt> becomes <span class="formula"><span class="unknown">\underset</span> + <i>M</i></span>.</p>
</div>
<div class="section" id="matrices">
<h2><a class="toc-backref" href="#toc-entry-24">3.4 Matrices</a></h2>
<p>The <tt class="docutils literal">matrix</tt> and <tt class="docutils literal">cases</tt> environments can also contain <tt class="docutils literal">\\</tt> and
<tt class="docutils literal">&</tt>:</p>
<pre class="literal-block">
.. math::
\left ( \begin{matrix} a & b \\ c & d \end{matrix}\right)
</pre>
<p>Result:</p>
<div class="formula">
<span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="array"><span class="arrayrow">
<span class="arraycell align-c">
<i>a</i>
</span>
<span class="arraycell align-c">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
</span>
<span class="arraycell align-c">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
<i>c</i>
</span>
<span class="arraycell align-c">
<i>d</i>
</span>
</span>
</span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span>
</div>
<p>The environments <tt class="docutils literal">pmatrix</tt>, <tt class="docutils literal">bmatrix</tt>, <tt class="docutils literal">Bmatrix</tt>, <tt class="docutils literal">vmatrix</tt>, and
<tt class="docutils literal">Vmatrix</tt> have (respectively) ( ), [ ], { }, | |, and <span class="formula">‖ ‖</span>
delimiters built in, e.g.</p>
<div class="formula">
<span class="unknown">\begin{pmatrix} <span class="arrayrow">
<span class="arraycell align-l">
<i>a</i>
</span>
<span class="arraycell align-l">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
<i>c</i>
</span>
<span class="arraycell align-l">
<i>d</i>
</span>
</span>
</span> <span class="unknown">\begin{bmatrix} <span class="arrayrow">
<span class="arraycell align-l">
<i>a</i>
</span>
<span class="arraycell align-l">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
<i>c</i>
</span>
<span class="arraycell align-l">
<i>d</i>
</span>
</span>
</span> <span class="unknown">\begin{Vmatrix} <span class="arrayrow">
<span class="arraycell align-l">
<i>a</i>
</span>
<span class="arraycell align-l">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
<i>c</i>
</span>
<span class="arraycell align-l">
<i>d</i>
</span>
</span>
</span>
</div>
<p>To produce a small matrix suitable for use in text, there is a
<tt class="docutils literal">smallmatrix</tt> environment
<span class="formula"><span class="bigdelimiter size1">(</span><span class="environment smallmatrix"><span class="arrayrow">
<span class="arraycell align-c">
<i>a</i>
</span>
<span class="arraycell align-c">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
</span>
<span class="arraycell align-c">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
<i>c</i>
</span>
<span class="arraycell align-c">
<i>d</i>
</span>
</span>
</span><span class="bigdelimiter size1">)</span></span>
that comes closer to fitting within a single text line than a normal
matrix.</p>
<p>For piecewise function definitions there is a <tt class="docutils literal">cases</tt> environment:</p>
<div class="formula">
<span class="mathrm">sgn</span>(<i>x</i>) = <span class="array"><span class="arrayrow"><span class="bracket align-l">⎧</span></span><span class="arrayrow"><span class="bracket align-l">⎨</span></span><span class="arrayrow"><span class="bracket align-l">⎩</span></span></span><span class="bracketcases">
<span class="arrayrow">
<span class="case align-l">
− 1
</span>
<span class="case align-l">
<i>x</i> < 0
</span>
</span>
<span class="arrayrow">
<span class="case align-l">
</span>
<span class="case align-l">
</span>
</span>
<span class="arrayrow">
<span class="case align-l">
<span class="phantom"> − </span>1
</span>
<span class="case align-l">
<i>x</i> > 0
</span>
</span>
</span>
</div>
</div>
<div class="section" id="spacing-commands">
<h2><a class="toc-backref" href="#toc-entry-25">3.5 Spacing commands</a></h2>
<p>Horizontal spacing of elements can be controlled with the following
commands:</p>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td><span class="m formula">3 4</span></td>
<td> </td>
<td><tt class="docutils literal">3\qquad 4</tt></td>
<td>= 2em</td>
</tr>
<tr><td><span class="m formula">3 4</span></td>
<td> </td>
<td><tt class="docutils literal">3\quad 4</tt></td>
<td>= 1em</td>
</tr>
<tr><td><span class="m formula">3 4</span></td>
<td><tt class="docutils literal">3~4</tt></td>
<td><tt class="docutils literal">3\nobreakspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">3 4</span></td>
<td><tt class="docutils literal">3\ 4</tt></td>
<td> </td>
<td>escaped space</td>
</tr>
<tr><td><span class="m formula">3<span class="thickspace"> </span>4</span></td>
<td><tt class="docutils literal"><span class="pre">3\;4</span></tt></td>
<td><tt class="docutils literal">3\thickspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">3 4</span></td>
<td><tt class="docutils literal"><span class="pre">3\:4</span></tt></td>
<td><tt class="docutils literal">3\medspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">3 4</span></td>
<td><tt class="docutils literal"><span class="pre">3\,4</span></tt></td>
<td><tt class="docutils literal">3\thinspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">34</span></td>
<td><tt class="docutils literal">3 4</tt></td>
<td> </td>
<td>regular space <a class="footnote-reference" href="#footnote-3" id="footnote-reference-5">[4]</a></td>
</tr>
<tr><td><span class="m formula">3<span class="unknown">\!</span>4</span></td>
<td><tt class="docutils literal"><span class="pre">3\!4</span></tt></td>
<td><tt class="docutils literal">3\negthinspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">3<span class="unknown">\negmedspace</span>4</span></td>
<td> </td>
<td><tt class="docutils literal">3\negmedspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="m formula">3<span class="unknown">\negthickspace</span>4</span></td>
<td> </td>
<td><tt class="docutils literal">3\negthickspace 4</tt></td>
<td> </td>
</tr>
<tr><td><span class="formula">3<span class="hspace" style="width: 1ex;"> </span>4</span></td>
<td> </td>
<td><tt class="docutils literal">3\hspace{1ex}4</tt></td>
<td>custom length</td>
</tr>
<tr><td><span class="formula">3<span class="unknown">\mspace</span>20<i>mu</i>4</span></td>
<td> </td>
<td><tt class="docutils literal">3\mspace{20mu}4</tt></td>
<td>custom length <a class="footnote-reference" href="#footnote-4" id="footnote-reference-6">[5]</a></td>
</tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="footnote-3" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-5">[4]</a></td><td>Whitespace characters are ignored in LaTeX math mode.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="footnote-4" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-6">[5]</a></td><td>Unit must be 'mu' (1 mu = 1/18em).</td></tr>
</tbody>
</table>
<p>Negative spacing does not work with MathML (in Firefox 78).</p>
<p>There are also three commands that leave a space equal to the height and
width of its argument. For example <tt class="docutils literal">\phantom{XXX}</tt> results in space as
wide and high as three X’s:</p>
<div class="formula">
<span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="phantom"><i>XXX</i></span> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>XXX</i> − 1</span><span class="ignored">)</span></span>
</div>
<p>The commands <tt class="docutils literal">\hphantom</tt> and <tt class="docutils literal">\vphantom</tt> insert space with the
width or height of the argument. They are not supported with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a>
MathML.</p>
</div>
<div class="section" id="roots">
<h2><a class="toc-backref" href="#toc-entry-26">3.6 Roots</a></h2>
<table border="1" class="docutils">
<thead valign="bottom">
<tr><th class="head">command</th>
<th class="head">example</th>
<th class="head">result</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal">\sqrt</tt></td>
<td><tt class="docutils literal"><span class="pre">\sqrt{x^2-1}</span></tt></td>
<td><span class="formula"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root"><i>x</i><sup>2</sup> − 1</span><span class="ignored">)</span></span></span></td>
</tr>
<tr><td><!-- -->
</td>
<td><tt class="docutils literal"><span class="pre">\sqrt[3n]{x^2-1}</span></tt></td>
<td><span class="formula"><span class="sqrt"><sup class="root">3<i>n</i></sup><span class="radical">√</span><span class="ignored">(</span><span class="root"><i>x</i><sup>2</sup> − 1</span><span class="ignored">)</span></span></span></td>
</tr>
<tr><td><!-- -->
</td>
<td><tt class="docutils literal"><span class="pre">\sqrt\frac{1}{2}</span></tt></td>
<td><span class="formula"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root"><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="boxed-formulas">
<h2><a class="toc-backref" href="#toc-entry-27">3.7 Boxed formulas</a></h2>
<p>The command <tt class="docutils literal">\boxed</tt> puts a box around its argument:</p>
<div class="formula">
<span class="boxed"><i>η</i> ≤ <i>C</i>(<i>δ</i>(<i>η</i>) + Λ<sub><i>M</i></sub>(0, <i>δ</i>))</span>
</div>
</div>
</div>
<div class="section" id="fractions-and-related-constructions">
<h1><a class="toc-backref" href="#toc-entry-28">4 Fractions and related constructions</a></h1>
<p>The <tt class="docutils literal">\frac</tt> command takes two ar guments, numerator and denominator,
and typesets them in normal fraction form. For example, <tt class="docutils literal">U = <span class="pre">\frac{R}{I}</span></tt>
produces <span class="formula"><i>U</i> = <span class="fraction"><span class="ignored">(</span><span class="numerator"><i>R</i></span><span class="ignored">)/(</span><span class="denominator"><i>I</i></span><span class="ignored">)</span></span></span>. Use <tt class="docutils literal">\dfrac</tt> or <tt class="docutils literal">\tfrac</tt> to
force text style and display style respectively.</p>
<div class="formula">
<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span> <span class="fullfraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span> <span class="textfraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span>
</div>
<p>and in text: <span class="formula"><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span></span>, <span class="formula"><span class="fullfraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span></span>, <span class="formula"><span class="textfraction"><span class="ignored">(</span><span class="numerator"><i>x</i> + 1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span></span>.</p>
<p>For binomial expressions such as <span class="formula"><span class="bigdelimiter size2">(</span><span class="binom"><span class="binomstack"><i>n</i></span><span class="binomstack"><i>k</i></span></span><span class="bigdelimiter size2">)</span></span>,
there are <tt class="docutils literal">\binom</tt>, <tt class="docutils literal">\dbinom</tt> and <tt class="docutils literal">\tbinom</tt> commands:</p>
<pre class="literal-block">
2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
</pre>
<p>prints</p>
<div class="formula">
2<sup><i>k</i></sup> − <span class="bigdelimiter size2">(</span><span class="binom"><span class="binomstack"><i>k</i></span><span class="binomstack">1</span></span><span class="bigdelimiter size2">)</span>2<sup><i>k</i> − 1</sup> + <span class="bigdelimiter size2">(</span><span class="binom"><span class="binomstack"><i>k</i></span><span class="binomstack">2</span></span><span class="bigdelimiter size2">)</span>2<sup><i>k</i> − 2</sup>
</div>
<p>The <tt class="docutils literal">\cfrac</tt> command for continued fractions uses displaystyle and
padding for sub-fractions:</p>
<div class="formula">
<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>π</i></span><span class="ignored">)/(</span><span class="denominator">4</span><span class="ignored">)</span></span> = 1 + <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-">1<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-">3<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-">5<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-">7<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + ⋯</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span> <span class="text"> vs.</span> <span class="fraction"><span class="ignored">(</span><span class="numerator"><i>π</i></span><span class="ignored">)/(</span><span class="denominator">4</span><span class="ignored">)</span></span> = 1 + <span class="fraction"><span class="ignored">(</span><span class="numerator">1<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fraction"><span class="ignored">(</span><span class="numerator">3<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fraction"><span class="ignored">(</span><span class="numerator">5<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + <span class="fraction"><span class="ignored">(</span><span class="numerator">7<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2 + ⋯</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span>
</div>
<p>It supports the optional argument <tt class="docutils literal">[l]</tt> or <tt class="docutils literal">[r]</tt> for
left or right placement of the numerator:</p>
<div class="formula">
<span class="fullfraction"><span class="ignored">(</span><span class="numerator align-l"><i>x</i></span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span> <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-"><i>x</i></span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span> <span class="fullfraction"><span class="ignored">(</span><span class="numerator align-r"><i>x</i></span><span class="ignored">)/(</span><span class="denominator"><i>x</i> − 1</span><span class="ignored">)</span></span>
</div>
</div>
<div class="section" id="delimiter-sizes">
<h1><a class="toc-backref" href="#toc-entry-29">5 Delimiter sizes</a></h1>
<p>Besides the automatic scaling of <a class="reference internal" href="#extensible-delimiters">extensible delimiters</a> with <tt class="docutils literal">\left</tt>
and <tt class="docutils literal">\right</tt>, there are four commands to manually select delimiters of
fixed size:</p>
<table border="1" class="docutils">
<tbody valign="top">
<tr><td>Sizing</td>
<td>no</td>
<td><tt class="docutils literal">\left</tt></td>
<td><tt class="docutils literal">\bigl</tt></td>
<td><tt class="docutils literal">\Bigl</tt></td>
<td><tt class="docutils literal">\biggl</tt></td>
<td><tt class="docutils literal">\Biggl</tt></td>
</tr>
<tr><td>command</td>
<td> </td>
<td><tt class="docutils literal">\right</tt></td>
<td><tt class="docutils literal">\bigr</tt></td>
<td><tt class="docutils literal">\Bigr</tt></td>
<td><tt class="docutils literal">\biggr</tt></td>
<td><tt class="docutils literal">\Biggr</tt></td>
</tr>
<tr><td>Result</td>
<td><span class="formula"><span class="displaystyle">(</span><i>b</i>)(<span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span>)</span></td>
<td><span class="formula"><span class="displaystyle"><span class="stretchy">(</span></span><i>b</i><span class="stretchy">)</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span></span></td>
<td><span class="formula"><span class="displaystyle"><span class="bigdelimiter size1">(</span></span><i>b</i><span class="bigdelimiter size1">)</span><span class="bigdelimiter size1">(</span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span><span class="bigdelimiter size1">)</span></span></td>
<td><span class="formula"><span class="displaystyle"><span class="bigdelimiter size2">(</span></span><i>b</i><span class="bigdelimiter size2">)</span><span class="bigdelimiter size2">(</span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span><span class="bigdelimiter size2">)</span></span></td>
<td><span class="formula"><span class="displaystyle"><span class="bigdelimiter size3">(</span></span><i>b</i><span class="bigdelimiter size3">)</span><span class="bigdelimiter size3">(</span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span><span class="bigdelimiter size3">)</span></span></td>
<td><span class="formula"><span class="displaystyle"><span class="bigdelimiter size4">(</span></span><i>b</i><span class="bigdelimiter size4">)</span><span class="bigdelimiter size4">(</span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>c</i></span><span class="ignored">)/(</span><span class="denominator"><i>d</i></span><span class="ignored">)</span></span><span class="bigdelimiter size4">)</span></span></td>
</tr>
</tbody>
</table>
<p>There are two or three situations where the delimiter size is commonly
adjusted using these commands:</p>
<p>The first kind of adjustment is done for cumulative operators with
limits, such as summation signs. With <tt class="docutils literal">\left</tt> and <tt class="docutils literal">\right</tt> the
delimiters usually turn out larger than necessary, and using the <tt class="docutils literal">Big</tt>
or <tt class="docutils literal">bigg</tt> sizes instead gives better results:</p>
<div class="formula">
<span class="stretchy">[</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>i</i></sub></span><i>a</i><sub><i>i</i></sub><span class="stretchy">|</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>j</i></sub></span><i>x</i><sub><i>ij</i></sub><span class="stretchy">|</span><sup><i>p</i></sup><span class="stretchy">]</span><sup>1 ⁄ <i>p</i></sup><span class="text"> versus </span><span class="bigdelimiter size3">[</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>i</i></sub></span><i>a</i><sub><i>i</i></sub><span class="bigdelimiter size2">|</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>j</i></sub></span><i>x</i><sub><i>ij</i></sub><span class="bigdelimiter size2">|</span><sup><i>p</i></sup><span class="bigdelimiter size3">]</span><sup>1 ⁄ <i>p</i></sup>
</div>
<p>The second kind of situation is clustered pairs of delimiters, where
left and right make them all the same size (because that is adequate to
cover the encompassed material), but what you really want is to make some
of the delimiters slightly larger to make the nesting easier to see.</p>
<div class="formula">
<span class="stretchy">(</span>(<i>a</i><sub>1</sub><i>b</i><sub>1</sub>) − (<i>a</i><sub>2</sub><i>b</i><sub>2</sub>)<span class="stretchy">)</span><span class="stretchy">(</span>(<i>a</i><sub>2</sub><i>b</i><sub>1</sub>) + (<i>a</i><sub>1</sub><i>b</i><sub>2</sub>)<span class="stretchy">)</span> <span class="text"> versus</span> <span class="bigdelimiter size1">(</span>(<i>a</i><sub>1</sub><i>b</i><sub>1</sub>) − (<i>a</i><sub>2</sub><i>b</i><sub>2</sub>)<span class="bigdelimiter size1">)</span><span class="bigdelimiter size1">(</span>(<i>a</i><sub>2</sub><i>b</i><sub>1</sub>) + (<i>a</i><sub>1</sub><i>b</i><sub>2</sub>)<span class="bigdelimiter size1">)</span>
</div>
<p>The third kind of situation is a slightly oversize object in running
text, such as <span class="formula"><span class="array"><span class="arrayrow"><span class="bracket align-left">|</span></span><span class="arrayrow"><span class="bracket align-left">|</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>b</i>’</span><span class="ignored">)/(</span><span class="denominator"><i>d</i>’</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">|</span></span><span class="arrayrow"><span class="bracket align-right">|</span></span></span></span> where the delimiters produced
by <tt class="docutils literal">\left</tt> and <tt class="docutils literal">\right</tt> cause too much line spreading. <a class="footnote-reference" href="#footnote-5" id="footnote-reference-7">[6]</a> In that case
<tt class="docutils literal">\bigl</tt> and <tt class="docutils literal">\bigr</tt> can be used to produce delimiters that are larger
than the base size but still able to fit within the normal line spacing:
<span class="formula"><span class="bigdelimiter size1">|</span><span class="fraction"><span class="ignored">(</span><span class="numerator"><i>b</i>’</span><span class="ignored">)/(</span><span class="denominator"><i>d</i>’</span><span class="ignored">)</span></span><span class="bigdelimiter size1">|</span></span>.</p>
<table class="docutils footnote" frame="void" id="footnote-5" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-7">[6]</a></td><td>With MathML, an example would be parentheses
around a <tt class="docutils literal">smallmatrix</tt> environment
<span class="formula"><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="environment smallmatrix"><span class="arrayrow">
<span class="arraycell align-c">
<i>a</i>
</span>
<span class="arraycell align-c">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
</span>
<span class="arraycell align-c">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
<i>c</i>
</span>
<span class="arraycell align-c">
<i>d</i>
</span>
</span>
</span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span></span>
vs. <span class="formula"><span class="bigdelimiter size2">(</span><span class="environment smallmatrix"><span class="arrayrow">
<span class="arraycell align-c">
<i>a</i>
</span>
<span class="arraycell align-c">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
</span>
<span class="arraycell align-c">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
<i>c</i>
</span>
<span class="arraycell align-c">
<i>d</i>
</span>
</span>
</span><span class="bigdelimiter size2">)</span></span>.</td></tr>
</tbody>
</table>
</div>
<div class="section" id="text">
<h1><a class="toc-backref" href="#toc-entry-30">6 Text</a></h1>
<p>The main use of the command <tt class="docutils literal">\text</tt> is for words or phrases in a
display. It is similar to <tt class="docutils literal">\mbox</tt> in its effects but, unlike <tt class="docutils literal">\mbox</tt>,
automatically produces subscript-size text if used in a subscript,
<tt class="docutils literal"><span class="pre">k_{\text{B}}T</span></tt> becomes <span class="formula"><i>k</i><sub><span class="text">B</span></sub><i>T</i></span>.</p>
<p>Whitespace is kept inside the argument:</p>
<div class="formula">
<i>f</i><sub>[<i>x</i><sub><i>i</i> − 1</sub>, <i>x</i><sub><i>i</i></sub>]</sub><span class="text"> is monotonic for </span><i>i</i> = 1, …, <i>c</i> + 1
</div>
<p>The text may contain math commands wrapped in <tt class="docutils literal">$</tt> signs, e.g.</p>
<div class="formula">
( − 1)<sup><i>n</i><sub><i>i</i></sub></sup> = <span class="array"><span class="arrayrow"><span class="bracket align-l">⎧</span></span><span class="arrayrow"><span class="bracket align-l">⎨</span></span><span class="arrayrow"><span class="bracket align-l">⎩</span></span></span><span class="bracketcases">
<span class="arrayrow">
<span class="case align-l">
− 1 <span class="text"> if $n<sub>i</sub>$ is odd,</span>
</span>
</span>
<span class="arrayrow">
<span class="case align-l">
</span>
</span>
<span class="arrayrow">
<span class="case align-l">
+ 1 <span class="text"> if $n<sub>i</sub>$ is even.</span>
</span>
</span>
</span>
</div>
<!-- TODO ignore {}, handle text-mode commands -->
<!-- TODO: ``\mod`` and its relatives
- - - - - - - - - - - - - - - - - - - - - - - - - -
Commands ``\mod``, ``\bmod``, ``\pmod``, ``\pod`` deal with the special
spacing conventions of “mod” notation. ``\mod`` and ``\pod`` are
variants of ``\pmod`` preferred by some authors; ``\mod`` omits the
parentheses, whereas ``\pod`` omits the “mod” and retains the
parentheses.
\gcd(n,m\bmod n) ;\quad x\equiv y\pmod b
;\quad x\equiv y\mod c ;\quad x\equiv y\pod d -->
</div>
<div class="section" id="integrals-and-sums">
<h1><a class="toc-backref" href="#toc-entry-31">7 Integrals and sums</a></h1>
<p>The limits on integrals, sums, and similar symbols are placed either to
the side of or above and below the base symbol, depending on convention
and context. In inline formulas and fractions, the limits on sums, and
similar symbols like</p>
<div class="formula">
<span class="limits"><sup class="limit"> </sup><span class="limit">lim</span><sub class="limit"><i>n</i> → ∞</sub></span><span class="limits"><sup class="limit"><i>n</i></sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit">1</sub></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span>
</div>
<p>move to index positions: <span class="formula"><span class="limits"><span class="limit">lim</span></span><sub><i>n</i> → ∞</sub><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><span class="scripts"><sup class="script"><i>n</i></sup><sub class="script">1</sub></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span></span>.</p>
<div class="section" id="altering-the-placement-of-limits">
<h2><a class="toc-backref" href="#toc-entry-32">7.1 Altering the placement of limits</a></h2>
<p>The commands <tt class="docutils literal">\intop</tt> and <tt class="docutils literal">\ointop</tt> produce integral signs with
limits as in sums and similar: <span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="scripts"><sup class="script">1</sup><sub class="script">0</sub></span></span>, <span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∮</span></span></span><sub><i>c</i></sub></span> and</p>
<div class="formula">
<span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∮</span></span><sub class="limit"><i>c</i></sub></span> <span class="text">vs.</span> <span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∮</span></span><sub class="limit"><i>c</i></sub></span>
</div>
<p>The commands <tt class="docutils literal">\limits</tt> and <tt class="docutils literal">\nolimits</tt> override the default placement
of the limits for any operator; <tt class="docutils literal">\displaylimits</tt> forces standard
positioning as for the sum command. They should follow immediately after
the operator to which they apply.</p>
<p>Compare the same term with default positions, <tt class="docutils literal">\limits</tt>, and
<tt class="docutils literal">\nolimits</tt> in inline and display mode: <span class="formula"><span class="limits"><span class="limit">lim</span></span><sub><i>x</i> → 0</sub><i>f</i>(<i>x</i>)</span>,
<span class="formula"><span class="limits"><span class="limit">lim</span></span><span class="unknown">\limits</span><sub><i>x</i> → 0</sub><i>f</i>(<i>x</i>)</span>, <span class="formula"><span class="limits"><span class="limit">lim</span></span><sub><i>x</i> → 0</sub><i>f</i>(<i>x</i>)</span>, vs.</p>
<div class="formula">
<span class="limits"><sup class="limit"> </sup><span class="limit">lim</span><sub class="limit"><i>x</i> → 0</sub></span><i>f</i>(<i>x</i>), <span class="limits"><span class="limit">lim</span></span><span class="unknown">\limits</span><sub><i>x</i> → 0</sub><i>f</i>(<i>x</i>) <span class="limits"><span class="limit">lim</span></span><sub><i>x</i> → 0</sub><i>f</i>(<i>x</i>).
</div>
<!-- TODO: \substack -->
<!-- TODO: \sideset -->
</div>
</div>
<div class="section" id="changing-the-size-of-elements-in-a-formula">
<h1><a class="toc-backref" href="#toc-entry-33">8 Changing the size of elements in a formula</a></h1>
<p>The declarations <a class="footnote-reference" href="#footnote-6" id="footnote-reference-8">[7]</a> <tt class="docutils literal">\displaystyle</tt>, <tt class="docutils literal">\textstyle</tt>,
<tt class="docutils literal">\scriptstyle</tt>, and <tt class="docutils literal">\scriptscriptstyle</tt>, select a symbol size and
spacing that would be applied in (respectively) display math, inline
math, first-order subscript, or second-order subscript, even when the
current context would normally yield some other size.</p>
<p>For example <tt class="docutils literal"><span class="pre">:math:`\displaystyle</span> <span class="pre">\sum_{n=0}^\infty</span>
<span class="pre">\frac{1}{n}`</span></tt> is printed as <span class="formula"><span class="displaystyle"><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span></span><span class="scripts"><sup class="script">∞</sup><sub class="script"><i>n</i> = 0</sub></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span></span>
rather than <span class="formula"><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><span class="scripts"><sup class="script">∞</sup><sub class="script"><i>n</i> = 0</sub></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span></span> and</p>
<pre class="literal-block">
\frac{\scriptstyle\sum_{n > 0} z^n}
{\displaystyle\prod_{1\leq k\leq n} (1-q^k)}
</pre>
<p>yields</p>
<div class="formula">
<span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="scriptstyle"><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span></span><sub><i>n</i> > 0</sub><i>z</i><sup><i>n</i></sup></span><span class="ignored">)/(</span><span class="denominator"><span class="displaystyle"><span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span></span><sub>1 ≤ <i>k</i> ≤ <i>n</i></sub>(1 − <i>q</i><sup><i>k</i></sup>)</span><span class="ignored">)</span></span><span class="text"> instead of the default </span><span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit"><i>n</i> > 0</sub></span><i>z</i><sup><i>n</i></sup></span><span class="ignored">)/(</span><span class="denominator"><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∏</span></span><sub class="limit">1 ≤ <i>k</i> ≤ <i>n</i></sub></span>(1 − <i>q</i><sup><i>k</i></sup>)</span><span class="ignored">)</span></span>.
</div>
<table class="docutils footnote" frame="void" id="footnote-6" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#footnote-reference-8">[7]</a></td><td><p class="first">"Declarations" are commands that affect processing of the current
"group". In particular, notice where the braces fall that delimit the
effect of the command: Right: <tt class="docutils literal">{\displaystyle <span class="pre">...}</span></tt> Wrong:
<tt class="docutils literal"><span class="pre">\displaystyle{...}</span></tt>.</p>
<p class="last">With <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> MathML, the declaration must be the first element
after the opening bracket.</p>
</td></tr>
</tbody>
</table>
</div>
<div class="section" id="appendix">
<h1><a class="toc-backref" href="#toc-entry-34">9 Appendix</a></h1>
<div class="section" id="tests">
<h2><a class="toc-backref" href="#toc-entry-35">9.1 Tests</a></h2>
<div class="section" id="font-changes">
<h3><a class="toc-backref" href="#toc-entry-36">9.1.1 Font changes</a></h3>
<p>Math alphabet macros change the default alphabet ("mathvariant" in
MathML), leaving some symbols unchanged:</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">normal:</th><td class="field-body"><span class="formula"><i>abs</i>(<i>x</i>)±<i>α</i> ≈ 3Γ ∀<i>x</i> ∈ <i>R</i></span></td>
</tr>
<tr class="field"><th class="field-name">mathrm:</th><td class="field-body"><span class="formula"><span class="mathrm">abs(x)±α ≈ 3Γ ∀x ∈ R</span></span></td>
</tr>
<tr class="field"><th class="field-name">mathit:</th><td class="field-body"><span class="formula"><i>abs(x)±α ≈ 3Γ ∀x ∈ R</i></span></td>
</tr>
<tr class="field"><th class="field-name">mathsf:</th><td class="field-body"><span class="formula"><span class="mathsf">abs(x)±α ≈ 3Γ ∀x ∈ R</span></span></td>
</tr>
<tr class="field"><th class="field-name">mathbb:</th><td class="field-body"><span class="formula"><span class="blackboard">abs(x)±α ≈ 3Γ ∀x ∈ R</span></span></td>
</tr>
<tr class="field"><th class="field-name">mathbf:</th><td class="field-body"><span class="formula"><b>abs(x)±α ≈ 3Γ ∀x ∈ R</b></span></td>
</tr>
<tr class="field"><th class="field-name">mathcal:</th><td class="field-body"><span class="formula"><span class="scriptfont">abs(x)±α ≈ 3Γ ∀x ∈ R</span></span></td>
</tr>
<tr class="field"><th class="field-name">mathscr:</th><td class="field-body"><span class="formula"><span class="mathscr">abs(x)±α ≈ 3Γ ∀x ∈ R</span></span></td>
</tr>
</tbody>
</table>
<p>Unicode supports the following blackboard-bold characters:
<span class="formula"><span class="blackboard">a…zA…Z0…9<span class="blackboard">Γ</span><span class="blackboard">Π</span><span class="blackboard">Σ</span><span class="blackboard">γ</span><span class="blackboard">π</span></span></span>.</p>
</div>
<div class="section" id="inferred-mrow-s-in-mathml">
<h3><a class="toc-backref" href="#toc-entry-37">9.1.2 Inferred <mrow>s in MathML</a></h3>
<p>The elements <msqrt>, <mstyle>, <merror>, <mpadded>, <mphantom>, <menclose>,
<mtd>, <mscarry>, and <math> treat their contents as a single inferred mrow
formed from all their children.</p>
<div class="formula">
<i>a</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2</span><span class="ignored">)</span></span> + <i>x</i>, <i>b</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">1 + <i>x</i><sup>2</sup></span><span class="ignored">)</span></span>, <i>c</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root"><span class="fraction"><span class="ignored">(</span><span class="numerator">sin(<i>x</i>)</span><span class="ignored">)/(</span><span class="denominator">23</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span>,
</div>
<p>inline: <span class="formula"><i>a</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2</span><span class="ignored">)</span></span> + <i>x</i>, <i>b</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">1 + <i>x</i><sup>2</sup></span><span class="ignored">)</span></span>, <i>c</i> = <span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root"><span class="fraction"><span class="ignored">(</span><span class="numerator">sin(<i>x</i>)</span><span class="ignored">)/(</span><span class="denominator">23</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span></span>.</p>
</div>
<div class="section" id="scripts-and-limits">
<h3><a class="toc-backref" href="#toc-entry-38">9.1.3 Scripts and Limits</a></h3>
<p>Accents should be nearer to the base (in MathML Firefox 78, it's vice versa!):
<span class="formula"><span class="embellished"><sup>‒</sup><i><span class="base">a</span></i></span><span class="overline"><i>a</i></span>, <span class="embellished"><sup>‒</sup><i><span class="base">l</span></i></span><span class="overline"><i>l</i></span>, <span class="embellished"><sup>‒</sup><i><span class="base">i</span></i></span><span class="overline"><i>i</i></span></span>,
<span class="formula"><span class="embellished"><sup><span class="smallsymbol">→</span></sup><span class="base"><i>r</i></span></span></span> <span class="formula"><span class="embellished"><sup>⟶</sup><span class="base"><i>r</i></span></span></span>.</p>
<p>Sub- and superscript may be given in any order:
<span class="formula"><i>x</i><span class="scripts"><sup class="script"><i>j</i></sup><sub class="script"><i>i</i></sub></span> = <i>x</i><span class="scripts"><sup class="script"><i>j</i></sup><sub class="script"><i>i</i></sub></span></span> and <span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="scripts"><sup class="script">1</sup><sub class="script">0</sub></span> = <span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="scripts"><sup class="script">1</sup><sub class="script">0</sub></span></span>.</p>
<p>Double exponent: <span class="formula"><i>x</i><sup>10<sup>4</sup></sup></span>, <span class="formula"><i>r</i><sub><i>T</i><sub><span class="mathrm">in</span></sub></sub></span> and <span class="formula"><i>x</i><span class="scripts"><sup class="script"><i>n</i><sup>2</sup></sup><sub class="script"><i>i</i></sub></span></span>.</p>
</div>
<div class="section" id="nested-groups">
<h3><a class="toc-backref" href="#toc-entry-39">9.1.4 Nested groups</a></h3>
<p>tex-token returns "{" for nested groups:</p>
<div class="formula">
<span class="text">das ist ein tollertext (unescaped {and }is
ignored by LaTeX)</span>
</div>
</div>
<div class="section" id="big-delimiters-and-symbols">
<h3><a class="toc-backref" href="#toc-entry-40">9.1.5 Big delimiters and symbols</a></h3>
<p>Compare automatic sizing with fixed sizes:</p>
<!-- math: \left( \frac{\frac1x}{\frac{1}{n}}\right) &= \Biggl(\text{Bigg}\Biggr)\\ -->
<div class="formula">
<span class="environment align"><span class="arrayrow">
<span class="arraycell align-r">
<span class="stretchy">(</span>3<span class="stretchy">)</span><span class="stretchy">(</span><i>f</i>(<i>x</i>)<span class="stretchy">)</span><span class="stretchy">(</span><span class="embellished"><sup>‒</sup><i><span class="base">x</span></i></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="overline"><i>x</i></span><span class="stretchy">)</span><span class="stretchy">(</span><i>n</i><sub><i>i</i></sub><span class="stretchy">)</span>
</span>
<span class="arraycell align-l">
= ()
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
<span class="stretchy">(</span><i>x</i><span class="stretchy">)</span>
</span>
<span class="arraycell align-l">
= <span class="bigdelimiter size1">(</span><span class="text">big</span><span class="bigdelimiter size1">)</span>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
<span class="stretchy">(</span>3<sup>2</sup><span class="stretchy">)</span><span class="stretchy">(</span><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">3</span><span class="ignored">)</span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">3<sup>2</sup></span><span class="ignored">)</span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">⨂</span></span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span><span class="stretchy">)</span>
</span>
<span class="arraycell align-l">
= <span class="bigdelimiter size2">(</span><span class="text"> Big</span><span class="bigdelimiter size2">)</span>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
<span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">3</span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">3<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2<sup>4</sup></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="bigdelimiter size2">(</span><span class="binom"><span class="binomstack">3</span><span class="binomstack">2</span></span><span class="bigdelimiter size2">)</span><span class="unknown">\begin{pmatrix} <span class="arrayrow">
<span class="arraycell align-l">
<i>a</i>
</span>
<span class="arraycell align-l">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-l">
<i>c</i>
</span>
<span class="arraycell align-l">
<i>d</i>
</span>
</span>
</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2</span><span class="ignored">)</span></span></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sup class="limit"> </sup></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span>
</span>
<span class="arraycell align-l">
= <span class="bigdelimiter size3">(</span><span class="text"> bigg</span><span class="bigdelimiter size3">)</span>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
<span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2</span><span class="ignored">)</span></span></span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="stretchy">(</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator">∑</span></span><sup class="limit"> </sup></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i></span><span class="ignored">)</span></span></span><span class="ignored">)/(</span><span class="denominator"><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span>
</span>
<span class="arraycell align-l">
= <span class="bigdelimiter size4">(</span><span class="text">Bigg</span><span class="bigdelimiter size4">)</span>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
</span>
<span class="arraycell align-l">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-r">
<span class="stretchy">(</span><span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sup class="limit"> </sup></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><sup class="limit">1</sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">0</sub></span><span class="stretchy">)</span>
</span>
</span>
</span>
</div>
<p>And in text:</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name"><span class="formula">()</span>:</th><td class="field-body"><span class="formula"><span class="stretchy">(</span>3<span class="stretchy">)</span><span class="stretchy">(</span><i>f</i>(<i>x</i>)<span class="stretchy">)</span><span class="stretchy">(</span><span class="embellished"><sup>‒</sup><i><span class="base">x</span></i></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="overline"><i>x</i></span><span class="stretchy">)</span><span class="stretchy">(</span><i>n</i><sub><i>i</i></sub><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><sub>0</sub><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span><span class="stretchy">)</span></span></td>
</tr>
<tr class="field"><th class="field-name" colspan="2"><span class="formula"><span class="bigdelimiter size1">(</span><span class="text">big</span><span class="bigdelimiter size1">)</span></span>:</th></tr>
<tr class="field"><td> </td><td class="field-body"><span class="formula"><span class="stretchy">(</span><i>x</i><span class="stretchy">)</span><span class="stretchy">(</span>3<sup>2</sup><span class="stretchy">)</span><span class="bigdelimiter size2">(</span><span class="binom"><span class="binomstack">3</span><span class="binomstack">2</span></span><span class="bigdelimiter size2">)</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="environment smallmatrix"><span class="arrayrow">
<span class="arraycell align-c">
<i>a</i>
</span>
<span class="arraycell align-c">
<i>b</i>
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
</span>
<span class="arraycell align-c">
</span>
</span>
<span class="arrayrow">
<span class="arraycell align-c">
<i>c</i>
</span>
<span class="arraycell align-c">
<i>d</i>
</span>
</span>
</span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">⨂</span></span></span><span class="stretchy">)</span></span></td>
</tr>
<tr class="field"><th class="field-name" colspan="2"><span class="formula"><span class="bigdelimiter size2">(</span><span class="text">Big</span><span class="bigdelimiter size2">)</span></span>:</th></tr>
<tr class="field"><td> </td><td class="field-body"><span class="formula"><span class="stretchy">(</span><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">3</span><span class="ignored">)</span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">3<sup>2</sup></span><span class="ignored">)</span></span><span class="stretchy">)</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">3</span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator">3<sup>2</sup></span><span class="ignored">)/(</span><span class="denominator">2<sup>4</sup></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="sqrt"><span class="radical">√</span><span class="ignored">(</span><span class="root">2</span><span class="ignored">)</span></span></span><span class="ignored">)/(</span><span class="denominator">2</span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><sub>0</sub><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><sup>1</sup><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span><span class="scripts"><sup class="script">1</sup><sub class="script">0</sub></span><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><sup>1</sup><span class="stretchy">)</span><span class="stretchy">(</span><span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span><span class="scripts"><sup class="script">1</sup><sub class="script">0</sub></span><span class="stretchy">)</span><span class="array"><span class="arrayrow"><span class="bracket align-left">⎛</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎜</span></span><span class="arrayrow"><span class="bracket align-left">⎝</span></span></span><span class="fraction"><span class="ignored">(</span><span class="numerator"><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>x</i></span><span class="ignored">)</span></span></span><span class="ignored">)/(</span><span class="denominator"><span class="fraction"><span class="ignored">(</span><span class="numerator">1</span><span class="ignored">)/(</span><span class="denominator"><i>n</i></span><span class="ignored">)</span></span></span><span class="ignored">)</span></span><span class="array"><span class="arrayrow"><span class="bracket align-right">⎞</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎟</span></span><span class="arrayrow"><span class="bracket align-right">⎠</span></span></span></span></td>
</tr>
</tbody>
</table>
<p>Test <tt class="docutils literal">\left</tt>, <tt class="docutils literal">\right</tt>, and the bigl/bigr, … size commands
with all extensible delimiters.</p>
<div class="formula">
<span class="emptydot"></span>(<i>b</i><span class="stretchy">)</span> <span class="bigdelimiter size1">(</span><i>b</i><span class="bigdelimiter size2">)</span> <span class="bigdelimiter size3">(</span><i>b</i><span class="bigdelimiter size4">)</span> <span class="emptydot"></span>[<i>b</i><span class="stretchy">]</span> <span class="bigdelimiter size1">[</span><i>b</i><span class="bigdelimiter size2">]</span> <span class="bigdelimiter size3">[</span><i>b</i><span class="bigdelimiter size4">]</span> <span class="emptydot"></span>{<i>b</i><span class="stretchy">}</span> <span class="bigdelimiter size1">{</span><i>b</i><span class="bigdelimiter size2">}</span> <span class="bigdelimiter size3">{</span><i>b</i><span class="bigdelimiter size4">}</span> <span class="emptydot"></span>⟨<i>b</i><span class="stretchy">⟩</span> <span class="bigdelimiter size1">⟨</span><i>b</i><span class="bigdelimiter size2">⟩</span> <span class="bigdelimiter size3">⟨</span><i>b</i><span class="bigdelimiter size4">⟩</span>
</div>
<div class="formula">
<span class="emptydot"></span>⌈<i>b</i><span class="stretchy">⌉</span> <span class="bigdelimiter size1">⌈</span><i>b</i><span class="bigdelimiter size2">⌉</span> <span class="bigdelimiter size3">⌈</span><i>b</i><span class="bigdelimiter size4">⌉</span> <span class="emptydot"></span>⌊<i>b</i><span class="stretchy">⌋</span> <span class="bigdelimiter size1">⌊</span><i>b</i><span class="bigdelimiter size2">⌋</span> <span class="bigdelimiter size3">⌊</span><i>b</i><span class="bigdelimiter size4">⌋</span> <span class="emptydot"></span>|<i>b</i><span class="stretchy">|</span> <span class="bigdelimiter size1">|</span><i>b</i><span class="bigdelimiter size2">|</span> <span class="bigdelimiter size3">|</span><i>b</i><span class="bigdelimiter size4">|</span> <span class="emptydot"></span>‖<i>b</i><span class="stretchy">‖</span> <span class="bigdelimiter size1">‖</span><i>b</i><span class="bigdelimiter size2">‖</span> <span class="bigdelimiter size3">‖</span><i>b</i><span class="bigdelimiter size4">‖</span>
</div>
<div class="formula">
<span class="emptydot"></span>⟮<i>b</i><span class="stretchy">⟯</span> <span class="bigdelimiter size1">⟮</span><i>b</i><span class="bigdelimiter size2">⟯</span> <span class="bigdelimiter size3">⟮</span><i>b</i><span class="bigdelimiter size4">⟯</span> <span class="emptydot"></span>⎰<i>b</i><span class="stretchy">⎱</span> <span class="bigdelimiter size1">⎰</span><i>b</i><span class="bigdelimiter size2">⎱</span> <span class="bigdelimiter size3">⎰</span><i>b</i><span class="bigdelimiter size4">⎱</span> <span class="emptydot"></span> ⁄ <i>b</i><span class="stretchy">\</span> <span class="bigdelimiter size1"> ⁄ </span><i>b</i><span class="bigdelimiter size2">\</span> <span class="bigdelimiter size3"> ⁄ </span><i>b</i><span class="bigdelimiter size4">\</span>
</div>
<div class="formula">
<span class="emptydot"></span>|<i>b</i><span class="stretchy">‖</span> <span class="bigdelimiter size1">|</span><i>b</i><span class="bigdelimiter size2">‖</span> <span class="bigdelimiter size3">|</span><i>b</i><span class="bigdelimiter size4">‖</span> <span class="emptydot"></span>|<i>b</i><span class="stretchy">‖</span> <span class="bigdelimiter size1">|</span><i>b</i><span class="bigdelimiter size2">‖</span> <span class="bigdelimiter size3">|</span><i>b</i><span class="bigdelimiter size4">‖</span> <span class="emptydot"></span>⏐<i>b</i><span class="stretchy">‖</span> <span class="bigdelimiter size1">⏐</span><i>b</i><span class="bigdelimiter size2">‖</span> <span class="bigdelimiter size3">⏐</span><i>b</i><span class="bigdelimiter size4">‖</span> <span class="emptydot"></span>⎪<i>b</i><span class="stretchy">⎪</span> <span class="bigdelimiter size1">⎪</span><i>b</i><span class="bigdelimiter size2">⎪</span> <span class="bigdelimiter size3">⎪</span><i>b</i><span class="bigdelimiter size4">⎪</span> <span class="emptydot"></span>|<i>b</i><span class="stretchy">‖</span> <span class="bigdelimiter size1">|</span><i>b</i><span class="bigdelimiter size2">‖</span> <span class="bigdelimiter size3">|</span><i>b</i><span class="bigdelimiter size4">‖</span>
</div>
<p>Variable-sized operators:</p>
<p>Inline: <span class="formula"><span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∬</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∭</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">⨌</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∫⋯∫</span></span></span><span class="limits"><span class="limit"><span class="bigoperator integral">∮</span></span></span> <span class="limits"><span class="limit"><span class="smallsymbol integral">∫</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∐</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋀</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋁</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋂</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋃</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨄</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨆</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨀</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨁</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨂</span></span></span></span> and Display:</p>
<div class="formula">
<span class="limits"><span class="limit"><span class="bigoperator integral">∫</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∬</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∭</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">⨌</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∫⋯∫</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator integral">∮</span></span></span> <span class="limits"><span class="limit"><span class="smallsymbol integral">∫</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∑</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∏</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">∐</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋀</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋁</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋂</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⋃</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨄</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨆</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨀</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨁</span></span></span> <span class="limits"><span class="limit"><span class="bigoperator">⨂</span></span></span>
</div>
<div class="formula">
<span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">1</sub></span><i>f</i> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">1</sub></span><i>f</i> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator integral">∬</span></span><sub class="limit">1</sub></span><i>f</i> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="smallsymbol integral">∫</span></span><sub class="limit">1</sub></span><i>f</i> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">∏</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">⋀</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">⋂</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">⨄</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"> </sup><span class="limit"><span class="bigoperator">⨀</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∫</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∫</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">⨌</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∮</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="smallsymbol integral">∫</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∑</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∐</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋁</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋃</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨆</span></span><sup class="limit"> </sup></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨂</span></span><sup class="limit"> </sup></span>
</div>
<div class="formula">
<span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∫</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∬</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∭</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">⨌</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∫⋯∫</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator integral">∮</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="smallsymbol integral">∫</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∑</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∏</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">∐</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋀</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋁</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋂</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⋃</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨄</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨆</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨀</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨁</span></span><sub class="limit">1</sub></span> <span class="limits"><sup class="limit"><i>N</i></sup><span class="limit"><span class="bigoperator">⨂</span></span><sub class="limit">1</sub></span>
</div>
</div>
<div class="section" id="text-1">
<h3><a class="toc-backref" href="#toc-entry-41">9.1.6 Text</a></h3>
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<p>Some text-mode LaTeX commands are supported with <a class="reference external" href="https://docutils.sourceforge.io/docs/user/config.html#math-output">math_output</a> "html".
In other output formats, use literal Unicode: <span class="formula"><span class="text">ç é è ë ê ñ ů ž ©</span></span>
to get the result of the accent macros
<span class="formula"><span class="text">çéèëêñůžc⃝</span></span>.</p>
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