jgm/undergradmath.html

## undergradmath.html
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<p><a href="https://github.com/johanvx/typst-undergradmath">
<strong>Typst Math for Undergrads</strong></a></p>
</div>
<p>This is a Typst port of <em><span class="box">L A <span class="box">T E X</span></span> Math for Undergrads</em> by Jim
Hefferon. The original version is available at <u><a href="https://gitlab.com/jim.hefferon/undergradmath">https://gitlab.com/jim.hefferon/undergradmath</a></u>.</p>
<p><strong>Meaning of annotations  </strong></p>
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<td style="text-align: left;"><p><span class="box">2023-05-22
❌</span></p></td>
<td style="text-align: left;"><p>This is unavailable. Last check date is
2023-05-22.</p></td>
</tr>
</tbody>
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<td style="text-align: left;"><p><span class="box">💦</span></p></td>
<td style="text-align: left;"><p>Get this in a tricky way. Need a
simpler method.</p></td>
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</tbody>
</table>
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<td style="text-align: left;"><p><span class="box">No idea
😕</span></p></td>
<td style="text-align: left;"><p>Don’t know how to get this.</p></td>
</tr>
</tbody>
</table>
<p><strong>Rule One  </strong>Any mathematics at all, even a single
character, gets a mathematical setting. Thus, for “the value of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>x</mi><annotation encoding="application/x-tex">x</annotation></semantics></math>
is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mn>7</mn><annotation encoding="application/x-tex">7</annotation></semantics></math>”
enter <code>the value of $x$ is $7$</code>.</p>
<p><strong>Template  </strong>Your document should contain at least
this.</p>
<table>
<tbody>
<tr class="odd">
<td></td>
<td><pre><code>-- document body here --
  </code></pre></td>
</tr>
</tbody>
</table>
<p><strong>Common constructs  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>x</mi><mn>2</mn></msup><annotation encoding="application/x-tex">x^{2}</annotation></semantics></math> <code>x^2</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msqrt><mn>2</mn></msqrt><annotation encoding="application/x-tex">\sqrt{2}</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mroot><mn>3</mn><mi>n</mi></mroot><annotation encoding="application/x-tex">\sqrt[n]{3}</annotation></semantics></math> <code>sqrt(2)</code>,
<code>root(n, 3)</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi>x</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><annotation encoding="application/x-tex">x_{i,j}</annotation></semantics></math> <code>x_(i, j)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfrac><mn>2</mn><mn>3</mn></mfrac><annotation encoding="application/x-tex">\frac{2}{3}</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>/</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">2/3</annotation></semantics></math> <code>2 / 3</code>,
<code>2 \/ 3</code> or <code>2 slash 3</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Calligraphic letters  </strong>Use as in
<code>$cal(A)$</code>.</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝒜</mi><mi>ℬ</mi><mi>𝒞</mi><mi>𝒟</mi><mi>ℰ</mi><mi>ℱ</mi><mi>𝒢</mi><mi>ℋ</mi><mi>ℐ</mi><mi>𝒥</mi><mi>𝒦</mi><mi>ℒ</mi><mi>ℳ</mi><mi>𝒩</mi><mi>𝒪</mi><mi>𝒫</mi><mi>𝒬</mi><mi>ℛ</mi><mi>𝒮</mi><mi>𝒯</mi><mi>𝒰</mi><mi>𝒱</mi><mi>𝒲</mi><mi>𝒳</mi><mi>𝒴</mi><mi>𝒵</mi></mrow><annotation encoding="application/x-tex">\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}</annotation></semantics></math></p>
<p>Getting script letters is</p>
<p><strong>Greek  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>α</mi><annotation encoding="application/x-tex">\alpha</annotation></semantics></math> <code>alpha</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ξ</mi><annotation encoding="application/x-tex">\xi</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ξ</mi><annotation encoding="application/x-tex">\Xi</annotation></semantics></math> <code>xi</code>,
<code>Xi</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>β</mi><annotation encoding="application/x-tex">\beta</annotation></semantics></math> <code>beta</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ο</mi><annotation encoding="application/x-tex">ο</annotation></semantics></math> <code>omicron</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>γ</mi><annotation encoding="application/x-tex">\gamma</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Γ</mi><annotation encoding="application/x-tex">\Gamma</annotation></semantics></math> <code>gamma</code>,
<code>Gamma</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>π</mi><annotation encoding="application/x-tex">\pi</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Π</mi><annotation encoding="application/x-tex">\Pi</annotation></semantics></math> <code>pi</code>,
<code>Pi</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>δ</mi><annotation encoding="application/x-tex">\delta</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Δ</mi><annotation encoding="application/x-tex">\Delta</annotation></semantics></math> <code>delta</code>,
<code>Delta</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ϖ</mo><annotation encoding="application/x-tex">\varpi</annotation></semantics></math> <code>pi.alt</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϵ</mi><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math> <code>epsilon.alt</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ρ</mi><annotation encoding="application/x-tex">\rho</annotation></semantics></math> <code>rho</code></span></p></td>
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<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ε</mi><annotation encoding="application/x-tex">\varepsilon</annotation></semantics></math> <code>epsilon</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>𝜚</mo><annotation encoding="application/x-tex">\varrho</annotation></semantics></math> <code>rho.alt</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ζ</mi><annotation encoding="application/x-tex">\zeta</annotation></semantics></math> <code>zeta</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>σ</mi><annotation encoding="application/x-tex">\sigma</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Σ</mi><annotation encoding="application/x-tex">\Sigma</annotation></semantics></math> <code>sigma</code>,
<code>Sigma</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>η</mi><annotation encoding="application/x-tex">\eta</annotation></semantics></math> <code>eta</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>𝜍</mo><annotation encoding="application/x-tex">\varsigma</annotation></semantics></math> <code>\u{03C2}</code>
</span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>θ</mi><annotation encoding="application/x-tex">\theta</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Θ</mi><annotation encoding="application/x-tex">\Theta</annotation></semantics></math> <code>theta</code>,
<code>Theta</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>τ</mi><annotation encoding="application/x-tex">\tau</annotation></semantics></math> <code>tau</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϑ</mi><annotation encoding="application/x-tex">\vartheta</annotation></semantics></math> <code>theta.alt</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>υ</mi><annotation encoding="application/x-tex">\upsilon</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Υ</mi><annotation encoding="application/x-tex">\Upsilon</annotation></semantics></math> <code>upsilon</code>,
<code>Upsilon</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ι</mi><annotation encoding="application/x-tex">\iota</annotation></semantics></math> <code>iota</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ϕ</mi><annotation encoding="application/x-tex">\phi</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Φ</mi><annotation encoding="application/x-tex">\Phi</annotation></semantics></math> <code>phi.alt</code>,
<code>Phi</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>κ</mi><annotation encoding="application/x-tex">\kappa</annotation></semantics></math> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Κ</mi><annotation encoding="application/x-tex">Κ</annotation></semantics></math></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>φ</mi><annotation encoding="application/x-tex">\varphi</annotation></semantics></math> <code>phi</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>λ</mi><annotation encoding="application/x-tex">\lambda</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Λ</mi><annotation encoding="application/x-tex">\Lambda</annotation></semantics></math> <code>lambda</code>,
<code>Lambda</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>χ</mi><annotation encoding="application/x-tex">\chi</annotation></semantics></math> <code>chi</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>μ</mi><annotation encoding="application/x-tex">\mu</annotation></semantics></math> <code>mu</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ψ</mi><annotation encoding="application/x-tex">\psi</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ψ</mi><annotation encoding="application/x-tex">\Psi</annotation></semantics></math> <code>psi</code>,
<code>Psi</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ν</mi><annotation encoding="application/x-tex">\nu</annotation></semantics></math> <code>nu</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ω</mi><annotation encoding="application/x-tex">\omega</annotation></semantics></math>,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>Ω</mi><annotation encoding="application/x-tex">\Omega</annotation></semantics></math> <code>omega</code>,
<code>Omega</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Sets and logic  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∪</mo><annotation encoding="application/x-tex">\cup</annotation></semantics></math> <code>union</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℝ</mi><annotation encoding="application/x-tex">\mathbb{R}</annotation></semantics></math> <code>RR</code>,
<code>bb(R)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∀</mo><annotation encoding="application/x-tex">\forall</annotation></semantics></math> <code>forall</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∩</mo><annotation encoding="application/x-tex">\cap</annotation></semantics></math> <code>sect</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℤ</mi><annotation encoding="application/x-tex">\mathbb{Z}</annotation></semantics></math> <code>ZZ</code>,
<code>bb(Z)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∃</mo><annotation encoding="application/x-tex">\exists</annotation></semantics></math> <code>exists</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊂</mo><annotation encoding="application/x-tex">\subset</annotation></semantics></math> <code>subset</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℚ</mi><annotation encoding="application/x-tex">\mathbb{Q}</annotation></semantics></math> <code>QQ</code>,
<code>bb(Q)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>¬</mo><annotation encoding="application/x-tex">\neg</annotation></semantics></math> <code>not</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊆</mo><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math> <code>subset.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℕ</mi><annotation encoding="application/x-tex">\mathbb{N}</annotation></semantics></math> <code>NN</code>,
<code>bb(N)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∨</mo><annotation encoding="application/x-tex">\vee</annotation></semantics></math> <code>or</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊃</mo><annotation encoding="application/x-tex">\supset</annotation></semantics></math> <code>supset</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>ℂ</mi><annotation encoding="application/x-tex">\mathbb{C}</annotation></semantics></math> <code>CC</code>,
<code>bb(C)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∧</mo><annotation encoding="application/x-tex">\land</annotation></semantics></math> <code>and</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊇</mo><annotation encoding="application/x-tex">\supseteq</annotation></semantics></math> <code>supset.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math> <code>diameter</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊢</mo><annotation encoding="application/x-tex">\vdash</annotation></semantics></math> <code>tack.r</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∈</mo><annotation encoding="application/x-tex">\in</annotation></semantics></math> <code>in</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math> <code>nothing</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊨</mo><annotation encoding="application/x-tex">\models</annotation></semantics></math> <code>models</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∉</mo><annotation encoding="application/x-tex">\notin</annotation></semantics></math> <code>in.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>א</mi><annotation encoding="application/x-tex">א</annotation></semantics></math> <code>alef</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∖</mo><annotation encoding="application/x-tex">\smallsetminus</annotation></semantics></math> <code>without</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p>Negate an operator, as in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊄</mo><annotation encoding="application/x-tex">⊄</annotation></semantics></math>,
with <code>subset.not</code>. Get the set complement
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>A</mi><mi>𝖼</mi></msup><annotation encoding="application/x-tex">A^{\mathsf{c}}</annotation></semantics></math>
with <code>A^(sans(c))</code> (or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>A</mi><mi>∁</mi></msup><annotation encoding="application/x-tex">A^{\complement}</annotation></semantics></math>
with <code>A^(complement)</code>, or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><mi>A</mi><mo accent="true">¯</mo></munder><annotation encoding="application/x-tex">\underset{¯}{A}</annotation></semantics></math>
with <code>overline(A)</code>).</p>
<dl>
<dt>Remark</dt>
<dd>
<p>Using <code>diameter</code> for <code>\varnothing</code> may cause
some confusion. However, <span class="box">L A <span class="box">T E X</span></span> also uses
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math>
(<code>\u{2300}</code>) instead of
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math>
(<code>\u{2205}</code>), see <u><a href="https://mirrors.sustech.edu.cn/CTAN/fonts/newcomputermodern/doc/newcm-doc.pdf">newcm
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>§</mi><annotation encoding="application/x-tex">§</annotation></semantics></math>13.3</a></u>.
Another solution is to use
<code>text(font: &quot;Fira Sans&quot;, nothing)</code>, but the resultant glyph
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>⌀</mi><annotation encoding="application/x-tex">\varnothing</annotation></semantics></math>
is subtly different from the widely used one. Ultimately, the choice is
always <strong>your decision</strong>.</p>
</dd>
</dl>
<p><strong>Decorations  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mi>′</mi></mrow><annotation encoding="application/x-tex">f\prime</annotation></semantics></math> <code>f&#39;</code>,
<code>f prime</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="false">⋅</mo></mover><annotation encoding="application/x-tex">\overset{\cdot}{a}</annotation></semantics></math> <code>dot(a)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="false">∼</mo></mover><annotation encoding="application/x-tex">\overset{\sim}{a}</annotation></semantics></math> <code>tilde(a)</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mi>″</mi></mrow><annotation encoding="application/x-tex">f&#39;&#39;</annotation></semantics></math> <code>f prime.double</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">¨</mo></mover><annotation encoding="application/x-tex">\overset{¨}{a}</annotation></semantics></math> <code>diaer(a)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">¯</mo></mover><annotation encoding="application/x-tex">\overline{a}</annotation></semantics></math> <code>macron(a)</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>Σ</mi><mo>*</mo></msup><annotation encoding="application/x-tex">\Sigma^{*}</annotation></semantics></math> <code>Sigma^*</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{a}</annotation></semantics></math> <code>hat(a)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">→</mo></mover><annotation encoding="application/x-tex">\overset{\rightarrow}{a}</annotation></semantics></math> <code>arrow(a)</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p>If the decorated letter is
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>i</mi><annotation encoding="application/x-tex">i</annotation></semantics></math>
or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>j</mi><annotation encoding="application/x-tex">j</annotation></semantics></math>
then some decorations need <code>\u{1D6A4}</code> and
<code>\u{1D6A5}</code> , as in
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mo>ı</mo><mo accent="true">→</mo></mover><annotation encoding="application/x-tex">\overset{\rightarrow}{\imath}</annotation></semantics></math>
with <code>arrow(\u{1D6A4})</code>. Some authors use boldface for
vectors: <code>bold(x)</code>.</p>
<p>Entering <code>overline(x + y)</code> produces
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo accent="true">¯</mo></munder><annotation encoding="application/x-tex">\underset{¯}{x + y}</annotation></semantics></math>,
and <code>hat(x + y)</code> gives
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo accent="true">̂</mo></mover><annotation encoding="application/x-tex">\hat{x + y}</annotation></semantics></math>.
Comment on an expression as here (there is also
<code>overbrace(..)</code>).</p>
<div data-align="center">
<p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><munder><munder><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mo accent="true">⏟</mo></munder><mrow><mo stretchy="true" form="prefix">|</mo><mi>A</mi><mo stretchy="true" form="postfix">|</mo></mrow></munder><annotation encoding="application/x-tex">\underset{|A|}{\underbrace{x + y}}</annotation></semantics></math> <code>underbrace(x + y, |A|)</code></span></p>
</div>
<p><strong>Dots  </strong>Use low dots in a list
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mi>…</mi><mo stretchy="true" form="postfix">}</mo></mrow><annotation encoding="application/x-tex">\left\{ 0,1,2,\ldots \right\}</annotation></semantics></math>,
entered as <code>{0, 1, 2, ...}</code>. Use centered dots in a sum or
product
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>+</mo><mi>⋯</mi><mo>+</mo><mn>100</mn></mrow><annotation encoding="application/x-tex">1 + \cdots + 100</annotation></semantics></math>,
entered as <code>1 + dots.h.c + 100</code>. You can also get vertical
dots <code>dots.v</code>, diagonal dots <code>dots.down</code> and
anti-diagonal dots <code>dots.up</code>.</p>
<p><strong>Roman names  </strong>Just type them!</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sin</mo><annotation encoding="application/x-tex">\sin</annotation></semantics></math> <code>sin</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sinh</mo><annotation encoding="application/x-tex">\sinh</annotation></semantics></math> <code>sinh</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arcsin</mo><annotation encoding="application/x-tex">\arcsin</annotation></semantics></math> <code>arcsin</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cos</mo><annotation encoding="application/x-tex">\cos</annotation></semantics></math> <code>cos</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cosh</mo><annotation encoding="application/x-tex">\cosh</annotation></semantics></math> <code>cosh</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arccos</mo><annotation encoding="application/x-tex">\arccos</annotation></semantics></math> <code>arccos</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>tan</mo><annotation encoding="application/x-tex">\tan</annotation></semantics></math> <code>tan</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>tanh</mo><annotation encoding="application/x-tex">\tanh</annotation></semantics></math> <code>tanh</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arctan</mo><annotation encoding="application/x-tex">\arctan</annotation></semantics></math> <code>arctan</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sec</mo><annotation encoding="application/x-tex">\sec</annotation></semantics></math> <code>sec</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>coth</mo><annotation encoding="application/x-tex">\coth</annotation></semantics></math> <code>coth</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>min</mo><annotation encoding="application/x-tex">\min</annotation></semantics></math> <code>min</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>csc</mo><annotation encoding="application/x-tex">\csc</annotation></semantics></math> <code>csc</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>det</mo><annotation encoding="application/x-tex">\det</annotation></semantics></math> <code>det</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>max</mo><annotation encoding="application/x-tex">\max</annotation></semantics></math> <code>max</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>cot</mo><annotation encoding="application/x-tex">\cot</annotation></semantics></math> <code>cot</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>dim</mo><annotation encoding="application/x-tex">\dim</annotation></semantics></math> <code>dim</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>inf</mo><annotation encoding="application/x-tex">\inf</annotation></semantics></math> <code>inf</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>exp</mo><annotation encoding="application/x-tex">\exp</annotation></semantics></math> <code>exp</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ker</mo><annotation encoding="application/x-tex">\ker</annotation></semantics></math> <code>ker</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>sup</mo><annotation encoding="application/x-tex">\sup</annotation></semantics></math> <code>sup</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>log</mo><annotation encoding="application/x-tex">\log</annotation></semantics></math> <code>log</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>deg</mo><annotation encoding="application/x-tex">\deg</annotation></semantics></math> <code>deg</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>liminf</mo><annotation encoding="application/x-tex">\liminf</annotation></semantics></math> <code>liminf</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ln</mo><annotation encoding="application/x-tex">\ln</annotation></semantics></math> <code>ln</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>arg</mo><annotation encoding="application/x-tex">\arg</annotation></semantics></math> <code>arg</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>limsup</mo><annotation encoding="application/x-tex">\limsup</annotation></semantics></math> <code>limsup</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>lg</mo><annotation encoding="application/x-tex">\lg</annotation></semantics></math> <code>lg</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>gcd</mo><annotation encoding="application/x-tex">\gcd</annotation></semantics></math> <code>gcd</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>lim</mo><annotation encoding="application/x-tex">\lim</annotation></semantics></math> <code>lim</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Other symbols  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>&lt;</mo><annotation encoding="application/x-tex">&lt;</annotation></semantics></math> <code>&lt;</code>,
<code>lt</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∠</mi><annotation encoding="application/x-tex">\angle</annotation></semantics></math> <code>angle</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋅</mo><annotation encoding="application/x-tex">\cdot</annotation></semantics></math> <code>dot</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≤</mo><annotation encoding="application/x-tex">\leq</annotation></semantics></math> <code>&lt;=</code>,
<code>lt.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∡</mi><annotation encoding="application/x-tex">\measuredangle</annotation></semantics></math> <code>angle.arc</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>±</mo><annotation encoding="application/x-tex">\pm</annotation></semantics></math> <code>plus.minus</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>&gt;</mo><annotation encoding="application/x-tex">&gt;</annotation></semantics></math> <code>&gt;</code>,
<code>gt</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℓ</mo><annotation encoding="application/x-tex">\ell</annotation></semantics></math> <code>ell</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∓</mo><annotation encoding="application/x-tex">\mp</annotation></semantics></math> <code>minus.plus</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≥</mo><annotation encoding="application/x-tex">\geq</annotation></semantics></math> <code>&gt;=</code>,
<code>gt.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∥</mo><annotation encoding="application/x-tex">\parallel</annotation></semantics></math> <code>parallel</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>×</mo><annotation encoding="application/x-tex">\times</annotation></semantics></math> <code>times</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≠</mo><annotation encoding="application/x-tex">\neq</annotation></semantics></math> <code>!=</code>,
<code>eq.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>45</mn><msup><mi></mi><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">45{^\circ}</annotation></semantics></math> <code>45 degree</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>÷</mo><annotation encoding="application/x-tex">\div</annotation></semantics></math> <code>div</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&lt;</mo><mo>&lt;</mo></mrow><annotation encoding="application/x-tex">&lt; &lt;</annotation></semantics></math> <code>&lt;&lt;</code>,
<code>lt.double</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≅</mo><annotation encoding="application/x-tex">\cong</annotation></semantics></math> <code>tilde.eqq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>*</mo><annotation encoding="application/x-tex">*</annotation></semantics></math> <code>*</code>,
<code>ast</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">&gt; &gt;</annotation></semantics></math> <code>&gt;&gt;</code>,
<code>gt.double</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≇</mo><annotation encoding="application/x-tex">\ncong</annotation></semantics></math> <code>tilde.eqq.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∣</mo><annotation encoding="application/x-tex">\mid</annotation></semantics></math> <code>divides</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≈</mo><annotation encoding="application/x-tex">\approx</annotation></semantics></math> <code>approx</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∼</mo><annotation encoding="application/x-tex">\sim</annotation></semantics></math> <code>tilde</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∤</mo><annotation encoding="application/x-tex">\nmid</annotation></semantics></math> <code>divides.not</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≍</mo><annotation encoding="application/x-tex">\asymp</annotation></semantics></math> <code>\u{224D}</code>
</span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≃</mo><annotation encoding="application/x-tex">\simeq</annotation></semantics></math> <code>tilde.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mi>!</mi></mrow><annotation encoding="application/x-tex">n!</annotation></semantics></math> <code>n!</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≡</mo><annotation encoding="application/x-tex">\equiv</annotation></semantics></math> <code>ident</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≁</mo><annotation encoding="application/x-tex">\nsim</annotation></semantics></math> <code>tilde.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∂</mi><annotation encoding="application/x-tex">\partial</annotation></semantics></math> <code>diff</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≺</mo><annotation encoding="application/x-tex">\prec</annotation></semantics></math> <code>prec</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊕</mo><annotation encoding="application/x-tex">\oplus</annotation></semantics></math> <code>plus.circle</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>∇</mi><annotation encoding="application/x-tex">\nabla</annotation></semantics></math> <code>nabla</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≼</mo><annotation encoding="application/x-tex">\preccurlyeq</annotation></semantics></math> <code>prec.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊖</mo><annotation encoding="application/x-tex">\ominus</annotation></semantics></math> <code>minus.cirle</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>ℏ</mo><annotation encoding="application/x-tex">\hslash</annotation></semantics></math> <code>planck.reduce</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≻</mo><annotation encoding="application/x-tex">\succ</annotation></semantics></math> <code>succ</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊙</mo><annotation encoding="application/x-tex">\odot</annotation></semantics></math> <code>dot.circle</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∘</mo><annotation encoding="application/x-tex">\circ</annotation></semantics></math> <code>circle.stroked.tiny</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≽</mo><annotation encoding="application/x-tex">\succcurlyeq</annotation></semantics></math> <code>succ.eq</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊗</mo><annotation encoding="application/x-tex">\otimes</annotation></semantics></math> <code>times.circle</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋆</mo><annotation encoding="application/x-tex">\star</annotation></semantics></math> <code>star</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∝</mo><annotation encoding="application/x-tex">\propto</annotation></semantics></math> <code>prop</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⊘</mo><annotation encoding="application/x-tex">\oslash</annotation></semantics></math> <code>\u{2298}</code>
</span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msqrt><mrow></mrow></msqrt><annotation encoding="application/x-tex">\sqrt{}</annotation></semantics></math> <code>sqrt(&quot;&quot;)</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≐</mo><annotation encoding="application/x-tex">\doteq</annotation></semantics></math> <code>\u{2250}</code>
</span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↾</mo><annotation encoding="application/x-tex">\upharpoonright</annotation></semantics></math> <code>harpoon.tr</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>✓</mi><annotation encoding="application/x-tex">✓</annotation></semantics></math> <code>checkmark</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p>Use <code>a divides b</code> for the divides relation,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>∣</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">a \mid b</annotation></semantics></math>,
and <code>a divides.not b</code> for the negation,
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>∤</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">a \nmid b</annotation></semantics></math>.
Use <code>|</code> to get set builder notation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">{</mo><mi>a</mi><mo>∈</mo><mi>S</mi><mspace width="0.222em"></mspace><mo stretchy="false" form="prefix">|</mo><mspace width="0.222em"></mspace><mi>a</mi><mrow><mspace width="0.333em"></mspace><mtext mathvariant="normal"> is odd</mtext></mrow><mo stretchy="true" form="postfix">}</mo></mrow><annotation encoding="application/x-tex">\left\{ a \in S~|~a\text{ is odd} \right\}</annotation></semantics></math>
with <code>{a in S | a &quot;is odd&quot;}</code>.</p>
<p><strong>Arrows  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>→</mo><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math> <code>-&gt;</code>,
<code>arrow.r</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mo>→</mo></mrow><annotation encoding="application/x-tex">| \rightarrow</annotation></semantics></math> <code>|-&gt;</code>,
<code>arrow.r.bar</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↛</mo><annotation encoding="application/x-tex">\nrightarrow</annotation></semantics></math> <code>arrow.r.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↦</mo><annotation encoding="application/x-tex">\longmapsto</annotation></semantics></math> <code>arrow.r.long.bar</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>→</mo><annotation encoding="application/x-tex">\longrightarrow</annotation></semantics></math> <code>arrow.r.long</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>←</mo><annotation encoding="application/x-tex">\leftarrow</annotation></semantics></math> <code>&lt;-</code>,
<code>arrow.l</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇒</mo><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math> <code>=&gt;</code>,
<code>arrow.r.double</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>←</mo><mo>&gt;</mo></mrow><annotation encoding="application/x-tex">\leftarrow &gt;</annotation></semantics></math> <code>&lt;-&gt;</code>,
<code>arrow.l.r</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇏</mo><annotation encoding="application/x-tex">\nRightarrow</annotation></semantics></math> <code>arrow.r.double.not</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↓</mo><annotation encoding="application/x-tex">\downarrow</annotation></semantics></math> <code>arrow.b</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇒</mo><annotation encoding="application/x-tex">\Longrightarrow</annotation></semantics></math> <code>arrow.r.double.long</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↑</mo><annotation encoding="application/x-tex">\uparrow</annotation></semantics></math> <code>arrow.t</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⇜</mo><annotation encoding="application/x-tex">⇜</annotation></semantics></math> <code>arrow.squiggly</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>↕</mo><annotation encoding="application/x-tex">\updownarrow</annotation></semantics></math> <code>arrow.t.b</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p>The right arrows in the first column have matching left arrows, such
as <code>arrow.l.not</code>, and there are some other matches for down
arrows, etc.</p>
<p><strong>Variable-sized operators  </strong>The summation
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mn>3</mn></msubsup><msup><mi>j</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\sum_{j = 0}^{3}j^{2}</annotation></semantics></math>
<code>sum_(j = 0)^3 j^2</code> and the integral
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∫</mo><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow><mn>3</mn></msubsup><msup><mi>x</mi><mn>2</mn></msup><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\int_{x = 0}^{3}x^{2}dx</annotation></semantics></math>
<code>integral_(x = 0)^3 x^2 dif x</code> expand when displayed.</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mn>3</mn></munderover><msup><mi>j</mi><mn>2</mn></msup><mspace width="2.0em"></mspace><msubsup><mo>∫</mo><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow><mn>3</mn></msubsup><msup><mi>x</mi><mn>2</mn></msup><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\sum_{j = 0}^{3}j^{2}\qquad\int_{x = 0}^{3}x^{2}dx</annotation></semantics></math></p>
<p>These do the same.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∫</mo><annotation encoding="application/x-tex">\int</annotation></semantics></math> <code>integral</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∭</mo><annotation encoding="application/x-tex">\iiint</annotation></semantics></math> <code>integral.triple</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋃</mo><annotation encoding="application/x-tex">\bigcup</annotation></semantics></math> <code>union.big</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∬</mo><annotation encoding="application/x-tex">\iint</annotation></semantics></math> <code>integral.double</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>∮</mo><annotation encoding="application/x-tex">\oint</annotation></semantics></math> <code>integral.cont</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>⋂</mo><annotation encoding="application/x-tex">\bigcap</annotation></semantics></math> <code>sect.big</code></span></p></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Fences  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">()</annotation></semantics></math> <code>()</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">⟨</mo><mo stretchy="false" form="postfix">⟩</mo></mrow><annotation encoding="application/x-tex">\langle\rangle</annotation></semantics></math> <code>angle.l angle.r</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">|</mo><mo stretchy="true" form="postfix">|</mo></mrow><annotation encoding="application/x-tex">\left| \right|</annotation></semantics></math> <code>abs(&quot;&quot;)</code></span></p></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">[</mo><mo stretchy="false" form="postfix">]</mo></mrow><annotation encoding="application/x-tex">\lbrack\rbrack</annotation></semantics></math> <code>[]</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">⌊</mo><mo stretchy="true" form="postfix">⌋</mo></mrow><annotation encoding="application/x-tex">\left\lfloor \right\rfloor</annotation></semantics></math> <code>floor(&quot;&quot;)</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo>∥</mo></mrow><mo>∥</mo></mrow><annotation encoding="application/x-tex">\left. \parallel \right.\parallel</annotation></semantics></math> <code>norm(&quot;&quot;)</code></span></p></td>
</tr>
<tr class="odd">
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">{</mo><mo stretchy="true" form="postfix">}</mo></mrow><annotation encoding="application/x-tex">\left\{ \right\}</annotation></semantics></math> <code>{}</code></span></p></td>
<td style="text-align: left;"><p><span class="box"><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">⌈</mo><mo stretchy="true" form="postfix">⌉</mo></mrow><annotation encoding="application/x-tex">\left\lceil \right\rceil</annotation></semantics></math> <code>ceil(&quot;&quot;)</code></span></p></td>
<td style="text-align: left;"></td>
</tr>
</tbody>
</table>
</div>
<p>Fix the size with the <code>lr</code> function.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo stretchy="true" form="prefix">[</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover><msup><mi>e</mi><msup><mi>k</mi><mn>2</mn></msup></msup><mo stretchy="true" form="postfix">]</mo></mrow></mrow><annotation encoding="application/x-tex">\left. \left\lbrack \sum_{k = 0}^{n}e^{k^{2}} \right\rbrack \right.</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>lr([sum_(k = 0)^n e^(k^2)], size: #50%)
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>To have them grow with the enclosed formula, also use the
<code>lr</code> function.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">⟨</mo><mi>i</mi><mo>,</mo><msup><mn>2</mn><msup><mn>2</mn><mi>i</mi></msup></msup><mo stretchy="true" form="postfix">⟩</mo></mrow><annotation encoding="application/x-tex">\left\langle i,2^{2^{i}} \right\rangle</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>lr(angle.l i, 2^(2^i) angle.r)
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>Fences scale by default if entered directly as codepoints, and don’t
scale automatically if entered as symbol notation.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mn>1</mn><msup><mi>n</mi><mi>α</mi></msup></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\left( \frac{1}{n^{\alpha}} \right)</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>(1 / n^(alpha))
  </code></pre></td>
</tr>
<tr class="even">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mfrac><mn>1</mn><msup><mi>n</mi><mi>α</mi></msup></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">(\frac{1}{n^{\alpha}})</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>paren.l 1 / n^(alpha) paren.r
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>The <code>lr</code> function also allows to scale unmatched
delimiters and one-side fences.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mrow><mfrac><mrow><mi>d</mi><mi>f</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo stretchy="true" form="postfix">|</mo></mrow><msub><mi>x</mi><mn>0</mn></msub></msub><annotation encoding="application/x-tex">\left. \frac{df}{dx} \right|_{x_{0}}</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>lr(frac(dif f, dif x) |)_(x_0)
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Arrays, Matrices  </strong>Get a matrix with the
<code>mat</code> function. You can pass an array to it.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mtable><mtr><mtd columnalign="center" style="text-align: center"><mi>a</mi></mtd><mtd columnalign="center" style="text-align: center"><mi>b</mi></mtd></mtr><mtr><mtd columnalign="center" style="text-align: center"><mi>c</mi></mtd><mtd columnalign="center" style="text-align: center"><mi>d</mi></mtd></mtr></mtable><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\begin{pmatrix}
a &amp; b \\
c &amp; d
\end{pmatrix}</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>$ mat(a, b; c, d) $
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>In Typst, <u><a href="https://typst.app/docs/reference/typst/array">array</a></u> is a
sequence of values, while in <span class="box">L A <span class="box">T E X</span></span>, array is a matrix without fences, which
is <code>$mat(delim: #none, ..)$</code> in Typst.</p>
<p>For the determinant use <code>|A|</code>, text operator
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>det</mo><annotation encoding="application/x-tex">\det</annotation></semantics></math>
<code>det</code> or <code>mat(delim: &quot;|&quot;, ..)</code>.</p>
<p>Definition by cases can be easily obtained with the
<code>cases</code> function.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>n</mi></msub><mo>=</mo><mrow><mo stretchy="true" form="prefix">{</mo><mtable><mtr><mtd columnalign="left" style="text-align: left"><mi>a</mi></mtd><mtd columnalign="left" style="text-align: left"><mrow><mtext mathvariant="normal">if </mtext><mspace width="0.333em"></mspace></mrow><mi>n</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd columnalign="left" style="text-align: left"><mi>r</mi><mo>⋅</mo><msub><mi>f</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mtd><mtd columnalign="left" style="text-align: left"><mrow><mtext mathvariant="normal">else </mtext><mspace width="0.333em"></mspace></mrow></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">f_{n} = \begin{cases}
a &amp; \text{if }n = 0 \\
r \cdot f_{n - 1} &amp; \text{else }
\end{cases}</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>$ f_n = cases(
    a &amp;&quot;if&quot; n = 0,
    r dot f_(n - 1) &amp;&quot;else&quot;
  ) $
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Spacing in mathematics  </strong>Improve
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>2</mn></msqrt><mi>x</mi></mrow><annotation encoding="application/x-tex">\sqrt{2}x</annotation></semantics></math>
to
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>2</mn></msqrt><mspace width="0.167em"></mspace><mi>x</mi></mrow><annotation encoding="application/x-tex">\sqrt{2}\, x</annotation></semantics></math>
with a thin space, as in <code>sqrt(2) thin x</code>. Slightly wider are
<code>medium</code> and <code>thick</code> (the three are in ratio
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>:</mo><mn>4</mn><mo>:</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">3:4:5</annotation></semantics></math>).
Bigger space is <code>quad</code> for
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo><mspace width="1.0em"></mspace><mo>←</mo></mrow><annotation encoding="application/x-tex">\rightarrow \quad \leftarrow</annotation></semantics></math>,
which is useful between parts of a display. Get arbitrary space with the
<code>h</code> function. For example, use <code>#h(2em)</code> for
<code>\qquad</code> in <span class="box">L A <span class="box">T E X</span></span> and <code>#h(-0.1667em)</code> for
<code>\!</code>.</p>
<p><strong>Displayed equations  </strong>Display equations in a block
level using <code>$ ... $</code> with at least one space separating the
math content and the <code>$</code>.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mo>=</mo><mi>k</mi><mo>⋅</mo><mo>lg</mo><mi>W</mi></mrow><annotation encoding="application/x-tex">S = k \cdot \lg W</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>$ S = k dot lg W $
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>You can break into multiple lines.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mo>sin</mo><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><mi>x</mi><mo>−</mo><mfrac><msup><mi>x</mi><mn>3</mn></msup><mn>3</mn></mfrac><mi>!</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"><mo>+</mo><mfrac><msup><mi>x</mi><mn>5</mn></msup><mn>5</mn></mfrac><mi>!</mi><mo>−</mo><mi>⋯</mi></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{array}{r}
\sin(x) = x - \frac{x^{3}}{3}! \\
 + \frac{x^{5}}{5}! - \cdots
\end{array}</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>$ sin(x) = x - x^3 / 3! \
      + x^5 / 5! - dots.h.c $
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>Align equations using <code>&amp;</code></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td style="text-align: left;"><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right" style="text-align: right"><mi>∇</mi><mo>⋅</mo><mi>𝐃</mi></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><mi>ρ</mi></mtd></mtr><mtr><mtd columnalign="right" style="text-align: right"><mi>∇</mi><mo>⋅</mo><mi>𝐁</mi></mtd><mtd columnalign="left" style="text-align: left"><mo>=</mo><mn>0</mn></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}
\nabla \cdot \mathbf{D} &amp; = \rho \\
\nabla \cdot \mathbf{B} &amp; = 0
\end{aligned}</annotation></semantics></math></p></td>
<td style="text-align: left;"><pre><code>$ nabla dot bold(D) &amp;= rho \
    nabla dot bold(B) &amp;= 0 $
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>(the left or right side of an alignment can be empty). Get a numbered
version by <code>#set math.equation(numbering: ..)</code>.</p>
<p><strong>Calculus examples  </strong>The last three here are display
style.</p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td><div>
<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo>:</mo><mi>ℝ</mi><mo>→</mo><mi>ℝ</mi></mrow><annotation encoding="application/x-tex">f:{\mathbb{R}} \rightarrow {\mathbb{R}}</annotation></semantics></math></p>
</div></td>
<td><pre><code>f: RR -&gt; RR
  </code></pre></td>
</tr>
<tr class="even">
<td><div>
<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9.8</mn><mspace width="0.222em"></mspace><msup><mrow><mspace width="0.333em"></mspace><mtext mathvariant="normal"> m/s</mtext></mrow><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">9.8\ \text{ m/s}^{2}</annotation></semantics></math></p>
</div></td>
<td><div>
<p><code>&quot;9.8&quot; &quot;m/s&quot;^2</code></p>
</div></td>
</tr>
<tr class="odd">
<td><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>lim</mo><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo>+</mo><mi>h</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>−</mo><mi>f</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">\lim_{h \rightarrow 0}\frac{f(x + h) - f(x)}{h}</annotation></semantics></math></p></td>
<td><pre><code>lim_(h -&gt; 0) (f(x + h) - f(x)) / h
  </code></pre></td>
</tr>
<tr class="even">
<td><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∫</mo><msup><mi>x</mi><mn>2</mn></msup><mi>d</mi><mi>x</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mi>/</mi><mn>3</mn><mo>+</mo><mi>C</mi></mrow><annotation encoding="application/x-tex">\int x^{2}dx = x^{3}/3 + C</annotation></semantics></math></p></td>
<td><pre><code>integral x^2 dif x = x^3 \/ 3 + C
  </code></pre></td>
</tr>
<tr class="odd">
<td><p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>∇</mi><mo>=</mo><mi>𝐢</mi><mfrac><mi>d</mi><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>+</mo><mi>𝐣</mi><mfrac><mi>d</mi><mrow><mi>d</mi><mi>y</mi></mrow></mfrac><mo>+</mo><mi>𝐤</mi><mfrac><mi>d</mi><mrow><mi>d</mi><mi>z</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\nabla = \mathbf{i}\frac{d}{dx} + \mathbf{j}\frac{d}{dy} + \mathbf{k}\frac{d}{dz}</annotation></semantics></math></p></td>
<td><pre><code>nabla = bold(i) dif / (dif x) + bold(j) dif / (dif y) + bold(k) dif / (dif z)
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p><strong>Discrete mathematics examples  </strong>For modulo, there is
a symbol
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>≡</mo><annotation encoding="application/x-tex">\equiv</annotation></semantics></math>
from <code>ident</code> and a text operator
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>mod</mo><annotation encoding="application/x-tex">\operatorname{mod}</annotation></semantics></math>
from <code>mod</code>.</p>
<p>For combinations the binomial symbol
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="true" form="prefix">(</mo><mfrac linethickness="0"><mi>n</mi><mi>k</mi></mfrac><mo stretchy="true" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\binom{n}{k}</annotation></semantics></math>
is from <code>binom(n, k)</code>. This resizes to be bigger in a
display.</p>
<p>For permutations use
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>n</mi><munder><mi>r</mi><mo accent="true">_</mo></munder></msup><annotation encoding="application/x-tex">n^{\underline{r}}</annotation></semantics></math>
from <code>n^(underline(r))</code> (some authors use
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>n</mi><mo>,</mo><mi>r</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">P(n,r)</annotation></semantics></math>,
or
<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi></mi><mi>n</mi></msub><msub><mi>P</mi><mi>r</mi></msub></mrow><annotation encoding="application/x-tex">_{n}P_{r}</annotation></semantics></math>
from <code>&quot;&quot;_n P_r</code>).</p>
<p><strong>Statistics examples  </strong></p>
<div data-align="center">
<table>
<tbody>
<tr class="odd">
<td><div>
<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><msqrt><mrow><msup><mrow><mo>∑</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><mn>2</mn></msup><mi>/</mi><mi>N</mi></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sigma^{2} = \sqrt{{\sum(x_{i} - \mu)}^{2}/N}</annotation></semantics></math></p>
</div></td>
<td><pre><code>sigma^2 = sqrt(sum(x_i - mu)^2 \/ N)
  </code></pre></td>
</tr>
<tr class="even">
<td><div>
<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>X</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>=</mo><msub><mi>μ</mi><mi>X</mi></msub><mo>=</mo><mo>∑</mo><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>P</mi><mrow><mo stretchy="true" form="prefix">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="true" form="postfix">)</mo></mrow><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">E(X) = \mu_{X} = \sum(x_{i} - P\left( x_{i} \right))</annotation></semantics></math></p>
</div></td>
<td><pre><code>E(X) = mu_X = sum(x_i - P(x_i))
  </code></pre></td>
</tr>
</tbody>
</table>
</div>
<p>The probability density of the normal distribution</p>
<p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><msqrt><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup><mi>π</mi></mrow></msqrt></mfrac><msup><mi>e</mi><mrow><mo>−</mo><mfrac><msup><mrow><mo stretchy="true" form="prefix">(</mo><mi>x</mi><mo>−</mo><mi>μ</mi><mo stretchy="true" form="postfix">)</mo></mrow><mn>2</mn></msup><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfrac></mrow></msup></mrow><annotation encoding="application/x-tex">\frac{1}{\sqrt{2\sigma^{2}\pi}}e^{- \frac{(x - \mu)^{2}}{2\sigma^{2}}}</annotation></semantics></math></p>
<p>comes from this.</p>
<table>
<tbody>
<tr class="odd">
<td></td>
<td><pre><code>1 / sqrt(2 sigma^2 pi)
    e^(- (x - mu)^2 / (2 sigma^2))
  </code></pre></td>
</tr>
</tbody>
</table>
<p><strong>For more  </strong>See also the Typst Documentation at <u><a href="https://typst.app/docs">https://typst.app/docs</a></u>.</p>
<div>
<hr />
<p>johanvx (<u><a href="https://github.com/johanvx">https://github.com/johanvx</a></u>)
2023-05-22</p>
</div>
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