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<a href="../precalc/calculator.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">1</span> <span class="chapter-title">From calculator to computer</span></a>
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<a href="../precalc/plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">8</span> <span class="chapter-title">The Graph of a Function</span></a>
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<a href="../precalc/transformations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">9</span> <span class="chapter-title">Function manipulations</span></a>
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<a href="../precalc/inversefunctions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">10</span> <span class="chapter-title">The Inverse of a Function</span></a>
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<a href="../precalc/polynomial.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">11</span> <span class="chapter-title">Polynomials</span></a>
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<a href="../precalc/polynomials_package.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">13</span> <span class="chapter-title">The Polynomials package</span></a>
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<a href="../precalc/julia_overview.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">17</span> <span class="chapter-title">Overview of Julia commands</span></a>
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<a href="../derivatives/numeric_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">23</span> <span class="chapter-title">Numeric derivatives</span></a>
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|
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</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/center_of_mass.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">44</span> <span class="chapter-title">Center of Mass</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/volumes_slice.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">45</span> <span class="chapter-title">Volumes by slicing</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/arc_length.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">46</span> <span class="chapter-title">Arc length</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/surface_area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">47</span> <span class="chapter-title">Surface Area</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">ODEs</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-5" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/euler.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">49</span> <span class="chapter-title">Euler’s method</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/solve.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">50</span> <span class="chapter-title">The problem-algorithm-solve interface</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/differential_equations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">51</span> <span class="chapter-title">The <code>DifferentialEquations</code> suite</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">Differential vector calculus</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-6" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/polar_coordinates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">52</span> <span class="chapter-title">Polar Coordinates and Curves</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">53</span> <span class="chapter-title">Vectors and matrices</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vector_valued_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">54</span> <span class="chapter-title">Vector-valued functions, <span class="math inline">\(f:R \rightarrow R^n\)</span></span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/scalar_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span> <span class="chapter-title">Scalar functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/scalar_functions_applications.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">56</span> <span class="chapter-title">Applications with scalar functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vector_fields.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">57</span> <span class="chapter-title">Functions <span class="math inline">\(R^n \rightarrow R^m\)</span></span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/plots_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">58</span> <span class="chapter-title">2D and 3D plots in Julia with Plots</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">Integral vector calculus</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
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</a>
|
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</div>
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<ul id="quarto-sidebar-section-7" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/double_triple_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">59</span> <span class="chapter-title">Multi-dimensional integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/line_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">60</span> <span class="chapter-title">Line and Surface Integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/div_grad_curl.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">61</span> <span class="chapter-title">The Gradient, Divergence, and Curl</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/stokes_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">62</span> <span class="chapter-title">Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/review.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">63</span> <span class="chapter-title">Quick Review of Vector Calculus</span></a>
|
||
</div>
|
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|
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</ul>
|
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</li>
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<div class="sidebar-item-container">
|
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<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-8" aria-expanded="false">Alternatives</a>
|
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<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-8" aria-expanded="false">
|
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<i class="bi bi-chevron-right ms-2"></i>
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<div class="sidebar-item-container">
|
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<a href="../alternatives/plotly_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">64</span> <span class="chapter-title">JavaScript based plotting libraries</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
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<a href="../alternatives/makie_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">65</span> <span class="chapter-title">Calculus plots with Makie</span></a>
|
||
</div>
|
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</li>
|
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</ul>
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</li>
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<div class="sidebar-item-container">
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<a class="sidebar-item-text sidebar-link text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-9" aria-expanded="true">Appendices</a>
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<a class="sidebar-item-toggle text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-9" aria-expanded="true">
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<i class="bi bi-chevron-right ms-2"></i>
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<ul id="quarto-sidebar-section-9" class="collapse list-unstyled sidebar-section depth1 show">
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<li class="sidebar-item">
|
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<div class="sidebar-item-container">
|
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<a href="../misc/getting_started_with_julia.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">66</span> <span class="chapter-title">Getting started with Julia</span></a>
|
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</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/julia_interfaces.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/calculus_with_julia.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/unicode.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/quick_notes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">70</span> <span class="chapter-title">Quick introduction to Calculus with Julia</span></a>
|
||
</div>
|
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</li>
|
||
</ul>
|
||
</li>
|
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<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../references.html" class="sidebar-item-text sidebar-link">References</a>
|
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</div>
|
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</li>
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</ul>
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</div>
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</nav>
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<!-- margin-sidebar -->
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<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
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</div>
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<!-- main -->
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<main class="content" id="quarto-document-content">
|
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<header id="title-block-header" class="quarto-title-block default">
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<div class="quarto-title">
|
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<h1 class="title d-none d-lg-block"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></h1>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="quarto-title-meta">
|
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</div>
|
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</header>
|
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|
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<p><code>Julia</code> allows the use of <em>Unicode</em> symbols to replace variable names and for function calls. Unicode operations are entered in this pattern <code>\name[tab]</code>. That is a slash, <code>\</code>, the name (e.g., <code>alpha</code>), and then a press of the <code>tab</code> key.</p>
|
||
<p>In these notes, the following may appear as variable or function names</p>
|
||
<table class="table">
|
||
<thead>
|
||
<tr class="header">
|
||
<th style="text-align: left;"><code>\Name</code></th>
|
||
<th style="text-align: left;">Symbol</th>
|
||
<th style="text-align: left;">Usage notes</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\euler</code></td>
|
||
<td style="text-align: left;"><code>ℯ</code></td>
|
||
<td style="text-align: left;">The variable <code>e</code></td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\pi</code></td>
|
||
<td style="text-align: left;"><code>π</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\alpha</code></td>
|
||
<td style="text-align: left;"><code>α</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\beta</code></td>
|
||
<td style="text-align: left;"><code>β</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\delta</code></td>
|
||
<td style="text-align: left;"><code>δ</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\Delta</code></td>
|
||
<td style="text-align: left;"><code>Δ</code></td>
|
||
<td style="text-align: left;">Change, as in <code>Δx</code></td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\gamma</code></td>
|
||
<td style="text-align: left;"><code>γ</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\phi</code></td>
|
||
<td style="text-align: left;"><code>ϕ</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\Phi</code></td>
|
||
<td style="text-align: left;"><code>Φ</code></td>
|
||
<td style="text-align: left;">Used for parameterized surfaces</td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>x\_1</code></td>
|
||
<td style="text-align: left;"><code>x₁</code></td>
|
||
<td style="text-align: left;">Subscripts</td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>r\vec</code></td>
|
||
<td style="text-align: left;"><code>r⃗</code></td>
|
||
<td style="text-align: left;">Vector annotation</td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>T\hat</code></td>
|
||
<td style="text-align: left;"><code>T̂</code></td>
|
||
<td style="text-align: left;">Unit vector annotation</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p>The following are associated with derivatives</p>
|
||
<table class="table">
|
||
<thead>
|
||
<tr class="header">
|
||
<th style="text-align: left;"><code>\Name</code></th>
|
||
<th style="text-align: left;">Symbol</th>
|
||
<th style="text-align: left;">Usage notes</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\partial</code></td>
|
||
<td style="text-align: left;"><code>∂</code></td>
|
||
<td style="text-align: left;"></td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\nabla</code></td>
|
||
<td style="text-align: left;"><code>∇</code></td>
|
||
<td style="text-align: left;">del operator in CwJ package</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p>The following are <em>infix</em> operators</p>
|
||
<table class="table">
|
||
<thead>
|
||
<tr class="header">
|
||
<th style="text-align: left;"><code>\Name</code></th>
|
||
<th style="text-align: left;">Symbol</th>
|
||
<th style="text-align: left;">Usage notes</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\circ</code></td>
|
||
<td style="text-align: left;"><code>∘</code></td>
|
||
<td style="text-align: left;">composition</td>
|
||
</tr>
|
||
<tr class="even">
|
||
<td style="text-align: left;"><code>\cdot</code></td>
|
||
<td style="text-align: left;"><code>⋅</code></td>
|
||
<td style="text-align: left;">dot product</td>
|
||
</tr>
|
||
<tr class="odd">
|
||
<td style="text-align: left;"><code>\times</code></td>
|
||
<td style="text-align: left;"><code>×</code></td>
|
||
<td style="text-align: left;">cross product</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p>Infix operators may need parentheses due to precedence rules. For example, to call a composition, one needs <code>(f ∘ g)(x)</code> so that composition happens before function evaluation (<code>g(x)</code>).</p>
|
||
|
||
|
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|
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</main> <!-- /main -->
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<script id="quarto-html-after-body" type="application/javascript">
|
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window.document.addEventListener("DOMContentLoaded", function (event) {
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const toggleBodyColorMode = (bsSheetEl) => {
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const mode = bsSheetEl.getAttribute("data-mode");
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const bodyEl = window.document.querySelector("body");
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if (mode === "dark") {
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bodyEl.classList.add("quarto-dark");
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} else {
|
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bodyEl.classList.add("quarto-light");
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bodyEl.classList.remove("quarto-dark");
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}
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const toggleBodyColorPrimary = () => {
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const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
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if (bsSheetEl) {
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toggleBodyColorMode(bsSheetEl);
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anchorJS.options = {
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anchorJS.add('.anchored');
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const clipboard = new window.ClipboardJS('.code-copy-button', {
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target: function(trigger) {
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return trigger.previousElementSibling;
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}
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});
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clipboard.on('success', function(e) {
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// button target
|
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const button = e.trigger;
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// don't keep focus
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button.blur();
|
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// flash "checked"
|
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button.classList.add('code-copy-button-checked');
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var currentTitle = button.getAttribute("title");
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