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2 changes: 1 addition & 1 deletion README.md
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A *Simplex Tree* is an ordered, [trie](https://en.wikipedia.org/wiki/Trie)-like structure whose nodes are in bijection with the faces of the complex. Here's a picture of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):

![simplex tree picture](./docs/pages/static/simplextree_pic.png)
![simplex tree picture](./docs/static/simplextree.png)

The *Simplex Tree* was originally introduced in the following paper:

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8 changes: 4 additions & 4 deletions docs/pages/index.html
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<p>A <em>Simplex Tree</em> is an ordered, <a href="https://en.wikipedia.org/wiki/Trie">trie</a>-like structure whose nodes are in bijection with the faces of the complex. Here’s a picture of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):</p>
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<p><img src="./static/simplextree_pic.png" class="preview-image img-fluid figure-img"></p>
<p><img src="../static/simplextree.png" class="preview-image img-fluid figure-img"></p>
<figcaption class="figure-caption">Picture taken from Boissonnat et al: “The simplex tree: An efficient data structure for general simplicial complexes”</figcaption>
</figure>
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18 changes: 9 additions & 9 deletions docs/pages/overview.html
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<p>Like graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a <em>Simplex Tree</em>: an ordered, <a href="https://en.wikipedia.org/wiki/Trie">trie</a>-like structure whose nodes are in bijection with the faces of the complex. Here’s a picture of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):</p>
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<p><img src="./static/simplextree_pic.png" class="preview-image img-fluid figure-img"></p>
<p><img src="../static/simplextree.png" class="preview-image img-fluid figure-img"></p>
<figcaption class="figure-caption">Picture taken from Boissonnat et al: “The simplex tree: An efficient data structure for general simplicial complexes”</figcaption>
</figure>
</div>
<p>To construct the complex above with a <code>simplextree</code> package, simply give the maximal simplices:</p>
<div class="cell" data-execution_count="1">
<div class="cell" data-execution_count="2">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> simplextree <span class="im">import</span> SimplexTree</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>st <span class="op">=</span> SimplexTree([[<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>],[<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">5</span>],[<span class="dv">6</span>,<span class="dv">7</span>,<span class="dv">9</span>],[<span class="dv">7</span>,<span class="dv">8</span>],[<span class="dv">10</span>]]) <span class="co"># complex form the picture</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(st)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</div>
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<p>To look at the tree structure, use <code>print_tree</code> (see also: <code>print_cousins</code>)</p>
<div class="cell" data-execution_count="2">
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<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>st.print_tree()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>1 (h = 2): .( 2 3 )..( 3 )
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</div>
</div>
<p>To maintain fast coface lookup and enumeration, extra links are added between nodes at the same level, which are shown by the dash-dotted lines in the figure above (only for the nodes with the label <span class="math inline">5</span>). To view these links with the <code>SimplexTree</code> class, use <code>print_cousins()</code>:</p>
<div class="cell" data-execution_count="3">
<div class="cell" data-execution_count="4">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>st.print_cousins()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>(last=2, depth=2): { 1 2 }
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