From 935026cf4360a251e84068aa0e72bb73f8f9a211 Mon Sep 17 00:00:00 2001
From: peekxc <matt.piekenbrock@gmail.com>
Date: Mon, 21 Aug 2023 21:35:26 -0400
Subject: [PATCH] Doc updates

---
 docs/pages/index.html                         | 107 ++-
 docs/pages/overview.html                      |  57 +-
 docs/pages/quickstart.html                    | 724 ++++++++++++++++++
 .../reference/SimplexTree.SimplexTree.html    |  19 +-
 docs/pages/reference/UnionFind.UnionFind.html |  21 +-
 docs/pages/reference/index.html               |  19 +-
 docs/reference/SimplexTree.SimplexTree.html   |  19 +-
 docs/reference/UnionFind.UnionFind.html       |  19 +-
 docs/reference/index.html                     |  29 +-
 docs/search.json                              | 165 ++--
 docs/static/styles.css                        |   7 +-
 docs_src/README.md                            |   7 +
 .../pages/overview/execute-results/html.json  |   4 +-
 .../quickstart/execute-results/html.json      |  11 +
 docs_src/_quarto.yml                          |   7 +-
 .../base.ipynb                                | 412 ++++++++++
 .../base.ipynb                                | 483 ++++++++++++
 .../base.ipynb                                | 481 ++++++++++++
 .../base.ipynb                                | 370 +++++++++
 .../base.ipynb                                | 428 +++++++++++
 .../base.ipynb                                | 331 ++++++++
 docs_src/pages/.jupyter_cache/global.db       | Bin 28672 -> 28672 bytes
 docs_src/pages/index.qmd                      | 118 +--
 docs_src/pages/overview.qmd                   |  11 +-
 docs_src/pages/quickstart.qmd                 | 100 +++
 docs_src/static/styles.css                    |   7 +-
 26 files changed, 3690 insertions(+), 266 deletions(-)
 create mode 100644 docs/pages/quickstart.html
 create mode 100644 docs_src/README.md
 create mode 100644 docs_src/_freeze/pages/quickstart/execute-results/html.json
 create mode 100644 docs_src/pages/.jupyter_cache/executed/87ea35e450ca33aa4dfbf936f10fa3ff/base.ipynb
 create mode 100644 docs_src/pages/.jupyter_cache/executed/a429fb4fec801f421aec0269aea0eeed/base.ipynb
 create mode 100644 docs_src/pages/.jupyter_cache/executed/a506d01bae855566e389b8497d151022/base.ipynb
 create mode 100644 docs_src/pages/.jupyter_cache/executed/acbf0e7a3056dde9fe641060139e060b/base.ipynb
 create mode 100644 docs_src/pages/.jupyter_cache/executed/be653243cbe262d890472aafedfcdd45/base.ipynb
 create mode 100644 docs_src/pages/.jupyter_cache/executed/fbb32eb408717b6f66aebf947b8c0726/base.ipynb
 create mode 100644 docs_src/pages/quickstart.qmd

diff --git a/docs/pages/index.html b/docs/pages/index.html
index ae189db..3d48c65 100644
--- a/docs/pages/index.html
+++ b/docs/pages/index.html
@@ -7,7 +7,7 @@
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 
-<title>simplextree – index</title>
+<title>index</title>
 <style>
 code{white-space: pre-wrap;}
 span.smallcaps{font-variant: small-caps;}
@@ -20,6 +20,40 @@
   margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */ 
   vertical-align: middle;
 }
+/* CSS for syntax highlighting */
+pre > code.sourceCode { white-space: pre; position: relative; }
+pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
+pre > code.sourceCode > span:empty { height: 1.2em; }
+.sourceCode { overflow: visible; }
+code.sourceCode > span { color: inherit; text-decoration: inherit; }
+div.sourceCode { margin: 1em 0; }
+pre.sourceCode { margin: 0; }
+@media screen {
+div.sourceCode { overflow: auto; }
+}
+@media print {
+pre > code.sourceCode { white-space: pre-wrap; }
+pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
+}
+pre.numberSource code
+  { counter-reset: source-line 0; }
+pre.numberSource code > span
+  { position: relative; left: -4em; counter-increment: source-line; }
+pre.numberSource code > span > a:first-child::before
+  { content: counter(source-line);
+    position: relative; left: -1em; text-align: right; vertical-align: baseline;
+    border: none; display: inline-block;
+    -webkit-touch-callout: none; -webkit-user-select: none;
+    -khtml-user-select: none; -moz-user-select: none;
+    -ms-user-select: none; user-select: none;
+    padding: 0 4px; width: 4em;
+  }
+pre.numberSource { margin-left: 3em;  padding-left: 4px; }
+div.sourceCode
+  {   }
+@media screen {
+pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
+}
 </style>
 
 
@@ -73,15 +107,16 @@
   <header id="quarto-header" class="headroom fixed-top">
     <nav class="navbar navbar-expand-lg navbar-dark ">
       <div class="navbar-container container-fluid">
-      <div class="navbar-brand-container">
-    <a class="navbar-brand" href="../index.html">
-    <span class="navbar-title">simplextree</span>
-    </a>
-  </div>
           <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
   <span class="navbar-toggler-icon"></span>
 </button>
           <div class="collapse navbar-collapse" id="navbarCollapse">
+            <ul class="navbar-nav navbar-nav-scroll me-auto">
+  <li class="nav-item">
+    <a class="nav-link active" href="../pages/index.html" rel="" target="" aria-current="page">
+ <span class="menu-text">simplextree</span></a>
+  </li>  
+</ul>
             <ul class="navbar-nav navbar-nav-scroll ms-auto">
   <li class="nav-item compact">
     <a class="nav-link" href="https://github.com/peekxc/simplextree-py" rel="" target=""><i class="bi bi-github" role="img">
@@ -105,7 +140,7 @@
       <button type="button" class="quarto-btn-toggle btn" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
         <i class="bi bi-layout-text-sidebar-reverse"></i>
       </button>
-      <nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item">Installation</li></ol></nav>
+      <nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item">simplextree</li></ol></nav>
       <a class="flex-grow-1" role="button" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">      
       </a>
       <button type="button" class="btn quarto-search-button" aria-label="" onclick="window.quartoOpenSearch();">
@@ -127,6 +162,12 @@
     <ul class="list-unstyled mt-1">
         <li class="sidebar-item">
   <div class="sidebar-item-container"> 
+  <a href="../pages/quickstart.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">Quick start</span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
   <a href="../pages/overview.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text">Overview</span></a>
   </div>
@@ -160,14 +201,22 @@
 <div id="quarto-sidebar-glass" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass"></div>
 <!-- margin-sidebar -->
     <div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
-        
+        <nav id="TOC" role="doc-toc" class="toc-active" data-toc-expanded="3">
+    <h2 id="toc-title">On this page</h2>
+   
+  <ul>
+  <li><a href="#install" id="toc-install" class="nav-link active" data-scroll-target="#install">Install</a></li>
+  <li><a href="#building-developing" id="toc-building-developing" class="nav-link" data-scroll-target="#building-developing">Building &amp; Developing</a></li>
+  <li><a href="#native-extensions" id="toc-native-extensions" class="nav-link" data-scroll-target="#native-extensions">Native Extensions</a></li>
+  </ul>
+</nav>
     </div>
 <!-- main -->
 <main class="content" id="quarto-document-content">
 
 <header id="title-block-header" class="quarto-title-block default">
 <div class="quarto-title">
-<h1 class="title">Installation</h1>
+<h1 class="title">simplextree</h1>
 </div>
 
 
@@ -182,22 +231,42 @@ <h1 class="title">Installation</h1>
 
 </header>
 
-<p><a href="https://github.com/peekxc/splex/actions/workflows/package.yml"><img src="https://github.com/peekxc/splex/actions/workflows/package.yml/badge.svg" class="img-fluid" alt="Tests"></a> <a href="https://coveralls.io/github/peekxc/splex"><img src="https://img.shields.io/endpoint?url=https://gist.githubusercontent.com/peekxc/ef42349965f40edf4232737026690c5f/raw/coverage_info.json" class="img-fluid" alt="coverage_badge"></a> <a href="https://github.com/peekxc/splex/actions/workflows/python-package.yml"><img src="https://img.shields.io/badge/python-3.9%20%7C%203.10%20%7C%203.11-blue" class="img-fluid" alt="python_badge"></a> <a href="https://github.com/peekxc/splex/actions/workflows/build-macos.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-macos.yml?logo=apple&amp;logoColor=white" class="img-fluid" alt="coverage_badge"></a> <a href="https://github.com/peekxc/splex/actions/workflows/build-windows.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-windows.yml?logo=windows&amp;logoColor=white" class="img-fluid" alt="coverage_badge"></a> <a href="https://github.com/peekxc/splex/actions/workflows/build-linux.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-linux.yml?logo=linux&amp;logoColor=white" class="img-fluid" alt="coverage_badge"></a></p>
-<p><code>simplextree</code> is a Python package aimed at simplifying computation for general simplicial complexes of any dimension. This package facilitates this aim by providing bindings to a Simplex Tree data structure implemented using modern C++ and exported an <a href="https://docs.python.org/3/extending/extending.html">extension module</a>. <!-- The underlying library implementation also exports a C++ header, which can be specified as a dependency and used in other packages. --></p>
-<p>The Simplex Tree was originally introduced in the following paper:</p>
-<blockquote class="blockquote">
-<p>Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.</p>
-</blockquote>
-<p>A Simplex Tree is an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. Here’s a picture (taken from the paper) of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):</p>
+<p><a href="https://coveralls.io/github/peekxc/simplextree-py"><img src="https://img.shields.io/endpoint?url=https://gist.githubusercontent.com/peekxc/ef42349965f40edf4232737026690c5f/raw/coverage_info.json" class="img-fluid" alt="coverage_badge"></a> <a href="https://github.com/peekxc/simplextree-py/actions/workflows/build-macos.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_macos.yml?logo=apple&amp;logoColor=white" class="img-fluid" alt="build_macos"></a> <a href="https://github.com/peekxc/simplextree-py/actions/workflows/build-windows.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_windows.yml?logo=windows&amp;logoColor=white" class="img-fluid" alt="build_windows"></a> <a href="https://github.com/peekxc/simplextree-py/actions/workflows/build-linux.yml"><img src="https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_linux.yml?logo=linux&amp;logoColor=white" class="img-fluid" alt="build_linux"></a></p>
+<p><code>simplextree</code> is an Python package that simplifies computation for general <a href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complexes</a> of any dimension by providing <a href="https://github.com/pybind/pybind11">pybind11</a> bindings to a <em>Simplex Tree</em> data structure implemented in modern C++17.</p>
+<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>
 <div class="quarto-figure quarto-figure-center">
 <figure class="figure">
-<p><img src="static/simplextree_pic.png" class="preview-image img-fluid figure-img"></p>
-<figcaption class="figure-caption">simplextree</figcaption>
+<p><img src="./static/simplextree_pic.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>TODO</p>
+<p>The <em>Simplex Tree</em> was originally introduced in the following paper:</p>
+<blockquote class="blockquote">
+<p>Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.</p>
+</blockquote>
+<p>The <code>SimplexTree</code> class exported by the package includes support for many tree operations, e.g.&nbsp;insertions, removals, expansions, collapses, star/link enumerations, and other traversals.</p>
+<section id="install" class="level2">
+<h2 class="anchored" data-anchor-id="install">Install</h2>
+<p>The easiest way to install the package is via the platform-specific <a href="https://pythonwheels.com/">wheels</a> on <a href="https://pypi.org/project/simplextree/">pypi</a>.</p>
+<div class="sourceCode" id="cb1"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="ex">python</span> <span class="at">-m</span> pip install simplextree </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>You can also <code>pip install</code> the package manually by downloading the appropriate wheel (or sdist) from the <a href="https://github.com/peekxc/simplextree-py/releases/">releases</a>.</p>
+<p>For installation instructions for developers looking to extend the package, see <a href="#building--developing">Building &amp; Developing</a>.</p>
+</section>
+<section id="building-developing" class="level2">
+<h2 class="anchored" data-anchor-id="building-developing">Building &amp; Developing</h2>
+<p>If you would like to build the package yourself for development reasons, a typical workflow is to install the <a href="https://pip.pypa.io/en/stable/reference/build-system/pyproject-toml/#build-time-dependencies">build-time dependencies</a> first:</p>
+<div class="sourceCode" id="cb2"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="ex">python</span> <span class="at">-m</span> pip install meson-python ninja pybind11 numpy</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>Then, build and install the package in <a href="https://peps.python.org/pep-0660/">editable mode</a> (see also <a href="https://meson-python.readthedocs.io/en/latest/how-to-guides/editable-installs.html">meson-python notes</a>), optionally without build isolation for speed:</p>
+<div class="sourceCode" id="cb3"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ex">python</span> <span class="at">-m</span> pip install <span class="at">--no-build-isolation</span> <span class="at">--editable</span> .</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>Unit testing is handled with <a href="https://docs.pytest.org/en/7.4.x/">pytest</a>. See the <a href="https://github.com/peekxc/simplextree-py/actions">gh-workflows</a> for platform-specific configuration.</p>
+</section>
+<section id="native-extensions" class="level2">
+<h2 class="anchored" data-anchor-id="native-extensions">Native Extensions</h2>
+<p>The underlying C++ library is <a href="https://en.wikipedia.org/wiki/Header-only">header-only</a> and may be included as a dependency by <a href="https://docs.python.org/3/extending/extending.html">extension modules</a> in other Python packages.</p>
+<p>Thus, to modify or extending the complex in C++, it is sufficient to add the package as a build-time dependency and append the include directory to the compilation target.</p>
 
 
+</section>
 
 </main> <!-- /main -->
 <script id="quarto-html-after-body" type="application/javascript">
diff --git a/docs/pages/overview.html b/docs/pages/overview.html
index 97785f6..49bd22c 100644
--- a/docs/pages/overview.html
+++ b/docs/pages/overview.html
@@ -7,7 +7,7 @@
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 
-<title>simplextree – overview</title>
+<title>overview</title>
 <style>
 code{white-space: pre-wrap;}
 span.smallcaps{font-variant: small-caps;}
@@ -65,6 +65,7 @@
 <script src="../site_libs/quarto-search/quarto-search.js"></script>
 <meta name="quarto:offset" content="../">
 <link href="../reference/index.html" rel="next">
+<link href="../pages/quickstart.html" rel="prev">
 <script src="../site_libs/quarto-html/quarto.js"></script>
 <script src="../site_libs/quarto-html/popper.min.js"></script>
 <script src="../site_libs/quarto-html/tippy.umd.min.js"></script>
@@ -124,15 +125,16 @@
   <header id="quarto-header" class="headroom fixed-top">
     <nav class="navbar navbar-expand-lg navbar-dark ">
       <div class="navbar-container container-fluid">
-      <div class="navbar-brand-container">
-    <a class="navbar-brand" href="../index.html">
-    <span class="navbar-title">simplextree</span>
-    </a>
-  </div>
           <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
   <span class="navbar-toggler-icon"></span>
 </button>
           <div class="collapse navbar-collapse" id="navbarCollapse">
+            <ul class="navbar-nav navbar-nav-scroll me-auto">
+  <li class="nav-item">
+    <a class="nav-link" href="../pages/index.html" rel="" target="">
+ <span class="menu-text">simplextree</span></a>
+  </li>  
+</ul>
             <ul class="navbar-nav navbar-nav-scroll ms-auto">
   <li class="nav-item compact">
     <a class="nav-link" href="https://github.com/peekxc/simplextree-py" rel="" target=""><i class="bi bi-github" role="img">
@@ -178,6 +180,12 @@
     <ul class="list-unstyled mt-1">
         <li class="sidebar-item">
   <div class="sidebar-item-container"> 
+  <a href="../pages/quickstart.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">Quick start</span></a>
+  </div>
+</li>
+        <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
   <a href="../pages/overview.html" class="sidebar-item-text sidebar-link active">
  <span class="menu-text">Overview</span></a>
   </div>
@@ -218,7 +226,7 @@
 
 <header id="title-block-header" class="quarto-title-block default">
 <div class="quarto-title">
-<h1 class="title">Overview: Simplicial Complexes</h1>
+<h1 class="title">Overview of the <code>simplextree</code> package</h1>
 </div>
 
 
@@ -239,15 +247,15 @@ <h1 class="title">Overview: Simplicial Complexes</h1>
 <li>If <span class="math inline">\tau \subset \sigma</span> and <span class="math inline">\sigma \in S</span>, then <span class="math inline">\tau \in S</span></li>
 </ol>
 <p>A simplicial complex is a natural generalization of a <a href="https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)">graph</a>—any graph can also be represented by a simplicial complex (though the converse is not true!).</p>
-<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, trie-like structure whose nodes are in bijection with the faces of the complex. Here’s a picture (from the paper) of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):</p>
+<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>
 <div class="quarto-figure quarto-figure-center">
 <figure class="figure">
-<p><img src="static/simplextree_pic.png" class="preview-image img-fluid figure-img"></p>
-<figcaption class="figure-caption">simplextree</figcaption>
+<p><img src="./static/simplextree_pic.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>The <code>simplextree</code> Python package exports an efficient class implementation of the <em>simplex tree</em> data structure. To construct the complex above with a simplex tree, it suffices to give the maximal simplices:</p>
-<div class="cell" data-execution_count="2">
+<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="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>
@@ -256,7 +264,7 @@ <h1 class="title">Overview: Simplicial Complexes</h1>
 </div>
 </div>
 <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="3">
+<div class="cell" data-execution_count="2">
 <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>
 <div class="cell-output cell-output-stdout">
 <pre><code>1 (h = 2): .( 2 3 )..( 3 )
@@ -271,7 +279,25 @@ <h1 class="title">Overview: Simplicial Complexes</h1>
 10 (h = 0): </code></pre>
 </div>
 </div>
-<p>The supported operations include:</p>
+<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="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>
+<div class="cell-output cell-output-stdout">
+<pre><code>(last=2, depth=2): { 1 2 } 
+(last=3, depth=2): { 1 3 } { 2 3 } 
+(last=4, depth=2): { 2 4 } { 3 4 } 
+(last=5, depth=2): { 2 5 } { 3 5 } { 4 5 } 
+(last=7, depth=2): { 6 7 } 
+(last=8, depth=2): { 7 8 } 
+(last=9, depth=2): { 6 9 } { 7 9 } 
+(last=3, depth=3): { 1 2 3 } 
+(last=4, depth=3): { 2 3 4 } 
+(last=5, depth=3): { 2 3 5 } { 2 4 5 } { 3 4 5 } 
+(last=9, depth=3): { 6 7 9 } 
+(last=5, depth=4): { 2 3 4 5 } </code></pre>
+</div>
+</div>
+<!-- Various subsets of the complex can be parameterized by a starting simplex.  -->
 
 
 
@@ -626,6 +652,9 @@ <h1 class="title">Overview: Simplicial Complexes</h1>
 </script>
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+ <span class="menu-text">Simplex Tree</span></a>
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+  <a href="../reference/UnionFind.UnionFind.html" class="sidebar-item-text sidebar-link">
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+
+<p>You can construct a <code>SimplexTree</code> by supplying simplices. Any collection of integer-valued <code>Iterable</code>’s will do, e.g.&nbsp;a list of lists:</p>
+<div class="cell" data-execution_count="1">
+<div class="sourceCode cell-code" id="cb1" data-caption="The SimplexTree class provides light wrapper around the extension module"><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">0</span>,<span class="dv">1</span>,<span class="dv">2</span>], [<span class="dv">0</span>,<span class="dv">1</span>], [<span class="dv">4</span>,<span class="dv">5</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>
+<div class="cell-output cell-output-stdout">
+<pre><code>Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices</code></pre>
+</div>
+</div>
+<p>Batch insertion, removal, and membership queries are supported</p>
+<div class="cell" data-execution_count="2">
+<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.insert([[<span class="dv">1</span>,<span class="dv">4</span>], [<span class="dv">1</span>,<span class="dv">5</span>], [<span class="dv">6</span>]])</span>
+<span id="cb3-2"><a href="#cb3-2" 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>
+<div class="cell-output cell-output-stdout">
+<pre><code>Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices</code></pre>
+</div>
+</div>
+<div class="cell" data-execution_count="3">
+<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.remove([[<span class="dv">6</span>]])</span>
+<span id="cb5-2"><a href="#cb5-2" 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>
+<div class="cell-output cell-output-stdout">
+<pre><code>Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices</code></pre>
+</div>
+</div>
+<div class="cell" data-execution_count="4">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(st.find([[<span class="dv">6</span>], [<span class="dv">0</span>,<span class="dv">1</span>]]))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[False  True]</code></pre>
+</div>
+</div>
+<p>Collections of simplices are returned as simple lists-of-lists:</p>
+<div class="cell" data-execution_count="5">
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(st.simplices())</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]</code></pre>
+</div>
+</div>
+<p>Various parameters can be given to restrict a given subset to certain subsets or orders:</p>
+<div class="cell" data-execution_count="6">
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(st.simplices(p<span class="op">=</span><span class="dv">1</span>)) </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[[0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5]]</code></pre>
+</div>
+</div>
+<p>Familiar Pythonic <a href="https://docs.python.org/3/library/collections.abc.html#collections-abstract-base-classes">Collection semantics</a> are supported, including __contains__, __iter__ support, and __len__:</p>
+<div class="cell" data-execution_count="7">
+<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>([<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">2</span>] <span class="kw">in</span> st)</span>
+<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>([<span class="bu">len</span>(simplex) <span class="cf">for</span> simplex <span class="kw">in</span> st])</span>
+<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="bu">len</span>(st))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>True
+[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]
+12</code></pre>
+</div>
+</div>
+<p>The cofaces of any simplex can be listed with <code>cofaces</code>:</p>
+<div class="cell" data-execution_count="8">
+<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"Cofaces([1]): "</span> <span class="op">+</span> <span class="bu">str</span>(st.cofaces([<span class="dv">1</span>])))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>Cofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]</code></pre>
+</div>
+</div>
+<p>The maximal simplices can be listed with <code>maximal</code>:</p>
+<div class="cell" data-execution_count="9">
+<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="st">"Maximal: "</span> <span class="op">+</span> <span class="bu">str</span>(st.maximal()))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>Maximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]</code></pre>
+</div>
+</div>
+<p>Basic properties are also available as attributes</p>
+<div class="cell" data-execution_count="10">
+<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>st.n_simplices, st.dimension, st.vertices, st.connected_components</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-display" data-execution_count="10">
+<pre><code>(array([5, 6, 1], dtype=uint64), 2, [0, 1, 2, 4, 5], [1, 1, 1, 1, 1])</code></pre>
+</div>
+</div>
+<p>Interoperability with numpy is provided whenever possible</p>
+<div class="cell" data-execution_count="11">
+<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np </span>
+<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a><span class="bu">all</span>(np.<span class="bu">all</span>(st.triangles <span class="op">==</span> np.array(st.simplices(p<span class="op">=</span><span class="dv">2</span>)), axis<span class="op">=</span><span class="dv">0</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-display" data-execution_count="11">
+<pre><code>True</code></pre>
+</div>
+</div>
+<p>Other complex-wide operations are supported, like <span class="math inline">k</span>-expansions</p>
+<div class="cell" data-execution_count="12">
+<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>st.insert([[<span class="dv">1</span>,<span class="dv">4</span>]]) </span>
+<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a>st.expand(<span class="dv">2</span>)       </span>
+<span id="cb23-3"><a href="#cb23-3" 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>
+<div class="cell-output cell-output-stdout">
+<pre><code>Simplex Tree with (5, 6, 2) (0, 1, 2)-simplices</code></pre>
+</div>
+</div>
+<p>The trie-structure can also be inspected on the python side:</p>
+<div class="cell" data-execution_count="13">
+<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb25-1"><a href="#cb25-1" 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>
+<div class="cell-output cell-output-stdout">
+<pre><code>0 (h = 2): .( 1 2 )..( 2 )
+1 (h = 2): .( 2 4 5 )..( 5 )
+2 (h = 0): 
+4 (h = 1): .( 5 )
+5 (h = 0): </code></pre>
+</div>
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+
+
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diff --git a/docs/pages/reference/SimplexTree.SimplexTree.html b/docs/pages/reference/SimplexTree.SimplexTree.html
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@@ -145,6 +146,12 @@
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+  <a href="../pages/quickstart.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">Quick start</span></a>
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diff --git a/docs/reference/UnionFind.UnionFind.html b/docs/reference/UnionFind.UnionFind.html
index d4d3dbc..9a8e411 100644
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@@ -7,7 +7,7 @@
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 
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+<title>unionfind.unionfind</title>
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@@ -128,6 +129,12 @@
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         <li class="sidebar-item">
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+  <a href="../pages/quickstart.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">Quick start</span></a>
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diff --git a/docs/reference/index.html b/docs/reference/index.html
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 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 
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@@ -129,6 +130,12 @@
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+  <a href="../pages/quickstart.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">Quick start</span></a>
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 <!-- margin-sidebar -->
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@@ -563,7 +570,7 @@ <h2 class="anchored" data-anchor-id="union-find">Union Find</h2>
       </a>          
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diff --git a/docs/search.json b/docs/search.json
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-    "text": "SimplexTree\n\n\n\n\n\nName\nDescription\n\n\n\n\nSimplexTree\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex.\n\n\n\n\n\nSimplexTree.SimplexTree(self, simplices=None)\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nn_simplices\nndarray\nnumber of simplices\n\n\ndimension\nint\nmaximal dimension of the complex\n\n\nid_policy\nstr\npolicy for generating new vertex ids\n\n\n\n\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nvertices\nndarray\nvertices of the complex\n\n\n\n\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=[])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=[])\nReturns the p-cofaces of a given simplex.\n\n\np : required\n\ncoface dimension to restrict to\n\nsigma : optional (default=[])\n\nthe simplex to obtain cofaces of\n\n\n\n\nlist :  list[Collection], \n\nthe p-cofaces of sigma\n\n\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\n\n\nsigma : required\n\nmaximal simplex to collapse\n\ntau : required\n\nface of sigma to collapse\n\n\n\n\nbool : None,\n\nwhether the pair was collapsed\n\n\n\n\nfrom splex import SimplexTree st = SimplexTree([[0,1,2]]) print(st)\nst.collapse([1,2], [0,1,2])\nprint(st)\n\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\n\n\nvertices :  numpy.typing.ArrayLike, optional (default=None)\n\nRetrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\n\n\n\n\nlist :  Union[numpy.typing.ArrayLike, int], \n\ndegree of each vertex id given in ‘vertices’\n\n\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\n\n\nk : required\n\nmaximum dimension to expand to.\n\n\n\n\nfrom simplextree import SimplexTree from itertools import combinations st = SimplexTree(combinations(range(8), 2)) print(st)\nst.expand(k=2) print(st)\n\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=[], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n**** :\n\nfound (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=[])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\n\n\n\nst = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=[])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=[], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nUNHANDLED ADMONITION\nTo select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\n\n\n\norder :  str, optional (default=‘preorder’)\n\nthe type of traversal of the simplex tree to execute.\n\nf :  Callable, optional (default=print)\n\na function to evaluate on every simplex in the traversal. 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This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nn_simplices\nndarray\nnumber of simplices\n\n\ndimension\nint\nmaximal dimension of the complex\n\n\nid_policy\nstr\npolicy for generating new vertex ids\n\n\n\n\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nvertices\nndarray\nvertices of the complex\n\n\n\n\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=[])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=[])\nReturns the p-cofaces of a given simplex.\n\n\np : required\n\ncoface dimension to restrict to\n\nsigma : optional (default=[])\n\nthe simplex to obtain cofaces of\n\n\n\n\nlist :  list[Collection], \n\nthe p-cofaces of sigma\n\n\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\n\n\nsigma : required\n\nmaximal simplex to collapse\n\ntau : required\n\nface of sigma to collapse\n\n\n\n\nbool : None,\n\nwhether the pair was collapsed\n\n\n\n\nfrom splex import SimplexTree st = SimplexTree([[0,1,2]]) print(st)\nst.collapse([1,2], [0,1,2])\nprint(st)\n\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\n\n\nvertices :  numpy.typing.ArrayLike, optional (default=None)\n\nRetrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\n\n\n\n\nlist :  Union[numpy.typing.ArrayLike, int], \n\ndegree of each vertex id given in ‘vertices’\n\n\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\n\n\nk : required\n\nmaximum dimension to expand to.\n\n\n\n\nfrom simplextree import SimplexTree from itertools import combinations st = SimplexTree(combinations(range(8), 2)) print(st)\nst.expand(k=2) print(st)\n\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=[], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n**** :\n\nfound (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=[])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\n\n\n\nst = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=[])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=[], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nUNHANDLED ADMONITION\nTo select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\n\n\n\norder :  str, optional (default=‘preorder’)\n\nthe type of traversal of the simplex tree to execute.\n\nf :  Callable, optional (default=print)\n\na function to evaluate on every simplex in the traversal. 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-    "text": "A simplicial complex S is a pair S = (V, \\Sigma) where V is a vertex set and \\Sigma a collection of simplices s \\in \\Sigma satisfying:\n\nIf v \\in V, then v \\in S\nIf \\tau \\subset \\sigma and \\sigma \\in S, then \\tau \\in S\n\nA simplicial complex is a natural generalization of a graph—any graph can also be represented by a simplicial complex (though the converse is not true!).\nLike graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a simplex tree: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. Here’s a picture (from the paper) of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):\n\n\n\nsimplextree\n\n\nThe simplextree Python package exports an efficient class implementation of the simplex tree data structure. To construct the complex above with a simplex tree, it suffices to give the maximal simplices:\n\nfrom simplextree import SimplexTree\nst = SimplexTree([[1,2,3],[2,3,4,5],[6,7,9],[7,8],[10]]) # complex form the picture\nprint(st)\n\nSimplex Tree with (10, 12, 6, 1) (0, 1, 2, 3)-simplices\n\n\nTo look at the tree structure, use print_tree (see also: print_cousins)\n\nst.print_tree()\n\n1 (h = 2): .( 2 3 )..( 3 )\n2 (h = 3): .( 3 4 5 )..( 4 5 5 )...( 5 )\n3 (h = 2): .( 4 5 )..( 5 )\n4 (h = 1): .( 5 )\n5 (h = 0): \n6 (h = 2): .( 7 9 )..( 9 )\n7 (h = 1): .( 8 9 )\n8 (h = 0): \n9 (h = 0): \n10 (h = 0): \n\n\nThe supported operations include:"
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-    "text": "splex promotes a common, pythonic interface for interacting with simplicial complexes that is independent of their internal representation.\nTo simplify usage, this interface incorporates the use of generics (inspired from R) and Protocol classes (to support duck-typing and structural subtyping).\nSee the design philosophy (todo) for more details."
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-    "text": "Out-of-the-box, splex comes with three distinct data structures for representing simplicial complexes: as sets of simplices, as (structured) arrays of integers, and as integer-valued tries. See the complexes overview page for more details."
+    "text": "SimplexTree.SimplexTree(self, simplices=None)\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\nAttributes: n_simplices (ndarray): number of simplices dimension (int): maximal dimension of the complex id_policy (str): policy for generating new vertex ids\nAttributes: Properties: vertices (ndarray): vertices of the complex\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\nParameters: p : coface dimension to restrict to sigma : the simplex to obtain cofaces of\nReturns: list: the p-cofaces of sigma\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\nParameters: sigma : maximal simplex to collapse tau : face of sigma to collapse\nReturns: bool: whether the pair was collapsed\nExamples:\n    from splex import SimplexTree \n    st = SimplexTree([[0,1,2]])\n    print(st)\n\n    st.collapse([1,2], [0,1,2])\n\n    print(st)\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\nParameters: vertices (ArrayLike): Retrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\nReturns: list: degree of each vertex id given in ‘vertices’\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\nParameters: k : maximum dimension to expand to.\nExamples:\n    from simplextree import SimplexTree \n    from itertools import combinations \n    st = SimplexTree(combinations(range(8), 2))\n    print(st)\n    \n    st.expand(k=2)\n    print(st)\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\nReturns: found (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\nExamples: st = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\nSupported traversals: - breadth-first / level order (“bfs”, “levelorder”) - depth-first / prefix (“dfs”, “preorder”) - faces - cofaces - coface roots (“coface_roots”) - p-skeleton - p-simplices - maximal simplices (“maximal”) - link To select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\nParameters: order: the type of traversal of the simplex tree to execute. f: a function to evaluate on every simplex in the traversal. Defaults to print. sigma: simplex to start the traversal at, where applicable. Defaults to the root node (empty set). p: dimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\nParameters: u (int): the first vertex in the free pair. v (int): the second vertex in the free pair. w (int): the target vertex to collapse to."
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-    "text": "The simplex tree is…\n\n\n\nsimplextree\n\n\n\n\nCode\nimport numpy as np \nimport matplotlib.pyplot as plt\n\nr = np.arange(0, 2, 0.01)\ntheta = 2 * np.pi * r\nfig, ax = plt.subplots(\n  subplot_kw = {'projection': 'polar'} \n)\nax.plot(theta, r)\nax.set_rticks([0.5, 1, 1.5, 2])\nax.grid(True)\nplt.show()"
+    "text": "Name\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\nParameters: p : coface dimension to restrict to sigma : the simplex to obtain cofaces of\nReturns: list: the p-cofaces of sigma\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\nParameters: sigma : maximal simplex to collapse tau : face of sigma to collapse\nReturns: bool: whether the pair was collapsed\nExamples:\n    from splex import SimplexTree \n    st = SimplexTree([[0,1,2]])\n    print(st)\n\n    st.collapse([1,2], [0,1,2])\n\n    print(st)\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\nParameters: vertices (ArrayLike): Retrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\nReturns: list: degree of each vertex id given in ‘vertices’\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\nParameters: k : maximum dimension to expand to.\nExamples:\n    from simplextree import SimplexTree \n    from itertools import combinations \n    st = SimplexTree(combinations(range(8), 2))\n    print(st)\n    \n    st.expand(k=2)\n    print(st)\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\nReturns: found (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\nExamples: st = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\nSupported traversals: - breadth-first / level order (“bfs”, “levelorder”) - depth-first / prefix (“dfs”, “preorder”) - faces - cofaces - coface roots (“coface_roots”) - p-skeleton - p-simplices - maximal simplices (“maximal”) - link To select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\nParameters: order: the type of traversal of the simplex tree to execute. f: a function to evaluate on every simplex in the traversal. Defaults to print. sigma: simplex to start the traversal at, where applicable. Defaults to the root node (empty set). p: dimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\nParameters: u (int): the first vertex in the free pair. v (int): the second vertex in the free pair. w (int): the target vertex to collapse to."
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     "text": "SimplexTree.SimplexTree\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex.\n\n\n\n\n\n\n\n\n\nUnionFind.UnionFind\nUnion Find data structure"
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     "text": "SimplexTree.SimplexTree\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex."
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-    "text": "The Simplex Tree data structure for constructing and modifying abstract simplicial complexes\n\n\n\nSimplexTree"
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+    "text": "A simplicial complex S is a pair S = (V, \\Sigma) where V is a vertex set and \\Sigma a collection of simplices s \\in \\Sigma satisfying:\n\nIf v \\in V, then v \\in S\nIf \\tau \\subset \\sigma and \\sigma \\in S, then \\tau \\in S\n\nA simplicial complex is a natural generalization of a graph—any graph can also be represented by a simplicial complex (though the converse is not true!).\nLike graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a Simplex Tree: an ordered, 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):\n\n\n\nPicture taken from Boissonnat et al: “The simplex tree: An efficient data structure for general simplicial complexes”\n\n\nTo construct the complex above with a simplextree package, simply give the maximal simplices:\n\nfrom simplextree import SimplexTree\nst = SimplexTree([[1,2,3],[2,3,4,5],[6,7,9],[7,8],[10]]) # complex form the picture\nprint(st)\n\nSimplex Tree with (10, 12, 6, 1) (0, 1, 2, 3)-simplices\n\n\nTo look at the tree structure, use print_tree (see also: print_cousins)\n\nst.print_tree()\n\n1 (h = 2): .( 2 3 )..( 3 )\n2 (h = 3): .( 3 4 5 )..( 4 5 5 )...( 5 )\n3 (h = 2): .( 4 5 )..( 5 )\n4 (h = 1): .( 5 )\n5 (h = 0): \n6 (h = 2): .( 7 9 )..( 9 )\n7 (h = 1): .( 8 9 )\n8 (h = 0): \n9 (h = 0): \n10 (h = 0): \n\n\nTo 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 5). To view these links with the SimplexTree class, use print_cousins():\n\nst.print_cousins()\n\n(last=2, depth=2): { 1 2 } \n(last=3, depth=2): { 1 3 } { 2 3 } \n(last=4, depth=2): { 2 4 } { 3 4 } \n(last=5, depth=2): { 2 5 } { 3 5 } { 4 5 } \n(last=7, depth=2): { 6 7 } \n(last=8, depth=2): { 7 8 } \n(last=9, depth=2): { 6 9 } { 7 9 } \n(last=3, depth=3): { 1 2 3 } \n(last=4, depth=3): { 2 3 4 } \n(last=5, depth=3): { 2 3 5 } { 2 4 5 } { 3 4 5 } \n(last=9, depth=3): { 6 7 9 } \n(last=5, depth=4): { 2 3 4 5 }"
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-    "text": "UnionFind\n\n\n\n\n\nName\nDescription\n\n\n\n\nUnionFind\nUnion Find data structure\n\n\n\n\n\nUnionFind.UnionFind(n)\nUnion Find data structure"
+    "text": "simplextree is an Python package that simplifies computation for general simplicial complexes of any dimension by providing pybind11 bindings to a Simplex Tree data structure implemented in modern C++17.\nA Simplex Tree is an ordered, 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):\nThe Simplex Tree was originally introduced in the following paper:\nThe SimplexTree class exported by the package includes support for many tree operations, e.g. insertions, removals, expansions, collapses, star/link enumerations, and other traversals."
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+    "text": "Install\nThe easiest way to install the package is via the platform-specific wheels on pypi.\npython -m pip install simplextree \nYou can also pip install the package manually by downloading the appropriate wheel (or sdist) from the releases.\nFor installation instructions for developers looking to extend the package, see Building & Developing."
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+    "text": "Building & Developing\nIf you would like to build the package yourself for development reasons, a typical workflow is to install the build-time dependencies first:\npython -m pip install meson-python ninja pybind11 numpy\nThen, build and install the package in editable mode (see also meson-python notes), optionally without build isolation for speed:\npython -m pip install --no-build-isolation --editable .\nUnit testing is handled with pytest. See the gh-workflows for platform-specific configuration."
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-    "text": "SimplexTree.SimplexTree(self, simplices=None)\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\nAttributes: n_simplices (ndarray): number of simplices dimension (int): maximal dimension of the complex id_policy (str): policy for generating new vertex ids\nAttributes: Properties: vertices (ndarray): vertices of the complex\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\nParameters: p : coface dimension to restrict to sigma : the simplex to obtain cofaces of\nReturns: list: the p-cofaces of sigma\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\nParameters: sigma : maximal simplex to collapse tau : face of sigma to collapse\nReturns: bool: whether the pair was collapsed\nExamples:\n    from splex import SimplexTree \n    st = SimplexTree([[0,1,2]])\n    print(st)\n\n    st.collapse([1,2], [0,1,2])\n\n    print(st)\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\nParameters: vertices (ArrayLike): Retrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\nReturns: list: degree of each vertex id given in ‘vertices’\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\nParameters: k : maximum dimension to expand to.\nExamples:\n    from simplextree import SimplexTree \n    from itertools import combinations \n    st = SimplexTree(combinations(range(8), 2))\n    print(st)\n    \n    st.expand(k=2)\n    print(st)\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\nReturns: found (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\nExamples: st = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\nSupported traversals: - breadth-first / level order (“bfs”, “levelorder”) - depth-first / prefix (“dfs”, “preorder”) - faces - cofaces - coface roots (“coface_roots”) - p-skeleton - p-simplices - maximal simplices (“maximal”) - link To select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\nParameters: order: the type of traversal of the simplex tree to execute. f: a function to evaluate on every simplex in the traversal. Defaults to print. sigma: simplex to start the traversal at, where applicable. Defaults to the root node (empty set). p: dimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\nParameters: u (int): the first vertex in the free pair. v (int): the second vertex in the free pair. w (int): the target vertex to collapse to."
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+    "text": "Native Extensions\nThe underlying C++ library is header-only and may be included as a dependency by extension modules in other Python packages.\nThus, to modify or extending the complex in C++, it is sufficient to add the package as a build-time dependency and append the include directory to the compilation target."
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-    "text": "Name\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\nParameters: p : coface dimension to restrict to sigma : the simplex to obtain cofaces of\nReturns: list: the p-cofaces of sigma\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\nParameters: sigma : maximal simplex to collapse tau : face of sigma to collapse\nReturns: bool: whether the pair was collapsed\nExamples:\n    from splex import SimplexTree \n    st = SimplexTree([[0,1,2]])\n    print(st)\n\n    st.collapse([1,2], [0,1,2])\n\n    print(st)\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\nParameters: vertices (ArrayLike): Retrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\nReturns: list: degree of each vertex id given in ‘vertices’\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\nParameters: k : maximum dimension to expand to.\nExamples:\n    from simplextree import SimplexTree \n    from itertools import combinations \n    st = SimplexTree(combinations(range(8), 2))\n    print(st)\n    \n    st.expand(k=2)\n    print(st)\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\nReturns: found (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\nParameters: simplices: Iterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\nExamples: st = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\nSupported traversals: - breadth-first / level order (“bfs”, “levelorder”) - depth-first / prefix (“dfs”, “preorder”) - faces - cofaces - coface roots (“coface_roots”) - p-skeleton - p-simplices - maximal simplices (“maximal”) - link To select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\nParameters: order: the type of traversal of the simplex tree to execute. f: a function to evaluate on every simplex in the traversal. Defaults to print. sigma: simplex to start the traversal at, where applicable. Defaults to the root node (empty set). p: dimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\nParameters: u (int): the first vertex in the free pair. v (int): the second vertex in the free pair. w (int): the target vertex to collapse to."
+    "text": "SimplexTree.SimplexTree(self, simplices=None)\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nn_simplices\nndarray\nnumber of simplices\n\n\ndimension\nint\nmaximal dimension of the complex\n\n\nid_policy\nstr\npolicy for generating new vertex ids\n\n\n\n\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nvertices\nndarray\nvertices of the complex\n\n\n\n\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\n\n\np : required\n\ncoface dimension to restrict to\n\nsigma : optional (default=[])\n\nthe simplex to obtain cofaces of\n\n\n\n\nlist :  list[Collection], \n\nthe p-cofaces of sigma\n\n\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\n\n\nsigma : required\n\nmaximal simplex to collapse\n\ntau : required\n\nface of sigma to collapse\n\n\n\n\nbool : None,\n\nwhether the pair was collapsed\n\n\n\n\nfrom splex import SimplexTree st = SimplexTree([[0,1,2]]) print(st)\nst.collapse([1,2], [0,1,2])\nprint(st)\n\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\n\n\nvertices :  numpy.typing.ArrayLike, optional (default=None)\n\nRetrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\n\n\n\n\nlist :  Union[numpy.typing.ArrayLike, int], \n\ndegree of each vertex id given in ‘vertices’\n\n\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\n\n\nk : required\n\nmaximum dimension to expand to.\n\n\n\n\nfrom simplextree import SimplexTree from itertools import combinations st = SimplexTree(combinations(range(8), 2)) print(st)\nst.expand(k=2) print(st)\n\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n**** :\n\nfound (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\n\n\n\nst = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nUNHANDLED ADMONITION\nTo select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\n\n\n\norder :  str, optional (default=‘preorder’)\n\nthe type of traversal of the simplex tree to execute.\n\nf :  Callable, optional (default=print)\n\na function to evaluate on every simplex in the traversal. Defaults to print.\n\nsigma :  Collection, optional (default=[])\n\nsimplex to start the traversal at, where applicable. Defaults to the root node (empty set).\n\np :  int, optional (default=0)\n\ndimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\n\n\nu :  int, required\n\nthe first vertex in the free pair.\n\nv :  int, required\n\nthe second vertex in the free pair.\n\nw :  int, required\n\nthe target vertex to collapse to."
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-    "text": "SimplexTree.SimplexTree(self, simplices=None)\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. This class exposes a native extension module wrapping a simplex tree implemented with modern C++.\nThe Simplex Tree was originally introduced in the paper &gt; Boissonnat, Jean-Daniel, and Clément Maria. “The simplex tree: An efficient data structure for general simplicial complexes.” Algorithmica 70.3 (2014): 406-427.\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nn_simplices\nndarray\nnumber of simplices\n\n\ndimension\nint\nmaximal dimension of the complex\n\n\nid_policy\nstr\npolicy for generating new vertex ids\n\n\n\n\n\n\n\n\n\nName\nType\nDescription\n\n\n\n\nvertices\nndarray\nvertices of the complex\n\n\n\n\n\n\n\n\n\nName\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\n\n\np : required\n\ncoface dimension to restrict to\n\nsigma : optional (default=[])\n\nthe simplex to obtain cofaces of\n\n\n\n\nlist :  list[Collection], \n\nthe p-cofaces of sigma\n\n\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\n\n\nsigma : required\n\nmaximal simplex to collapse\n\ntau : required\n\nface of sigma to collapse\n\n\n\n\nbool : None,\n\nwhether the pair was collapsed\n\n\n\n\nfrom splex import SimplexTree st = SimplexTree([[0,1,2]]) print(st)\nst.collapse([1,2], [0,1,2])\nprint(st)\n\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\n\n\nvertices :  numpy.typing.ArrayLike, optional (default=None)\n\nRetrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\n\n\n\n\nlist :  Union[numpy.typing.ArrayLike, int], \n\ndegree of each vertex id given in ‘vertices’\n\n\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\n\n\nk : required\n\nmaximum dimension to expand to.\n\n\n\n\nfrom simplextree import SimplexTree from itertools import combinations st = SimplexTree(combinations(range(8), 2)) print(st)\nst.expand(k=2) print(st)\n\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n**** :\n\nfound (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\n\n\n\nst = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nUNHANDLED ADMONITION\nTo select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\n\n\n\norder :  str, optional (default=‘preorder’)\n\nthe type of traversal of the simplex tree to execute.\n\nf :  Callable, optional (default=print)\n\na function to evaluate on every simplex in the traversal. Defaults to print.\n\nsigma :  Collection, optional (default=[])\n\nsimplex to start the traversal at, where applicable. Defaults to the root node (empty set).\n\np :  int, optional (default=0)\n\ndimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\n\n\nu :  int, required\n\nthe first vertex in the free pair.\n\nv :  int, required\n\nthe second vertex in the free pair.\n\nw :  int, required\n\nthe target vertex to collapse to."
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     "text": "Name\nDescription\n\n\n\n\nadjacent\nChecks for adjacencies between simplices.\n\n\ncard\nReturns the cardinality of various skeleta of the complex.\n\n\ncoface_roots\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\ncofaces\nReturns the p-cofaces of a given simplex.\n\n\ncollapse\nPerforms an elementary collapse on two given simplices.\n\n\ndegree\nComputes the degree of select vertices in the trie.\n\n\nexpand\nPerforms a k-expansion of the complex.\n\n\nfaces\nWrapper for simplices function.\n\n\nfind\nFinds whether simplices exist in Simplex Tree.\n\n\ninsert\nInserts simplices into the Simplex Tree.\n\n\nlink\nReturns all simplices in the link of a given simplex.\n\n\nmaximal\nReturns the maximal simplices in the complex.\n\n\nremove\nRemoves simplices into the Simplex Tree.\n\n\nsimplices\nReturns the p-simplices in the complex.\n\n\nskeleton\nReturns the simplices in the p-skeleton of the complex.\n\n\ntraverse\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nvertex_collapse\nMaps a pair of vertices into a single vertex.\n\n\n\n\n\nSimplexTree.SimplexTree.adjacent(self, simplices)\nChecks for adjacencies between simplices.\n\n\n\nSimplexTree.SimplexTree.card(self, p=None)\nReturns the cardinality of various skeleta of the complex.\n\n\n\nSimplexTree.SimplexTree.coface_roots(self, sigma=\\[\\])\nReturns the simplex ‘roots’ of a given simplex whose subtrees generate its cofaces.\n\n\n\nSimplexTree.SimplexTree.cofaces(self, sigma=\\[\\])\nReturns the p-cofaces of a given simplex.\n\n\np : required\n\ncoface dimension to restrict to\n\nsigma : optional (default=[])\n\nthe simplex to obtain cofaces of\n\n\n\n\nlist :  list[Collection], \n\nthe p-cofaces of sigma\n\n\n\n\n\nSimplexTree.SimplexTree.collapse(self, tau, sigma)\nPerforms an elementary collapse on two given simplices.\nChecks whether its possible to collapse \\sigma through \\tau, and if so, both simplices are removed. A simplex \\sigma is said to be collapsible through one of its faces \\tau if \\sigma is the only coface of \\tau (excluding \\tau itself).\n\n\nsigma : required\n\nmaximal simplex to collapse\n\ntau : required\n\nface of sigma to collapse\n\n\n\n\nbool : None,\n\nwhether the pair was collapsed\n\n\n\n\nfrom splex import SimplexTree st = SimplexTree([[0,1,2]]) print(st)\nst.collapse([1,2], [0,1,2])\nprint(st)\n\n\n\n\nSimplexTree.SimplexTree.degree(self, vertices=None)\nComputes the degree of select vertices in the trie.\n\n\nvertices :  numpy.typing.ArrayLike, optional (default=None)\n\nRetrieves vertex degrees If no vertices are specified, all degrees are computed. Non-existing vertices by default have degree 0.\n\n\n\n\nlist :  Union[numpy.typing.ArrayLike, int], \n\ndegree of each vertex id given in ‘vertices’\n\n\n\n\n\nSimplexTree.SimplexTree.expand(self, k)\nPerforms a k-expansion of the complex.\nThis function is particularly useful for expanding clique complexes beyond their 1-skeleton.\n\n\nk : required\n\nmaximum dimension to expand to.\n\n\n\n\nfrom simplextree import SimplexTree from itertools import combinations st = SimplexTree(combinations(range(8), 2)) print(st)\nst.expand(k=2) print(st)\n\n\n\n\nSimplexTree.SimplexTree.faces(self, p=None, sigma=\\[\\], **kwargs)\nWrapper for simplices function.\n\n\n\nSimplexTree.SimplexTree.find(self, simplices)\nFinds whether simplices exist in Simplex Tree.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n**** :\n\nfound (ndarray) : boolean array indicating whether each simplex was found in the complex\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then the p-simplex to find is given by each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then searched for in the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.insert(self, simplices)\nInserts simplices into the Simplex Tree.\nBy definition, inserting a simplex also inserts all of its faces. If the simplex already exists in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike)\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is inserted along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then inserted into the tree. \n\n\n\n\n\n\nSimplexTree.SimplexTree.link(self, sigma=\\[\\])\nReturns all simplices in the link of a given simplex.\n\n\n\nSimplexTree.SimplexTree.maximal(self)\nReturns the maximal simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.remove(self, simplices)\nRemoves simplices into the Simplex Tree.\nBy definition, removing a face also removes all of its cofaces. If the simplex does not exist in the complex, the tree is not modified.\n\n\nsimplices :  Iterable[Collection], required\n\nIterable of simplices to insert (each of which are SimplexLike).\n\n\n\n\n\n\n\nNote\n\n\n\n    If the iterable is an 2-dim np.ndarray, then a p-simplex is removed along each contiguous p+1 stride.\n    Otherwise, each element of the iterable to casted to a Simplex and then removed from the tree. \n\n\n\n\n\nst = SimplexTree([range(3)]) print(st) st.remove([[0,1]]) print(st)\n\n\n\n\nSimplexTree.SimplexTree.simplices(self, p=None)\nReturns the p-simplices in the complex.\n\n\n\nSimplexTree.SimplexTree.skeleton(self, p=None, sigma=\\[\\])\nReturns the simplices in the p-skeleton of the complex.\n\n\n\nSimplexTree.SimplexTree.traverse(self, order='preorder', f=print, sigma=\\[\\], p=0)\nTraverses the simplex tree in the specified order, calling ‘f’ on each simplex encountered.\n\n\nUNHANDLED ADMONITION\nTo select one of these options, set order to one of [“bfs”, “levelorder”, “dfs”, “preorder”]\n\n\n\norder :  str, optional (default=‘preorder’)\n\nthe type of traversal of the simplex tree to execute.\n\nf :  Callable, optional (default=print)\n\na function to evaluate on every simplex in the traversal. Defaults to print.\n\nsigma :  Collection, optional (default=[])\n\nsimplex to start the traversal at, where applicable. Defaults to the root node (empty set).\n\np :  int, optional (default=0)\n\ndimension of simplices to restrict to, where applicable. Defaults to 0.\n\n\n\n\n\nSimplexTree.SimplexTree.vertex_collapse(self, u, v, w)\nMaps a pair of vertices into a single vertex.\n\n\nu :  int, required\n\nthe first vertex in the free pair.\n\nv :  int, required\n\nthe second vertex in the free pair.\n\nw :  int, required\n\nthe target vertex to collapse to."
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+    "href": "pages/reference/UnionFind.UnionFind.html",
+    "title": "UnionFind.UnionFind",
+    "section": "",
+    "text": "UnionFind.UnionFind\nUnionFind.UnionFind(n)\nUnion Find data structure"
+  },
+  {
+    "objectID": "reference/index.html",
+    "href": "reference/index.html",
     "title": "API Reference",
     "section": "",
     "text": "SimplexTree.SimplexTree\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex.\n\n\n\n\n\n\n\n\n\nUnionFind.UnionFind\nUnion Find data structure"
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     "text": "SimplexTree.SimplexTree\nSimplexTree provides lightweight wrapper around a Simplex Tree data structure: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex."
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     "title": "API Reference",
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     "text": "UnionFind.UnionFind\nUnion Find data structure"
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-    "text": "Name\nType\nDescription\n\n\n\n\nn_simplices\nndarray\nnumber of simplices\n\n\ndimension\nint\nmaximal dimension of the complex\n\n\nid_policy\nstr\npolicy for generating new vertex ids"
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-    "text": "Name\nType\nDescription\n\n\n\n\nvertices\nndarray\nvertices of the complex"
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diff --git a/docs/static/styles.css b/docs/static/styles.css
index 8b05631..fef3495 100644
--- a/docs/static/styles.css
+++ b/docs/static/styles.css
@@ -46,7 +46,12 @@ section[id^=returns] > p {
   margin-top: 0.5em; 
 }
 
+.sourceCode {
+  background-color: #d3d3d357;
+}
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   color:#9753b8;
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\ No newline at end of file
+}
+
diff --git a/docs_src/README.md b/docs_src/README.md
new file mode 100644
index 0000000..eb57ef8
--- /dev/null
+++ b/docs_src/README.md
@@ -0,0 +1,7 @@
+Build the docs with:
+
+> python gen_api.py & quarto render 
+
+Optionally preview with: 
+
+> quarto preview
\ No newline at end of file
diff --git a/docs_src/_freeze/pages/overview/execute-results/html.json b/docs_src/_freeze/pages/overview/execute-results/html.json
index 3ceb21a..e9a1234 100644
--- a/docs_src/_freeze/pages/overview/execute-results/html.json
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@@ -1,7 +1,7 @@
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-    "markdown": "---\nformat:\n  html:\n    code-fold: false\nexecute:\n  freeze: auto\n  enabled: true\ntitle: 'Overview: Simplicial Complexes'\n---\n\n\n\n\n\nA _simplicial complex_ $S$ is a pair $S = (V, \\Sigma)$ where $V$ is a vertex set and $\\Sigma$ a collection of _simplices_ $s \\in \\Sigma$ satisfying: \n\n1. If $v \\in V$, then $v \\in S$\n2. If $\\tau \\subset \\sigma$ and $\\sigma \\in S$, then $\\tau \\in S$\n\nA simplicial complex is a natural generalization of a [graph](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics))---any graph can also be represented by a simplicial complex (though the converse is not true!). \n\nLike graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a _simplex tree_: an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. Here's a picture (from the paper) of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):\n\n![simplextree](static/simplextree_pic.png){.preview-image}\n\nThe `simplextree` Python package exports an efficient class implementation of the _simplex tree_ data structure. \nTo construct the complex above with a simplex tree, it suffices to give the maximal simplices: \n\n\n::: {.cell execution_count=2}\n``` {.python .cell-code}\nfrom simplextree import SimplexTree\nst = SimplexTree([[1,2,3],[2,3,4,5],[6,7,9],[7,8],[10]]) # complex form the picture\nprint(st)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (10, 12, 6, 1) (0, 1, 2, 3)-simplices\n```\n:::\n:::\n\n\nTo look at the tree structure, use `print_tree` (see also: `print_cousins`)\n\n::: {.cell execution_count=3}\n``` {.python .cell-code}\nst.print_tree()\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n1 (h = 2): .( 2 3 )..( 3 )\n2 (h = 3): .( 3 4 5 )..( 4 5 5 )...( 5 )\n3 (h = 2): .( 4 5 )..( 5 )\n4 (h = 1): .( 5 )\n5 (h = 0): \n6 (h = 2): .( 7 9 )..( 9 )\n7 (h = 1): .( 8 9 )\n8 (h = 0): \n9 (h = 0): \n10 (h = 0): \n```\n:::\n:::\n\n\nThe supported operations include: \n\n",
+    "markdown": "---\nformat:\n  html:\n    code-fold: false\nexecute:\n  freeze: auto\n  enabled: true\ntitle: Overview of the `simplextree` package\n---\n\n\n\n\n\nA _simplicial complex_ $S$ is a pair $S = (V, \\Sigma)$ where $V$ is a vertex set and $\\Sigma$ a collection of _simplices_ $s \\in \\Sigma$ satisfying: \n\n1. If $v \\in V$, then $v \\in S$\n2. If $\\tau \\subset \\sigma$ and $\\sigma \\in S$, then $\\tau \\in S$\n\nA simplicial complex is a natural generalization of a [graph](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics))---any graph can also be represented by a simplicial complex (though the converse is not true!). \n\nLike graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a _Simplex Tree_: 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):\n\n![Picture taken from Boissonnat et al: \"The simplex tree: An efficient data structure for general simplicial complexes\"](./static/simplextree_pic.png){.preview-image}\n\nTo construct the complex above with a `simplextree` package, simply give the maximal simplices: \n\n\n::: {.cell execution_count=1}\n``` {.python .cell-code}\nfrom simplextree import SimplexTree\nst = SimplexTree([[1,2,3],[2,3,4,5],[6,7,9],[7,8],[10]]) # complex form the picture\nprint(st)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (10, 12, 6, 1) (0, 1, 2, 3)-simplices\n```\n:::\n:::\n\n\nTo look at the tree structure, use `print_tree` (see also: `print_cousins`)\n\n::: {.cell execution_count=2}\n``` {.python .cell-code}\nst.print_tree()\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n1 (h = 2): .( 2 3 )..( 3 )\n2 (h = 3): .( 3 4 5 )..( 4 5 5 )...( 5 )\n3 (h = 2): .( 4 5 )..( 5 )\n4 (h = 1): .( 5 )\n5 (h = 0): \n6 (h = 2): .( 7 9 )..( 9 )\n7 (h = 1): .( 8 9 )\n8 (h = 0): \n9 (h = 0): \n10 (h = 0): \n```\n:::\n:::\n\n\nTo 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 $5$). To view these links with the `SimplexTree` class, use `print_cousins()`:\n\n::: {.cell execution_count=3}\n``` {.python .cell-code}\nst.print_cousins()\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n(last=2, depth=2): { 1 2 } \n(last=3, depth=2): { 1 3 } { 2 3 } \n(last=4, depth=2): { 2 4 } { 3 4 } \n(last=5, depth=2): { 2 5 } { 3 5 } { 4 5 } \n(last=7, depth=2): { 6 7 } \n(last=8, depth=2): { 7 8 } \n(last=9, depth=2): { 6 9 } { 7 9 } \n(last=3, depth=3): { 1 2 3 } \n(last=4, depth=3): { 2 3 4 } \n(last=5, depth=3): { 2 3 5 } { 2 4 5 } { 3 4 5 } \n(last=9, depth=3): { 6 7 9 } \n(last=5, depth=4): { 2 3 4 5 } \n```\n:::\n:::\n\n\n<!-- Various subsets of the complex can be parameterized by a starting simplex.  -->\n\n",
     "supporting": [
       "overview_files/figure-html"
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diff --git a/docs_src/_freeze/pages/quickstart/execute-results/html.json b/docs_src/_freeze/pages/quickstart/execute-results/html.json
new file mode 100644
index 0000000..fb8de7d
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+  "hash": "6cb97ebb040e05ca9d323340c574f898",
+  "result": {
+    "markdown": "---\nformat:\n  html:\n    code-fold: false\nexecute:\n  freeze: auto\n  enabled: true\ndraft: true\ntitle: Quick Start\n---\n\n\n\n\n\nYou can construct a `SimplexTree` by supplying simplices. Any collection of integer-valued `Iterable`'s will do, e.g. a list of lists: \n\n\n::: {.cell execution_count=1}\n``` {.python .cell-code caption=\"The SimplexTree class provides light wrapper around the extension module\" code-summary=\"SimplexTree constructor\"}\nfrom simplextree import SimplexTree \nst = SimplexTree([[0,1,2], [0,1], [4,5]]) \nprint(st) \n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n```\n:::\n:::\n\n\nBatch insertion, removal, and membership queries are supported\n\n::: {.cell execution_count=2}\n``` {.python .cell-code code-summary=\"Batch operations\"}\nst.insert([[1,4], [1,5], [6]])\nprint(st)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n```\n:::\n:::\n\n\n::: {.cell execution_count=3}\n``` {.python .cell-code}\nst.remove([[6]])\nprint(st)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (5, 6, 1) (0, 1, 2)-simplices\n```\n:::\n:::\n\n\n::: {.cell execution_count=4}\n``` {.python .cell-code}\nprint(st.find([[6], [0,1]]))\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n[False  True]\n```\n:::\n:::\n\n\nCollections of simplices are returned as simple lists-of-lists:\n\n::: {.cell execution_count=5}\n``` {.python .cell-code code-summary=\"Complex collections\"}\nprint(st.simplices())\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n```\n:::\n:::\n\n\nVarious parameters can be given to restrict a given subset to certain subsets or orders: \n\n::: {.cell execution_count=6}\n``` {.python .cell-code}\nprint(st.simplices(p=1)) \n```\n\n::: {.cell-output .cell-output-stdout}\n```\n[[0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5]]\n```\n:::\n:::\n\n\nFamiliar Pythonic [Collection semantics](https://docs.python.org/3/library/collections.abc.html#collections-abstract-base-classes) are supported, including \\_\\_contains\\_\\_, \\_\\_iter\\_\\_ support, and \\_\\_len\\_\\_:\n\n::: {.cell execution_count=7}\n``` {.python .cell-code}\nprint([0,1,2] in st)\nprint([len(simplex) for simplex in st])\nprint(len(st))\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nTrue\n[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n12\n```\n:::\n:::\n\n\nThe cofaces of any simplex can be listed with `cofaces`:\n\n::: {.cell execution_count=8}\n``` {.python .cell-code}\nprint(\"Cofaces([1]): \" + str(st.cofaces([1])))\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nCofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]\n```\n:::\n:::\n\n\nThe maximal simplices can be listed with `maximal`:\n\n::: {.cell execution_count=9}\n``` {.python .cell-code}\nprint(\"Maximal: \" + str(st.maximal()))\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nMaximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n```\n:::\n:::\n\n\nBasic properties are also available as attributes \n\n::: {.cell execution_count=10}\n``` {.python .cell-code}\nst.n_simplices, st.dimension, st.vertices, st.connected_components\n```\n\n::: {.cell-output .cell-output-display execution_count=10}\n```\n(array([5, 6, 1], dtype=uint64), 2, [0, 1, 2, 4, 5], [1, 1, 1, 1, 1])\n```\n:::\n:::\n\n\nInteroperability with numpy is provided whenever possible\n\n::: {.cell execution_count=11}\n``` {.python .cell-code}\nimport numpy as np \nall(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))\n```\n\n::: {.cell-output .cell-output-display execution_count=11}\n```\nTrue\n```\n:::\n:::\n\n\nOther complex-wide operations are supported, like $k$-expansions \n\n::: {.cell execution_count=12}\n``` {.python .cell-code}\nst.insert([[1,4]]) \nst.expand(2)       \nprint(st)\n```\n\n::: {.cell-output .cell-output-stdout}\n```\nSimplex Tree with (5, 6, 2) (0, 1, 2)-simplices\n```\n:::\n:::\n\n\nThe trie-structure can also be inspected on the python side:\n\n::: {.cell execution_count=13}\n``` {.python .cell-code}\nst.print_tree()\n```\n\n::: {.cell-output .cell-output-stdout}\n```\n0 (h = 2): .( 1 2 )..( 2 )\n1 (h = 2): .( 2 4 5 )..( 5 )\n2 (h = 0): \n4 (h = 1): .( 5 )\n5 (h = 0): \n```\n:::\n:::\n\n\n",
+    "supporting": [
+      "quickstart_files/figure-html"
+    ],
+    "filters": [],
+    "includes": {}
+  }
+}
\ No newline at end of file
diff --git a/docs_src/_quarto.yml b/docs_src/_quarto.yml
index da3cde2..6423d6c 100644
--- a/docs_src/_quarto.yml
+++ b/docs_src/_quarto.yml
@@ -29,11 +29,13 @@ quartodoc:
         - UnionFind.UnionFind
 
 website:
-  title: simplextree
   search: 
     location: sidebar
     type: textbox
   navbar:
+    left: 
+      - text: simplextree
+        href: "pages/index.html"
     background: light
     right: 
       - icon: github
@@ -48,6 +50,8 @@ website:
     border: true 
     collapse-level: 2
     contents: 
+      - text: Quick start 
+        href: pages/quickstart.qmd
       - text: Overview 
         href: pages/overview.qmd
       - section: API Reference
@@ -89,5 +93,6 @@ format:
     linestretch: 1.2
     margin-top: "0px" 
     css: /static/styles.css
+    # monobackgroundcolor: "#d3d3d357"
 # out_index: pages/index.qmd
 # sphinx-build . ./_build/html -b html
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/87ea35e450ca33aa4dfbf936f10fa3ff/base.ipynb b/docs_src/pages/.jupyter_cache/executed/87ea35e450ca33aa4dfbf936f10fa3ff/base.ipynb
new file mode 100644
index 0000000..147e88b
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/87ea35e450ca33aa4dfbf936f10fa3ff/base.ipynb
@@ -0,0 +1,412 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "6a80b9db",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
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\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/api.py\": 1692138182.4017549, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/tseries/api.py\": 1692138182.505042, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/common.py\": 1692138182.4381795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/align.py\": 1692138182.435933, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/scope.py\": 1692138182.438822, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/ops.py\": 1692138182.4378428, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/engines.py\": 1692138182.4364808, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/parsing.py\": 1692138182.4354477, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/expr.py\": 1692138182.439189, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/eval.py\": 1692138182.4385064, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/computation/api.py\": 1692138182.4373705, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/reshape/encoding.py\": 1692138182.408996, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/reshape/merge.py\": 1692138182.4086566, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/reshape/pivot.py\": 1692138182.4114964, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/reshape/tile.py\": 1692138182.4079792, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/reshape/api.py\": 1692138182.410623, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/api/extensions/__init__.py\": 1692138182.9699655, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/api/indexers/__init__.py\": 1692138182.969085, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/interchange/__init__.py\": 1692138182.4210947, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/interchange/dataframe_protocol.py\": 1692138182.4214342, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/dtypes/api.py\": 1692138182.4254737, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/api/types/__init__.py\": 1692138182.9693809, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/interchange/utils.py\": 1692138182.4217417, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/core/interchange/from_dataframe.py\": 1692138182.4205694, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/api/interchange/__init__.py\": 1692138182.9696739, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/api/__init__.py\": 1692138182.9687946, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/_random.py\": 1692138182.823019, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/contexts.py\": 1692138182.8236432, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/_io.py\": 1692138182.82212, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/_warnings.py\": 1692138182.822785, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/lib-dynload/cmath.cpython-39-darwin.so\": 1688592120.413391, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_libs/testing.cpython-39-darwin.so\": 1692138182.911092, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/asserters.py\": 1692138182.8233826, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/compat.py\": 1692138182.8217711, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/site-packages/pandas/_testing/__init__.py\": 1692138182.8225126, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "5b2da0cc",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| lst-cap: The SimplexTree class provides light wrapper around the extension module\n",
+    "#| output: true\n",
+    "#| code-summary: SimplexTree constructor\n",
+    "from simplextree import SimplexTree \n",
+    "st = SimplexTree([[0,1,2], [0,1], [4,5]]) \n",
+    "print(st) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "49607b35",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n",
+      "Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([False,  True])"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Batch operations\n",
+    "st.insert([[1,4], [1,5], [6]])\n",
+    "print(st)\n",
+    "st.remove([[6]])\n",
+    "print(st)\n",
+    "st.find([[6], [0,1]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7092a859",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n",
+      "[[0], [0, 1], [0, 2], [1], [1, 2], [1, 4], [1, 5], [2], [4], [4, 5], [5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Complex collections \n",
+    "print(st.simplices())\n",
+    "print(st.skeleton(1)) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "12b4a0a7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n",
+      "[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n",
+      "12\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print([0,1,2] in st)\n",
+    "print([len(simplex) for simplex in st])\n",
+    "print(len(st))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "9f579f4b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Cofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]\n",
+      "Maximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Cofaces([1]): \" + str(st.cofaces([1])))\n",
+    "print(\"Maximal: \" + str(st.maximal()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cd55889a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 1, 1, 1, 1]\n",
+      "[0, 1, 2, 4, 5]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(array([5, 6, 1], dtype=uint64), 2)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "print(st.connected_components)\n",
+    "print(st.vertices)\n",
+    "st.n_simplices, st.dimension"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "9a8d0275",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "## Interoperability with numpy is provided whenever possible\n",
+    "import numpy as np \n",
+    "all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))\n",
+    "# True \n",
+    "\n",
+    "## Other complex-wide operations are supported, like k-expansions \n",
+    "st.insert([[1,4]]) \n",
+    "st.expand(2)       \n",
+    "# Simplex Tree with (6, 6, 2) (0, 1, 2)-simplices"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "97f42e6a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 (h = 2): .( 1 2 )..( 2 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=1, depth=2): { 0 1 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=2): { 0 2 } { 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=2): { 1 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=2): { 4 5 } { 1 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=3): { 0 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=3): { 1 4 5 } \n"
+     ]
+    }
+   ],
+   "source": [
+    "## The trie-structure can also be inspected on the python side \n",
+    "st.print_tree()\n",
+    "# 0 (h = 2): .( 1 2 )..( 2 )\n",
+    "# 1 (h = 1): .( 2 4 5 )\n",
+    "# 2 (h = 0): \n",
+    "# 4 (h = 1): .( 5 )\n",
+    "# 5 (h = 0): \n",
+    "\n",
+    "st.print_cousins()\n",
+    "# (last=1, depth=2): { 0 1 } \n",
+    "# (last=2, depth=2): { 0 2 } { 1 2 } \n",
+    "# (last=4, depth=2): { 1 4 } \n",
+    "# (last=5, depth=2): { 4 5 } { 1 5 } \n",
+    "# (last=2, depth=3): { 0 1 2 } "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/a429fb4fec801f421aec0269aea0eeed/base.ipynb b/docs_src/pages/.jupyter_cache/executed/a429fb4fec801f421aec0269aea0eeed/base.ipynb
new file mode 100644
index 0000000..b24cc5e
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/a429fb4fec801f421aec0269aea0eeed/base.ipynb
@@ -0,0 +1,483 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "cf1a02f1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap.py\": 1688592098.220885, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap_external.py\": 1688592098.223086, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/codecs.py\": 1688592096.019708, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/aliases.py\": 1688592098.717748, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/__init__.py\": 1688592098.715795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/utf_8.py\": 1688592098.947974, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/latin_1.py\": 1688592098.886754, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/abc.py\": 1688592095.983326, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/io.py\": 1688592096.09689, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "035a4f47",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| lst-cap: The SimplexTree class provides light wrapper around the extension module\n",
+    "#| output: true\n",
+    "#| code-summary: SimplexTree constructor\n",
+    "from simplextree import SimplexTree \n",
+    "st = SimplexTree([[0,1,2], [0,1], [4,5]]) \n",
+    "print(st) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "39174624",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "None\n",
+      "Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Batch operations\n",
+    "print(st.insert([[1,4], [1,5], [6]]))\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "eadaa200",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "None\n",
+      "Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(st.remove([[6]]))\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "4f2aaedf",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[False  True]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(st.find([[6], [0,1]]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "b148be12",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Complex collections \n",
+    "print(st.simplices())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "bd1a21ed",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print(st.simplices(p=1)) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "4c7587c3",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n",
+      "[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n",
+      "12\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print([0,1,2] in st)\n",
+    "print([len(simplex) for simplex in st])\n",
+    "print(len(st))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "58e15595",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Cofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Cofaces([1]): \" + str(st.cofaces([1])))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "6041a312",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Maximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Maximal: \" + str(st.maximal()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "0680c4e2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([5, 6, 1], dtype=uint64), 2, [0, 1, 2, 4, 5], [1, 1, 1, 1, 1])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "st.n_simplices, st.dimension, st.vertices, st.connected_components"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "e15f31e9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np \n",
+    "all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "83e1e7c7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 6, 2) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "st.insert([[1,4]]) \n",
+    "st.expand(2)       \n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "59678c0e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 (h = 2): .( 1 2 )..( 2 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_tree()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "f4e6a20b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=1, depth=2): { 0 1 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=2): { 0 2 } { 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=2): { 1 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=2): { 4 5 } { 1 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=3): { 0 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=3): { 1 4 5 } \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_cousins()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/a506d01bae855566e389b8497d151022/base.ipynb b/docs_src/pages/.jupyter_cache/executed/a506d01bae855566e389b8497d151022/base.ipynb
new file mode 100644
index 0000000..bc9ea57
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/a506d01bae855566e389b8497d151022/base.ipynb
@@ -0,0 +1,481 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "fd60495a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap.py\": 1688592098.220885, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap_external.py\": 1688592098.223086, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/codecs.py\": 1688592096.019708, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/aliases.py\": 1688592098.717748, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/__init__.py\": 1688592098.715795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/utf_8.py\": 1688592098.947974, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/latin_1.py\": 1688592098.886754, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/abc.py\": 1688592095.983326, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/io.py\": 1688592096.09689, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "e4a8cfe0",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| lst-cap: The SimplexTree class provides light wrapper around the extension module\n",
+    "#| output: true\n",
+    "#| code-summary: SimplexTree constructor\n",
+    "from simplextree import SimplexTree \n",
+    "st = SimplexTree([[0,1,2], [0,1], [4,5]]) \n",
+    "print(st) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "7d4b6cad",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Batch operations\n",
+    "st.insert([[1,4], [1,5], [6]])\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "e406759d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "st.remove([[6]])\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "29b8dad8",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[False  True]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(st.find([[6], [0,1]]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "f8dce77b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Complex collections \n",
+    "print(st.simplices())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cebae634",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print(st.simplices(p=1)) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "4fdfca20",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n",
+      "[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n",
+      "12\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print([0,1,2] in st)\n",
+    "print([len(simplex) for simplex in st])\n",
+    "print(len(st))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "9b0837e2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Cofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Cofaces([1]): \" + str(st.cofaces([1])))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "4a4ce3ec",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Maximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Maximal: \" + str(st.maximal()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "49fc4ea4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([5, 6, 1], dtype=uint64), 2, [0, 1, 2, 4, 5], [1, 1, 1, 1, 1])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "st.n_simplices, st.dimension, st.vertices, st.connected_components"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "f556b2df",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np \n",
+    "all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "757a894d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 6, 2) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "st.insert([[1,4]]) \n",
+    "st.expand(2)       \n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "4c607126",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 (h = 2): .( 1 2 )..( 2 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_tree()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "4dbd92d6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=1, depth=2): { 0 1 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=2): { 0 2 } { 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=2): { 1 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=2): { 4 5 } { 1 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=3): { 0 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=3): { 1 4 5 } \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_cousins()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/acbf0e7a3056dde9fe641060139e060b/base.ipynb b/docs_src/pages/.jupyter_cache/executed/acbf0e7a3056dde9fe641060139e060b/base.ipynb
new file mode 100644
index 0000000..bd039b8
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/acbf0e7a3056dde9fe641060139e060b/base.ipynb
@@ -0,0 +1,370 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9ebd97cd",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap.py\": 1688592098.220885, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap_external.py\": 1688592098.223086, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/codecs.py\": 1688592096.019708, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/aliases.py\": 1688592098.717748, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/__init__.py\": 1688592098.715795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/utf_8.py\": 1688592098.947974, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/latin_1.py\": 1688592098.886754, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/abc.py\": 1688592095.983326, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/io.py\": 1688592096.09689, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "50b2cace",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| lst-cap: The SimplexTree class provides light wrapper around the extension module\n",
+    "#| output: true\n",
+    "#| code-summary: SimplexTree constructor\n",
+    "from simplextree import SimplexTree \n",
+    "st = SimplexTree([[0,1,2], [0,1], [4,5]]) \n",
+    "print(st) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "57d5a4b2",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "## Batch insertion, removal, and membership queries are supported\n",
+    "st.insert([[1,4], [1,5], [6]])\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "c2fc0370",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "st.remove([[6]])\n",
+    "# Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "130874ee",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n",
+      "[[0], [0, 1], [0, 2], [1], [1, 2], [1, 4], [1, 5], [2], [4], [4, 5], [5]]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(array([5, 6, 1], dtype=uint64), 2)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "st.find([[6], [0,1]])\n",
+    "# array([False,  True])\n",
+    "\n",
+    "## Collections of simplices are returned as simple lists-of-lists\n",
+    "print(st.simplices())\n",
+    "# [[0],[1],[2],[4],[5], [0,1],[0,2],[1,2],[1,4],[1,5],[4,5],[0,1,2]])\n",
+    "\n",
+    "print(st.skeleton(1)) \n",
+    "# [[0],[1],[2],[4],[5], [0,1],[0,2],[1,2],[1,4],[1,5],[4,5]])\n",
+    "\n",
+    "## Familiar Pythonic collection semantics are supported, including contains and iteration\n",
+    "[0,1,2] in st\n",
+    "# True \n",
+    "\n",
+    "[len(simplex) for simplex in st]\n",
+    "# [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n",
+    "\n",
+    "## Various subsets of the complex can be enumerated\n",
+    "st.cofaces([1])\n",
+    "# [[1], [0,1], [1,2], [1,4], [1,5], [0,1,2], [1,4,5]]\n",
+    "\n",
+    "st.maximal()\n",
+    "# [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n",
+    "\n",
+    "## Basic properties are also available as attributes \n",
+    "st.connected_components \n",
+    "# [1,1,1,1,1]\n",
+    "\n",
+    "st.vertices\n",
+    "# [0,1,2,4,5]\n",
+    "\n",
+    "st.n_simplices, st.dimension\n",
+    "# [5, 6, 1], 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "c666aef5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "## Interoperability with numpy is provided whenever possible\n",
+    "import numpy as np \n",
+    "all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))\n",
+    "# True \n",
+    "\n",
+    "## Other complex-wide operations are supported, like k-expansions \n",
+    "st.insert([[1,4]]) \n",
+    "st.expand(2)       \n",
+    "# Simplex Tree with (6, 6, 2) (0, 1, 2)-simplices"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "2c35cc0c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 (h = 2): .( 1 2 )..( 2 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=1, depth=2): { 0 1 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=2): { 0 2 } { 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=2): { 1 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=2): { 4 5 } { 1 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=3): { 0 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=3): { 1 4 5 } \n"
+     ]
+    }
+   ],
+   "source": [
+    "## The trie-structure can also be inspected on the python side \n",
+    "st.print_tree()\n",
+    "# 0 (h = 2): .( 1 2 )..( 2 )\n",
+    "# 1 (h = 1): .( 2 4 5 )\n",
+    "# 2 (h = 0): \n",
+    "# 4 (h = 1): .( 5 )\n",
+    "# 5 (h = 0): \n",
+    "\n",
+    "st.print_cousins()\n",
+    "# (last=1, depth=2): { 0 1 } \n",
+    "# (last=2, depth=2): { 0 2 } { 1 2 } \n",
+    "# (last=4, depth=2): { 1 4 } \n",
+    "# (last=5, depth=2): { 4 5 } { 1 5 } \n",
+    "# (last=2, depth=3): { 0 1 2 } "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/be653243cbe262d890472aafedfcdd45/base.ipynb b/docs_src/pages/.jupyter_cache/executed/be653243cbe262d890472aafedfcdd45/base.ipynb
new file mode 100644
index 0000000..c9e086a
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/be653243cbe262d890472aafedfcdd45/base.ipynb
@@ -0,0 +1,428 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "38c9bc9b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap.py\": 1688592098.220885, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap_external.py\": 1688592098.223086, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/codecs.py\": 1688592096.019708, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/aliases.py\": 1688592098.717748, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/__init__.py\": 1688592098.715795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/utf_8.py\": 1688592098.947974, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/latin_1.py\": 1688592098.886754, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/abc.py\": 1688592095.983326, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/io.py\": 1688592096.09689, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "1aeecfd4",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 4, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| lst-cap: The SimplexTree class provides light wrapper around the extension module\n",
+    "#| output: true\n",
+    "#| code-summary: SimplexTree constructor\n",
+    "from simplextree import SimplexTree \n",
+    "st = SimplexTree([[0,1,2], [0,1], [4,5]]) \n",
+    "print(st) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "184e1c99",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (6, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Batch operations\n",
+    "st.insert([[1,4], [1,5], [6]])\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7d744918",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "st.remove([[6]])\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "df47a173",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[False  True]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(st.find([[6], [0,1]]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "0455bd12",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0], [1], [2], [4], [5], [0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "#| code-summary: Complex collections \n",
+    "print(st.simplices())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "cee48d4a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0, 1], [0, 2], [1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print(st.simplices(p=1)) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "517f7aae",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n",
+      "[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]\n",
+      "12\n"
+     ]
+    }
+   ],
+   "source": [
+    "#| echo: true\n",
+    "#| output: true\n",
+    "print([0,1,2] in st)\n",
+    "print([len(simplex) for simplex in st])\n",
+    "print(len(st))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "e1d22130",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Cofaces([1]): [[1], [1, 2], [1, 4], [1, 5], [0, 1], [0, 1, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Cofaces([1]): \" + str(st.cofaces([1])))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "2a9eecb5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Maximal: [[0, 1, 2], [1, 4], [1, 5], [4, 5]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Maximal: \" + str(st.maximal()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "0f3c7598",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array([5, 6, 1], dtype=uint64), 2, [0, 1, 2, 4, 5], [1, 1, 1, 1, 1])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "st.n_simplices, st.dimension, st.vertices, st.connected_components"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "83153e6f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np \n",
+    "all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "cd5ceb70",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (5, 6, 2) (0, 1, 2)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "st.insert([[1,4]]) \n",
+    "st.expand(2)       \n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "9f96eb20",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 (h = 2): .( 1 2 )..( 2 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_tree()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/docs_src/pages/.jupyter_cache/executed/fbb32eb408717b6f66aebf947b8c0726/base.ipynb b/docs_src/pages/.jupyter_cache/executed/fbb32eb408717b6f66aebf947b8c0726/base.ipynb
new file mode 100644
index 0000000..2ec6255
--- /dev/null
+++ b/docs_src/pages/.jupyter_cache/executed/fbb32eb408717b6f66aebf947b8c0726/base.ipynb
@@ -0,0 +1,331 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9156c302",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap.py\": 1688592098.220885, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/importlib/_bootstrap_external.py\": 1688592098.223086, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/codecs.py\": 1688592096.019708, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/aliases.py\": 1688592098.717748, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/__init__.py\": 1688592098.715795, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/utf_8.py\": 1688592098.947974, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/encodings/latin_1.py\": 1688592098.886754, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/abc.py\": 1688592095.983326, \"/Users/mpiekenbrock/opt/miniconda3/envs/simplextree/lib/python3.9/io.py\": 1688592096.09689, 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+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "# imports\n",
+    "import os\n",
+    "import sys\n",
+    "import types\n",
+    "import json\n",
+    "\n",
+    "# figure size/format\n",
+    "fig_width = 7\n",
+    "fig_height = 5\n",
+    "fig_format = 'retina'\n",
+    "fig_dpi = 96\n",
+    "\n",
+    "# matplotlib defaults / format\n",
+    "try:\n",
+    "  import matplotlib.pyplot as plt\n",
+    "  plt.rcParams['figure.figsize'] = (fig_width, fig_height)\n",
+    "  plt.rcParams['figure.dpi'] = fig_dpi\n",
+    "  plt.rcParams['savefig.dpi'] = fig_dpi\n",
+    "  from IPython.display import set_matplotlib_formats\n",
+    "  set_matplotlib_formats(fig_format)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# plotly use connected mode\n",
+    "try:\n",
+    "  import plotly.io as pio\n",
+    "  pio.renderers.default = \"notebook_connected\"\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "# enable pandas latex repr when targeting pdfs\n",
+    "try:\n",
+    "  import pandas as pd\n",
+    "  if fig_format == 'pdf':\n",
+    "    pd.set_option('display.latex.repr', True)\n",
+    "except Exception:\n",
+    "  pass\n",
+    "\n",
+    "\n",
+    "\n",
+    "# output kernel dependencies\n",
+    "kernel_deps = dict()\n",
+    "for module in list(sys.modules.values()):\n",
+    "  # Some modules play games with sys.modules (e.g. email/__init__.py\n",
+    "  # in the standard library), and occasionally this can cause strange\n",
+    "  # failures in getattr.  Just ignore anything that's not an ordinary\n",
+    "  # module.\n",
+    "  if not isinstance(module, types.ModuleType):\n",
+    "    continue\n",
+    "  path = getattr(module, \"__file__\", None)\n",
+    "  if not path:\n",
+    "    continue\n",
+    "  if path.endswith(\".pyc\") or path.endswith(\".pyo\"):\n",
+    "    path = path[:-1]\n",
+    "  if not os.path.exists(path):\n",
+    "    continue\n",
+    "  kernel_deps[path] = os.stat(path).st_mtime\n",
+    "print(json.dumps(kernel_deps))\n",
+    "\n",
+    "# set run_path if requested\n",
+    "if r'/Users/mpiekenbrock/simplextree-py/docs_src/pages':\n",
+    "  os.chdir(r'/Users/mpiekenbrock/simplextree-py/docs_src/pages')\n",
+    "\n",
+    "# reset state\n",
+    "%reset\n",
+    "\n",
+    "def ojs_define(**kwargs):\n",
+    "  import json\n",
+    "  try:\n",
+    "    # IPython 7.14 preferred import\n",
+    "    from IPython.display import display, HTML\n",
+    "  except:\n",
+    "    from IPython.core.display import display, HTML\n",
+    "\n",
+    "  # do some minor magic for convenience when handling pandas\n",
+    "  # dataframes\n",
+    "  def convert(v):\n",
+    "    try:\n",
+    "      import pandas as pd\n",
+    "    except ModuleNotFoundError: # don't do the magic when pandas is not available\n",
+    "      return v\n",
+    "    if type(v) == pd.Series:\n",
+    "      v = pd.DataFrame(v)\n",
+    "    if type(v) == pd.DataFrame:\n",
+    "      j = json.loads(v.T.to_json(orient='split'))\n",
+    "      return dict((k,v) for (k,v) in zip(j[\"index\"], j[\"data\"]))\n",
+    "    else:\n",
+    "      return v\n",
+    "  \n",
+    "  v = dict(contents=list(dict(name=key, value=convert(value)) for (key, value) in kwargs.items()))\n",
+    "  display(HTML('<script type=\"ojs-define\">' + json.dumps(v) + '</script>'), metadata=dict(ojs_define = True))\n",
+    "globals()[\"ojs_define\"] = ojs_define\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "348179d7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Simplex Tree with (10, 12, 6, 1) (0, 1, 2, 3)-simplices\n"
+     ]
+    }
+   ],
+   "source": [
+    "from simplextree import SimplexTree\n",
+    "st = SimplexTree([[1,2,3],[2,3,4,5],[6,7,9],[7,8],[10]]) # complex form the picture\n",
+    "print(st)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "96128ada",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 (h = 2): .( 2 3 )..( 3 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2 (h = 3): .( 3 4 5 )..( 4 5 5 )...( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3 (h = 2): .( 4 5 )..( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 (h = 1): .( 5 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "6 (h = 2): .( 7 9 )..( 9 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7 (h = 1): .( 8 9 )\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "9 (h = 0): \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 (h = 0): \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_tree()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "afb70f6f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=2, depth=2): { 1 2 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=3, depth=2): { 1 3 } { 2 3 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=2): { 2 4 } { 3 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=2): { 2 5 } { 3 5 } { 4 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=7, depth=2): { 6 7 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=8, depth=2): { 7 8 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=9, depth=2): { 6 9 } { 7 9 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=3, depth=3): { 1 2 3 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=4, depth=3): { 2 3 4 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=3): { 2 3 5 } { 2 4 5 } { 3 4 5 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=9, depth=3): { 6 7 9 } \n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(last=5, depth=4): { 2 3 4 5 } \n"
+     ]
+    }
+   ],
+   "source": [
+    "st.print_cousins()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "simplextree",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
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diff --git a/docs_src/pages/index.qmd b/docs_src/pages/index.qmd
index f569388..d2dda1d 100644
--- a/docs_src/pages/index.qmd
+++ b/docs_src/pages/index.qmd
@@ -2,112 +2,64 @@
 format:
   html:
     code-fold: false
-jupyter: python3
+jupyter: 
+  kernelspec:
+    display_name: simplextree
+    language: python
+    name: python3
 execute: 
   freeze: auto
   enabled: false
-draft: true
 ---
 
-[![Tests](https://github.com/peekxc/splex/actions/workflows/package.yml/badge.svg)](https://github.com/peekxc/splex/actions/workflows/package.yml)
-[![coverage_badge](https://img.shields.io/endpoint?url=https://gist.githubusercontent.com/peekxc/ef42349965f40edf4232737026690c5f/raw/coverage_info.json)](https://coveralls.io/github/peekxc/splex)
-[![python_badge](https://img.shields.io/badge/python-3.9%20%7C%203.10%20%7C%203.11-blue)](https://github.com/peekxc/splex/actions/workflows/python-package.yml)
-[![coverage_badge](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-macos.yml?logo=apple&logoColor=white)](https://github.com/peekxc/splex/actions/workflows/build-macos.yml)
-[![coverage_badge](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-windows.yml?logo=windows&logoColor=white)](https://github.com/peekxc/splex/actions/workflows/build-windows.yml)
-[![coverage_badge](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build-linux.yml?logo=linux&logoColor=white)](https://github.com/peekxc/splex/actions/workflows/build-linux.yml)
+# simplextree
+[![coverage_badge](https://img.shields.io/endpoint?url=https://gist.githubusercontent.com/peekxc/ef42349965f40edf4232737026690c5f/raw/coverage_info.json)](https://coveralls.io/github/peekxc/simplextree-py)
+[![build_macos](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_macos.yml?logo=apple&logoColor=white)](https://github.com/peekxc/simplextree-py/actions/workflows/build-macos.yml)
+[![build_windows](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_windows.yml?logo=windows&logoColor=white)](https://github.com/peekxc/simplextree-py/actions/workflows/build-windows.yml)
+[![build_linux](https://img.shields.io/github/actions/workflow/status/peekxc/simplextree-py/build_linux.yml?logo=linux&logoColor=white)](https://github.com/peekxc/simplextree-py/actions/workflows/build-linux.yml)
 
-`simplextree` is a Python package aimed at simplifying computation for general simplicial complexes of any dimension. This package facilitates this aim by providing bindings to a Simplex Tree data structure implemented using modern C++ and exported an [extension module](https://docs.python.org/3/extending/extending.html). 
-<!-- The underlying library implementation also exports a C++ header, which can be specified as a dependency and used in other packages. -->
+`simplextree` is an Python package that simplifies computation for general [simplicial complexes](https://en.wikipedia.org/wiki/Simplicial_complex) of any dimension by providing [pybind11](https://github.com/pybind/pybind11) bindings to a _Simplex Tree_ data structure implemented in modern C++17. 
 
-The Simplex Tree was originally introduced in the following paper:
+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):
 
-> Boissonnat, Jean-Daniel, and Clément Maria. "The simplex tree: An efficient data structure for general simplicial complexes." Algorithmica 70.3 (2014): 406-427.
-
-A Simplex Tree is an ordered, trie-like structure whose nodes are in bijection with the faces of the complex. Here's a picture (taken from the paper) of a simplicial 3-complex (left) and its corresponding Simplex Tree (right):
-
-![simplextree](static/simplextree_pic.png){.preview-image}
-
-## Installation
+![Picture taken from Boissonnat et al: "The simplex tree: An efficient data structure for general simplicial complexes"](./static/simplextree_pic.png){.preview-image}
 
-TODO
+The _Simplex Tree_ was originally introduced in the following paper:
 
+> Boissonnat, Jean-Daniel, and Clément Maria. "The simplex tree: An efficient data structure for general simplicial complexes." Algorithmica 70.3 (2014): 406-427.
 
-## Quick Start 
+The `SimplexTree` class exported by the package includes support for many tree operations, e.g. insertions, removals, expansions, collapses, star/link enumerations, and other traversals. 
 
-```{python}
-## The SimplexTree class provides light wrapper around the extension module
-from simplextree import SimplexTree 
-st = SimplexTree([[0,1,2], [0,1], [4,5]]) 
-print(st) 
-```
+## Install 
 
-```{python}
-## Batch insertion, removal, and membership queries are supported
-st.insert([[1,4], [1,5], [6]])
-print(st)
-```
+The easiest way to install the package is via the platform-specific [wheels](https://pythonwheels.com/) on [pypi](https://pypi.org/project/simplextree/). 
 
-```{python}
-st.remove([[6]])
-# Simplex Tree with (5, 6, 1) (0, 1, 2)-simplices
+```bash 
+python -m pip install simplextree 
 ```
 
-```{python}
-st.find([[6], [0,1]])
-# array([False,  True])
+You can also `pip install` the package manually by downloading the appropriate wheel (or sdist) from the [releases](https://github.com/peekxc/simplextree-py/releases/). 
 
-## Collections of simplices are returned as simple lists-of-lists
-print(st.simplices())
-# [[0],[1],[2],[4],[5], [0,1],[0,2],[1,2],[1,4],[1,5],[4,5],[0,1,2]])
+For installation instructions for developers looking to extend the package, see [Building & Developing](#building--developing). 
 
-print(st.skeleton(1)) 
-# [[0],[1],[2],[4],[5], [0,1],[0,2],[1,2],[1,4],[1,5],[4,5]])
+## Building & Developing 
 
-## Familiar Pythonic collection semantics are supported, including contains and iteration
-[0,1,2] in st
-# True 
+If you would like to build the package yourself for development reasons, a typical workflow is to install the [build-time dependencies](https://pip.pypa.io/en/stable/reference/build-system/pyproject-toml/#build-time-dependencies) first: 
 
-[len(simplex) for simplex in st]
-# [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3]
-
-## Various subsets of the complex can be enumerated
-st.cofaces([1])
-# [[1], [0,1], [1,2], [1,4], [1,5], [0,1,2], [1,4,5]]
-
-st.maximal()
-# [[0, 1, 2], [1, 4], [1, 5], [4, 5]]
-
-## Basic properties are also available as attributes 
-st.connected_components 
-# [1,1,1,1,1]
+```bash
+python -m pip install meson-python ninja pybind11 numpy
+```
 
-st.vertices
-# [0,1,2,4,5]
+Then, build and install the package in [editable mode](https://peps.python.org/pep-0660/) (see also [meson-python notes](https://meson-python.readthedocs.io/en/latest/how-to-guides/editable-installs.html)), optionally without build isolation for speed:
 
-st.n_simplices, st.dimension
-# [5, 6, 1], 2
+```bash
+python -m pip install --no-build-isolation --editable .
+```
 
-## Interoperability with numpy is provided whenever possible
-all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))
-# True 
+Unit testing is handled with [pytest](https://docs.pytest.org/en/7.4.x/). See the [gh-workflows](https://github.com/peekxc/simplextree-py/actions) for platform-specific configuration. 
 
-## Other complex-wide operations are supported, like k-expansions 
-st.insert([[1,4]]) 
-st.expand(2)       
-# Simplex Tree with (6, 6, 2) (0, 1, 2)-simplices
+## Native Extensions 
 
-## The trie-structure can also be inspected on the python side 
-st.print_tree()
-# 0 (h = 2): .( 1 2 )..( 2 )
-# 1 (h = 1): .( 2 4 5 )
-# 2 (h = 0): 
-# 4 (h = 1): .( 5 )
-# 5 (h = 0): 
+The underlying C++ library is [header-only](https://en.wikipedia.org/wiki/Header-only) and may be included as a dependency by [extension modules](https://docs.python.org/3/extending/extending.html) in other Python packages.
 
-st.print_cousins()
-# (last=1, depth=2): { 0 1 } 
-# (last=2, depth=2): { 0 2 } { 1 2 } 
-# (last=4, depth=2): { 1 4 } 
-# (last=5, depth=2): { 4 5 } { 1 5 } 
-# (last=2, depth=3): { 0 1 2 } 
-```
+Thus, to modify or extending the complex in C++, it is sufficient to add the package as a build-time dependency and append the include directory to the compilation target.
\ No newline at end of file
diff --git a/docs_src/pages/overview.qmd b/docs_src/pages/overview.qmd
index 7fd3d74..cf414ec 100644
--- a/docs_src/pages/overview.qmd
+++ b/docs_src/pages/overview.qmd
@@ -12,7 +12,7 @@ execute:
   enabled: true
 ---
 
-# Overview: Simplicial Complexes
+# Overview of the `simplextree` package
 
 A _simplicial complex_ $S$ is a pair $S = (V, \Sigma)$ where $V$ is a vertex set and $\Sigma$ a collection of _simplices_ $s \in \Sigma$ satisfying: 
 
@@ -21,9 +21,9 @@ A _simplicial complex_ $S$ is a pair $S = (V, \Sigma)$ where $V$ is a vertex set
 
 A simplicial complex is a natural generalization of a [graph](https://en.wikipedia.org/wiki/Graph_(discrete_mathematics))---any graph can also be represented by a simplicial complex (though the converse is not true!). 
 
-Like graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a _simplex tree_: an ordered, 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):
+Like graphs, there are many ways to represent simplicial complexes in memory. One such way is to use a _Simplex Tree_: 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):
 
-![simplextree](static/simplextree_pic.png){.preview-image}
+![Picture taken from Boissonnat et al: "The simplex tree: An efficient data structure for general simplicial complexes"](./static/simplextree_pic.png){.preview-image}
 
 To construct the complex above with a `simplextree` package, simply give the maximal simplices: 
 
@@ -38,4 +38,9 @@ To look at the tree structure, use `print_tree` (see also: `print_cousins`)
 st.print_tree()
 ```
 
+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 $5$). To view these links with the `SimplexTree` class, use `print_cousins()`:
+```{python}
+st.print_cousins()
+```
 
+<!-- Various subsets of the complex can be parameterized by a starting simplex.  -->
\ No newline at end of file
diff --git a/docs_src/pages/quickstart.qmd b/docs_src/pages/quickstart.qmd
new file mode 100644
index 0000000..3eb7c75
--- /dev/null
+++ b/docs_src/pages/quickstart.qmd
@@ -0,0 +1,100 @@
+---
+format:
+  html:
+    code-fold: false
+jupyter: python3
+execute: 
+  freeze: auto
+  enabled: true
+draft: true
+---
+
+## Quick Start 
+
+You can construct a `SimplexTree` by supplying simplices. Any collection of integer-valued `Iterable`'s will do, e.g. a list of lists: 
+```{python}
+#| echo: true
+#| lst-cap: The SimplexTree class provides light wrapper around the extension module
+#| output: true
+#| code-summary: SimplexTree constructor
+from simplextree import SimplexTree 
+st = SimplexTree([[0,1,2], [0,1], [4,5]]) 
+print(st) 
+```
+
+Batch insertion, removal, and membership queries are supported
+
+```{python}
+#| echo: true
+#| output: true
+#| code-summary: Batch operations
+st.insert([[1,4], [1,5], [6]])
+print(st)
+```
+
+```{python}
+st.remove([[6]])
+print(st)
+```
+
+```{python}
+print(st.find([[6], [0,1]]))
+```
+
+Collections of simplices are returned as simple lists-of-lists:
+```{python}
+#| echo: true
+#| output: true
+#| code-summary: Complex collections 
+print(st.simplices())
+```
+
+Various parameters can be given to restrict a given subset to certain subsets or orders: 
+```{python}
+#| echo: true
+#| output: true
+print(st.simplices(p=1)) 
+```
+
+Familiar Pythonic [Collection semantics](https://docs.python.org/3/library/collections.abc.html#collections-abstract-base-classes) are supported, including \_\_contains\_\_, \_\_iter\_\_ support, and \_\_len\_\_:
+```{python}
+#| echo: true
+#| output: true
+print([0,1,2] in st)
+print([len(simplex) for simplex in st])
+print(len(st))
+```
+
+The cofaces of any simplex can be listed with `cofaces`:
+
+```{python}
+print("Cofaces([1]): " + str(st.cofaces([1])))
+```
+
+The maximal simplices can be listed with `maximal`:
+```{python}
+print("Maximal: " + str(st.maximal()))
+```
+
+Basic properties are also available as attributes 
+```{python}
+st.n_simplices, st.dimension, st.vertices, st.connected_components
+```
+
+Interoperability with numpy is provided whenever possible
+```{python}
+import numpy as np 
+all(np.all(st.triangles == np.array(st.simplices(p=2)), axis=0))
+```
+
+Other complex-wide operations are supported, like $k$-expansions 
+```{python}
+st.insert([[1,4]]) 
+st.expand(2)       
+print(st)
+```
+
+The trie-structure can also be inspected on the python side:
+```{python}
+st.print_tree()
+```
diff --git a/docs_src/static/styles.css b/docs_src/static/styles.css
index 8b05631..fef3495 100644
--- a/docs_src/static/styles.css
+++ b/docs_src/static/styles.css
@@ -46,7 +46,12 @@ section[id^=returns] > p {
   margin-top: 0.5em; 
 }
 
+.sourceCode {
+  background-color: #d3d3d357;
+}
+
 .type_annotation {
   color:#9753b8;
   font-style: italic;
-}
\ No newline at end of file
+}
+