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<!DOCTYPE html> <html lang="en"> <head> <title>elimTree -- elimination tree of a chordal graph</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="exploiting chordal structure in polynomial ideals" href="index.html">Chordal</a> :: <a title="elimination tree of a chordal graph" href="_elim__Tree.html">elimTree</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="___Get__Table.html">next</a> | <a href="___Elim__Tree.html">previous</a> | <a href="___Get__Table.html">forward</a> | <a href="___Elim__Tree.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>elimTree -- elimination tree of a chordal graph</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">elimTree G</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">G</span>, <span>an instance of the type <a title="a chordal graph" href="___Chordal__Graph.html">ChordalGraph</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="the elimination tree of a chordal graph" href="___Elim__Tree.html">ElimTree</a></span>, the elimination tree of G</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method computes the elimination tree of some given chordal graph.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : G = graph(toList(0..9),{ {0,{6,7}},{1,{4,9}},{2,{3,5}},{3,{7,8}}, {4,{5,8}},{5,{8}},{6,{8,9}},{7,{8}},{8,{9}} });</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : Gc = chordalGraph G o2 = ChordalGraph{0 => {6, 7} } 1 => {4, 9} 2 => {3, 5} 3 => {5, 7, 8} 4 => {5, 8, 9} 5 => {7, 8, 9} 6 => {7, 8, 9} 7 => {8, 9} 8 => {9} 9 => {} o2 : ChordalGraph</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : elimTree Gc o3 = ElimTree{0 => 6 } 1 => 4 2 => 3 3 => 5 4 => 5 5 => 7 6 => 7 7 => 8 8 => 9 9 => null o3 : ElimTree</code></pre> </td> </tr> </table> <pre></pre> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">elimTree</span>:</h2> <ul> <li><span><kbd>elimTree(ChordalNet)</kbd> -- see <span><a title="the elimination tree of a chordal graph" href="___Elim__Tree.html">ElimTree</a> -- the elimination tree of a chordal graph</span></span></li> <li><kbd>elimTree(ChordalGraph)</kbd></li> <li><span><span class="tt">elimTree(List,HashTable,HashTable)</span> (missing documentation)<!--tag: (elimTree,List,HashTable,HashTable)--> </span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="elimination tree of a chordal graph" href="_elim__Tree.html">elimTree</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Chordal/ChordalDoc.m2:430:0</span>.</p> </div> </div> </div> </body> </html>