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<!DOCTYPE html> <html lang="en"> <head> <title>ChordalNet -- a chordal network</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="a chordal network" href="___Chordal__Net.html">ChordalNet</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="_chordal__Net.html">next</a> | <a href="_chordal__Graph.html">previous</a> | <a href="_chordal__Net.html">forward</a> | <a href="_chordal__Graph.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>ChordalNet -- a chordal network</h1> <div> <h2>Description</h2> This type describes a chordal network representation of a polynomial ideal. The constructor of this type is <a title="constructs a chordal network from a polynomial set" href="_chordal__Net.html">chordalNet</a> <h3>Examples</h3> <ul> <li><span><a title="a new representation of polynomial ideals" href="_chordal_spnetworks_spexamples.html">chordal networks examples</a> -- a new representation of polynomial ideals</span></li> </ul> <h3>Overview of chordal networks methods</h3> Methods to visualize a chordal network: <ul> <li><span><a title="displays a chordal network using Graphivz" href="_display__Net.html">displayNet</a> -- displays a chordal network using Graphivz</span></li> <li><a title="a chordal network" href="___Chordal__Net.html">net</a> -- print a chordal network</li> <li><span><a title="digraph associated to a chordal network" href="_digraph_lp__Chordal__Net_rp.html">digraph(ChordalNet)</a> -- digraph associated to a chordal network</span></li> </ul> Methods to access properties of a chordal network: <ul> <li><span><a title="list of nodes of a chordal network" href="_nodes.html">nodes</a> -- list of nodes of a chordal network</span></li> <li><a title="the elimination tree of a chordal graph" href="___Elim__Tree.html">elimTree</a> -- get the underlying elimination tree</li> <li><a title="a chordal network" href="___Chordal__Net.html">ring</a> -- get the underlying ring</li> <li><span><a title="whether a chordal network is triangular" href="_is__Triangular.html">isTriangular</a> -- whether a chordal network is triangular</span></li> <li><a title="a chordal network" href="___Chordal__Net.html">structure</a> -- either "Monomial", "Binomial" or "None" </li> </ul> Elimination routines using chordal structure: <ul> <li><span><a title="performs elimination on the chordal network" href="_chordal__Elim.html">chordalElim</a> -- performs elimination on the chordal network</span></li> <li><span><a title="makes a chordal network triangular" href="_chordal__Tria.html">chordalTria</a> -- makes a chordal network triangular</span></li> </ul> Methods for triangular chordal networks: <ul> <li><span><a title="counts the number of roots of a chordal network" href="_root__Count.html">rootCount</a> -- counts the number of roots of a chordal network</span></li> <li><span><a title="dimension of a chordal network" href="_dim_lp__Chordal__Net_rp.html">dim(ChordalNet)</a> -- dimension of a chordal network</span></li> <li><span><a title="dimension of a chordal network" href="_dim_lp__Chordal__Net_rp.html">codim(ChordalNet)</a> -- dimension of a chordal network</span></li> <li><span><a title="codimension counts of the chains of a chordal network" href="_codim__Count.html">codimCount</a> -- codimension counts of the chains of a chordal network</span></li> <li><span><a title="top dimension of a chordal network" href="_top__Components_lp__Chordal__Net_rp.html">topComponents(ChordalNet)</a> -- top dimension of a chordal network</span></li> <li><span><a title="ideal membership test" href="___Ring__Element_sp_pc_sp__Chordal__Net.html">RingElement % ChordalNet</a> -- ideal membership test</span></li> <li><span><a title="iterates over the chains of a chordal network" href="_next__Chain.html">nextChain</a> -- iterates over the chains of a chordal network</span></li> <li><span><a title="components of a chordal network" href="_components_lp__Chordal__Net_cm__Z__Z_rp.html">components(ChordalNet)</a> -- components of a chordal network</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Functions and methods returning an object of class ChordalNet:</h2> <ul> <li><span><kbd>chordalNet(Ideal)</kbd> -- see <span><a title="constructs a chordal network from a polynomial set" href="_chordal__Net.html">chordalNet</a> -- constructs a chordal network from a polynomial set</span></span></li> <li><span><kbd>chordalNet(Ideal,List)</kbd> -- see <span><a title="constructs a chordal network from a polynomial set" href="_chordal__Net.html">chordalNet</a> -- constructs a chordal network from a polynomial set</span></span></li> <li><span><kbd>chordalNet(Ideal,String)</kbd> -- see <span><a title="constructs a chordal network from a polynomial set" href="_chordal__Net.html">chordalNet</a> -- constructs a chordal network from a polynomial set</span></span></li> <li><span><a title="construct chordal network from a digraph" href="_chordal__Net_lp__Hash__Table_cm__Hash__Table_cm__Elim__Tree_cm__Digraph_rp.html">chordalNet(HashTable,HashTable,ElimTree,Digraph)</a> -- construct chordal network from a digraph</span></li> <li><span><a title="apply ring map to a chordal network" href="___Ring__Map_sp__Chordal__Net.html">RingMap ChordalNet</a> -- apply ring map to a chordal network</span></li> </ul> <h2>Methods that use an object of class ChordalNet:</h2> <ul> <li><span><kbd>chordalElim(ChordalNet)</kbd> -- see <span><a title="performs elimination on the chordal network" href="_chordal__Elim.html">chordalElim</a> -- performs elimination on the chordal network</span></span></li> <li><kbd>net(ChordalNet)</kbd></li> <li><kbd>ring(ChordalNet)</kbd></li> <li><span><kbd>triaSystem(ChordalNet,ChordalNetChain)</kbd> -- see <span><a title="a chain of a chordal network" href="___Chordal__Net__Chain.html">ChordalNetChain</a> -- a chain of a chordal network</span></span></li> <li><span><kbd>chordalTria(ChordalNet)</kbd> -- see <span><a title="makes a chordal network triangular" href="_chordal__Tria.html">chordalTria</a> -- makes a chordal network triangular</span></span></li> <li><span><kbd>codimCount(ChordalNet)</kbd> -- see <span><a title="codimension counts of the chains of a chordal network" href="_codim__Count.html">codimCount</a> -- codimension counts of the chains of a chordal network</span></span></li> <li><span><kbd>components(ChordalNet)</kbd> -- see <span><a title="components of a chordal network" href="_components_lp__Chordal__Net_cm__Z__Z_rp.html">components(ChordalNet,ZZ)</a> -- components of a chordal network</span></span></li> <li><span><a title="components of a chordal network" href="_components_lp__Chordal__Net_cm__Z__Z_rp.html">components(ChordalNet,ZZ)</a> -- components of a chordal network</span></li> <li><span><a title="digraph associated to a chordal network" href="_digraph_lp__Chordal__Net_rp.html">digraph(ChordalNet)</a> -- digraph associated to a chordal network</span></li> <li><span><kbd>codim(ChordalNet)</kbd> -- see <span><a title="dimension of a chordal network" href="_dim_lp__Chordal__Net_rp.html">dim(ChordalNet)</a> -- dimension of a chordal network</span></span></li> <li><span><a title="dimension of a chordal network" href="_dim_lp__Chordal__Net_rp.html">dim(ChordalNet)</a> -- dimension of a chordal network</span></li> <li><span><kbd>displayNet(ChordalNet)</kbd> -- see <span><a title="displays a chordal network using Graphivz" href="_display__Net.html">displayNet</a> -- displays a chordal network using Graphivz</span></span></li> <li><span><kbd>displayNet(Function,ChordalNet)</kbd> -- see <span><a title="displays a chordal network using Graphivz" href="_display__Net.html">displayNet</a> -- displays a chordal network using Graphivz</span></span></li> <li><span><kbd>displayNet(String,String,Function,ChordalNet)</kbd> -- see <span><a title="displays a chordal network using Graphivz" href="_display__Net.html">displayNet</a> -- displays a chordal network using Graphivz</span></span></li> <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><span><a title="simple primality test of a chordal network" href="_is__Prime__Simple_lp__Chordal__Net_rp.html">isPrimeSimple(ChordalNet)</a> -- simple primality test of a chordal network</span></li> <li><span><kbd>isTriangular(ChordalNet)</kbd> -- see <span><a title="whether a chordal network is triangular" href="_is__Triangular.html">isTriangular</a> -- whether a chordal network is triangular</span></span></li> <li><span><kbd>nextChain(ChordalNet)</kbd> -- see <span><a title="iterates over the chains of a chordal network" href="_next__Chain.html">nextChain</a> -- iterates over the chains of a chordal network</span></span></li> <li><span><kbd>nextChain(ChordalNetChain,ChordalNet)</kbd> -- see <span><a title="iterates over the chains of a chordal network" href="_next__Chain.html">nextChain</a> -- iterates over the chains of a chordal network</span></span></li> <li><span><kbd>nextChain(ChordalNetChain,Sequence,ZZ,ChordalNet)</kbd> -- see <span><a title="iterates over the chains of a chordal network" href="_next__Chain.html">nextChain</a> -- iterates over the chains of a chordal network</span></span></li> <li><span><kbd>nextChain(ZZ,ChordalNet)</kbd> -- see <span><a title="iterates over the chains of a chordal network" href="_next__Chain.html">nextChain</a> -- iterates over the chains of a chordal network</span></span></li> <li><span><kbd>nodes(ChordalNet)</kbd> -- see <span><a title="list of nodes of a chordal network" href="_nodes.html">nodes</a> -- list of nodes of a chordal network</span></span></li> <li><span><kbd>nodes(ChordalNet,RingElement)</kbd> -- see <span><a title="list of nodes of a chordal network" href="_nodes.html">nodes</a> -- list of nodes of a chordal network</span></span></li> <li><span><kbd>reduceNet(ChordalNet)</kbd> -- see <span><a title="reduces a chordal network" href="_reduce__Net.html">reduceNet</a> -- reduces a chordal network</span></span></li> <li><span><kbd>pseudoRemainder(RingElement,ChordalNet)</kbd> -- see <span><a title="ideal membership test" href="___Ring__Element_sp_pc_sp__Chordal__Net.html">RingElement % ChordalNet</a> -- ideal membership test</span></span></li> <li><span><a title="ideal membership test" href="___Ring__Element_sp_pc_sp__Chordal__Net.html">RingElement % ChordalNet</a> -- ideal membership test</span></li> <li><span><kbd>rootCount(ChordalNet)</kbd> -- see <span><a title="counts the number of roots of a chordal network" href="_root__Count.html">rootCount</a> -- counts the number of roots of a chordal network</span></span></li> <li><span><a title="size of a chordal network" href="_size_lp__Chordal__Net_rp.html">size(ChordalNet)</a> -- size of a chordal network</span></li> <li><span><a title="writes a chordal network to a dot file" href="_write__Dot__File_lp__String_cm__Function_cm__Chordal__Net_rp.html">writeDotFile(String,Function,ChordalNet)</a> -- writes a chordal network to a dot file</span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a chordal network" href="___Chordal__Net.html">ChordalNet</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all mutable hash tables" href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">MutableHashTable</a> < <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Chordal/ChordalDoc.m2:221:0</span>.</p> </div> </div> </div> </body> </html>