<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>isCM -- determines if a (hyper)graph is Cohen-Macaulay</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Connected.html">next</a> | <a href="_is__Chordal.html">previous</a> | <a href="_is__Connected.html">forward</a> | <a href="_is__Chordal.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>isCM -- determines if a (hyper)graph is Cohen-Macaulay</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>b = isCM H</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>H</tt>, <span>a <a href="___Hyper__Graph.html">hypergraph</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>true</tt> if the <a href="_edge__Ideal.html" title="creates the edge ideal of a (hyper)graph">edgeIdeal</a> of <tt>H</tt> is Cohen-Macaulay</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>This uses the edge ideal notion of Cohen-Macaulayness; a hypergraph is called C-M if and only if its edge ideal is C-M.</div> <table class="examples"><tr><td><pre>i1 : R = QQ[a..e];</pre> </td></tr> <tr><td><pre>i2 : C = cycle R;</pre> </td></tr> <tr><td><pre>i3 : UnmixedTree = graph {a*b, b*c, c*d};</pre> </td></tr> <tr><td><pre>i4 : MixedTree = graph {a*b, a*c, a*d};</pre> </td></tr> <tr><td><pre>i5 : isCM C o5 = true</pre> </td></tr> <tr><td><pre>i6 : isCM UnmixedTree o6 = true</pre> </td></tr> <tr><td><pre>i7 : isCM MixedTree o7 = false</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_is__S__C__M.html" title="determines if a (hyper)graph is sequentially Cohen-Macaulay">isSCM</a> -- determines if a (hyper)graph is sequentially Cohen-Macaulay</span></li> <li><span><a href="_edge__Ideal.html" title="creates the edge ideal of a (hyper)graph">edgeIdeal</a> -- creates the edge ideal of a (hyper)graph</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>isCM</tt> :</h2> <ul><li>isCM(HyperGraph)</li> </ul> </div> </div> </body> </html>