<?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>GroundSet -- underlying set of a poset</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Lattice.html">next</a> | <a href="_filter.html">previous</a> | <a href="_is__Lattice.html">forward</a> | <a href="_filter.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>GroundSet -- underlying set of a poset</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>G = P.GroundSet</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>an object of class <a href="___Poset.html" title="a class for partially ordered sets (posets)">Poset</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>G</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, list of elements in P without the data of how they are partially ordered</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>Since any poset is in fact a HashTable this symbol denotes the data in the HashTable consisting of the elements of the set.</div> <table class="examples"><tr><td><pre>i1 : S = QQ[a,b,c,d];</pre> </td></tr> <tr><td><pre>i2 : M = monomialIdeal (b^2, b*c, c^2); o2 : MonomialIdeal of S</pre> </td></tr> <tr><td><pre>i3 : L = lcmLattice (M);</pre> </td></tr> <tr><td><pre>i4 : L.GroundSet 2 2 2 2 2 2 o4 = {b , b*c, c , b c, b c , b*c } o4 : List</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Relation__Matrix.html" title="the matrix expressing all of the relations between elements in a Poset">RelationMatrix</a> -- the matrix expressing all of the relations between elements in a Poset</span></li> <li><span><a href="___Relations.html" title="a set of relations in the poset that generates all other relations">Relations</a> -- a set of relations in the poset that generates all other relations</span></li> <li><span><a href="_poset.html" title="creating a poset">poset</a> -- creating a poset</span></li> <li><span><a href="___Poset.html" title="a class for partially ordered sets (posets)">Poset</a> -- a class for partially ordered sets (posets)</span></li> </ul> </div> <div class="waystouse"><h2>For the programmer</h2> <p>The object <a href="___Ground__Set.html" title="underlying set of a poset">GroundSet</a> is <span>a <a href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p> </div> </div> </body> </html>