<?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>isLattice -- determines if a poset is a lattice</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_join__Exists.html">next</a> | <a href="___Ground__Set.html">previous</a> | <a href="_join__Exists.html">forward</a> | <a href="___Ground__Set.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>isLattice -- determines if a poset is a lattice</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>isLattice (P)</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>true</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, if P is a lattice</span></li> <li><span><tt>false</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, otherwise</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>This function examines the entire poset to determine whether or not every pair of elements has both a meet and a join.</div> <table class="examples"><tr><td><pre>i1 : P = poset ({a,b,c,d,e,f}, {(a,d),(d,f),(b,d),(b,e),(c,e),(e,f)});</pre> </td></tr> <tr><td><pre>i2 : isLattice (P) o2 = false</pre> </td></tr> </table> <div>And by adding an element to the above example, we can create a poset which is a lattice.</div> <table class="examples"><tr><td><pre>i3 : P = poset ({a,b,c,d,e,f,x}, {(a,d),(d,f),(b,d),(b,e),(c,e),(e,f), (x,a), (x,b), (x,c)});</pre> </td></tr> <tr><td><pre>i4 : isLattice (P) o4 = true</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>isLattice</tt> :</h2> <ul><li>isLattice(Poset)</li> </ul> </div> </div> </body> </html>