<?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>isEmpty -- checks if a Polyhedron is empty</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Face.html">next</a> | <a href="_is__Complete.html">previous</a> | <a href="_is__Face.html">forward</a> | <a href="_is__Complete.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>isEmpty -- checks if a Polyhedron is empty</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 = isEmpty P</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</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>, <a href="../../Macaulay2Doc/html/_true.html" title="">true</a> if the <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a> is empty, <a href="../../Macaulay2Doc/html/_false.html" title="">false</a> otherwise</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p/> The polyhedron is empty if the dimension is -1.<table class="examples"><tr><td><pre>i1 : P = intersection(matrix{{1,0},{0,1},{-1,-1}},matrix{{-1},{1},{-1}}) o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => -1 number of facets => 0 number of rays => 0 number of vertices => 0 o1 : Polyhedron</pre> </td></tr> <tr><td><pre>i2 : isEmpty P o2 = true</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>isEmpty</tt> :</h2> <ul><li>isEmpty(Polyhedron)</li> </ul> </div> </div> </body> </html>