<?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>inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_interior__Point.html">next</a> | <a href="_incomp__Cones.html">previous</a> | <a href="_interior__Point.html">forward</a> | <a href="_incomp__Cones.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>inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron</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 = inInterior(p,C) </tt><br/><tt>b = inInterior(p,P)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>p</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, over <a href="../../Macaulay2Doc/html/___Z__Z.html" title="the class of all integers">ZZ</a> or <a href="../../Macaulay2Doc/html/___Q__Q.html" title="the class of all rational numbers">QQ</a> with only one column representing a point</span></li>
<li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<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 <tt>p</tt> lies in the relative interior of the
Cone/Polyhedron, <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/>
<tt>inInterior</tt> checks if the smallest face of the <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or
the <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a> containing <tt>p</tt> is the <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or
the <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a> itself. For this the number of rows of <tt>p</tt> must
equal the ambient dimension of the second argument.<table class="examples"><tr><td><pre>i1 : P = cyclicPolytope(3,5)
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 0
number of vertices => 5
o1 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i2 : p = matrix{{2},{4},{8}}
o2 = | 2 |
| 4 |
| 8 |
3 1
o2 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i3 : q = matrix{{2},{6},{20}}
o3 = | 2 |
| 6 |
| 20 |
3 1
o3 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i4 : inInterior(p,P)
o4 = false</pre>
</td></tr>
<tr><td><pre>i5 : inInterior(q,P)
o5 = true</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>inInterior</tt> :</h2>
<ul><li>inInterior(Matrix,Cone)</li>
<li>inInterior(Matrix,Polyhedron)</li>
</ul>
</div>
</div>
</body>
</html>
