<?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>rays -- displays all rays of a Cone, a Fan, or a Polyhedron</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_save__Session.html">next</a> | <a href="___Q__Q_sp_st_sp__Polyhedron.html">previous</a> | <a href="_save__Session.html">forward</a> | <a href="___Q__Q_sp_st_sp__Polyhedron.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>rays -- displays all rays of a Cone, a Fan, or a 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> R = rays C </tt><br/><tt>R = rays F </tt><br/><tt>R = rays P</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<li><span><tt>F</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</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>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p/>
<tt>rays</tt> returns the rays of the input as the columns of the
matrix <tt>R</tt>.<table class="examples"><tr><td><pre>i1 : P = convexHull(matrix {{1,-1,2,-2},{1,1,2,2}}, matrix {{0},{1}})
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 5
number of rays => 1
number of vertices => 4
o1 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i2 : rays P
o2 = | 0 |
| 1 |
2 1
o2 : Matrix QQ <--- QQ</pre>
</td></tr>
<tr><td><pre>i3 : C = posHull P
o3 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
o3 : Cone</pre>
</td></tr>
<tr><td><pre>i4 : rays C
o4 = | -1 1 |
| 1 1 |
2 2
o4 : Matrix QQ <--- QQ</pre>
</td></tr>
<tr><td><pre>i5 : F = normalFan P
o5 = {ambient dimension => 2 }
number of generating cones => 4
number of rays => 5
top dimension of the cones => 2
o5 : Fan</pre>
</td></tr>
<tr><td><pre>i6 : rays F
o6 = {| -1 |, | 1 |, | 1 |, | -1 |, | 0 |}
| 0 | | 1 | | 0 | | 1 | | 1 |
o6 : List</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>rays</tt> :</h2>
<ul><li>rays(Cone)</li>
<li>rays(Fan)</li>
<li>rays(Polyhedron)</li>
</ul>
</div>
</div>
</body>
</html>
