<?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>Polyhedron * Polyhedron -- computes the direct product of two polyhedra</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="___Polyhedron_sp_pl_sp__Cone.html">next</a> | <a href="___Polyhedron_sp_st_sp__Cone.html">previous</a> | <a href="___Polyhedron_sp_pl_sp__Cone.html">forward</a> | <a href="___Polyhedron_sp_st_sp__Cone.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>Polyhedron * Polyhedron -- computes the direct product of two polyhedra</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> Q = P1 * P2</tt></div>
</dd></dl>
</div>
</li>
<li><span>Operator: <a href="../../Macaulay2Doc/html/__st.html" title="a binary operator, usually used for multiplication">*</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>P1</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
<li><span><tt>P2</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>Q</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p/>
Computes the direct product of <tt>P1</tt> and <tt>P2</tt>.This is the polyhedron
<tt>{(x,y) | x in P1, y in P2}</tt>, in the direct product of the ambient spaces.<p/>
See also <a href="_direct__Product.html" title="computes the direct product of two convex objects">directProduct</a>.<table class="examples"><tr><td><pre>i1 : P1 = convexHull matrix {{1,-1,0,0},{0,0,1,-1}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i2 : P2 = convexHull matrix {{1},{-1}}
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 0
number of facets => 1
number of rays => 0
number of vertices => 1
o2 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i3 : P = P1 * P2
o3 = {ambient dimension => 4 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o3 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i4 : vertices P
o4 = | -1 1 0 0 |
| 0 0 -1 1 |
| 1 1 1 1 |
| -1 -1 -1 -1 |
4 4
o4 : Matrix QQ <--- QQ</pre>
</td></tr>
</table>
</div>
</div>
</div>
</body>
</html>
