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<head><title>Polyhedron * Cone -- computes the direct product of a polyhedron and a cone</title>
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<div><h1>Polyhedron * Cone -- computes the direct product of a polyhedron and a cone</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 = P * C</tt></div>
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<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>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>Q</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
Computes the direct product of <tt>P</tt> and <tt>C</tt>. This is the polyhedron
<tt>{(p,c) | p in P, x in C}</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 : P =convexHull matrix {{1},{-1}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 0
number of facets => 1
number of rays => 0
number of vertices => 1
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : C = posHull matrix {{1,2},{2,1}}
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
o2 : Cone</pre>
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<tr><td><pre>i3 : Q = P * C
o3 = {ambient dimension => 4 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 3
number of rays => 2
number of vertices => 1
o3 : Polyhedron</pre>
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<tr><td><pre>i4 : (vertices Q,rays Q)
o4 = (| 1 |, | 0 0 |)
| -1 | | 0 0 |
| 0 | | 2 1 |
| 0 | | 1 2 |
o4 : Sequence</pre>
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