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<head><title>directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones</title>
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<div><h1>directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones</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> P = directProduct(X,Y)</tt></div>
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<li><span>Function: <a href="_direct__Product.html" title="computes the direct product of two convex objects">directProduct</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>X</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span>, <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a></span></li>
<li><span><tt>Y</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span>, <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>P</tt>, <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a></span></li>
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<div class="single"><h2>Description</h2>
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The <tt>directProduct</tt> of <tt>X</tt> and <tt>Y</tt> is the polyhedron
<tt>{(x,y) | x in X, y in Y}</tt> in the direct product of the ambient spaces. If
<tt>X</tt> and <tt>Y</tt> are both cones, then the direct product is again a cone
and the output is then also given as a <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a>, otherwise as a <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a>.<table class="examples"><tr><td><pre>i1 : P = hypercube 1
o1 = {ambient dimension => 1 }
dimension of lineality space => 0
dimension of polyhedron => 1
number of facets => 2
number of rays => 0
number of vertices => 2
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : Q = hypercube 2
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o2 : Polyhedron</pre>
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<tr><td><pre>i3 : directProduct(P,Q) == hypercube 3
o3 = true</pre>
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See also <a href="___Cone_sp_st_sp__Cone.html" title="computes the direct product of two cones">Cone * Cone</a>, <a href="___Cone_sp_st_sp__Polyhedron.html" title="computes the direct product of a cone and a polyhedron">Cone * Polyhedron</a>, <a href="___Polyhedron_sp_st_sp__Cone.html" title="computes the direct product of a polyhedron and a cone">Polyhedron * Cone</a>, and <a href="___Polyhedron_sp_st_sp__Polyhedron.html" title="computes the direct product of two polyhedra">Polyhedron * Polyhedron</a>.</div>
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