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<head><title>Cone + Polyhedron -- computes the Minkowski sum of a cone and a polyhedron</title>
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<div><h1>Cone + Polyhedron -- computes the Minkowski sum of a cone and 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> Q = C + P</tt></div>
</dd></dl>
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</li>
<li><span>Operator: <a href="../../Macaulay2Doc/html/__pl.html" title="a unary or binary operator, usually used for addition">+</a></span></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>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
</ul>
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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 Minkowski sum of <tt>C</tt> and <tt>P</tt>.This is the polyhedron
<tt>C + P = {c + p | c in C, p in P}</tt>. Note that <tt>C</tt> and <tt>P</tt> have
to lie in the same ambient space.<p/>
See also <a href="_minkowski__Sum.html" title=" computes the Minkowski sum of two convex objects">minkowskiSum</a>.<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{1},{2},{0}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o1 : Cone</pre>
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<tr><td><pre>i2 : P = hypercube 3
o2 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 0
number of vertices => 8
o2 : Polyhedron</pre>
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<tr><td><pre>i3 : Q = C + P
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 1
number of vertices => 6
o3 : Polyhedron</pre>
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<tr><td><pre>i4 : (vertices Q,rays Q)
o4 = (| -1 1 -1 -1 1 -1 |, | 1 |)
| -1 -1 1 -1 -1 1 | | 2 |
| -1 -1 -1 1 1 1 | | 0 |
o4 : Sequence</pre>
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