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<head><title>Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra</title>
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<div><h1>Polyhedron + Polyhedron -- computes the Minkowski sum 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>
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<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>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>
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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>P1</tt> and <tt>P2</tt>.This is the polyhedron
<tt>P1 + P2 = {x + y | x in P1, y in P2}</tt>. Note that <tt>P1</tt> and <tt>P2</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 : P1 = convexHull matrix {{1,0,0},{0,1,0}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 3
number of rays => 0
number of vertices => 3
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : P2 = convexHull matrix {{-1,0,0},{0,-1,0}}
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 3
number of rays => 0
number of vertices => 3
o2 : Polyhedron</pre>
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<tr><td><pre>i3 : P = P1 + P2
o3 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 6
number of rays => 0
number of vertices => 6
o3 : Polyhedron</pre>
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<tr><td><pre>i4 : vertices P
o4 = | -1 1 0 1 0 -1 |
| 0 0 -1 -1 1 1 |
2 6
o4 : Matrix QQ <--- QQ</pre>
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