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<head><title>Cone + Cone -- computes the Minkowski sum of two cones</title>
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<div><h1>Cone + Cone -- computes the Minkowski sum of two 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> C = C1 + C2</tt></div>
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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>C1</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<li><span><tt>C2</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>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
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<div class="single"><h2>Description</h2>
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Computes the Minkowski sum of <tt>C1</tt> and <tt>C2</tt>. This is the cone
<tt>C1 + C2 = {x + y | x in C1, y in C2}</tt>. Note that <tt>C1</tt> and <tt>C2</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 : C1 = posHull matrix {{1,2,3},{2,3,1},{3,1,2}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 3
number of rays => 3
o1 : Cone</pre>
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<tr><td><pre>i2 : C2 = posHull matrix {{1},{0},{0}}
o2 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o2 : Cone</pre>
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<tr><td><pre>i3 : C = C1 + C2
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 4
number of rays => 4
o3 : Cone</pre>
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<tr><td><pre>i4 : rays C
o4 = | 1 2 3 1 |
| 0 3 1 2 |
| 0 1 2 3 |
3 4
o4 : Matrix QQ <--- QQ</pre>
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