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<head><title>normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron</title>
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<div><h1>normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of 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> C = normalCone(P,Q)</tt></div>
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<li><span>Function: <a href="../../ReesAlgebra/html/_normal__Cone.html" title="the normal cone of a subscheme">normalCone</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>Q</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span>, which must be a face of <tt>P</tt></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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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="../../ReesAlgebra/html/_symmetric__Kernel_lp..._cm_sp__Variable_sp_eq_gt_sp..._rp.html">Variable => ...</a>, -- Choose name for variables in the created ring</span></li>
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<div class="single"><h2>Description</h2>
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The normal cone of a face <tt>Q</tt> of a polyhedron <tt>P</tt> is the cone in the normal fan (see <a href="_normal__Fan.html" title="computes the normalFan of a polyhedron">normalFan</a>)
that corresponds to this face. This is the cone of all vectors attaining their maximum on this face.<table class="examples"><tr><td><pre>i1 : P = hypercube 3
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 0
number of vertices => 8
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}
o2 = {ambient dimension => 3 }
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 : C = normalCone(P,Q)
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o3 : Cone</pre>
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<tr><td><pre>i4 : rays C
o4 = | 0 |
| 0 |
| -1 |
3 1
o4 : Matrix QQ <--- QQ</pre>
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