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<head><title>isFace -- tests if the first argument is a face of the second</title>
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<div><h1>isFace -- tests if the first argument is a face of the second</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>b = isFace(X,Y)</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><li><span><tt>X</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span>, or <a href="___Polyhedron.html" title="the class of all convex polyhedra">Polyhedron</a></span></li>
<li><span><tt>Y</tt>, an element of the same class as <tt>X</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <a href="../../Macaulay2Doc/html/_true.html" title="">true</a> if <tt>X</tt> is a face of <tt>Y</tt>, false otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
Both arguments must lie in the same ambient space. Then <tt>isFace</tt> computes all
faces of <tt>Y</tt> with the dimension of <tt>X</tt> and checks if one of them is <tt>X</tt>.<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}}
o2 = {ambient dimension => 3 }
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 : isFace(Q,P)
o3 = false</pre>
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Thus, <tt>Q</tt> is not a face of <tt>P</tt>, but we can extend it to a face.<table class="examples"><tr><td><pre>i4 : v = matrix{{1},{-1},{-1}};
3 1
o4 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i5 : Q = convexHull{Q,v}
o5 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o5 : Polyhedron</pre>
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<tr><td><pre>i6 : isFace(Q,P)
o6 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isFace</tt> :</h2>
<ul><li>isFace(Cone,Cone)</li>
<li>isFace(Polyhedron,Polyhedron)</li>
</ul>
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