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<head><title>skeleton -- computes the k-skeleton of a Fan</title>
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<div><h1>skeleton -- computes the k-skeleton of a Fan</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> F1 = skeleton(k,F)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>k</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>F</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>F1</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
For an integer <tt>k</tt> between 0 and the dimension of <tt>F</tt>,
<tt>skeleton</tt> computes the <tt>k</tt>-skeleton of the <a href="___Fan.html" title="the class of all fans">Fan</a> <tt>F</tt>,
i.e. the <a href="___Fan.html" title="the class of all fans">Fan</a> <tt>F1</tt> generated by all cones of dimension
<tt>k</tt> in <tt>F</tt>.<p/>
For example, we can look at the 2-skeleton of the fan of projective
3-space:<table class="examples"><tr><td><pre>i1 : P = convexHull matrix{{1,0,0,0},{0,1,0,0},{0,0,1,0}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron</pre>
</td></tr>
<tr><td><pre>i2 : F = normalFan P
o2 = {ambient dimension => 3 }
number of generating cones => 4
number of rays => 4
top dimension of the cones => 3
o2 : Fan</pre>
</td></tr>
<tr><td><pre>i3 : F1 = skeleton(2,F)
o3 = {ambient dimension => 3 }
number of generating cones => 6
number of rays => 4
top dimension of the cones => 2
o3 : Fan</pre>
</td></tr>
<tr><td><pre>i4 : apply(genCones F1,rays)
o4 = {| 0 0 |, | 1 0 |, | 1 -1 |, | -1 0 |, | 0 -1 |, | 1 0 |}
| 1 0 | | 0 1 | | 0 -1 | | -1 0 | | 1 -1 | | 0 0 |
| 0 1 | | 0 0 | | 0 -1 | | -1 1 | | 0 -1 | | 0 1 |
o4 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>skeleton</tt> :</h2>
<ul><li>skeleton(ZZ,Fan)</li>
</ul>
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