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<head><title>smoothSubfan -- computes the subfan of all smooth cones</title>
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<div><h1>smoothSubfan -- computes the subfan of all smooth 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> F1 = smoothSubfan F</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><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>
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<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 a given <a href="___Fan.html" title="the class of all fans">Fan</a> <tt>F</tt> the function computes the subfan <tt>F1</tt> of
all smooth cones.<p/>
Let's consider the fan consisting of the following three dimensional cone and all
of its faces:<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{1,-1,0},{1,1,0},{1,1,1}}
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 : F = fan C
o2 = {ambient dimension => 3 }
number of generating cones => 1
number of rays => 3
top dimension of the cones => 3
o2 : Fan</pre>
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This cone is not smooth, therefore also the fan is not. But if we remove the interior and one
of the two dimensional faces the resulting subfan is smooth.<table class="examples"><tr><td><pre>i3 : F1 = smoothSubfan F
o3 = {ambient dimension => 3 }
number of generating cones => 2
number of rays => 3
top dimension of the cones => 2
o3 : Fan</pre>
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<tr><td><pre>i4 : apply(genCones F1, rays)
o4 = {| 0 1 |, | 0 -1 |}
| 0 1 | | 0 1 |
| 1 1 | | 1 1 |
o4 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>smoothSubfan</tt> :</h2>
<ul><li>smoothSubfan(Fan)</li>
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