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<head><title>fan -- generates a Fan</title>
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<div><h1>fan -- generates 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> F = fan C </tt><br/><tt>F = fan L</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, with elements of class <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or <a href="___Fan.html" title="the class of all fans">Fan</a></span></li>
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<li><div class="single">Outputs:<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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<div class="single"><h2>Description</h2>
<div><p/>
If <tt>fan</tt> is applied to a <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> it generates
the <a href="___Fan.html" title="the class of all fans">Fan</a> given by the the Cone and all of its faces. If applied to
a <a href="../../Macaulay2Doc/html/___List.html" title="the class of all lists -- {...}">List</a> the list must only contain Cones and Fans in the same
ambient space. Then it adds the Cones in the List and the generating Cones
of the Fans in the List one by one to the Fan, checking each time if the
new Cone is compatible with the cones that have already been added, i.e.
that the intersection with each of them is a face of both Cones
(intersection condition).<p/>
If one of the cones is in the wrong ambient space, there will be an
error and no fan will be returned. If the intersection condition fails, there
will also be an error. The pairs of incompatible cones can be accessed with the
function <a href="_incomp__Cones.html" title="returns the pairs of incompatible cones">incompCones</a>.<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{1,-1},{0,-1}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
o1 : Cone</pre>
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<tr><td><pre>i2 : F = fan C
o2 = {ambient dimension => 2 }
number of generating cones => 1
number of rays => 2
top dimension of the cones => 2
o2 : Fan</pre>
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<tr><td><pre>i3 : C1 = posHull matrix {{1,0},{0,1}};</pre>
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<tr><td><pre>i4 : C2 = posHull matrix {{0,-1},{1,-1}};</pre>
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<tr><td><pre>i5 : F = fan {C,C1,C2}
o5 = {ambient dimension => 2 }
number of generating cones => 3
number of rays => 3
top dimension of the cones => 2
o5 : Fan</pre>
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<div class="waystouse"><h2>Ways to use <tt>fan</tt> :</h2>
<ul><li>fan(Cone)</li>
<li>fan(List)</li>
</ul>
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