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<head><title>imageFan -- computes the fan of the image</title>
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<div><h1>imageFan -- computes the fan of the image</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 = imageFan(M,C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
<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">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>
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<tt>M</tt> must be a matrix from the ambient space of the <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> <tt>C</tt> to some
target space. The <tt>imageFan</tt> is the common refinement of the images of all faces of <tt>C</tt>.<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{2,1,-1,-3},{1,1,1,1},{0,1,-1,0}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 4
number of rays => 4
o1 : Cone</pre>
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<tr><td><pre>i2 : M = matrix {{1,0,0},{0,1,0}}
o2 = | 1 0 0 |
| 0 1 0 |
2 3
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : F = imageFan(M,C)
o3 = {ambient dimension => 2 }
number of generating cones => 3
number of rays => 4
top dimension of the cones => 2
o3 : Fan</pre>
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<tr><td><pre>i4 : rays F
o4 = {| -3 |, | -1 |, | 2 |, | 1 |}
| 1 | | 1 | | 1 | | 1 |
o4 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>imageFan</tt> :</h2>
<ul><li>imageFan(Matrix,Cone)</li>
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