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<head><title>ccRefinement -- computes the coarsest common refinement of a set of rays</title>
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<div><h1>ccRefinement -- computes the coarsest common refinement of a set of rays</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 = ccRefinement R</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</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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The coarsest common refinement of a set of rays <tt>R</tt> is the common refinement
of all possible triangulations of the rays.<p/>
For example, consider a three dimensional cone with four rays:<table class="examples"><tr><td><pre>i1 : R = matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}
o1 = | 1 1 -1 -1 |
| 1 -1 1 -1 |
| 1 1 1 1 |
3 4
o1 : Matrix ZZ <--- ZZ</pre>
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The coarsest common refinement has a fifth ray and consists of four cones.<table class="examples"><tr><td><pre>i2 : F = ccRefinement R
o2 = {ambient dimension => 3 }
number of generating cones => 4
number of rays => 5
top dimension of the cones => 3
o2 : Fan</pre>
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<tr><td><pre>i3 : rays F
o3 = {| 1 |, | 1 |, | -1 |, | 0 |, | -1 |}
| -1 | | 1 | | -1 | | 0 | | 1 |
| 1 | | 1 | | 1 | | 1 | | 1 |
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>ccRefinement</tt> :</h2>
<ul><li>ccRefinement(Matrix)</li>
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