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<head><title>isPure -- checks if a Fan is of pure dimension</title>
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<div><h1>isPure -- checks if a Fan is of pure dimension</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> b = isPure F</tt></div>
</dd></dl>
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</li>
<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>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <a href="../../Macaulay2Doc/html/_true.html" title="">true</a> if the <a href="___Fan.html" title="the class of all fans">Fan</a> is of pure dimension, <a href="../../Macaulay2Doc/html/_false.html" title="">false</a> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
<tt>isPure</tt> tests if the <a href="___Fan.html" title="the class of all fans">Fan</a> is pure by checking if the first and the last entry in
the list of generating Cones are of the same dimension.<p/>
Let us construct a fan consisting of the positive orthant and the ray <tt>v</tt> that is the
negative sum of the canonical basis, which is obviously not pure:<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{1,0,0},{0,1,0},{0,0,1}}
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>
</td></tr>
<tr><td><pre>i2 : v = posHull matrix {{-1},{-1},{-1}}
o2 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o2 : Cone</pre>
</td></tr>
<tr><td><pre>i3 : F = fan {C,v}
o3 = {ambient dimension => 3 }
number of generating cones => 2
number of rays => 4
top dimension of the cones => 3
o3 : Fan</pre>
</td></tr>
<tr><td><pre>i4 : isPure F
o4 = true</pre>
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<p/>
But we can make a pure fan if we choose any two dimensional face of the positive
orthant and take the cone generated by this face and <tt>v</tt> and add it to the cone:<table class="examples"><tr><td><pre>i5 : C1 = posHull{(faces(1,C))#0,v}
o5 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 3
number of rays => 3
o5 : Cone</pre>
</td></tr>
<tr><td><pre>i6 : F = addCone(C1,F)
o6 = {ambient dimension => 3 }
number of generating cones => 2
number of rays => 4
top dimension of the cones => 3
o6 : Fan</pre>
</td></tr>
<tr><td><pre>i7 : isPure F
o7 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isPure</tt> :</h2>
<ul><li>isPure(Fan)</li>
</ul>
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