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<head><title>isSmooth -- checks if a Cone or Fan is smooth</title>
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<div><h1>isSmooth -- checks if a Cone or Fan is smooth</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 = isSmooth C </tt><br/><tt>b = isSmooth F</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>
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<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="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a>/<a href="___Fan.html" title="the class of all fans">Fan</a> is smooth, <a href="../../Macaulay2Doc/html/_false.html" title="">false</a> otherwise</span></li>
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<div class="single"><h2>Description</h2>
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<tt>isSmooth</tt> checks for a <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> if the rays are a subset of a basis of the
lattice. For a <a href="___Fan.html" title="the class of all fans">Fan</a> it checks smoothness for every <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a>.<table class="examples"><tr><td><pre>i1 : C = posHull matrix {{1,2,3},{3,1,2},{2,3,1}}
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 : isSmooth C
o2 = false</pre>
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<tr><td><pre>i3 : F = hirzebruch 3
o3 = {ambient dimension => 2 }
number of generating cones => 4
number of rays => 4
top dimension of the cones => 2
o3 : Fan</pre>
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<tr><td><pre>i4 : isSmooth F
o4 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isSmooth</tt> :</h2>
<ul><li>isSmooth(Cone)</li>
<li>isSmooth(Fan)</li>
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