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<head><title>isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice</title>
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<div><h1>isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice</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 = isNormal P</tt></div>
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<li><span>Function: <a href="../../IntegralClosure/html/_is__Normal.html" title="determine if a reduced ring is normal">isNormal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span>, which must be compact</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>, true if P is normal in the ambient lattice</span></li>
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<div class="single"><h2>Description</h2>
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<tt>isNormal</tt> can only be applied to polytopes, i.e. compact polyhedra. It
embeds the polytope on height 1 in a space of dimension plus 1 and takes the Cone over
this polytope. Then it checks if all elements of the Hilbert basis lie in height 1.<table class="examples"><tr><td><pre>i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : isNormal P
o2 = false</pre>
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