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<head><title>volume -- computes the volume of a polytope</title>
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<div><h1>volume -- computes the volume of a polytope</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> v = volume P</tt></div>
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<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>v</tt>, <span>a <a href="../../Macaulay2Doc/html/___Q__Q.html">rational number</a></span></span></li>
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<div class="single"><h2>Description</h2>
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<tt>volume</tt> computes the volume of a polytope. To do this, it triangulates the polytope first. The volume
of a simplex is |det(v_1-v_0,..,v_n-v_0)|/n!, where v_0,..,v_n are the vertices of the simplex.<table class="examples"><tr><td><pre>i1 : P = crossPolytope 3
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 8
number of rays => 0
number of vertices => 6
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : volume P
4
o2 = -
3
o2 : QQ</pre>
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<div class="waystouse"><h2>Ways to use <tt>volume</tt> :</h2>
<ul><li>volume(Polyhedron)</li>
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