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<head><title>minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum</title>
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<div><h1>minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum</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 = minFace(w,P) </tt><br/><tt>F = minFace(w,C)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>w</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, over <a href="../../Macaulay2Doc/html/___Z__Z.html" title="the class of all integers">ZZ</a> or <a href="../../Macaulay2Doc/html/___Q__Q.html" title="the class of all rational numbers">QQ</a> with only one column representing a
weight vector</span></li>
<li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>F</tt>, Depending on the input, a Cone or a Polyhedron, the face where <tt>w</tt> attains
its minimum</span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
<tt>minFace</tt> computes the face of the given Polyhedron <tt>P</tt> or Cone <tt>C</tt>
where <tt>w</tt> attains its minimum.<table class="examples"><tr><td><pre>i1 : P = hypercube 3
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 0
number of vertices => 8
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : w = matrix {{1},{2},{0}}
o2 = | 1 |
| 2 |
| 0 |
3 1
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : F = minFace(w,P)
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 1
number of facets => 2
number of rays => 0
number of vertices => 2
o3 : Polyhedron</pre>
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<tr><td><pre>i4 : vertices F
o4 = | -1 -1 |
| -1 -1 |
| -1 1 |
3 2
o4 : Matrix QQ <--- QQ</pre>
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<div class="waystouse"><h2>Ways to use <tt>minFace</tt> :</h2>
<ul><li>minFace(Matrix,Cone)</li>
<li>minFace(Matrix,Polyhedron)</li>
</ul>
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