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<head><title>commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans</title>
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<div><h1>commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans</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 = commonFace(C1,C2) </tt><br/><tt>b = commonFace(P1,P2) </tt><br/><tt>b = commonFace(X,F) </tt><br/><tt>b = commonFace(F,X) </tt><br/><tt>b = commonFace L</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><li><span><tt>C1</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<li><span><tt>C2</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li>
<li><span><tt>P1</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
<li><span><tt>P2</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
<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>
<li><span><tt>X</tt>, <a href="___Cone.html" title="the class of all rational convex polyhedral cones">Cone</a> or <a href="___Fan.html" title="the class of all fans">Fan</a></span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</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 intersection is a face both,
and <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>commonFace</tt> checks if the intersection of <tt>C1</tt>
and <tt>C2</tt> or the intersection of <tt>P1</tt> and <tt>P2</tt> is
a face of both. If it is applied to a pair of a cone <tt>C</tt> and a fan <tt>F</tt> then
it checks if the intersection of <tt>C</tt> with every generating cone of <tt>F</tt> is
a face of each. For two fans it checks this condition for every pair of generating cones.
If applied to a list then the list must contain Fans and Cones and it checks pairwise for
a common face.<p/>
For example, consider the following three cones:<table class="examples"><tr><td><pre>i1 : C1 = posHull matrix {{1,0},{0,1}};</pre>
</td></tr>
<tr><td><pre>i2 : C2 = posHull matrix {{1,-1},{0,-1}};</pre>
</td></tr>
<tr><td><pre>i3 : C3 = posHull matrix {{1,-1},{2,-1}};</pre>
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for each pair of two of them we can check if their intersection is a common face:<table class="examples"><tr><td><pre>i4 : commonFace(C1,C2)
o4 = true</pre>
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<tr><td><pre>i5 : commonFace(C2,C3)
o5 = true</pre>
</td></tr>
<tr><td><pre>i6 : commonFace(C3,C1)
o6 = false</pre>
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<div class="waystouse"><h2>Ways to use <tt>commonFace</tt> :</h2>
<ul><li>commonFace(Cone,Cone)</li>
<li>commonFace(Cone,Fan)</li>
<li>commonFace(Fan,Cone)</li>
<li>commonFace(Fan,Fan)</li>
<li>commonFace(List)</li>
<li>commonFace(Polyhedron,Polyhedron)</li>
</ul>
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