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<head><title>areCompatible -- checks if the intersection of two cones is a face of each</title>
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<div><h1>areCompatible -- checks if the intersection of two cones is a face of each</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,C) = areCompatible(C1,C2)</tt></div>
</dd></dl>
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</li>
<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>
</ul>
</div>
</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 of each cone,
and <a href="../../Macaulay2Doc/html/_false.html" title="">false</a> otherwise.</span></li>
<li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span>, the intersection of both Cones if they are compatible, otherwise
the empty polyhedron.</span></li>
</ul>
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</li>
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<div class="single"><h2>Description</h2>
<div><p/>
<tt>areCompatible</tt> is an extension of <a href="_common__Face.html" title="checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans">commonFace</a> for Cones. It
also checks if the intersection <tt>C</tt> of <tt>C1</tt> and <tt>C2</tt> is a
face of each and the answer is given by <tt>b</tt>. Furthermore, the intersection
is given for further calculations if the two cones lie in the same ambient space. Otherwise,
the empty polyhedron in the ambient space of <tt>C1</tt> is given.<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>
</td></tr>
</table>
<p/>
These might form a fan, but if we check if they are compatible, we see they
are not:<table class="examples"><tr><td><pre>i4 : areCompatible(C1,C2)
o4 = (true, {ambient dimension => 2 })
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o4 : Sequence</pre>
</td></tr>
<tr><td><pre>i5 : areCompatible(C2,C3)
o5 = (true, {ambient dimension => 2 })
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o5 : Sequence</pre>
</td></tr>
<tr><td><pre>i6 : areCompatible(C3,C1)
o6 = (false, {ambient dimension => 2 })
dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
o6 : Sequence</pre>
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<div class="waystouse"><h2>Ways to use <tt>areCompatible</tt> :</h2>
<ul><li>areCompatible(Cone,Cone)</li>
</ul>
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