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<head><title>incompCones -- returns the pairs of incompatible cones</title>
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<div><h1>incompCones -- returns the pairs of incompatible cones</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> Lpairs = incompCones L </tt><br/><tt>Lpairs = incompCones(X,F) </tt><br/><tt>Lpairs = incompCones(F,X)</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</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>
</ul>
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<li><div class="single">Outputs:<ul><li><span><tt>Lpairs</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
If <tt>incompCones</tt> is applied to a list of cones and fans, then it returns the pairs of elements
whose intersection is not a face of each. For a cone <tt>C</tt> and a fan <tt>F</tt> in the list this means there
is at least one generating cone of <tt>F</tt> whose intersection with <tt>C</tt> is not a face of each. For two
fans in the list this means there is at least one generating cone each such that their intersection is not a face
of each. If applied to a pair consisting of a cone and a fan or two fans, then it returns the pairs of cones that
do not share a common face.<table class="examples"><tr><td><pre>i1 : C1 = posHull matrix{{1,0},{1,1}};</pre>
</td></tr>
<tr><td><pre>i2 : C2 = posHull matrix{{1,0},{0,-1}};</pre>
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<tr><td><pre>i3 : C3 = posHull matrix{{-1,0},{0,1}};</pre>
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<tr><td><pre>i4 : C4 = posHull matrix{{1,1},{0,1}};</pre>
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<tr><td><pre>i5 : C5 = posHull matrix {{1,2},{2,1}};</pre>
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<tr><td><pre>i6 : L = {C1,C2,C3,C4,C5};</pre>
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<tr><td><pre>i7 : Lpairs = incompCones L
o7 = {({ambient dimension => 2 }, {ambient dimension => 2
dimension of lineality space => 0 dimension of lineality space =>
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}), ({ambient dimension => 2 }, {ambient dimension => 2
0 dimension of lineality space => 0 dimension of lineality space
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
})}
=> 0
o7 : List</pre>
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<tr><td><pre>i8 : Lpairs == {(C1,C4),(C1,C5)}
o8 = false</pre>
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<div class="waystouse"><h2>Ways to use <tt>incompCones</tt> :</h2>
<ul><li>incompCones(Cone,Fan)</li>
<li>incompCones(Fan,Cone)</li>
<li>incompCones(Fan,Fan)</li>
<li>incompCones(List)</li>
</ul>
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