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<head><title>isComplete -- checks completeness of a Fan</title>
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<div><h1>isComplete -- checks completeness of a Fan</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 = isComplete F</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><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>
</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 <a href="___Fan.html" title="the class of all fans">Fan</a> is complete, <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>isComplete</tt> just calls an entry in the hash table of the Fan. The check for completeness
is done while generating the fan. Whenever a full dimensional Cone is added (see <a href="_fan.html" title="generates a Fan">fan</a>
or <a href="_add__Cone.html" title="adds cones to a Fan">addCone</a>) the set of faces of codimension 1 that appear only in one full dimensional Cone
is updated. The Fan is then complete if and only if this set is empty and there is at least one
full dimensional Cone.<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,-2}};</pre>
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<tr><td><pre>i3 : C3 = posHull matrix {{0,-2},{1,-1}};</pre>
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<tr><td><pre>i4 : F = fan {C1,C2,C3}
o4 = {ambient dimension => 2 }
number of generating cones => 3
number of rays => 4
top dimension of the cones => 2
o4 : Fan</pre>
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<tr><td><pre>i5 : isComplete F
o5 = false</pre>
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Hence the fan above is not complete, but we can add the missing cone:<table class="examples"><tr><td><pre>i6 : C4 = posHull matrix {{-1,-2},{-2,-1}};</pre>
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<tr><td><pre>i7 : F = addCone(C4,F)
o7 = {ambient dimension => 2 }
number of generating cones => 4
number of rays => 4
top dimension of the cones => 2
o7 : Fan</pre>
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<tr><td><pre>i8 : isComplete F
o8 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isComplete</tt> :</h2>
<ul><li>isComplete(Fan)</li>
</ul>
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