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<head><title>flats -- list the flats of an arrangement of given rank</title>
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<div><h1>flats -- list the flats of an arrangement of given rank</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>flats(n,A)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, rank</span></li>
<li><span><tt>A</tt>, <span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, hyperplane arrangement</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, A list of <a href="___Flat.html">flats</a> of rank <tt>n</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>If the rank is omitted, the <a href="___Flat.html">flats</a> of each rank are listed.<table class="examples"><tr><td><pre>i1 : A := typeA(3)
o1 = {x - x , x - x , x - x , x - x , x - x , x - x }
1 2 1 3 1 4 2 3 2 4 3 4
o1 : Hyperplane Arrangement </pre>
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<tr><td><pre>i2 : flats(2,A)
o2 = {{0, 1, 3}, {0, 2, 4}, {0, 5}, {1, 4}, {1, 2, 5}, {2, 3}, {3, 4, 5}}
o2 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_circuits.html" title="list the circuits of an arrangement">circuits</a> -- list the circuits of an arrangement</span></li>
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<div class="waystouse"><h2>Ways to use <tt>flats</tt> :</h2>
<ul><li>flats(Arrangement)</li>
<li>flats(ZZ,Arrangement)</li>
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