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<head><title>isDecomposable -- test if an arrangement is decomposable</title>
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<div><h1>isDecomposable -- test if an arrangement is decomposable</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>isDecomposable(A) or isDecomposable(A,k)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, a hyperplane arrangement</span></li>
<li><span><tt>k</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, an optional coefficient ring, by default the coefficient ring of the arrangement</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, whether or not the arrangement decomposes in the sense of Papadima and Suciu [Comment. Helv. 2006]</span></li>
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<div class="single"><h2>Description</h2>
<div>An arrangement is said to be decomposable if the derived subalgebra of its holonomy Lie algebra is a direct sum of the derived subalgebras of free Lie algebras, indexed by the rank-2 <a href="___Flat.html">flats</a> of the arrangement.<table class="examples"><tr><td><pre>i1 : X3 = arrangement "X3"
o1 = {x , x , x , x + x , x + x , x + x }
1 2 3 1 2 1 3 2 3
o1 : Hyperplane Arrangement </pre>
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<tr><td><pre>i2 : isDecomposable X3
o2 = true</pre>
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<tr><td><pre>i3 : isDecomposable(X3,ZZ/5)
o3 = true</pre>
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<tr><td><pre>i4 : isDecomposable typeA(3)
o4 = false</pre>
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<div class="waystouse"><h2>Ways to use <tt>isDecomposable</tt> :</h2>
<ul><li>isDecomposable(Arrangement)</li>
<li>isDecomposable(Arrangement,Ring)</li>
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