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<head><title>arrangement(String,PolynomialRing) -- look up a built-in hyperplane arrangement</title>
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<div><h1>arrangement(String,PolynomialRing) -- look up a built-in hyperplane arrangement</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>arrangement(s) or arrangement(s,R) or arrangement(s,k)</tt></div>
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<li><span>Function: <a href="_arrangement.html" title="create a hyperplane arrangement">arrangement</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>s</tt>, <span>a <a href="../../Macaulay2Doc/html/___String.html">string</a></span>, the name of a built-in arrangement</span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, an optional coordinate ring for the arrangement</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, the hyperplane arrangement named <tt>s</tt>.</span></li>
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<div class="single"><h2>Description</h2>
<div>The built-in arrangements are stored in a global <a href="../../Macaulay2Doc/html/___Hash__Table.html" title="the class of all hash tables">HashTable</a> called <tt>arrangementLibrary</tt>. Accordingly, the user can see what arrangements are available by examining the keys:<table class="examples"><tr><td><pre>i1 : keys arrangementLibrary
o1 = {prism, (9_3)_2, notTame, Ziegler1, Hessian, nonFano, Ziegler2, X2,
------------------------------------------------------------------------
MacLane, X3, braid, Pappus}
o1 : List</pre>
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<tr><td><pre>i2 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i3 : A = arrangement("Pappus",R)
o3 = {x, y, z, x - y, y - z, x - y - z, 2x + y + z, 2x + y - z, 2x - 5y + z}
o3 : Hyperplane Arrangement </pre>
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<tr><td><pre>i4 : poincare A
2 3
o4 = 1 + 9T + 27T + 19T
o4 : ZZ[T]</pre>
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<tr><td><pre>i5 : isDecomposable A
o5 = false</pre>
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<tr><td><pre>i6 : A = arrangement("prism", ZZ/101) -- can also specify coefficient ring
o6 = {x , x , x , x , x + x + x , x + x + x }
1 2 3 4 1 2 4 1 3 4
o6 : Hyperplane Arrangement </pre>
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<tr><td><pre>i7 : ring A
ZZ
o7 = ---[x , x , x , x ]
101 1 2 3 4
o7 : PolynomialRing</pre>
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<div class="single"><h2>Caveat</h2>
<div>The arrangements <tt>MacLane</tt> and <tt>Hessian</tt> are defined over <tt>ZZ/31627</tt>, where <tt>6419</tt> is a cube root of unity.</div>
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