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<head><title>graphic -- Make a graphic arrangement</title>
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<div><h1>graphic -- Make a graphic 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>graphic(G) or graphic(G,k) or graphic(G,R)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>G</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a graph, expressed as a list of pairs of vertices</span></li>
<li><span><tt>k</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, an optional coefficient ring, by default <tt>QQ</tt></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 graphic arrangement from graph <tt>G</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>A graph <tt>G</tt> has vertices 1, 2, ..., n, and its edges are a list of lists of length 2. The graphic arrangement <tt>A(G)</tt> of <tt>G</tt> is, by definition, the subarrangement of the type A_(n-1) arrangement with hyperplanes <tt>x_i-x_j</tt> for each edge <tt>{i,j}</tt> of <tt>G</tt><table class="examples"><tr><td><pre>i1 : G = {{1,2},{2,3},{3,4},{4,1}}; -- a four-cycle</pre>
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<tr><td><pre>i2 : AG = graphic G
o2 = {- x + x , - x + x , - x + x , x - x }
1 2 2 3 3 4 1 4
o2 : Hyperplane Arrangement </pre>
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<tr><td><pre>i3 : describe AG
o3 = {- x + x , - x + x , - x + x , x - x }
1 2 2 3 3 4 1 4</pre>
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<tr><td><pre>i4 : rank AG -- the number of vertices minus number of components
o4 = 3</pre>
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<tr><td><pre>i5 : ring AG
o5 = QQ[x , x , x , x ]
1 2 3 4
o5 : PolynomialRing</pre>
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<tr><td><pre>i6 : ring graphic(G,ZZ[x,y,z,w])
o6 = ZZ[x, y, z, w]
o6 : PolynomialRing</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_type__A.html" title="Type A reflection arrangement">typeA</a> -- Type A reflection arrangement</span></li>
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<div class="waystouse"><h2>Ways to use <tt>graphic</tt> :</h2>
<ul><li>graphic(List)</li>
<li>graphic(List,PolynomialRing)</li>
<li>graphic(List,Ring)</li>
</ul>
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