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<head><title>link -- link of a face in a simplicial complex</title>
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<div><h1>link -- link of a face in a simplicial complex</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>link(D,f)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>D</tt>, <span>a <a href="___Simplicial__Complex.html">simplicial complex</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a monomial representing a face of the simplicial complex <tt>D</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Simplicial__Complex.html">simplicial complex</a></span>, the link of <tt>f</tt> in <tt>D</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>The link of a face <i>f</i> in <i>D</i> is the simplicial complex whose faces are the subsets <i>g</i> whose intersection with <i>f</i> is empty, where <i>f ∪g</i> is a face of <i>D</i>.<table class="examples"><tr><td><pre>i1 : R = QQ[x0,x1,x2,x3,x4,x5,x6];</pre>
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<tr><td><pre>i2 : D = simplicialComplex {x0*x1*x3, x1*x3*x4, x1*x2*x4, x2*x4*x5,
x2*x3*x5, x3*x5*x6, x3*x4*x6, x0*x4*x6,
x0*x4*x5, x0*x1*x5, x1*x5*x6, x1*x2*x6,
x0*x2*x6, x0*x2*x3}
o2 = | x3x5x6 x1x5x6 x3x4x6 x0x4x6 x1x2x6 x0x2x6 x2x4x5 x0x4x5 x2x3x5 x0x1x5 x1x3x4 x1x2x4 x0x2x3 x0x1x3 |
o2 : SimplicialComplex</pre>
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<tr><td><pre>i3 : link(D,x0)
o3 = | x4x6 x2x6 x4x5 x1x5 x2x3 x1x3 |
o3 : SimplicialComplex</pre>
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<tr><td><pre>i4 : link(D,x0*x2)
o4 = | x6 x3 |
o4 : SimplicialComplex</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="index.html" title="simplicial complexes">SimplicialComplexes</a> -- simplicial complexes</span></li>
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<div class="waystouse"><h2>Ways to use <tt>link</tt> :</h2>
<ul><li>link(SimplicialComplex,RingElement)</li>
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