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<head><title>facets -- the facets of a simplicial complex</title>
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<div><h1>facets -- the facets of 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>facets D</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>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, with one row, whose entries are squarefree monomials representing the facets (maximal faces) of <tt>D</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>In Macaulay2, every <a href="___Simplicial__Complex.html">simplicial complex</a> is equipped with a polynomial ring, and the resulting matrix of facets is defined over this ring.<table class="examples"><tr><td><pre>i1 : loadPackage "SimplicialComplexes";</pre>
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The 3-dimensional sphere has a unique minimal nonface which corresponds to the interior.<table class="examples"><tr><td><pre>i2 : R = ZZ[a..e];</pre>
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<tr><td><pre>i3 : sphere = simplicialComplex monomialIdeal(a*b*c*d*e)
o3 = | bcde acde abde abce abcd |
o3 : SimplicialComplex</pre>
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<tr><td><pre>i4 : facets sphere
o4 = | bcde acde abde abce abcd |
1 5
o4 : Matrix R <--- R</pre>
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The following <a href="_faces.html" title="the i-faces of a simplicial complex ">faces</a> generate a simplicial complex consisting of a triangle (on vertices <tt>a,b,c</tt>), two edges connecting <tt>c</tt> to <tt>d</tt> and <tt>b</tt> to <tt>d</tt>, and an isolated vertex <tt>e</tt>.<table class="examples"><tr><td><pre>i5 : D = simplicialComplex {e, c*d, b*d, a*b*c, a*b, c}
o5 = | e cd bd abc |
o5 : SimplicialComplex</pre>
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<tr><td><pre>i6 : facets D
o6 = | e cd bd abc |
1 4
o6 : Matrix R <--- R</pre>
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There are four facets of <tt>D</tt>.<p/>
Note that no computatation is performed by this routine; all the computation was done while constructing the simplicial complex.<p/>
A simplicial complex is displayed by listing its facets, and so this function is frequently unnecessary.</div>
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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>
<li><span><a href="_simplicial__Complex.html" title="create a simplicial complex">simplicialComplex</a> -- create a simplicial complex</span></li>
<li><span><a href="_faces.html" title="the i-faces of a simplicial complex ">faces</a> -- the i-faces of a simplicial complex </span></li>
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<div class="waystouse"><h2>Ways to use <tt>facets</tt> :</h2>
<ul><li>facets(SimplicialComplex)</li>
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