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<head><title>ring(SimplicialComplex) -- get the associated ring of an object</title>
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<div><h1>ring(SimplicialComplex) -- get the associated ring of an object</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>R = ring D</tt></div>
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<li><span>Function: <a href="../../Macaulay2Doc/html/_ring.html" title="get the associated ring of an object">ring</a></span></li>
<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><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the polynomial ring used to define <tt>D</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>The vertices of every simplicial complex are variables in the polynomial ring <tt>R</tt>, and subsets of vertices, such as faces, are represented as squarefree monomials in <tt>R</tt>.<table class="examples"><tr><td><pre>i1 : loadPackage "SimplicialComplexes";</pre>
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<table class="examples"><tr><td><pre>i2 : R = QQ[a..d];</pre>
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<tr><td><pre>i3 : D = simplicialComplex monomialIdeal(a*b*c*d);</pre>
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<tr><td><pre>i4 : ring D
o4 = R
o4 : PolynomialRing</pre>
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<tr><td><pre>i5 : coefficientRing D
o5 = QQ
o5 : Ring</pre>
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<tr><td><pre>i6 : S = ZZ[w..z];</pre>
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<tr><td><pre>i7 : E = simplicialComplex monomialIdeal(w*x*y*z);</pre>
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<tr><td><pre>i8 : ring E
o8 = S
o8 : PolynomialRing</pre>
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<tr><td><pre>i9 : coefficientRing E
o9 = ZZ
o9 : Ring</pre>
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There is a bijection between simplicial complexes and squarefree monomial ideals. This package exploits this correspondence by using commutative algebra routines to perform most of the necessary computations.</div>
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<div class="single"><h2>Caveat</h2>
<div>Some operations depend on the choice of ring, or its coefficient ring</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="_coefficient__Ring_lp__Simplicial__Complex_rp.html" title="get the coefficient ring">coefficientRing(SimplicialComplex)</a> -- get the coefficient ring</span></li>
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