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<head><title>coefficientRing(SimplicialComplex) -- get the coefficient ring</title>
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<div><h1>coefficientRing(SimplicialComplex) -- get the coefficient ring</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>coefficientRing D</tt></div>
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<li><span>Function: <a href="../../Macaulay2Doc/html/_coefficient__Ring.html" title="get the coefficient ring">coefficientRing</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><span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the coefficients of the defining <a href="_ring_lp__Simplicial__Complex_rp.html">polynomial ring</a> of <tt>D</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><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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Some computations depend on the choice of coefficient ring, for example, the boundary maps and the chain complex of D.<table class="examples"><tr><td><pre>i10 : chainComplex D
1 4 6 4
o10 = QQ <-- QQ <-- QQ <-- QQ
-1 0 1 2
o10 : ChainComplex</pre>
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<tr><td><pre>i11 : chainComplex E
1 4 6 4
o11 = ZZ <-- ZZ <-- ZZ <-- ZZ
-1 0 1 2
o11 : ChainComplex</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>
<li><span><a href="_ring_lp__Simplicial__Complex_rp.html" title="get the associated ring of an object">ring(SimplicialComplex)</a> -- get the associated ring of an object</span></li>
<li><span><tt>chainComplex(SimplicialComplex)</tt> (missing documentation<!-- tag: (chainComplex,SimplicialComplex) -->)</span></li>
<li><span><a href="_boundary.html" title="boundary operator">boundary</a> -- boundary operator</span></li>
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