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<head><title>isCM -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay</title>
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<div><h1>isCM -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay</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>B=isCM I</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, a homogeneous ideal in a polynomial ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>true</tt> if <tt>(ring I)/I</tt> is Cohen-Macaulay and <tt>false</tt> otherwise</span></li>
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<div class="single"><h2>Description</h2>
<div><div><tt>isCM</tt> takes a homogeneous ideal <tt>I</tt> in a polynomial ring <tt>R</tt> and, by computing the projective dimension and codimension of <tt>I</tt>, determines whether <tt>R/I</tt> is Cohen-Macaulay. Of course, <tt>isCM</tt> works only if <i>Macaulay2</i> can compute the projective dimension of <tt>I</tt>.</div>
<table class="examples"><tr><td><pre>i1 : R=ZZ/32003[a..c];</pre>
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<tr><td><pre>i2 : isCM(ideal(a^2,b^4)) --complete intersection
o2 = true</pre>
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<tr><td><pre>i3 : isCM(ideal(a^3,b^5,c^4,a*c^3)) --Artinian
o3 = true</pre>
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<tr><td><pre>i4 : isCM(ideal(a^3,a*b^2))
o4 = false</pre>
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<div class="waystouse"><h2>Ways to use <tt>isCM</tt> :</h2>
<ul><li>isCM(Ideal)</li>
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