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<head><title>isCM -- whether a ring or module is Cohen-Macaulay</title>
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<div><h1>isCM -- whether a ring or module 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>isCM(A)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, a <a href="../../Macaulay2Doc/html/___Ring.html" title="the class of all rings">Ring</a> or <a href="../../Macaulay2Doc/html/___Module.html" title="the class of all modules">Module</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><a href="../../Macaulay2Doc/html/___Boolean.html" title="the class of Boolean values">Boolean</a></span></li>
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<div class="single"><h2>Description</h2>
<div>This command merely checks if the depth of <tt>A</tt> equals the Krull dimension of <tt>A</tt>.<table class="examples"><tr><td><pre>i1 : A = ZZ/2[x,y,z];</pre>
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<tr><td><pre>i2 : isCM(A)
o2 = true</pre>
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<tr><td><pre>i3 : A = ZZ/2[x,y]/(x^2,x*y);</pre>
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<tr><td><pre>i4 : isCM(A)
o4 = false</pre>
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<tr><td><pre>i5 : A = ZZ/101[a_1,a_2,b_1,b_2,c_1]/ideal(a_1*b_1,a_2*b_2,b_1*c_1);</pre>
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<tr><td><pre>i6 : isCM(A)
o6 = false</pre>
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<p>This symbol is provided by the package <a href="index.html" title="computations involving regular sequences">Depth</a>.</p>
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<div class="single"><h2>Caveat</h2>
<div>Typically when one thinks of a Cohen-Macaulay ring or module, one is in the local case. Since the local case is not yet implemented into Macaulay 2, we compute over the ideal generated by by <a href="../../Macaulay2Doc/html/_generators_lp__Ring_rp.html" title="the list of generators of a ring">generators(Ring)</a>.</div>
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<div class="waystouse"><h2>Ways to use <tt>isCM</tt> :</h2>
<ul><li>isCM(Module)</li>
<li>isCM(Ring)</li>
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