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<head><title>pdim(Module) -- calculate the projective dimension of a module</title>
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<div><h1>pdim(Module) -- calculate the projective dimension of a module</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>pdim M</tt></div>
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<li><span>Function: <a href="_pdim.html" title="calculate the projective dimension">pdim</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the projective dimension</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : I = ideal(x^2, x*y, y*z);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : M = R^1/I
o3 = cokernel | x2 xy yz |
1
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : res M
1 3 2
o4 = R <-- R <-- R <-- 0
0 1 2 3
o4 : ChainComplex</pre>
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<tr><td><pre>i5 : pdim M
o5 = 2</pre>
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Notice this is one more than the projective dimension of I as an R-module.<table class="examples"><tr><td><pre>i6 : res(module I)
3 2
o6 = R <-- R <-- 0
0 1 2
o6 : ChainComplex</pre>
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<tr><td><pre>i7 : pdim(module I)
o7 = 1</pre>
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