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<head><title>codim(Module) -- codimension of the support of a module</title>
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<div><h1>codim(Module) -- codimension of the support 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>codim M</tt></div>
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<li><span>Function: <a href="_codim.html" title="compute the codimension">codim</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span>, a module over a ring <tt>R</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_codim_lp__Ideal_cm_sp__Generic_sp_eq_gt_sp..._rp.html">Generic => ...</a>, </span></li>
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<div class="single"><h2>Description</h2>
<div>Computes the codimension of the support of the module as given by <tt>dim(R) - dim(M)</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d];</pre>
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<tr><td><pre>i2 : M = coker matrix{{a,b},{c,d}}
o2 = cokernel | a b |
| c d |
2
o2 : R-module, quotient of R</pre>
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<tr><td><pre>i3 : codim M
o3 = 1</pre>
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<p>The returned value is the usual codimension if <tt>R</tt> is an integral domain or, more generally, equidimensional.</p>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dim_lp__Module_rp.html" title="compute the Krull dimension">dim(Module)</a> -- compute the Krull dimension</span></li>
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