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<head><title>codim(QuotientRing) -- compute the codimension</title>
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<div><h1>codim(QuotientRing) -- compute the codimension</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 R</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>R</tt>, <span>a <a href="___Quotient__Ring.html">quotient ring</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 codimension of <tt>R</tt></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 presentation ideal of <tt>R</tt> over its ambient polynomial ring.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))
o1 = R
o1 : QuotientRing</pre>
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<tr><td><pre>i2 : codim R
o2 = 1</pre>
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However, the following may not be the expected result.<table class="examples"><tr><td><pre>i3 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))
o3 = R
o3 : QuotientRing</pre>
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<tr><td><pre>i4 : codim R
o4 = 1</pre>
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<tr><td><pre>i5 : codim (R/x)
o5 = 2</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dim_lp__Ring_rp.html" title="compute the Krull dimension">dim(QuotientRing)</a> -- compute the Krull dimension</span></li>
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