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<head><title>codim(ProjectiveVariety) -- codimension of the projective variety</title>
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<div><h1>codim(ProjectiveVariety) -- codimension of the projective variety</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 V</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>V</tt>, <span>a <a href="___Projective__Variety.html">projective variety</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></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 projective variety <tt>V</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x_0..x_3];</pre>
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<tr><td><pre>i2 : M = matrix{{x_0,x_1,x_2},{x_1,x_2,x_3}}
o2 = | x_0 x_1 x_2 |
| x_1 x_2 x_3 |
2 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : V = Proj(R/minors(2,M));</pre>
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<tr><td><pre>i4 : codim V
o4 = 2</pre>
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<div class="single"><h2>Caveat</h2>
<div>The returned value is the usual codimension if the base graded ring is an integral domain or, more generally, equidimensional.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_codim_lp__Quotient__Ring_rp.html" title="compute the codimension">codim(QuotientRing)</a> -- compute the codimension</span></li>
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