<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>codim(Ideal) -- compute the codimension</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_codim_lp__Ideal_cm_sp__Generic_sp_eq_gt_sp..._rp.html">next</a> | <a href="_codim_lp__Coherent__Sheaf_rp.html">previous</a> | <a href="_codim_lp__Ideal_cm_sp__Generic_sp_eq_gt_sp..._rp.html">forward</a> | <a href="_codim_lp__Coherent__Sheaf_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>codim(Ideal) -- 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 I</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_codim.html" title="compute the codimension">codim</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, <tt>dim(R) - dim(R/I)</tt>, where <tt>R</tt> is the ring containing <tt>I</tt>.</span></li>
</ul>
</div>
</li>
<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>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p>When R is equidimensional, this quantity is the codimension of the ideal <tt>I</tt>.</p>
<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..e];</pre>
</td></tr>
<tr><td><pre>i2 : I = monomialCurveIdeal(R,{2,3,5,7})
2 2 2 3 3 2
o2 = ideal (d - c*e, b*d - a*e, b*c - a*d, c d - b e, c - a*b*e, b - a*c )
o2 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i3 : J = ideal presentation singularLocus(R/I);
o3 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i4 : codim J
o4 = 4</pre>
</td></tr>
<tr><td><pre>i5 : radical J
o5 = ideal (d, c, b, a*e)
o5 : Ideal of R</pre>
</td></tr>
</table>
The following may not be the expected result, because the ring is not equidimensional.<table class="examples"><tr><td><pre>i6 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))
o6 = R
o6 : QuotientRing</pre>
</td></tr>
<tr><td><pre>i7 : codim ideal(x,y)
o7 = 1</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dim_lp__Ideal_rp.html" title="compute the Krull dimension">dim(Ideal)</a> -- compute the Krull dimension</span></li>
<li><span><a href="_dim_lp__Ideal_rp.html" title="compute the Krull dimension">dim(MonomialIdeal)</a> -- compute the Krull dimension</span></li>
<li><span><a href="_codim_lp__Monomial__Ideal_rp.html" title="compute the codimension">codim(MonomialIdeal)</a> -- compute the codimension</span></li>
</ul>
</div>
</div>
</body>
</html>
