<?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>primaryComponent(Ideal,Ideal) -- find a primary component corresponding to an associated prime</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_primary__Component_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">next</a> | <a href="_localize_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">previous</a> | <a href="_primary__Component_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">forward</a> | <a href="_localize_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">backward</a> | <a href="index.html">up</a> | <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>
<div><a href="index.html" title="">PrimaryDecomposition</a> > <a href="_primary__Component_lp__Ideal_cm__Ideal_rp.html" title="find a primary component corresponding to an associated prime">primaryComponent(Ideal,Ideal)</a></div>
<hr/>
<div><h1>primaryComponent(Ideal,Ideal) -- find a primary component corresponding to an associated prime</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>Q = primaryComponent(I,P)</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_primary__Component_lp__Ideal_cm__Ideal_rp.html" title="find a primary component corresponding to an associated prime">primaryComponent</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, an ideal in a (quotient of a) polynomial ring <tt>R</tt></span></li>
<li><span><tt>P</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, an associated prime of <tt>I</tt></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>Q</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, a <tt>P</tt>-primary ideal of <tt>I</tt>.</span></li>
</ul>
</div>
</li>
<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_primary__Component_lp..._cm_sp__Increment_sp_eq_gt_sp..._rp.html">Increment => ...</a>, </span></li>
<li><span><a href="_primary__Component_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, </span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>Q is topComponents(I + P^m), for sufficiently large m. The criterion that Q is primary is given in Eisenbud-Huneke-Vasconcelos, Invent. Math. 110 (1992) 207-235. However, we use <a href="_localize_lp__Ideal_cm__Ideal_rp.html" title="localize an ideal at a prime ideal">localize(Ideal,Ideal)</a>.<p><b>Author and maintainer: </b>C. Yackel, cyackel@math.indiana.edu. Last modified June, 2000.</p>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_associated__Primes_lp__Ideal_rp.html" title="find the associated primes of an ideal">associatedPrimes(Ideal)</a> -- find the associated primes of an ideal</span></li>
<li><span><a href="_primary__Decomposition.html" title="irredundant primary decomposition of an ideal">primaryDecomposition(Ideal)</a> -- irredundant primary decomposition of an ideal</span></li>
<li><span><a href="../../Macaulay2Doc/html/_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></li>
<li><span><a href="../../Macaulay2Doc/html/_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a> -- minimal associated primes of an ideal</span></li>
<li><span><a href="../../Macaulay2Doc/html/_top__Components.html" title="compute top dimensional component">topComponents</a> -- compute top dimensional component</span></li>
<li><span><a href="../../Macaulay2Doc/html/_remove__Lowest__Dimension.html" title="remove components of lowest dimension">removeLowestDimension</a> -- remove components of lowest dimension</span></li>
</ul>
</div>
</div>
</body>
</html>
