<?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>radical of an ideal</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_minimal_spprimes_spof_span_spideal.html">next</a> | <a href="_ideal_spquotients_spand_spsaturation.html">previous</a> | <a href="_minimal_spprimes_spof_span_spideal.html">forward</a> | <a href="_ideal_spquotients_spand_spsaturation.html">backward</a> | <a href="_ideals.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="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a> > <a href="_radical_spof_span_spideal.html" title="">radical of an ideal</a></div>
<hr/>
<div><h1>radical of an ideal</h1>
<div>There are two main ways to find the radical of an ideal. The first is to use the function <a href="_radical.html" title="the radical of an ideal">radical</a> and the second is to find the intersection of the minimal prime ideals. On some large examples the second method is faster.<h2>using radical</h2>
<table class="examples"><tr><td><pre>i1 : S = ZZ/101[x,y,z]
o1 = S
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : I = ideal(x^3-y^2,y^2*z^2)
3 2 2 2
o2 = ideal (x - y , y z )
o2 : Ideal of S</pre>
</td></tr>
<tr><td><pre>i3 : radical I
3 2
o3 = ideal (y*z, x*z, - x + y )
o3 : Ideal of S</pre>
</td></tr>
</table>
<h2>using minimal prime ideals</h2>
An alternate way to find the radical of an ideal <tt>I</tt> is to take the intersection of its minimal prime ideals. To find the <a href="_minimal_spprimes_spof_span_spideal.html" title="">minimal primes of an ideal</a><tt>I</tt> use the function <a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a>. Then use <a href="_intersect.html" title="compute an intersection">intersect</a>.<table class="examples"><tr><td><pre>i4 : intersect minimalPrimes I
3 2
o4 = ideal (y*z, x*z, - x + y )
o4 : Ideal of S</pre>
</td></tr>
</table>
</div>
</div>
</body>
</html>
