<?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>intclToricRing -- integral closure of a toric ring</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_intmat2mons.html">next</a> | <a href="_intcl__Mon__Ideal.html">previous</a> | <a href="_intmat2mons.html">forward</a> | <a href="_intcl__Mon__Ideal.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>intclToricRing -- integral closure of a toric ring</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>intclToricRing(I)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the leading monomials of the elements of the ideal generate the toric ring</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the generators of the ideal are the generators of the integral closure</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>This function computes the integral closure of the toric ring generated by the leading monomials of the elements of <tt>I</tt>. The function returns an <a href="../../Macaulay2Doc/html/___Ideal.html" title="the class of all ideals">Ideal</a> listing the generators of the integral closure.<br/><br/><em>A mathematical remark:</em> the toric ring (and the other rings computed) depends on the list of monomials given, and not only on the ideal they generate!<table class="examples"><tr><td><pre>i1 : R=ZZ/37[x,y,t];</pre>
</td></tr>
<tr><td><pre>i2 : I=ideal(x^3, x^2*y, y^3, x*y^2);
o2 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i3 : intclToricRing(I)
o3 = ideal (y, x)
o3 : Ideal of R</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>intclToricRing</tt> :</h2>
<ul><li>intclToricRing(Ideal)</li>
</ul>
</div>
</div>
</body>
</html>
