<?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>localMingens -- finds a minimal set of generators</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_local__Modulo.html">next</a> | <a href="_local__Complement.html">previous</a> | <a href="_local__Modulo.html">forward</a> | <a href="_local__Complement.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>localMingens -- finds a minimal set of generators</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>localMingens m</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>m</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, the matrix of minimal generators</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>We get a minimal set for the homogeneous case, but not necessarily otherwise.<table class="examples"><tr><td><pre>i1 : R=QQ[a,b]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : setMaxIdeal ideal gens R
o2 = ideal (a, b)
o2 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i3 : mingens image matrix{{a-1,a,b},{a-1,a,b}}
o3 = | 1 b a-1 |
| 1 b a-1 |
2 3
o3 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i4 : localMingens matrix {{a-1,a,b},{a-1,a,b}}
o4 = | a-1 |
| a-1 |
2 1
o4 : Matrix R <--- R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_set__Max__Ideal.html" title="set the maximal ideal for local ring methods">setMaxIdeal</a> -- set the maximal ideal for local ring methods</span></li>
<li><span><a href="_local__Complement.html" title="find the splitting of the target of a map">localComplement</a> -- find the splitting of the target of a map</span></li>
<li><span><a href="_localsyz.html" title="find syzygies">localsyz</a> -- find syzygies</span></li>
<li><span><a href="_local__Modulo.html" title="find the pre-image (pullback) of image of a map over a local ring">localModulo</a> -- find the pre-image (pullback) of image of a map over a local ring</span></li>
<li><span><a href="_local__Prune.html" title="find a minimal presentation">localPrune</a> -- find a minimal presentation</span></li>
<li><span><a href="_local__Resolution.html" title="find a resolution over a local ring">localResolution</a> -- find a resolution over a local ring</span></li>
<li><span><tt>residueMap</tt> (missing documentation<!-- tag: residueMap -->)</span></li>
<li><span><tt>maxIdeal</tt> (missing documentation<!-- tag: maxIdeal -->)</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>localMingens</tt> :</h2>
<ul><li>localMingens(Matrix)</li>
</ul>
</div>
</div>
</body>
</html>
