<?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>invSyzygies -- compute involutive basis of syzygies</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_is__Pommaret__Basis.html">next</a> | <a href="_inv__Reduce.html">previous</a> | <a href="_is__Pommaret__Basis.html">forward</a> | <a href="_inv__Reduce.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>invSyzygies -- compute involutive basis of syzygies</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>invSyzygies J</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span>J, <span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span>, <span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span>, an involutive basis for the syzygies of J</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre>
</td></tr>
<tr><td><pre>i2 : I = ideal(x,y,z);
o2 : Ideal of R</pre>
</td></tr>
<tr><td><pre>i3 : J = janetBasis I
+-+---------+
o3 = |z|{z} |
+-+---------+
|y|{z, y} |
+-+---------+
|x|{z, y, x}|
+-+---------+
o3 : InvolutiveBasis</pre>
</td></tr>
<tr><td><pre>i4 : invSyzygies J
+----------+---------+
o4 = |{1} | x ||{z, y, x}|
|{1} | 0 || |
|{1} | -z || |
+----------+---------+
|{1} | y ||{z, y} |
|{1} | -z || |
|{1} | 0 || |
+----------+---------+
|{1} | 0 ||{z, y, x}|
|{1} | x || |
|{1} | -y || |
+----------+---------+
o4 : InvolutiveBasis</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div>cannot be iterated because <a href="../../Macaulay2Doc/html/_schreyer__Order.html" title="create or obtain free modules with Schryer monomial orders">schreyerOrder</a> is not used; call <a href="_janet__Resolution.html" title="construct a free resolution for a given ideal or module using Janet bases">janetResolution</a> instead</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_janet__Basis.html" title="compute Janet basis for an ideal or a submodule of a free module">janetBasis</a> -- compute Janet basis for an ideal or a submodule of a free module</span></li>
<li><span><a href="_janet__Resolution.html" title="construct a free resolution for a given ideal or module using Janet bases">janetResolution</a> -- construct a free resolution for a given ideal or module using Janet bases</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>invSyzygies</tt> :</h2>
<ul><li>invSyzygies(InvolutiveBasis)</li>
</ul>
</div>
</div>
</body>
</html>
