<?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>bgg -- the ith differential of the complex R(M)</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_cohomology__Table.html">next</a> | <a href="_beilinson.html">previous</a> | <a href="_cohomology__Table.html">forward</a> | <a href="_beilinson.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>bgg -- the ith differential of the complex R(M)</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>bgg(i,M,E)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the cohomological index</span></li>
<li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, graded <tt>S</tt>-module</span></li>
<li><span><tt>E</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, exterior algebra</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, a matrix representing the ith differential</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>This function takes as input an integer <tt>i</tt> and a finitely generated graded <tt>S</tt>-module <tt>M</tt>, and returns the ith map in <tt>R(M)</tt>, which is an adjoint of the multiplication map between <tt>M_i</tt> and <tt>M_{i+1}</tt>.<table class="examples"><tr><td><pre>i1 : S = ZZ/32003[x_0..x_2]; </pre>
</td></tr>
<tr><td><pre>i2 : E = ZZ/32003[e_0..e_2, SkewCommutative=>true];</pre>
</td></tr>
<tr><td><pre>i3 : M = coker matrix {{x_0^2, x_1^2, x_2^2}};</pre>
</td></tr>
<tr><td><pre>i4 : bgg(1,M,E)
o4 = {-2} | e_1 e_0 0 |
{-2} | e_2 0 e_0 |
{-2} | 0 e_2 e_1 |
3 3
o4 : Matrix E <--- E</pre>
</td></tr>
<tr><td><pre>i5 : bgg(2,M,E)
o5 = {-3} | e_2 e_1 e_0 |
1 3
o5 : Matrix E <--- E</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_sym__Ext.html" title="the first differential of the complex R(M)">symExt</a> -- the first differential of the complex R(M)</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>bgg</tt> :</h2>
<ul><li>bgg(ZZ,Module,PolynomialRing)</li>
</ul>
</div>
</div>
</body>
</html>
