<?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>sum(ChainComplex) -- direct sum of the components of a chain complex</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_sum_lp__Chain__Complex__Map_rp.html">next</a> | <a href="_sum.html">previous</a> | <a href="_sum_lp__Chain__Complex__Map_rp.html">forward</a> | <a href="_sum.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>sum(ChainComplex) -- direct sum of the components of a chain complex</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><span>Function: <a href="_sum.html" title="compute the sum">sum</a></span></li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><tt>sum C</tt> -- yields the sum of the modules in a chain complex.<p/>
The degrees of the components are preserved.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d];</pre>
</td></tr>
<tr><td><pre>i2 : C = res coker vars R
1 4 6 4 1
o2 = R <-- R <-- R <-- R <-- R <-- 0
0 1 2 3 4 5
o2 : ChainComplex</pre>
</td></tr>
<tr><td><pre>i3 : sum C
16
o3 = R
o3 : R-module, free, degrees {0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4}</pre>
</td></tr>
<tr><td><pre>i4 : degrees oo
o4 = {{0}, {1}, {1}, {1}, {1}, {2}, {2}, {2}, {2}, {2}, {2}, {3}, {3}, {3},
------------------------------------------------------------------------
{3}, {4}}
o4 : List</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_sum.html" title="compute the sum">sum</a> -- compute the sum</span></li>
<li><span><a href="_sum_lp__Chain__Complex__Map_rp.html" title="direct sum of the components of a chain map">sum(ChainComplexMap)</a> -- direct sum of the components of a chain map</span></li>
</ul>
</div>
</div>
</body>
</html>
