<?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>Hom(Module,ChainComplex)</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="___Hom_lp__Module_cm__Module_rp.html">next</a> | <a href="___Hom_lp__Matrix_cm__Module_rp.html">previous</a> | <a href="___Hom_lp__Module_cm__Module_rp.html">forward</a> | <a href="___Hom_lp__Matrix_cm__Module_rp.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>Hom(Module,ChainComplex)</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>Hom(M,C)</tt><br/><tt>Hom(C,M)</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="___Hom.html" title="module of homomorphisms">Hom</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Chain__Complex.html">chain complex</a></span>, The chain complex whose <tt>i</tt>-th spot is <tt>Hom(M,C_i)</tt>, in the first case, or <tt>Hom(C_(-i),M)</tt> in the second case</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[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 : M = R^1/(a,b)
o3 = cokernel | a b |
1
o3 : R-module, quotient of R</pre>
</td></tr>
<tr><td><pre>i4 : C' = Hom(C,M)
o4 = cokernel {-4} | a b | <-- cokernel {-3} | a b 0 0 0 0 0 0 | <-- cokernel {-2} | a b 0 0 0 0 0 0 0 0 0 0 | <-- cokernel {-1} | a b 0 0 0 0 0 0 | <-- cokernel | a b |
{-3} | 0 0 a b 0 0 0 0 | {-2} | 0 0 a b 0 0 0 0 0 0 0 0 | {-1} | 0 0 a b 0 0 0 0 |
-4 {-3} | 0 0 0 0 a b 0 0 | {-2} | 0 0 0 0 a b 0 0 0 0 0 0 | {-1} | 0 0 0 0 a b 0 0 | 0
{-3} | 0 0 0 0 0 0 a b | {-2} | 0 0 0 0 0 0 a b 0 0 0 0 | {-1} | 0 0 0 0 0 0 a b |
{-2} | 0 0 0 0 0 0 0 0 a b 0 0 |
-3 {-2} | 0 0 0 0 0 0 0 0 0 0 a b | -1
-2
o4 : ChainComplex</pre>
</td></tr>
<tr><td><pre>i5 : C'.dd_-1
o5 = {-2} | 0 0 0 0 |
{-2} | c 0 0 0 |
{-2} | 0 c 0 0 |
{-2} | d 0 0 0 |
{-2} | 0 d 0 0 |
{-2} | 0 0 d -c |
o5 : Matrix</pre>
</td></tr>
<tr><td><pre>i6 : C'.dd^2 == 0
o6 = true</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div>Hom of two chain complexes is not yet implemented</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_resolution.html" title="projective resolution">resolution</a> -- projective resolution</span></li>
</ul>
</div>
</div>
</body>
</html>
