<?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>HH ChainComplex -- homology 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="___H__H_sp__Chain__Complex__Map.html">next</a> | <a href="_hh.html">previous</a> | <a href="___H__H_sp__Chain__Complex__Map.html">forward</a> | <a href="_hh.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>HH ChainComplex -- homology of a chain complex</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>HH C</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_homology.html" title="general homology functor">homology</a></span></li> <li><div class="single">Inputs:<ul><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="___Graded__Module.html">graded module</a></span>, the homology of <tt>C</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[x]/x^5;</pre> </td></tr> <tr><td><pre>i2 : C = res coker vars R 1 1 1 o2 = R <-- R <-- R 0 1 2 o2 : ChainComplex</pre> </td></tr> <tr><td><pre>i3 : M = HH C o3 = 0 : cokernel | x | 1 : subquotient ({1} | x4 |, {1} | x4 |) 2 : image {5} | x | o3 : GradedModule</pre> </td></tr> <tr><td><pre>i4 : prune M o4 = 0 : cokernel | x | 1 : 0 2 : cokernel {6} | x4 | o4 : GradedModule</pre> </td></tr> </table> </div> </div> </div> </body> </html>