<?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>dd -- differential in 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="_debug.html">next</a> | <a href="___Database_sp_sh_qu_sp__String.html">previous</a> | <a href="_debug.html">forward</a> | <a href="___Database_sp_sh_qu_sp__String.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>dd -- differential in a chain complex</h1> <div class="single"><h2>Description</h2> <div><tt>dd</tt> -- a symbol used as a key in a chain complex, under which are stored the differentials.<p/> The differentials are stored as the members in a chain complex map of degree <tt>-1</tt>. The map <tt>C.dd_i</tt> is the one whose source is the module <tt>C_i</tt>, and it is arranged to be zero if no map has been stored in that spot.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b];</pre> </td></tr> <tr><td><pre>i2 : C = resolution cokernel vars R 1 2 1 o2 = R <-- R <-- R <-- 0 0 1 2 3 o2 : ChainComplex</pre> </td></tr> <tr><td><pre>i3 : C.dd 1 2 o3 = 0 : R <----------- R : 1 | a b | 2 1 1 : R <-------------- R : 2 {1} | -b | {1} | a | 1 2 : R <----- 0 : 3 0 o3 : ChainComplexMap</pre> </td></tr> <tr><td><pre>i4 : C.dd_2 o4 = {1} | -b | {1} | a | 2 1 o4 : Matrix R <--- R</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Chain__Complex.html" title="the class of all chain complexes">ChainComplex</a> -- the class of all chain complexes</span></li> </ul> </div> <div class="waystouse"><h2>For the programmer</h2> <p>The object <a href="_dd.html" title="differential in a chain complex">dd</a> is <span>a <a href="___Symbol.html">symbol</a></span>.</p> </div> </div> </body> </html>