<?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>ChainComplexMap Array -- degree shift</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Change__Matrix.html">next</a> | <a href="___Chain__Complex__Map_sp_us_sp__Z__Z_sp_eq_sp__Thing.html">previous</a> | <a href="___Change__Matrix.html">forward</a> | <a href="___Chain__Complex__Map_sp_us_sp__Z__Z_sp_eq_sp__Thing.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>ChainComplexMap Array -- degree shift</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>g = f[i]</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="___S__P__A__C__E.html" title="blank operator; often used for function application, making polynomial rings">SPACE</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, </span></li> <li><span><tt>i</tt>, <span>an <a href="___Array.html">array</a></span>, an array <tt>[i]</tt> containing an integer <tt>i</tt></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>g</tt>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, a new chain complex map <tt>g</tt> in which <tt>g_j</tt> is <tt>f_(i+j)</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..z];</pre> </td></tr> <tr><td><pre>i2 : C = res coker vars R;</pre> </td></tr> <tr><td><pre>i3 : f = id_C 1 1 o3 = 0 : R <--------- R : 0 | 1 | 3 3 1 : R <----------------- R : 1 {1} | 1 0 0 | {1} | 0 1 0 | {1} | 0 0 1 | 3 3 2 : R <----------------- R : 2 {2} | 1 0 0 | {2} | 0 1 0 | {2} | 0 0 1 | 1 1 3 : R <------------- R : 3 {3} | 1 | 4 : 0 <----- 0 : 4 0 o3 : ChainComplexMap</pre> </td></tr> <tr><td><pre>i4 : f[3] 1 1 o4 = -3 : R <--------- R : -3 | 1 | 3 3 -2 : R <----------------- R : -2 {1} | 1 0 0 | {1} | 0 1 0 | {1} | 0 0 1 | 3 3 -1 : R <----------------- R : -1 {2} | 1 0 0 | {2} | 0 1 0 | {2} | 0 0 1 | 1 1 0 : R <------------- R : 0 {3} | 1 | 1 : 0 <----- 0 : 1 0 o4 : ChainComplexMap</pre> </td></tr> </table> </div> </div> </div> </body> </html>