<?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>ChainComplex ^ ZZ -- access member, cohomological degree</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Chain__Complex_sp_us_sp__Z__Z.html">next</a> | <a href="___Chain__Complex_sp_pl_pl_sp__Chain__Complex.html">previous</a> | <a href="___Chain__Complex_sp_us_sp__Z__Z.html">forward</a> | <a href="___Chain__Complex_sp_pl_pl_sp__Chain__Complex.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>ChainComplex ^ ZZ -- access member, cohomological degree</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>C^n</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="_^.html" title="a binary operator, usually used for powers">^</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> <li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Module.html">module</a></span>, The <tt>(-n)</tt>-th component <tt>C_(-n)</tt> of <tt>C</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Subscripts refer to homological degree, and superscripts refer to cohomological degree. It is only a matter of notation: <tt>C_(-n)</tt> is always the same as <tt>C^n</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z];</pre> </td></tr> <tr><td><pre>i2 : C = res coker vars R 1 3 3 1 o2 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o2 : ChainComplex</pre> </td></tr> <tr><td><pre>i3 : C = dual C 1 3 3 1 o3 = R <-- R <-- R <-- R -3 -2 -1 0 o3 : ChainComplex</pre> </td></tr> <tr><td><pre>i4 : C^2 3 o4 = R o4 : R-module, free, degrees {-2, -2, -2}</pre> </td></tr> <tr><td><pre>i5 : C^2 == C_(-2) o5 = true</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> <li><span><a href="___Module_sp^_sp__Array.html" title="projection onto summand">ChainComplex ^ Array</a> -- projection onto summand</span></li> </ul> </div> </div> </body> </html>