<?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>Module ^ ZZ -- direct sum</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Module_sp^_st_st_sp__Z__Z.html">next</a> | <a href="___Module_sp^_sp__List.html">previous</a> | <a href="___Module_sp^_st_st_sp__Z__Z.html">forward</a> | <a href="___Module_sp^_sp__List.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>Module ^ ZZ -- direct sum</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>M^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>M</tt>, <span>a <a href="___Module.html">module</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 direct sum of <tt>n</tt> copies of <tt>M</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : M = coker matrix{{1,2,3}} o1 = cokernel | 1 2 3 | 1 o1 : ZZ-module, quotient of ZZ</pre> </td></tr> <tr><td><pre>i2 : M^3 o2 = cokernel | 1 2 3 0 0 0 0 0 0 | | 0 0 0 1 2 3 0 0 0 | | 0 0 0 0 0 0 1 2 3 | 3 o2 : ZZ-module, quotient of ZZ</pre> </td></tr> <tr><td><pre>i3 : directSum(3:M) o3 = cokernel | 1 2 3 0 0 0 0 0 0 | | 0 0 0 1 2 3 0 0 0 | | 0 0 0 0 0 0 1 2 3 | 3 o3 : ZZ-module, quotient of ZZ</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></li> <li><span><a href="__pl_pl.html" title="a binary operator, usually used for direct sum">++</a> -- a binary operator, usually used for direct sum</span></li> </ul> </div> </div> </body> </html>