<?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 ^ List -- projection onto summand</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Module_sp^_sp__Z__Z.html">next</a> | <a href="___Module_sp^_sp__Array.html">previous</a> | <a href="___Module_sp^_sp__Z__Z.html">forward</a> | <a href="___Module_sp^_sp__Array.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 ^ List -- projection onto summand</h1> <div class="single"><h2>Synopsis</h2> <ul><li><span>Operator: <a href="_^.html" title="a binary operator, usually used for powers">^</a></span></li> </ul> </div> <div class="single"><h2>Description</h2> <div><tt>M^{i,j,k,...}</tt> -- provides the projection map from a free module <tt>M</tt> to the free module corresponding to the basis vectors whose index numbers are listed.<p/> <table class="examples"><tr><td><pre>i1 : (ZZ^5)^{2,3} o1 = | 0 0 1 0 0 | | 0 0 0 1 0 | 2 5 o1 : Matrix ZZ <--- ZZ</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</a> -- a binary operator, used for subscripting and access to elements</span></li> <li><span><a href="___Module.html" title="the class of all modules">Module</a> -- the class of all modules</span></li> <li><span><a href="___List.html" title="the class of all lists -- {...}">List</a> -- the class of all lists -- {...}</span></li> </ul> </div> </div> </body> </html>