<?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>Ring ^ ZZ -- make a free module</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Ring_sp_us_sp__List.html">next</a> | <a href="___Ring_sp^_sp__List.html">previous</a> | <a href="___Ring_sp_us_sp__List.html">forward</a> | <a href="___Ring_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>Ring ^ ZZ -- make a free module</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>R^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>R</tt>, <span>a <a href="___Ring.html">ring</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>, a new free <tt>R</tt>-module of rank <tt>n</tt>.</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The new free module has basis elements of degree zero. To specify the degrees explicitly, see <a href="___Ring_sp^_sp__List.html" title="make a free module">Ring ^ List</a>.<table class="examples"><tr><td><pre>i1 : R = ZZ[x,y,z]/(x^2-y*x) o1 = R o1 : QuotientRing</pre> </td></tr> <tr><td><pre>i2 : F = R^4 4 o2 = R o2 : R-module, free</pre> </td></tr> <tr><td><pre>i3 : degrees F o3 = {{0}, {0}, {0}, {0}} o3 : List</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Module)</a> -- degrees of generators</span></li> <li><span><a href="___Ring_sp^_sp__List.html" title="make a free module">Ring ^ List</a> -- make a free module</span></li> <li><span><a href="_graded_spand_spmultigraded_sppolynomial_springs.html" title="">graded and multigraded polynomial rings</a></span></li> </ul> </div> </div> </body> </html>