<?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>cover(Module) -- get the covering free module</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_cover__Map_lp__Module_rp.html">next</a> | <a href="_cover_lp__Matrix_rp.html">previous</a> | <a href="_cover__Map_lp__Module_rp.html">forward</a> | <a href="_cover_lp__Matrix_rp.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>cover(Module) -- get the covering 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>F = cover M</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_cover.html" title="get the covering free module">cover</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> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Module.html">module</a></span>, the free module whose basis elements correspond to the generators of <tt>M</tt>.</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The free module <tt>F</tt> is the source of the generator matrix of <tt>M</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[a..f];</pre> </td></tr> <tr><td><pre>i2 : g = matrix{{a,b},{c,d},{e,f}} o2 = | a b | | c d | | e f | 3 2 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : M = subquotient(g,matrix{{b},{c},{d}}) o3 = subquotient (| a b |, | b |) | c d | | c | | e f | | d | 3 o3 : R-module, subquotient of R</pre> </td></tr> <tr><td><pre>i4 : cover M 2 o4 = R o4 : R-module, free, degrees {1, 1}</pre> </td></tr> <tr><td><pre>i5 : cover M == source generators M o5 = true</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_ambient_lp__Module_rp.html" title="ambient free module">ambient(Module)</a> -- ambient free module</span></li> <li><span><a href="_super.html" title="get the ambient module">super(Module)</a> -- get the ambient module</span></li> </ul> </div> </div> </body> </html>