<?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>isSubmodule -- whether a module is evidently a submodule of 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="_is__Subquotient_lp__Module_cm__Module_rp.html">next</a> | <a href="_is__Square__Free.html">previous</a> | <a href="_is__Subquotient_lp__Module_cm__Module_rp.html">forward</a> | <a href="_is__Square__Free.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>isSubmodule -- whether a module is evidently a submodule of 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>isSubmodule M</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Thing.html">thing</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Boolean.html">Boolean value</a></span>, <a href="_true.html" title="">true</a> if <tt>M</tt> is evidently a submodule of a free module and <a href="_false.html" title="">false</a> otherwise</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>No computation is done -- <tt>M</tt> may be a isomorphic to a submodule of a free module although this function will not detect it.<table class="examples"><tr><td><pre>i1 : R = ZZ/5[a,b,c];</pre> </td></tr> <tr><td><pre>i2 : M = R^3;</pre> </td></tr> <tr><td><pre>i3 : isSubmodule M o3 = true</pre> </td></tr> <tr><td><pre>i4 : N = ideal(a,b) * M o4 = image | a 0 0 b 0 0 | | 0 a 0 0 b 0 | | 0 0 a 0 0 b | 3 o4 : R-module, submodule of R</pre> </td></tr> <tr><td><pre>i5 : isSubmodule N o5 = true</pre> </td></tr> <tr><td><pre>i6 : N' = ideal(a,b) * (R^1 / ideal(a^2,b^2,c^2)) o6 = subquotient (| a b |, | a2 b2 c2 |) 1 o6 : R-module, subquotient of R</pre> </td></tr> <tr><td><pre>i7 : isSubmodule N' o7 = false</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>isSubmodule</tt> :</h2> <ul><li>isSubmodule(Module)</li> <li>isSubmodule(Thing)</li> </ul> </div> </div> </body> </html>