<?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>isSubquotient(Module,Module) -- check whether a module is a subquotient of another</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Subset.html">next</a> | <a href="_is__Submodule.html">previous</a> | <a href="_is__Subset.html">forward</a> | <a href="_is__Submodule.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>isSubquotient(Module,Module) -- check whether a module is a subquotient of another</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>isSubquotient(M,N)</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_is__Subquotient_lp__Module_cm__Module_rp.html" title="check whether a module is a subquotient of another">isSubquotient</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>a <a href="___Module.html">module</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>, returns true if M is a subquotient module of N</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre> </td></tr> <tr><td><pre>i2 : N = coker matrix{{a,b},{c,d}} o2 = cokernel | a b | | c d | 2 o2 : R-module, quotient of R</pre> </td></tr> <tr><td><pre>i3 : N1 = N/(a^4*N) o3 = cokernel | a4 0 a b | | 0 a4 c d | 2 o3 : R-module, quotient of R</pre> </td></tr> <tr><td><pre>i4 : M = a*N/(R*a*N_0+a*b*N) o4 = subquotient (| a 0 |, | 0 ab 0 a b |) | 0 a | | -c 0 ab c d | 2 o4 : R-module, subquotient of R</pre> </td></tr> <tr><td><pre>i5 : isSubquotient(M,N) o5 = true</pre> </td></tr> <tr><td><pre>i6 : isSubquotient(M,N1) o6 = false</pre> </td></tr> </table> </div> </div> </div> </body> </html>