<?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>trim -- minimize generators and relations</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_trim_lp__Ideal_rp.html">next</a> | <a href="___Tree__Node.html">previous</a> | <a href="_trim_lp__Ideal_rp.html">forward</a> | <a href="___Tree__Node.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>trim -- minimize generators and relations</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="___Complement.html">Strategy => ...</a>, </span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>There are two ways to present a module <tt>M</tt> over a ring. One way is to take a free module F (whose generators are called the generators) and form the quotient M = F/H by a submodule H of F (whose generators are called the relations). Another way is take a free module F, a submodule G of F (whose generators are called the relations), a submodule H of F (whose generators are called the relations), and form the subquotient module M = (G+H)/H, obtained also as the image of G in F/H. The purpose of <tt>trim</tt> is to minimize presentations of the latter type. This applies also to rings and ideals.</div> </div> <div class="waystouse"><h2>Ways to use <tt>trim</tt> :</h2> <ul><li><span><a href="_trim_lp__Ideal_rp.html" title="">trim(Ideal)</a></span></li> <li><span><a href="_trim_lp__Module_rp.html" title="">trim(Module)</a></span></li> <li><span><a href="_trim_lp__Quotient__Ring_rp.html" title="">trim(QuotientRing)</a></span></li> <li><span><a href="_trim_lp__Ring_rp.html" title="">trim(Ring)</a></span></li> </ul> </div> </div> </body> </html>