<?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>generators(Ring) -- the list of generators of a ring</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Generic.html">next</a> | <a href="_generators_lp__Module_rp.html">previous</a> | <a href="___Generic.html">forward</a> | <a href="_generators_lp__Module_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>generators(Ring) -- the list of generators of a ring</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>generators R</tt><br/><tt>gens R</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_generators.html" title="provide matrix or list of generators">generators</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> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of generators</span></li> </ul> </div> </li> <li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>CoefficientRing => </tt><span><span>a <a href="___Ring.html">ring</a></span>, <span>default value null</span>, the coefficient ring over which to provide the generators of <tt>R</tt>, if different from the most recent one</span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : A = QQ[x,y];</pre> </td></tr> <tr><td><pre>i2 : gens A o2 = {x, y} o2 : List</pre> </td></tr> <tr><td><pre>i3 : kk = toField(QQ[t]/(t^3-t-1));</pre> </td></tr> <tr><td><pre>i4 : B = kk[x,y,z];</pre> </td></tr> <tr><td><pre>i5 : generators B o5 = {x, y, z} o5 : List</pre> </td></tr> <tr><td><pre>i6 : generators(B, CoefficientRing => QQ) o6 = {x, y, z, t} o6 : List</pre> </td></tr> </table> </div> </div> </div> </body> </html>