<?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>associatedGradedRing -- the associated graded ring of an ideal</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_distinguished.html">next</a> | <a href="_analytic__Spread.html">previous</a> | <a href="_distinguished.html">forward</a> | <a href="_analytic__Spread.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>associatedGradedRing -- the associated graded ring of an ideal</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>associatedGradedRing I</tt><br/><tt>associatedGradedRing(I,f)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li> <li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, optional argument, if given it should be a non-zero divisor in the ideal <tt>I</tt></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the associated graded ring <i>R[It] ⊗R/I</i></span></li> </ul> </div> </li> <li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_symmetric__Kernel_lp..._cm_sp__Variable_sp_eq_gt_sp..._rp.html">Variable => ...</a>, -- Choose name for variables in the created ring</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>associatedGradedRing is a synonym for <a href="_normal__Cone.html" title="the normal cone of a subscheme">normalCone</a>.</div> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_rees__Algebra.html" title="compute the defining ideal of the Rees Algebra">reesAlgebra</a> -- compute the defining ideal of the Rees Algebra</span></li> <li><span><a href="_normal__Cone.html" title="the normal cone of a subscheme">normalCone</a> -- the normal cone of a subscheme</span></li> <li><span><tt>tangentCone</tt> (missing documentation<!-- tag: tangentCone -->)</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>associatedGradedRing</tt> :</h2> <ul><li>associatedGradedRing(Ideal)</li> <li>associatedGradedRing(Ideal,RingElement)</li> </ul> </div> </div> </body> </html>