<?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>macaulayLowerOperator -- the a_<d> operator used in Green's proof of Macaulay's Theorem</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_macaulay__Rep.html">next</a> | <a href="_macaulay__Bound.html">previous</a> | <a href="_macaulay__Rep.html">forward</a> | <a href="_macaulay__Bound.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>macaulayLowerOperator -- the a_<d> operator used in Green's proof of Macaulay's Theorem</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>h=macaulayLowerOperator(a,d)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>a</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a positive integer</span></li> <li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a positive integer</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>h</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, a nonnegative integer representing <tt>a<sub>-</sub>-TEMPORARY AMPERSAND--lt;d></tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>Given positive integers <tt>a</tt> and <tt>d</tt>, <tt>macaulayLowerOperator</tt> yields <tt>a<sub>-</sub>-TEMPORARY AMPERSAND--lt;d></tt>, the operation from Green’s proof of Macaulay’s Theorem. See Bruns and Herzog, <em>Cohen-Macaulay Rings</em>, page 161.</div> <table class="examples"><tr><td><pre>i1 : macaulayLowerOperator(3,1) o1 = 2</pre> </td></tr> <tr><td><pre>i2 : macaulayLowerOperator(15,5) o2 = 3</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_macaulay__Rep.html" title="the Macaulay representation of an integer">macaulayRep</a> -- the Macaulay representation of an integer</span></li> <li><span><a href="_macaulay__Bound.html" title="the bound on the growth of a Hilbert function from Macaulay's Theorem">macaulayBound</a> -- the bound on the growth of a Hilbert function from Macaulay's Theorem</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>macaulayLowerOperator</tt> :</h2> <ul><li>macaulayLowerOperator(ZZ,ZZ)</li> </ul> </div> </div> </body> </html>