<?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>macaulayBound -- the bound on the growth of a Hilbert function from 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__Lower__Operator.html">next</a> | <a href="___L__P__P.html">previous</a> | <a href="_macaulay__Lower__Operator.html">forward</a> | <a href="___L__P__P.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>macaulayBound -- the bound on the growth of a Hilbert function from 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=macaulayBound(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>, the Macaulay upper bound for the Hilbert function in degree <tt>d+1</tt> given that it is <tt>a</tt> in degree <tt>d</tt>.</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><div>Given a Hilbert function of <tt>a</tt> in degree <tt>d</tt>, <tt>macaulayBound</tt> yields the upper bound from Macaulay’s Theorem for the Hilbert function in degree <tt>d+1</tt>.</div> <table class="examples"><tr><td><pre>i1 : macaulayBound(3,1) o1 = 6</pre> </td></tr> <tr><td><pre>i2 : macaulayBound(15,5) o2 = 18</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__Lower__Operator.html" title="the a_<d> operator used in Green's proof of Macaulay's Theorem">macaulayLowerOperator</a> -- the a_<d> operator used in Green's proof of Macaulay's Theorem</span></li> <li><span><a href="_is__H__F.html" title="is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal">isHF</a> -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>macaulayBound</tt> :</h2> <ul><li>macaulayBound(ZZ,ZZ)</li> </ul> </div> </div> </body> </html>