<?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>dual(MonomialIdeal,RingElement) -- the Alexander dual</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_eagon__Northcott_lp__Matrix_rp.html">next</a> | <a href="_dual_lp__Monomial__Ideal_cm__List_rp.html">previous</a> | <a href="_eagon__Northcott_lp__Matrix_rp.html">forward</a> | <a href="_dual_lp__Monomial__Ideal_cm__List_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>dual(MonomialIdeal,RingElement) -- the Alexander dual</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>dual(I,m)</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_dual.html" title="dual module or map">dual</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span>, a monomial ideal</span></li> <li><span><tt>m</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, a monomial</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span>the Alexander dual of <tt>I</tt> formed with respect to <tt>m</tt>.</span></li> </ul> </div> </li> <li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_dual_lp__Monomial__Ideal_cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, </span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The monomial <tt>m</tt> should be divisible by all of the minimal generators of <tt>I</tt>.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_dual_lp__Monomial__Ideal_rp.html" title="the Alexander dual of a monomial ideal">dual(MonomialIdeal)</a> -- the Alexander dual of a monomial ideal</span></li> </ul> </div> </div> </body> </html>