<?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 -- dual module or map</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_dual_lp__Chain__Complex_rp.html">next</a> | <a href="_drop_lp__Basic__List_cm__Z__Z_rp.html">previous</a> | <a href="_dual_lp__Chain__Complex_rp.html">forward</a> | <a href="_drop_lp__Basic__List_cm__Z__Z_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 -- dual module or map</h1> <div><!--empty documentation body--></div> <div class="waystouse"><h2>Ways to use <tt>dual</tt> :</h2> <ul><li><span>dual(BettiTally), see <span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></span></li> <li><span><a href="_dual_lp__Chain__Complex_rp.html" title="dual">dual(ChainComplex)</a> -- dual</span></li> <li><span><a href="_dual_lp__Chain__Complex__Map_rp.html" title="dual of a chain complex">dual(ChainComplexMap)</a> -- dual of a chain complex</span></li> <li><span><a href="_dual_lp__Coherent__Sheaf_rp.html" title="dual coherent sheaf">dual(CoherentSheaf)</a> -- dual coherent sheaf</span></li> <li><span><a href="_dual_lp__Matrix_rp.html" title="dual of a map">dual(Matrix)</a> -- dual of a map</span></li> <li><span><a href="_dual_lp__Module_rp.html" title="dual module">dual(Module)</a> -- dual module</span></li> <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> <li><span><a href="_dual_lp__Monomial__Ideal_cm__List_rp.html" title="the Alexander dual">dual(MonomialIdeal,List)</a> -- the Alexander dual</span></li> <li><span><a href="_dual_lp__Monomial__Ideal_cm__Ring__Element_rp.html" title="the Alexander dual">dual(MonomialIdeal,RingElement)</a> -- the Alexander dual</span></li> </ul> </div> </div> </body> </html>