<?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>DintegrationClasses -- integration classes of a D-module</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Dintegration__Complex.html">next</a> | <a href="___Dintegration__All.html">previous</a> | <a href="___Dintegration__Complex.html">forward</a> | <a href="___Dintegration__All.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>DintegrationClasses -- integration classes of a D-module</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>N = DintegrationClasses(M,w), NI = DintegrationClasses(I,w), Ni = DintegrationClasses(i,M,w),</tt><br/><tt> NIi = DintegrationClasses(i,I,w), </tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, over the Weyl algebra <em>D</em></span></li> <li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, which represents the module <em>M = D/I</em></span></li> <li><span><tt>w</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a weight vector</span></li> <li><span><tt>i</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, nonnegative</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>Ni</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span></span></li> <li><span><tt>N</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span></span></li> <li><span><tt>NIi</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span></span></li> <li><span><tt>NI</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span></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="___Dintegration__Ideal_lp..._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>An extension of <a href="___Dintegration.html" title="integration modules of a D-module">Dintegration</a> that computes the explicit cohomology classes of a derived integration complex.<table class="examples"><tr><td><pre>i1 : R = QQ[x_1,x_2,D_1,D_2,WeylAlgebra=>{x_1=>D_1,x_2=>D_2}] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : I = ideal(x_1, D_2-1) o2 = ideal (x , D - 1) 1 2 o2 : Ideal of R</pre> </td></tr> <tr><td><pre>i3 : DintegrationClasses(I,{1,0}) o3 = HashTable{Boundaries => HashTable{0 => | D_2-1 |}} 1 => 0 Cycles => HashTable{0 => | 1 |} 1 => 0 1 2 1 VResolution => R <-- R <-- R 0 1 2 o3 : HashTable</pre> </td></tr> </table> </div> </div> <div class="single"><h2>Caveat</h2> <div>The module M should be specializable to the subspace. This is true for holonomic modules.The weight vector w should be a list of n numbers if M is a module over the nth Weyl algebra.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Dintegration.html" title="integration modules of a D-module">Dintegration</a> -- integration modules of a D-module</span></li> <li><span><a href="___Dintegration__All.html" title="integration modules of a D-module (extended version)">DintegrationAll</a> -- integration modules of a D-module (extended version)</span></li> <li><span><a href="___Drestriction.html" title="restriction modules of a D-module">Drestriction</a> -- restriction modules of a D-module</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>DintegrationClasses</tt> :</h2> <ul><li>DintegrationClasses(Ideal,List)</li> <li>DintegrationClasses(Module,List)</li> <li>DintegrationClasses(ZZ,Ideal,List)</li> <li>DintegrationClasses(ZZ,Module,List)</li> </ul> </div> </div> </body> </html>