<?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>Ddim -- dimension 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="___Ddual.html">next</a> | <a href="___Cycles.html">previous</a> | <a href="___Ddual.html">forward</a> | <a href="___Cycles.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>Ddim -- dimension 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>Ddim M, Ddim I</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> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the dimension of <em>M</em></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>The dimension of <em>M</em> is equal to the dimension of the associated graded module with respect to the Bernstein filtration.</p> <table class="examples"><tr><td><pre>i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}] o1 = W o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : I = ideal (x*Dx+2*y*Dy-3, Dx^2-Dy) 2 o2 = ideal (x*Dx + 2y*Dy - 3, Dx - Dy) o2 : Ideal of W</pre> </td></tr> <tr><td><pre>i3 : Ddim I o3 = 2</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_char__Ideal.html" title="characteristic ideal of a D-module">charIdeal</a> -- characteristic ideal of a D-module</span></li> <li><span><a href="_holonomic__Rank.html" title="rank of a D-module">holonomicRank</a> -- rank of a D-module</span></li> <li><span><a href="_sing__Locus.html" title="singular locus of a D-module">singLocus</a> -- singular locus of a D-module</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>Ddim</tt> :</h2> <ul><li>Ddim(Ideal)</li> <li>Ddim(Module)</li> </ul> </div> </div> </body> </html>