<?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>localCohom(ZZ,Ideal) -- local cohomology of a polynomial ring</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_local__Cohom_lp__Z__Z_cm__Ideal_cm__Module_rp.html">next</a> | <a href="_local__Cohom_lp__List_cm__Ideal_cm__Module_rp.html">previous</a> | <a href="_local__Cohom_lp__Z__Z_cm__Ideal_cm__Module_rp.html">forward</a> | <a href="_local__Cohom_lp__List_cm__Ideal_cm__Module_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>localCohom(ZZ,Ideal) -- local cohomology of a polynomial ring</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>localCohom(d,I)</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_local__Cohom.html" title="local cohomology">localCohom</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li> <li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, the local cohomology of <tt>I</tt> in degree <em>d</em></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="_local__Cohom_lp..._cm_sp__Loc__Strategy_sp_eq_gt_sp..._rp.html">LocStrategy => ...</a>, -- specify localization strategy for local cohomology</span></li> <li><span><a href="_local__Cohom_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, -- specify strategy for local cohomology</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>See <a href="_local__Cohom_lp__Ideal_rp.html" title="local cohomology of a polynomial ring">localCohom(Ideal)</a> for the full description.<table class="examples"><tr><td><pre>i1 : W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}] o1 = W o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : I = ideal (X*(Y-Z), X*Y*Z) o2 = ideal (X*Y - X*Z, X*Y*Z) o2 : Ideal of W</pre> </td></tr> <tr><td><pre>i3 : h = localCohom (2,I) o3 = HashTable{2 => cokernel | -XYZ XY-XZ 3XdX-2YdY-2ZdZ YdY+ZdZ+3 Y2dY-2YdYZ-2YZdZ+Z2dZ |} o3 : HashTable</pre> </td></tr> <tr><td><pre>i4 : pruneLocalCohom h o4 = HashTable{2 => | Y-Z Z2 dYZ+ZdZ+2 XdX+2 |} o4 : HashTable</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_prune__Local__Cohom_lp__Hash__Table_rp.html" title="prunes local cohomology modules">pruneLocalCohom</a> -- prunes local cohomology modules</span></li> </ul> </div> </div> </body> </html>