<?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>euler(CoherentSheaf) -- Euler characteristic of coherent sheaf</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_euler_lp__Ideal_rp.html">next</a> | <a href="_euler.html">previous</a> | <a href="_euler_lp__Ideal_rp.html">forward</a> | <a href="_euler.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>euler(CoherentSheaf) -- Euler characteristic of coherent sheaf</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>euler F</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_euler.html" title="Euler characteristic">euler</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the Euler characteristic of the cohomology of the sheaf</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The command returns <tt>chi(F)</tt> the Euler characteristic of the sheaf <tt>F</tt> i.e. the alternated sum of the dimensions of its cohomology groups<p/> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_eulers_lp__Coherent__Sheaf_rp.html" title="list the sectional Euler characteristics">eulers(CoherentSheaf)</a> -- list the sectional Euler characteristics</span></li> <li><span><a href="_genus.html" title="arithmetic genus">genus</a> -- arithmetic genus</span></li> </ul> </div> </div> </body> </html>