<?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>eulerCharacteristic -- The Euler characteristic of a complex.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Example_spfirst_sporder_spdeformation.html">next</a> | <a href="_embedding__Complex.html">previous</a> | <a href="___Example_spfirst_sporder_spdeformation.html">forward</a> | <a href="_embedding__Complex.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>eulerCharacteristic -- The Euler characteristic of a complex.</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>eulerCharacteristic(C)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></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></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>The Euler characteristic of C. This is printed always when printing a complex and the faces are known.</p> <div/> <table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_5];</pre> </td></tr> <tr><td><pre>i2 : C=fullCyclicPolytope(3,R);</pre> </td></tr> <tr><td><pre>i3 : fvector C o3 = {1, 6, 12, 8, 1} o3 : List</pre> </td></tr> <tr><td><pre>i4 : eulerCharacteristic C o4 = 0</pre> </td></tr> <tr><td><pre>i5 : dC=boundaryOfPolytope(C);</pre> </td></tr> <tr><td><pre>i6 : fvector dC o6 = {1, 6, 12, 8, 0} o6 : List</pre> </td></tr> <tr><td><pre>i7 : eulerCharacteristic dC o7 = 1</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_fvector.html" title="The F-vector of a complex.">fvector</a> -- The F-vector of a complex.</span></li> <li><span><a href="_fc.html" title="The faces of a complex.">fc</a> -- The faces of a complex.</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>eulerCharacteristic</tt> :</h2> <ul><li>eulerCharacteristic(Complex)</li> <li>eulerCharacteristic(List)</li> </ul> </div> </div> </body> </html>