<?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>Complex == Complex -- Compare two complexes.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_complex__From__Facets.html">next</a> | <a href="_complex.html">previous</a> | <a href="_complex__From__Facets.html">forward</a> | <a href="_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>Complex == Complex -- Compare two complexes.</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>C1==C2</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="../../Macaulay2Doc/html/__eq_eq.html" title="equality">==</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>C1</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></span></li> <li><span><tt>C2</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>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>Checks whether C1 and C2 are equal.</p> <p>Uses the facets of C1 and C2 (as in many examples the Stanley-Reisner ideal cannot be computed as it is too big to write down).</p> <div/> <table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4];</pre> </td></tr> <tr><td><pre>i2 : C=simplex R;</pre> </td></tr> <tr><td><pre>i3 : bC=boundaryOfPolytope C o3 = 3: x x x x x x x x x x x x x x x x x x x x 0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4 1 2 3 4 o3 : complex of dim 3 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1</pre> </td></tr> <tr><td><pre>i4 : dbC=dualize bC o4 = 0: v v v v v 0 1 2 3 4 o4 : co-complex of dim 0 embedded in dim 4 (printing facets) equidimensional, simplicial, F-vector {0, 5, 10, 10, 5, 1}, Euler = 1</pre> </td></tr> <tr><td><pre>i5 : bC==dualize dbC o5 = true</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Face_sp_eq_eq_sp__Face.html" title="Compare two faces.">Face == Face</a> -- Compare two faces.</span></li> <li><span><a href="___Complex.html" title="The class of all embedded complexes.">Complex</a> -- The class of all embedded complexes.</span></li> <li><span><a href="_dualize.html" title="The dual of a face or complex.">dualize</a> -- The dual of a face or complex.</span></li> <li><span><a href="_facets.html" title="The maximal faces of a complex.">facets</a> -- The maximal faces of a complex.</span></li> </ul> </div> </div> </body> </html>