<?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>vertexFacetMatrix -- computes the vertex-facet-relations matrix</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_vertices.html">next</a> | <a href="_vertex__Edge__Matrix.html">previous</a> | <a href="_vertices.html">forward</a> | <a href="_vertex__Edge__Matrix.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>vertexFacetMatrix -- computes the vertex-facet-relations matrix</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> M = vertexFacetMatrix P</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p/> <tt>vertexFacetMatrix</tt> computes the matrix <tt>M</tt> where the columns are indexed by the facets and the rows are indexed by the vertices of <tt>P</tt> and has 1 as an entry if the corresponding facet contains this vertex and 0 otherwise.<table class="examples"><tr><td><pre>i1 : P = cyclicPolytope(3,5) o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 5 o1 : Polyhedron</pre> </td></tr> <tr><td><pre>i2 : vertexFacetMatrix P o2 = | 0 1 2 3 4 5 6 | | 1 1 1 1 0 0 1 | | 2 1 0 0 0 1 1 | | 3 1 1 0 1 1 0 | | 4 0 1 1 1 0 0 | | 5 0 0 1 1 1 1 | 6 7 o2 : Matrix ZZ <--- ZZ</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>vertexFacetMatrix</tt> :</h2> <ul><li>vertexFacetMatrix(Polyhedron)</li> </ul> </div> </div> </body> </html>