<?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>hypercube -- computes the d-dimensional hypercube with edge length 2*s</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_hyperplanes.html">next</a> | <a href="_hirzebruch.html">previous</a> | <a href="_hyperplanes.html">forward</a> | <a href="_hirzebruch.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>hypercube -- computes the d-dimensional hypercube with edge length 2*s</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> P = hypercube(d,s)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, , strictly positive</span></li> <li><span><tt>s</tt>, <a href="../../Macaulay2Doc/html/___Z__Z.html" title="the class of all integers">ZZ</a> or <a href="../../Macaulay2Doc/html/___Q__Q.html" title="the class of all rational numbers">QQ</a>, positive (optional)</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p/> The <tt>d</tt>-dimensional <tt>hypercube</tt> with edge length 2*<tt>s</tt> is the convex hull of all points in <tt>{+/- s}^d</tt> in <a href="../../Macaulay2Doc/html/___Q__Q.html" title="the class of all rational numbers">QQ</a>^d. If <tt>s</tt> is omitted it is set to 1.<table class="examples"><tr><td><pre>i1 : P = hypercube 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 8 o1 : Polyhedron</pre> </td></tr> <tr><td><pre>i2 : vertices P o2 = | -1 1 -1 1 -1 1 -1 1 | | -1 -1 1 1 -1 -1 1 1 | | -1 -1 -1 -1 1 1 1 1 | 3 8 o2 : Matrix QQ <--- QQ</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>hypercube</tt> :</h2> <ul><li>hypercube(ZZ)</li> <li>hypercube(ZZ,QQ)</li> <li>hypercube(ZZ,ZZ)</li> </ul> </div> </div> </body> </html>