<?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>typeD -- Type D reflection arrangement</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_vee.html">next</a> | <a href="_type__B.html">previous</a> | <a href="_vee.html">forward</a> | <a href="_type__B.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>typeD -- Type D reflection arrangement</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>typeD(n) or typeD(n,R) or typeD(n,k)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the rank</span></li> <li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a polynomial (coordinate) ring in n variables</span></li> <li><span><tt>k</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, a coefficient ring; by default, <tt>QQ</tt></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, the D_n reflection arrangement</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The hyperplane arrangement with hyperplanes defined by the type D_n root system: for example,<table class="examples"><tr><td><pre>i1 : D4 = typeD(4) o1 = {x - x , x + x , x - x , x + x , x - x , x + x , x - x , x + x , x - x , x + x , x - x , x + x } 1 2 1 2 1 3 1 3 1 4 1 4 2 3 2 3 2 4 2 4 3 4 3 4 o1 : Hyperplane Arrangement </pre> </td></tr> <tr><td><pre>i2 : describe D4 o2 = {x - x , x + x , x - x , x + x , x - x , x + x , x - x , x + x , 1 2 1 2 1 3 1 3 1 4 1 4 2 3 2 3 ------------------------------------------------------------------------ x - x , x + x , x - x , x + x } 2 4 2 4 3 4 3 4</pre> </td></tr> <tr><td><pre>i3 : ring D4 o3 = QQ[x , x , x , x ] 1 2 3 4 o3 : PolynomialRing</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_type__A.html" title="Type A reflection arrangement">typeA</a> -- Type A reflection arrangement</span></li> <li><span><a href="_type__B.html" title="Type B reflection arrangement">typeB</a> -- Type B reflection arrangement</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>typeD</tt> :</h2> <ul><li>typeD(ZZ)</li> <li>typeD(ZZ,PolynomialRing)</li> <li>typeD(ZZ,Ring)</li> </ul> </div> </div> </body> </html>