<?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>Cone ? Cone -- compares the Cones</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_cones.html">next</a> | <a href="___Cone_sp_eq_eq_sp__Cone.html">previous</a> | <a href="_cones.html">forward</a> | <a href="___Cone_sp_eq_eq_sp__Cone.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>Cone ? Cone -- compares the Cones</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> b = C1 ? C2</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="../../Macaulay2Doc/html/__qu.html" title="comparison operator">?</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>C1</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li> <li><span><tt>C2</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <tt>></tt> or <tt><</tt> or <tt>=</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p/> This induces an order on Cones. <tt>C1</tt> is greater then <tt>C2</tt> if its ambient dimension is greater, if this is equal then if its dimension is higher and if this is equal if it has the higher ordered rays and lineality space.<table class="examples"><tr><td><pre>i1 : C1 = posHull matrix {{1,0},{0,1},{1,1}} o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of the cone => 2 number of facets => 2 number of rays => 2 o1 : Cone</pre> </td></tr> <tr><td><pre>i2 : C2 = posHull matrix {{1,0,1},{0,1,0},{1,1,0}} o2 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of the cone => 3 number of facets => 3 number of rays => 3 o2 : Cone</pre> </td></tr> <tr><td><pre>i3 : C1 ? C2 o3 = < o3 : Keyword</pre> </td></tr> </table> </div> </div> </div> </body> </html>