<?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>mLatticePoints -- Compute the lattice points of a convex hull.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_m__Pos__Hull__Faces.html">next</a> | <a href="_m__Homology.html">previous</a> | <a href="_m__Pos__Hull__Faces.html">forward</a> | <a href="_m__Homology.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>mLatticePoints -- Compute the lattice points of a convex hull.</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>mLatticePoints(L)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of <a href="../../Macaulay2Doc/html/___Vector.html" title="the class of all elements of free modules that are handled by the engine">Vector</a>s.</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p>Returns a list with the lattice points of the convex hull of L.</p> <p>This uses the Convex functions convHull and hilbertbasis.</p> <div/> <table class="examples"><tr><td><pre>i1 : L={vector {3,-1,-1},vector {-1,3,-1},vector {-1,-1,3},vector {-1,-1,-1}};</pre> </td></tr> <tr><td><pre>i2 : P=mLatticePoints(L) o2 = {| -1 |, | -1 |, | -1 |, | 0 |, | -1 |, | -1 |, | 0 |, | -1 |, | 0 |, | 3 | | 2 | | 2 | | 2 | | 1 | | 1 | | 1 | | 1 | | 1 | | -1 | | 0 | | -1 | | -1 | | 1 | | 0 | | 0 | | -1 | | -1 | ------------------------------------------------------------------------ | 1 |, | -1 |, | -1 |, | 0 |, | -1 |, 0, | 1 |, | -1 |, | 0 |, | 1 |, | 1 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | 0 | | -1 | | 2 | | 1 | | 1 | | 0 | | 0 | | -1 | | -1 | | -1 | ------------------------------------------------------------------------ | 2 |, | -1 |, | -1 |, | 0 |, | -1 |, | 0 |, | 1 |, | -1 |, | 0 |, | 0 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | 3 | | 2 | | 2 | | 1 | | 1 | | 1 | | 0 | | 0 | ------------------------------------------------------------------------ | 1 |, | 2 |, | -1 |, | 0 |, | 1 |, | 2 |, | 3 |} | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | -1 | | 0 | | 0 | | -1 | | -1 | | -1 | | -1 | | -1 | o2 : List</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>mLatticePoints</tt> :</h2> <ul><li>mLatticePoints(List)</li> </ul> </div> </div> </body> </html>