<?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>hull -- The positive hull complex.</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_ideal__To__Co__Complex.html">next</a> | <a href="___H__H_sp__Complex.html">previous</a> | <a href="_ideal__To__Co__Complex.html">forward</a> | <a href="___H__H_sp__Complex.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>hull -- The positive hull complex.</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>hull(L)</tt><br/><tt>hull(fn)</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 lying all in the same space.</span></li>
<li><span><tt>fn</tt>, <span>a <a href="../../Macaulay2Doc/html/___String.html">string</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_file.html">file => ...</a>, -- Store result of a computation in a file.</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p>Returns the cone which is the hull of lattice vectors in L. The output has C.isPolytope==true.</p>
<p>If applied to the string fn the result of a previous computation stored via the option <a href="_file.html" title="Store result of a computation in a file.">file</a> is read from the file fn.</p>
<p>The hull of L has to be strictly convex.</p>
<div/>
<table class="examples"><tr><td><pre>i1 : L= {{0,1,1,0,0},{0,1,0,1,0},{0,1,0,0,0},{1,0,0,0,1},{1,0,-1,-1,-1},{1,0,0,0,0}};</pre>
</td></tr>
<tr><td><pre>i2 : L=apply(L,vector)
o2 = {| 0 |, | 0 |, | 0 |, | 1 |, | 1 |, | 1 |}
| 1 | | 1 | | 1 | | 0 | | 0 | | 0 |
| 1 | | 0 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 1 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 0 | | 0 | | 1 | | -1 | | 0 |
o2 : List</pre>
</td></tr>
<tr><td><pre>i3 : C=hull L
o3 = 4: y y y y y y
0 1 2 3 4 5
o3 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 6, 14, 16, 8, 1}, Euler = 0</pre>
</td></tr>
<tr><td><pre>i4 : C.grading
o4 = | 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 1 0 0 |
| 0 1 0 1 0 |
| 1 0 -1 -1 -1 |
| 1 0 0 0 1 |
6 5
o4 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i5 : dC=dualize C
o5 = 4: v v v v v v v v
0 1 2 3 4 5 6 7
o5 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, non-simplicial, F-vector {1, 8, 16, 14, 6, 1}, Euler = 0</pre>
</td></tr>
<tr><td><pre>i6 : dC.grading
o6 = | 0 1 -1 -1 0 |
| 0 1 1 -1 0 |
| 0 1 -1 1 0 |
| 1 0 0 0 -1 |
| 1 0 2 0 -1 |
| 1 0 0 2 -1 |
| 1 0 0 0 1 |
| 0 1 -1 -1 2 |
8 5
o6 : Matrix ZZ <--- ZZ</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div><p>The cone is represented as a complex on its rays, hence if <a href="_dim_lp__Face_rp.html" title="Compute the dimension of a face.">dim(Face)</a> is applied to a <a href="___Face.html" title="The class of all faces of complexes or co-complexes.">Face</a> it will return the dimension of the corresponding cone minus one.</p>
<p>This uses the package Polyhedra.m2 to compute the facets. Too slow compared to Maple/convex.</p>
<div>If the package <i>ConvexInterface</i> is loaded, then this command calls Maple/Convex. See the corresponding option explained at <a href="index.html" title="Deformations of Stanley-Reisner rings and related computations.">SRdeformations</a>.</div>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Complex.html" title="The class of all embedded complexes.">Complex</a> -- The class of all embedded complexes.</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>hull</tt> :</h2>
<ul><li>hull(List)</li>
<li>hull(String)</li>
</ul>
</div>
</div>
</body>
</html>
