<?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>complexFromFacets -- Make a complex from its facets.</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_complex__To__Ideal.html">next</a> | <a href="___Complex_sp_eq_eq_sp__Complex.html">previous</a> | <a href="_complex__To__Ideal.html">forward</a> | <a href="___Complex_sp_eq_eq_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>complexFromFacets -- Make a complex from its facets.</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>complexFromFacets(R,facetlist)</tt><br/><tt>complexFromFacets(R,facetlist,Rdual)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span></span></li>
<li><span><tt>facetlist</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of the facets, sorted by dimension</span></li>
<li><span><tt>Rdual</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Complex.html">embedded complex</a></span></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><p>Make a complex from a list of faces and/or facets.</p>
<p>This is mostly used internally but may be occasionally useful for the end user.</p>
<div/>
<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_5]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : C=boundaryCyclicPolytope(3,R)
o2 = 2: x x x x x x x x x x x x x x x x x x x x x x x x
0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5
o2 : complex of dim 2 embedded in dim 5 (printing facets)
equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1</pre>
</td></tr>
<tr><td><pre>i3 : fC=facets C
o3 = {{}, {}, {}, {x x x , x x x , x x x , x x x , x x x , x x x , x x x ,
0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5
------------------------------------------------------------------------
x x x }, {}, {}, {}}
3 4 5
o3 : List</pre>
</td></tr>
<tr><td><pre>i4 : C1=complexFromFacets(R,fC)
o4 = 2: x x x x x x x x x x x x x x x x x x x x x x x x
0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5
o4 : complex of dim 2 embedded in dim 5 (printing facets)
equidimensional, simplicial</pre>
</td></tr>
<tr><td><pre>i5 : C1==C
o5 = true</pre>
</td></tr>
<tr><td><pre>i6 : fc C1;</pre>
</td></tr>
<tr><td><pre>i7 : C1
o7 = 2: x x x x x x x x x x x x x x x x x x x x x x x x
0 1 2 0 2 3 0 3 4 0 1 5 1 2 5 2 3 5 0 4 5 3 4 5
o7 : complex of dim 2 embedded in dim 5 (printing facets)
equidimensional, simplicial, F-vector {1, 6, 12, 8, 0, 0, 0}, Euler = 1</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div><div>If both the list of faces and facets is specified there is no consistency check.</div>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Face.html" title="The class of all faces of complexes or co-complexes.">Face</a> -- The class of all faces of complexes or co-complexes.</span></li>
<li><span><a href="_complex.html" title="Make a complex.">complex</a> -- Make a complex.</span></li>
<li><span><a href="_fc.html" title="The faces of a complex.">fc</a> -- The faces of a complex.</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>complexFromFacets</tt> :</h2>
<ul><li>complexFromFacets(PolynomialRing,List)</li>
<li>complexFromFacets(PolynomialRing,List,PolynomialRing)</li>
</ul>
</div>
</div>
</body>
</html>
