<?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>subArrangement -- Subarrangement containing a fixed flat</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_tolist.html">next</a> | <a href="_ring_lp__Arrangement_rp.html">previous</a> | <a href="_tolist.html">forward</a> | <a href="_ring_lp__Arrangement_rp.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>subArrangement -- Subarrangement containing a fixed flat</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>subArrangement(A,F) or subArrangement(F)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="___Arrangement.html">hyperplane arrangement</a></span></span></li>
<li><span><tt>F</tt>, <span>an <a href="___Flat.html">intersection of hyperplane(s)</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, the subarrangement of <tt>A</tt> contained in <tt>F</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>If <tt>X</tt> is the linear subspace indexed by the flat <tt>F</tt>, then the subarrangement <tt>A_F</tt> consists of those hyperplanes in <tt>A</tt> that contain <tt>X</tt>.<table class="examples"><tr><td><pre>i1 : A := typeA(3)
o1 = {x - x , x - x , x - x , x - x , x - x , x - x }
1 2 1 3 1 4 2 3 2 4 3 4
o1 : Hyperplane Arrangement </pre>
</td></tr>
<tr><td><pre>i2 : flats(2,A)
o2 = {{0, 1, 3}, {0, 2, 4}, {0, 5}, {1, 4}, {1, 2, 5}, {2, 3}, {3, 4, 5}}
o2 : List</pre>
</td></tr>
<tr><td><pre>i3 : B := subArrangement first oo
o3 = {x - x , x - x , x - x }
1 2 1 3 2 3
o3 : Hyperplane Arrangement </pre>
</td></tr>
</table>
Note that the ambient vector space of <tt>A_F</tt> is the same as that of <tt>A</tt>; subarrangements are essential in general.<table class="examples"><tr><td><pre>i4 : ring B
o4 = QQ[x , x , x , x ]
1 2 3 4
o4 : PolynomialRing</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Arrangement_sp_us_sp__Flat.html" title="Subarrangement containing a fixed flat">Arrangement _ Flat</a> -- Subarrangement containing a fixed flat</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>subArrangement</tt> :</h2>
<ul><li>subArrangement(Arrangement,Flat)</li>
<li>subArrangement(Flat)</li>
</ul>
</div>
</div>
</body>
</html>
