<?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>ambient(Matrix)</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_ambient_lp__Module_rp.html">next</a> | <a href="_ambient_lp__Graded__Module_rp.html">previous</a> | <a href="_ambient_lp__Module_rp.html">forward</a> | <a href="_ambient_lp__Graded__Module_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>ambient(Matrix)</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>ambient f</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_ambient.html" title="ambient free module of a subquotient, or ambient ring">ambient</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, M --> N, where M is a free module or quotient of a free module F.</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, ambient M --> ambient N</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
</td></tr>
<tr><td><pre>i2 : f = map(image vars R, coker matrix{{a,b},{c,d}}, transpose matrix{{a,b,c,d},{d,c,b,a}})
o2 = {1} | a 2d |
{1} | b 2c |
{1} | c 0 |
{1} | d 0 |
o2 : Matrix</pre>
</td></tr>
<tr><td><pre>i3 : target f
o3 = image | a b c d |
1
o3 : R-module, submodule of R</pre>
</td></tr>
<tr><td><pre>i4 : source f
o4 = cokernel | a b |
| c d |
2
o4 : R-module, quotient of R</pre>
</td></tr>
<tr><td><pre>i5 : ambient f
o5 = | a2+b2+c2+d2 2bc+2ad |
1 2
o5 : Matrix R <--- R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></li>
<li><span><a href="_cover_lp__Matrix_rp.html" title="get the covering free module">cover(Matrix)</a> -- get the covering free module</span></li>
<li><span><a href="_matrix_lp__Matrix_rp.html" title="the matrix between generators">matrix(Matrix)</a> -- the matrix between generators</span></li>
</ul>
</div>
</div>
</body>
</html>
