<?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>minimalPresentation(Matrix) -- minimally present source and target of a matrix</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_minimal__Presentation_lp__Module_rp.html">next</a> | <a href="_minimal__Presentation_lp__Ideal_rp.html">previous</a> | <a href="_minimal__Presentation_lp__Module_rp.html">forward</a> | <a href="_minimal__Presentation_lp__Ideal_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>minimalPresentation(Matrix) -- minimally present source and target of a 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>minimalPresentation f</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_minimal__Presentation.html" title="compute a minimal presentation">minimalPresentation</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>g</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>Exclude => ...</tt> (missing documentation<!-- tag: minimalPresentation(..., Exclude => ...) -->), </span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>If the source and target of <tt>f</tt> are graded, then minimal presentations of the source and target modules for <tt>f</tt> are computed using <a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> and <tt>g</tt> is the matrix corresponding to <tt>f</tt> with source and target the minimally presented source and target. If either the source or target of <tt>f</tt> is not graded then an attempt is made to improve their presentations and <tt>g</tt>is the matrix with resulting source and target. An example follows.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..d];</pre>
</td></tr>
<tr><td><pre>i2 : f = inducedMap(coker matrix {{a,1,b},{c,3,b+d}},R^2)
o2 = | 1 -10668 |
| 0 0 |
o2 : Matrix</pre>
</td></tr>
<tr><td><pre>i3 : g = prune f
o3 = | -3 1 |
o3 : Matrix</pre>
</td></tr>
<tr><td><pre>i4 : source g
2
o4 = R
o4 : R-module, free</pre>
</td></tr>
<tr><td><pre>i5 : target g
o5 = cokernel | b+16001d a-10668c |
1
o5 : R-module, quotient of R</pre>
</td></tr>
</table>
<p>This function does not remove elements from the base field from the matrix, but rather minimally presents the source and target and gives the corresponding new map. For example:</p>
<table class="examples"><tr><td><pre>i6 : m = matrix{{a,1,b},{c,3,b+d}}
o6 = | a 1 b |
| c 3 b+d |
2 3
o6 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i7 : prune m
o7 = | a 1 b |
| c 3 b+d |
2 3
o7 : Matrix R <--- R</pre>
</td></tr>
</table>
Unlike above, nothing changes.</div>
</div>
<div class="single"><h2>Caveat</h2>
<div>Check out the example just above.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></li>
</ul>
</div>
</div>
</body>
</html>
