<?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>genericSymmetricMatrix -- make a generic symmetric matrix</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_genus.html">next</a> | <a href="_generic__Skew__Matrix.html">previous</a> | <a href="_genus.html">forward</a> | <a href="_generic__Skew__Matrix.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>genericSymmetricMatrix -- make a generic symmetric 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>genericSymmetricMatrix(R,r,n)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li>
<li><span><tt>r</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, which is a variable in the ring <tt>R</tt> (this input is optional)</span></li>
<li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, a symmetric <a href="___Matrix.html">matrix</a> with <tt>n</tt> rows whose entries on and above the diagonal are the variables of <tt>R</tt> starting with <tt>r</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>A square <a href="___Matrix.html">matrix</a> <tt>M</tt> is <em>symmetric</em> if <tt>transpose(M) - M == 0</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..z];</pre>
</td></tr>
<tr><td><pre>i2 : M = genericSymmetricMatrix(R,a,3)
o2 = | a b c |
| b d e |
| c e f |
3 3
o2 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i3 : transpose(M) - M == 0
o3 = true</pre>
</td></tr>
<tr><td><pre>i4 : genericSymmetricMatrix(R,d,5)
o4 = | d e f g h |
| e i j k l |
| f j m n o |
| g k n p q |
| h l o q r |
5 5
o4 : Matrix R <--- R</pre>
</td></tr>
</table>
<p/>
Omitting the input <tt>r</tt> is the same as having <tt>r</tt> be the first variable in <tt>R</tt>.<table class="examples"><tr><td><pre>i5 : genericSymmetricMatrix(R,3)
o5 = | a b c |
| b d e |
| c e f |
3 3
o5 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i6 : genericSymmetricMatrix(R,5)
o6 = | a b c d e |
| b f g h i |
| c g j k l |
| d h k m n |
| e i l n o |
5 5
o6 : Matrix R <--- R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_vars_lp__Ring_rp.html" title="row matrix of the variables">vars(Ring)</a> -- row matrix of the variables</span></li>
<li><span><a href="_generic__Matrix.html" title="make a generic matrix of variables">genericMatrix</a> -- make a generic matrix of variables</span></li>
<li><span><a href="_generic__Skew__Matrix.html" title="make a generic skew symmetric matrix of variables">genericSkewMatrix</a> -- make a generic skew symmetric matrix of variables</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>genericSymmetricMatrix</tt> :</h2>
<ul><li>genericSymmetricMatrix(Ring,RingElement,ZZ)</li>
<li>genericSymmetricMatrix(Ring,ZZ)</li>
</ul>
</div>
</div>
</body>
</html>
