<?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>ConwayPolynomials -- database of Conway polynomials for use with GF</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_conway__Polynomial.html">next</a> | previous | <a href="_conway__Polynomial.html">forward</a> | backward | up | top | <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>ConwayPolynomials -- database of Conway polynomials for use with GF</h1>
<div class="single"><h2>Description</h2>
<div><p><em>ConwayPolynomials</em> is a package that provides a database of Conway polynomials. A Conway polynomial for a prime p and an exponent n is a particular monic polynomial whose roots are primitive elements of a finite field with p^n elements. They can take a very long time to compute, so the package comes with just a publicly available database of Conway polynomials provided by Frank Luebeck.</p>
<p>After the package is loaded, the function <a href="../../Macaulay2Doc/html/___G__F.html" title="make a finite field">GF</a> will return Galois fields presented by Conway polynomials, provided they are in the table. Moreover, <a href="../../Macaulay2Doc/html/_map.html" title="make a map">map</a> can be used to produce the canonical maps between Conway Galois fields.</p>
<table class="examples"><tr><td><pre>i1 : conwayPolynomial 125
3
o1 = a - 2a - 2
ZZ
o1 : --[a]
5</pre>
</td></tr>
<tr><td><pre>i2 : GF 125
o2 = GF 125
o2 : GaloisField</pre>
</td></tr>
<tr><td><pre>i3 : ambient oo
ZZ
--[a]
5
o3 = -----------
3
a - 2a - 2
o3 : QuotientRing</pre>
</td></tr>
<tr><td><pre>i4 : map(GF 125^2, GF 125)
5 4 3 2
o4 = map(GF 15625,GF 125,{- a + a - a - a - 2a - 2})
o4 : RingMap GF 15625 <--- GF 125</pre>
</td></tr>
<tr><td><pre>i5 : isWellDefined oo
o5 = true</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Author</h2>
<ul><li><div class="single">Daniel R. Grayson<span> <<a href="mailto:dan@math.uiuc.edu">dan@math.uiuc.edu</a>></span></div>
</li>
</ul>
</div>
<div class="single"><h2>Version</h2>
This documentation describes version <b>1.0</b> of ConwayPolynomials.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/ConwayPolynomials.m2">ConwayPolynomials.m2</a>. The auxiliary files accompanying it are in the directory <a href="../../../../Macaulay2/ConwayPolynomials/">ConwayPolynomials/</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Functions<ul><li><span><a href="_conway__Polynomial.html" title="provide a Conway polynomial">conwayPolynomial</a> -- provide a Conway polynomial</span></li>
</ul>
</div>
</li>
</ul>
</div>
</div>
</body>
</html>
