<?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>isPrimitive -- whether an element is a primitive element of a finite field</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_is__Pseudoprime_lp__Z__Z_rp.html">next</a> | <a href="_is__Prime.html">previous</a> | <a href="_is__Pseudoprime_lp__Z__Z_rp.html">forward</a> | <a href="_is__Prime.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>isPrimitive -- whether an element is a primitive element of a finite field</h1> <div class="single"><h2>Description</h2> <div><tt>isPrimitive(f)</tt> -- Given an element <tt>f</tt> in a quotient of a polynomial ring <tt>R</tt> over a finite field <tt>K</tt>which is itself a finite field, with the ring being finite dimensional over the field, determine if <tt>f</tt> generates the multiplicative group of this field.<table class="examples"><tr><td><pre>i1 : R = ZZ/5[t]/(t^2+t+1);</pre> </td></tr> <tr><td><pre>i2 : isPrimitive t o2 = false</pre> </td></tr> <tr><td><pre>i3 : isPrimitive (t-1) o3 = true</pre> </td></tr> </table> </div> </div> </div> </body> </html>