<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">


<html xmlns="http://www.w3.org/1999/xhtml">
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
    
    <title>Frank Luebeck’s tables of Conway polynomials over finite fields &mdash; Sage Reference Manual v6.8: Databases</title>
    
    <link rel="stylesheet" href="../../_static/sage.css" type="text/css" />
    <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../../',
        VERSION:     '6.8',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  true
      };
    </script>
    <script type="text/javascript" src="../../_static/jquery.js"></script>
    <script type="text/javascript" src="../../_static/underscore.js"></script>
    <script type="text/javascript" src="../../_static/doctools.js"></script>
    <script type="text/javascript" src="../../_static/MathJax.js?config=TeX-AMS_HTML-full,../mathjax_sage.js"></script>
    <script type="text/javascript" src="../../_static/MathJax.js?config=TeX-AMS_HTML-full,../mathjax_sage.js"></script>
    <link rel="shortcut icon" href="../../_static/favicon.ico"/>
    <link rel="top" title="Sage Reference Manual v6.8: Databases" href="../../index.html" />
    <link rel="next" title="Tables of zeros of the Riemann-Zeta function" href="odlyzko.html" />
    <link rel="prev" title="Local copy of Sloane On-Line Encyclopedia of Integer Sequences" href="sloane.html" />
    <link rel="icon" href="../../_static/sageicon.png" type="image/x-icon" />

  </head>
  <body>
    <div class="related">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="../../../genindex.html" title="General Index"
             accesskey="I">index</a></li>
        <li class="right" >
          <a href="../../py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="odlyzko.html" title="Tables of zeros of the Riemann-Zeta function"
             accesskey="N">next</a> |</li>
        <li class="right" >
          <a href="sloane.html" title="Local copy of Sloane On-Line Encyclopedia of Integer Sequences"
             accesskey="P">previous</a> |</li>
  
    
      <a href="../../../../index.html"><img src="../../_static/sagelogo.png" style="vertical-align: middle" title="Sage Logo"></a>
    
  
  
        <li><a href="../../index.html">Databases</a> &raquo;</li>
 
      </ul>
    </div>  

    <div class="document">
      <div class="documentwrapper">
        <div class="bodywrapper">
          <div class="body">
            
  <div class="section" id="frank-luebeck-s-tables-of-conway-polynomials-over-finite-fields">
<span id="sage-databases-conway"></span><h1>Frank Luebeck&#8217;s tables of Conway polynomials over finite fields<a class="headerlink" href="#frank-luebeck-s-tables-of-conway-polynomials-over-finite-fields" title="Permalink to this headline">¶</a></h1>
<span class="target" id="module-sage.databases.conway"></span><dl class="class">
<dt id="sage.databases.conway.ConwayPolynomials">
<em class="property">class </em><tt class="descclassname">sage.databases.conway.</tt><tt class="descname">ConwayPolynomials</tt><a class="headerlink" href="#sage.databases.conway.ConwayPolynomials" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">_abcoll.Mapping</span></tt></p>
<p>Initialize the database.</p>
<p>TESTS:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="n">c</span> <span class="o">=</span> <span class="n">ConwayPolynomials</span><span class="p">()</span>
<span class="gp">sage: </span><span class="n">c</span>
<span class="go">Frank Luebeck&#39;s database of Conway polynomials</span>
</pre></div>
</div>
<dl class="method">
<dt id="sage.databases.conway.ConwayPolynomials.degrees">
<tt class="descname">degrees</tt><big>(</big><em>p</em><big>)</big><a class="headerlink" href="#sage.databases.conway.ConwayPolynomials.degrees" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the list of integers <tt class="docutils literal"><span class="pre">n</span></tt> for which the database of Conway
polynomials contains the polynomial of degree <tt class="docutils literal"><span class="pre">n</span></tt> over <tt class="docutils literal"><span class="pre">GF(p)</span></tt>.</p>
<p>EXAMPLES:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="n">c</span> <span class="o">=</span> <span class="n">ConwayPolynomials</span><span class="p">()</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">degrees</span><span class="p">(</span><span class="mi">60821</span><span class="p">)</span>
<span class="go">[1, 2, 3, 4]</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">degrees</span><span class="p">(</span><span class="n">next_prime</span><span class="p">(</span><span class="mi">10</span><span class="o">^</span><span class="mi">7</span><span class="p">))</span>
<span class="go">[]</span>
</pre></div>
</div>
</dd></dl>

<dl class="method">
<dt id="sage.databases.conway.ConwayPolynomials.has_polynomial">
<tt class="descname">has_polynomial</tt><big>(</big><em>p</em>, <em>n</em><big>)</big><a class="headerlink" href="#sage.databases.conway.ConwayPolynomials.has_polynomial" title="Permalink to this definition">¶</a></dt>
<dd><p>Return True if the database of Conway polynomials contains the
polynomial of degree <tt class="docutils literal"><span class="pre">n</span></tt> over <tt class="docutils literal"><span class="pre">GF(p)</span></tt>.</p>
<p>INPUT:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">p</span></tt> &#8211; prime number</li>
<li><tt class="docutils literal"><span class="pre">n</span></tt> &#8211; positive integer</li>
</ul>
<p>EXAMPLES:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="n">c</span> <span class="o">=</span> <span class="n">ConwayPolynomials</span><span class="p">()</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">has_polynomial</span><span class="p">(</span><span class="mi">97</span><span class="p">,</span> <span class="mi">12</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">has_polynomial</span><span class="p">(</span><span class="mi">60821</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>

<dl class="method">
<dt id="sage.databases.conway.ConwayPolynomials.polynomial">
<tt class="descname">polynomial</tt><big>(</big><em>p</em>, <em>n</em><big>)</big><a class="headerlink" href="#sage.databases.conway.ConwayPolynomials.polynomial" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Conway polynomial of degree <tt class="docutils literal"><span class="pre">n</span></tt> over <tt class="docutils literal"><span class="pre">GF(p)</span></tt>,
or raise a RuntimeError if this polynomial is not in the
database.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">See also the global function <tt class="docutils literal"><span class="pre">conway_polynomial</span></tt> for
a more user-friendly way of accessing the polynomial.</p>
</div>
<p>INPUT:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">p</span></tt> &#8211; prime number</li>
<li><tt class="docutils literal"><span class="pre">n</span></tt> &#8211; positive integer</li>
</ul>
<p>OUTPUT:</p>
<p>List of Python int&#8217;s giving the coefficients of the corresponding
Conway polynomial in ascending order of degree.</p>
<p>EXAMPLES:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="n">c</span> <span class="o">=</span> <span class="n">ConwayPolynomials</span><span class="p">()</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">polynomial</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">21</span><span class="p">)</span>
<span class="go">(1, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)</span>
<span class="gp">sage: </span><span class="n">c</span><span class="o">.</span><span class="n">polynomial</span><span class="p">(</span><span class="mi">97</span><span class="p">,</span> <span class="mi">128</span><span class="p">)</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="c">...</span>
<span class="gr">RuntimeError</span>: <span class="n">Conway polynomial over F_97 of degree 128 not in database.</span>
</pre></div>
</div>
</dd></dl>

<dl class="method">
<dt id="sage.databases.conway.ConwayPolynomials.primes">
<tt class="descname">primes</tt><big>(</big><big>)</big><a class="headerlink" href="#sage.databases.conway.ConwayPolynomials.primes" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the list of prime numbers <tt class="docutils literal"><span class="pre">p</span></tt> for which the database of
Conway polynomials contains polynomials over <tt class="docutils literal"><span class="pre">GF(p)</span></tt>.</p>
<p>EXAMPLES:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="n">c</span> <span class="o">=</span> <span class="n">ConwayPolynomials</span><span class="p">()</span>
<span class="gp">sage: </span><span class="n">P</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">primes</span><span class="p">()</span>
<span class="gp">sage: </span><span class="mi">2</span> <span class="ow">in</span> <span class="n">P</span>
<span class="go">True</span>
<span class="gp">sage: </span><span class="n">next_prime</span><span class="p">(</span><span class="mi">10</span><span class="o">^</span><span class="mi">7</span><span class="p">)</span> <span class="ow">in</span> <span class="n">P</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

<dl class="class">
<dt id="sage.databases.conway.DictInMapping">
<em class="property">class </em><tt class="descclassname">sage.databases.conway.</tt><tt class="descname">DictInMapping</tt><big>(</big><em>dict</em><big>)</big><a class="headerlink" href="#sage.databases.conway.DictInMapping" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">_abcoll.Mapping</span></tt></p>
<p>Places dict into a non-mutable mapping.</p>
<p>TESTS:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">sage: </span><span class="kn">from</span> <span class="nn">sage.databases.conway</span> <span class="kn">import</span> <span class="n">DictInMapping</span>
<span class="gp">sage: </span><span class="n">d</span> <span class="o">=</span> <span class="p">{}</span>
<span class="gp">sage: </span><span class="n">m</span> <span class="o">=</span> <span class="n">DictInMapping</span><span class="p">(</span><span class="n">d</span><span class="p">);</span> <span class="n">m</span>
<span class="go">{}</span>
<span class="gp">sage: </span><span class="n">d</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span> <span class="n">m</span>
<span class="go">{0: 1}</span>
<span class="gp">sage: </span><span class="n">m</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">3</span>
<span class="gt">Traceback (most recent call last):</span>
<span class="c">...</span>
<span class="gr">TypeError</span>: <span class="n">&#39;DictInMapping&#39; object does not support item assignment</span>
</pre></div>
</div>
</dd></dl>

</div>


          </div>
        </div>
      </div>
      <div class="sphinxsidebar">
        <div class="sphinxsidebarwrapper">
            <h4>Previous topic</h4>
            <p class="topless"><a href="sloane.html"
                                  title="previous chapter">Local copy of Sloane On-Line Encyclopedia of Integer Sequences</a></p>
            <h4>Next topic</h4>
            <p class="topless"><a href="odlyzko.html"
                                  title="next chapter">Tables of zeros of the Riemann-Zeta function</a></p>
            <h3>This Page</h3>
            <ul class="this-page-menu">
              <li><a href="../../_sources/sage/databases/conway.txt"
                     rel="nofollow">Show Source</a></li>
            </ul>
          <div id="searchbox" style="display: none">
            <h3>Quick search</h3>
              <form class="search" action="../../../search.html" method="get">
                <input type="text" name="q" size="18" />
               
               
               
               
                <input type="submit" style="background-color: #B8B9F6" value="Go" />
                <input type="hidden" name="check_keywords" value="yes" />
                <input type="hidden" name="area" value="default" />
              </form>
              <p class="searchtip" style="font-size: 90%">
              Enter search terms or a module, class or function name.
              </p>
          </div>
          <script type="text/javascript">$('#searchbox').show(0);</script>
        </div>
      </div>
      <div class="clearer"></div>
    </div>
    <div class="related">
      <h3>Navigation</h3>
      <ul>
        <li class="right" style="margin-right: 10px">
          <a href="../../../genindex.html" title="General Index"
             >index</a></li>
        <li class="right" >
          <a href="../../py-modindex.html" title="Python Module Index"
             >modules</a> |</li>
        <li class="right" >
          <a href="odlyzko.html" title="Tables of zeros of the Riemann-Zeta function"
             >next</a> |</li>
        <li class="right" >
          <a href="sloane.html" title="Local copy of Sloane On-Line Encyclopedia of Integer Sequences"
             >previous</a> |</li>
  
    
      <a href="../../../../index.html"><img src="../../_static/sagelogo.png" style="vertical-align: middle" title="Sage Logo"></a>
    
  
  
        <li><a href="../../index.html">Databases</a> &raquo;</li>
 
      </ul>
    </div>
    
    <div class="footer">
        &copy; Copyright 2005--2015, The Sage Development Team.
      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.2.2.
    </div>
    <script type="text/javascript">
/*global jQuery, window */
/* Sphinx sidebar toggle.  Putting this code at the end of the body
 * enables the toggle for the live, static, and offline docs.  Note:
 * sage.misc.html.math_parse() eats jQuery's dollar-sign shortcut. */
var jq = jQuery;
jq(document).ready(function () {
    var bar, bod, bg, fg, key, tog, wid_old, wid_new, resize, get_state, set_state;
    bod = jq('div.bodywrapper');
    bar = jq('div.sphinxsidebar');
    tog = jq('<div class="sphinxsidebartoggle"></div>');

    /* Delayed resize helper.  Not perfect but good enough. */
    resize = function () {
        setTimeout(function () {
            tog.height(bod.height());
        }, 100);
    };
    jq(window).resize(function () {
        resize();
    });

    /* Setup and add the toggle. See Sphinx v0.5.1 default.css. */
    fg = jq('div.sphinxsidebar p a').css('color') || 'rgb(152, 219, 204)';
    bg = jq('div.document').css('background-color') || 'rgb(28, 78, 99)';
    wid_old = '230px';
    wid_new = '5px';
    tog.css('background-color', bg)
        .css('border-width', '0px')
        .css('border-right', wid_new + ' ridge ' + bg)
        .css('cursor', 'pointer')
        .css('position', 'absolute')
        .css('left', '-' + wid_new)
        .css('top', '0px')
        .css('width', wid_new);
    bod.css('position', 'relative');
    bod.prepend(tog);
    resize();

    /* Cookie helpers. */
    key = 'sphinxsidebar=';
    set_state = function (s) {
        var date = new Date();
        /* Expiry in 7 days. */
        date.setTime(date.getTime() + (7 * 24 * 3600 * 1000));
        document.cookie = key + encodeURIComponent(s) + '; expires=' +
            date.toUTCString() + '; path=/';
    };
    get_state = function () {
        var i, c, crumbs = document.cookie.split(';');
        for (i = 0; i < crumbs.length; i += 1) {
            c = crumbs[i].replace(/^\s+/, '');
            if (c.indexOf(key) === 0) {
                return decodeURIComponent(c.substring(key.length, c.length));
            }
        }
        return null;
    };

    /* Event handlers. */
    tog.mouseover(function (ev) {
        tog.css('border-right-color', fg);
    }).mouseout(function (ev) {
        tog.css('border-right-color', bg);
    }).click(function (ev) {
        if (bod.hasClass('wide')) {
            bod.removeClass('wide');
            bod.css('margin-left', wid_old);
            bar.css('width', wid_old);
            bar.show();
            set_state('visible');
        } else {
            set_state('hidden');
            bar.hide();
            bar.css('width', '0px');
            bod.css('margin-left', wid_new);
            bod.addClass('wide');
        }
        resize();
    });

    /* Hide the normally visible sidebar? */
    if (get_state() === 'hidden') {
        tog.trigger('click');
    } else {
        set_state('visible');
    }
});
    </script>
  </body>
</html>

Collaborative Calculation and Data Science

colby

sagemath

Product

Resources

Company