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<title>GAP (GAPDoc) - Appendix A: The File 3k+1.xml</title>
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<div class="ChapSects"><a href="chapA.html#X830C58F97F9CD901">A <span class="Heading">The File <code class="file">3k+1.xml</code></span></a>
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<h3>A <span class="Heading">The File <code class="file">3k+1.xml</code></span></h3>

<p>Here is the complete source of the example <strong class="pkg">GAPDoc</strong> document <code class="file">3k+1.xml</code> discussed in Section <a href="chap1.html#X7B47AFA881BFC9DC"><span class="RefLink">1.2</span></a>.</p>


<div class="example"><pre>
&lt;?xml version="1.0" encoding="UTF-8"?&gt;

&lt;!--   A complete "fake package" documentation   
--&gt;

&lt;!DOCTYPE Book SYSTEM "gapdoc.dtd"&gt;

&lt;Book Name="3k+1"&gt;

&lt;TitlePage&gt;
  &lt;Title&gt;The &lt;Package&gt;ThreeKPlusOne&lt;/Package&gt; Package&lt;/Title&gt;
  &lt;Version&gt;Version 42&lt;/Version&gt;
  &lt;Author&gt;Dummy Authör
    &lt;Email&gt;3kplusone@dev.null&lt;/Email&gt;
  &lt;/Author&gt;

  &lt;Copyright&gt;&amp;copyright; 2000 The Author. &lt;P/&gt;
    You can do with this package what you want.&lt;P/&gt; Really.
  &lt;/Copyright&gt;
&lt;/TitlePage&gt;

&lt;TableOfContents/&gt;

&lt;Body&gt;
  &lt;Chapter&gt; &lt;Heading&gt;The &lt;M&gt;3k+1&lt;/M&gt; Problem&lt;/Heading&gt;
    &lt;Section Label="sec:theory"&gt; &lt;Heading&gt;Theory&lt;/Heading&gt;
      Let  &lt;M&gt;k \in  &amp;NN;&lt;/M&gt; be  a  natural number.  We consider  the
      sequence &lt;M&gt;n(i, k), i \in &amp;NN;,&lt;/M&gt; with &lt;M&gt;n(1, k) = k&lt;/M&gt; and
      else &lt;M&gt;n(i+1,  k) = n(i, k)  / 2&lt;/M&gt; if &lt;M&gt;n(i,  k)&lt;/M&gt; is even
      and &lt;M&gt;n(i+1, k) =  3 n(i, k) + 1&lt;/M&gt; if  &lt;M&gt;n(i, k)&lt;/M&gt; is odd.
      &lt;P/&gt; It  is not known  whether for  any natural number  &lt;M&gt;k \in
      &amp;NN;&lt;/M&gt; there is an &lt;M&gt;m \in &amp;NN;&lt;/M&gt; with &lt;M&gt;n(m, k) = 1&lt;/M&gt;.
      &lt;P/&gt;
      &lt;Package&gt;ThreeKPlusOne&lt;/Package&gt;  provides   the  function  &lt;Ref
      Func="ThreeKPlusOneSequence"/&gt;   to  explore   this  for   given
      &lt;M&gt;n&lt;/M&gt;.  If  you really  want  to  know something  about  this
      problem, see &lt;Cite Key="Wi98"/&gt; or
      &lt;URL Text="this homepage"&gt;https://www.ku.de/mgf/mathematik/statistik/personen-des-lehrstuhls/prof-dr-guenther-wirsching&lt;/URL&gt;
      for more details (and forget this package).
    &lt;/Section&gt;

    &lt;Section&gt; &lt;Heading&gt;Program&lt;/Heading&gt;
      In this section we describe the main function of this package.
      &lt;ManSection&gt; 
        &lt;Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/&gt;
        &lt;Description&gt;
          This  function computes  for a  natural number  &lt;A&gt;k&lt;/A&gt; the
          beginning of the sequence  &lt;M&gt;n(i, k)&lt;/M&gt; defined in section
          &lt;Ref Sect="sec:theory"/&gt;.  The sequence  stops at  the first
          &lt;M&gt;1&lt;/M&gt;  or at  &lt;M&gt;n(&lt;A&gt;max&lt;/A&gt;, k)&lt;/M&gt;,  if &lt;A&gt;max&lt;/A&gt;  is
          given.
&lt;Example&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">ThreeKPlusOneSequence(101);</span>
"Sorry, not yet implemented. Wait for Version 84 of the package"
&lt;/Example&gt;
        &lt;/Description&gt;
      &lt;/ManSection&gt;
    &lt;/Section&gt;
  &lt;/Chapter&gt;
&lt;/Body&gt;

&lt;Bibliography Databases="3k+1" /&gt;
&lt;TheIndex/&gt;

&lt;/Book&gt;

</pre></div>


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