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A The File 3k+1.xml

Here is the complete source of the example GAPDoc document 3k+1.xml discussed in Section 1.2.

<?xml version="1.0" encoding="UTF-8"?>

<!--   A complete "fake package" documentation
-->

<!DOCTYPE Book SYSTEM "gapdoc.dtd">

<Book Name="3k+1">

<TitlePage>
<Title>The <Package>ThreeKPlusOne</Package> Package</Title>
<Version>Version 42</Version>
<Author>Dummy Authör
<Email>3kplusone@dev.null</Email>
</Author>

You can do with this package what you want.<P/> Really.
</TitlePage>

<TableOfContents/>

<Body>
Let  <M>k \in  &NN;</M> be  a  natural number.  We consider  the
sequence <M>n(i, k), i \in &NN;,</M> with <M>n(1, k) = k</M> and
else <M>n(i+1,  k) = n(i, k)  / 2</M> if <M>n(i,  k)</M> is even
and <M>n(i+1, k) =  3 n(i, k) + 1</M> if  <M>n(i, k)</M> is odd.
<P/> It  is not known  whether for  any natural number  <M>k \in
&NN;</M> there is an <M>m \in &NN;</M> with <M>n(m, k) = 1</M>.
<P/>
<Package>ThreeKPlusOne</Package>  provides   the  function  <Ref
Func="ThreeKPlusOneSequence"/>   to  explore   this  for   given
<M>n</M>.  If  you really  want  to  know something  about  this
problem, see <Cite Key="Wi98"/> or
<URL>http://www.ku.de/mgf/mathematik/lehrstuhlstatistik/team/dr-guenther-wirsching/</URL>
for more details (and forget this package).
</Section>

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

<Bibliography Databases="3k+1" />
<TheIndex/>

</Book>


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