3k+1.xmlHere is the complete source of the example GAPDoc document 3k+1.xml discussed in Section 1.2.
<?xml version="1.0" encoding="ISO-8859-1"?>
<!-- A complete "fake package" documentation
$Id: app3k1.xml,v 1.1.1.1 2001/01/05 13:37:49 gap Exp $
-->
<!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>
<Copyright>©right; 2000 The Author. <P/>
You can do with this package what you want.<P/> Really.
</Copyright>
</TitlePage>
<TableOfContents/>
<Body>
<Chapter> <Heading>The <M>3k+1</M> Problem</Heading>
<Section Label="sec:theory"> <Heading>Theory</Heading>
Let <M>k \in \N</M> be a natural number. We consider the sequence
<M>n(i, k), i \in \N,</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 \N</M>
there is an <M>m \in \N</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://mathsrv.ku-eichstaett.de/MGF/homes/wirsching/</URL>
for more details (and forget this package).
</Section>
<Section> <Heading>Program</Heading>
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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