  
  [1m[4m[31mA. The File [1m3k+1.xml[1m[4m[31m[0m
  
  Here  is  the  complete  source  of  the  example  [1mGAPDoc[0m  document [1m3k+1.xml[0m
  discussed in Section [1m1.2[0m.
  
  [22m[35m---------------------------  3k+1.xml  ---------------------------[0m
    [22m[35m<?xml version="1.0" encoding="ISO-8859-1"?>[0m
    [22m[35m[0m
    [22m[35m<!--   A complete "fake package" documentation   [0m
    [22m[35m   $Id: app3k1.xml,v 1.2 2002/05/29 07:58:58 gap Exp $[0m
    [22m[35m-->[0m
    [22m[35m[0m
    [22m[35m<!DOCTYPE Book SYSTEM "gapdoc.dtd">[0m
    [22m[35m[0m
    [22m[35m<Book Name="3k+1">[0m
    [22m[35m[0m
    [22m[35m<TitlePage>[0m
    [22m[35m  <Title>The <Package>ThreeKPlusOne</Package> Package</Title>[0m
    [22m[35m  <Version>Version 42</Version>[0m
    [22m[35m  <Author>Dummy Authör[0m
    [22m[35m    <Email>3kplusone@dev.null</Email>[0m
    [22m[35m  </Author>[0m
    [22m[35m[0m
    [22m[35m  <Copyright>&copyright; 2000 The Author. <P/>[0m
    [22m[35m    You can do with this package what you want.<P/> Really.[0m
    [22m[35m  </Copyright>[0m
    [22m[35m</TitlePage>[0m
    [22m[35m[0m
    [22m[35m<TableOfContents/>[0m
    [22m[35m[0m
    [22m[35m<Body>[0m
    [22m[35m  <Chapter> <Heading>The <M>3k+1</M> Problem</Heading>[0m
    [22m[35m    <Section Label="sec:theory"> <Heading>Theory</Heading>[0m
    [22m[35m      Let <M>k \in \N</M> be a natural number. We consider the sequence[0m
    [22m[35m      <M>n(i,  k), i  \in  \N,</M> with  <M>n(1, k)  =  k</M> and  else[0m
    [22m[35m      <M>n(i+1, k)  = n(i, k)  / 2</M> if  <M>n(i, k)</M> is  even and[0m
    [22m[35m      <M>n(i+1, k) = 3 n(i, k) + 1</M> if <M>n(i, k)</M> is odd.[0m
    [22m[35m      <P/>[0m
    [22m[35m      It is  not known whether for  any natural number <M>k  \in \N</M> [0m
    [22m[35m      there is an <M>m \in \N</M> with <M>n(m, k) = 1</M>.              [0m
    [22m[35m      <P/>[0m
    [22m[35m      <Package>ThreeKPlusOne</Package>  provides   the  function  <Ref[0m
    [22m[35m      Func="ThreeKPlusOneSequence"/>   to  explore   this  for   given[0m
    [22m[35m      <M>n</M>.  If  you really  want  to  know something  about  this[0m
    [22m[35m      problem, see <Cite Key="Wi98"/> or[0m
    [22m[35m      <URL>http://mathsrv.ku-eichstaett.de/MGF/homes/wirsching/</URL>[0m
    [22m[35m      for more details (and forget this package).[0m
    [22m[35m    </Section>[0m
    [22m[35m[0m
    [22m[35m    <Section> <Heading>Program</Heading>[0m
    [22m[35m      In this section we describe the main function of this package.[0m
    [22m[35m      <ManSection> [0m
    [22m[35m        <Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/>[0m
    [22m[35m        <Description>[0m
    [22m[35m          This  function computes  for a  natural number  <A>k</A> the[0m
    [22m[35m          beginning of the sequence  <M>n(i, k)</M> defined in section[0m
    [22m[35m          <Ref Sect="sec:theory"/>.  The sequence  stops at  the first[0m
    [22m[35m          <M>1</M>  or at  <M>n(<A>max</A>, k)</M>,  if <A>max</A>  is[0m
    [22m[35m          given.[0m
    [22m[35m<Example>[0m
    [22m[35mgap> ThreeKPlusOneSequence(101);[0m
    [22m[35m"Sorry, not yet implemented. Wait for Version 84 of the package"[0m
    [22m[35m</Example>[0m
    [22m[35m        </Description>[0m
    [22m[35m      </ManSection>[0m
    [22m[35m    </Section>[0m
    [22m[35m  </Chapter>[0m
    [22m[35m</Body>[0m
    [22m[35m[0m
    [22m[35m<Bibliography Databases="3k+1" />[0m
    [22m[35m<TheIndex/>[0m
    [22m[35m[0m
    [22m[35m</Book>[0m
  [22m[35m------------------------------------------------------------------[0m
  
