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A The File 3k+1.xml

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">

  <Title>The <Package>ThreeKPlusOne</Package> Package</Title>
  <Version>Version 42</Version>
  <Author>Dummy Authör

  <Copyright>&copyright; 2000 The Author. <P/>
    You can do with this package what you want.<P/> Really.


  <Chapter> <Heading>The <M>3k+1</M> Problem</Heading>
    <Section Label="sec:theory"> <Heading>Theory</Heading>
      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>.
      <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
      for more details (and forget this package).

    <Section> <Heading>Program</Heading>
      In this section we describe the main function of this package.
        <Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/>
          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
gap> ThreeKPlusOneSequence(101);
"Sorry, not yet implemented. Wait for Version 84 of the package"

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


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