GAP (GAPDoc) - Appendix A: The File 3k+1.xml

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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">

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

      <Copyright>&copyright; 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  &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 Text="this homepage">https://www.ku.de/mgf/mathematik/statistik/personen-des-lehrstuhls/prof-dr-guenther-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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