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>[email protected]</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 &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> <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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