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<!DOCTYPE Book SYSTEM "gapdoc.dtd">

<Book Name="NumericalSgps">

<TitlePage>
  <Title>Numerical Semigroups</Title>
  <Version>( Version <#Include SYSTEM "../version"> )
  </Version>
  <Author> Manuel Delgado
    <Email>mdelgado@fc.up.pt</Email>
    <Homepage>http://www.fc.up.pt/cmup/mdelgado</Homepage>
  </Author>
  <Author> Pedro A. García-Sánchez
    <Email>pedro@ugr.es</Email>
    <Homepage>http://www.ugr.es/~pedro</Homepage>
  </Author>
  <Author> José João Morais
    <Email>josejoao@fc.up.pt</Email>
  </Author>
  <Copyright> &copyright; 2005 by Manuel Delgado, Pedro A. García-Sánchez and José João Morais<P/>
              We adopt the copyright regulations of &GAP; as detailed in the
              copyright notice in the &GAP; manual. </Copyright>


<Acknowledgements>

The first author's work was (partially) supported by the <E>Centro de Matemática da Universidade do
Porto</E> (CMUP), financed by FCT (Portugal) through the programmes POCTI
(Programa Operacional "Ciência, Tecnologia, Inovação") and POSI (Programa
Operacional Sociedade da Informação), with national and European Community
structural funds and a sabbatical grant of FCT.
<P/>
The second author was supported by the project MTM2004-01446
and FEDER founds.
<P/>
The third author acknowledges financial support of FCT and the POCTI program
through a scholarship given by <E>Centro de Matemática da Universidade do Porto</E>.
<P/>
The authors whish to thank J. I. García-García for many helpfull discussions
and for helping in the programming of preliminary versions of some functions.

</Acknowledgements>

<Colophon>
This work started when the first author visited the University of Granada in part of a sabbatical year.

Bug reports, suggestions and comments are, of course, welcome. Please use our
email addresses to this effect.

</Colophon>


</TitlePage>

<TableOfContents/>

<Body>

<#Include SYSTEM "introduction.xml">

<Chapter>
            <Heading>
                Numerical Semigroups
            </Heading>
            This chapter describes how to create numerical semigroups in &GAP;
            and perform some basic tests.

<#Include SYSTEM "Generating_Numerical_Semigroups.xml">
<#Include SYSTEM "Some_basic_tests.xml">

</Chapter>


        <Chapter>
            <Heading>
                Basic operations with numerical semigroups
            </Heading>

<#Include SYSTEM "The_definitions.xml">
<#Include SYSTEM "Frobenius_Number.xml">
<#Include SYSTEM "Gaps.xml">

</Chapter>


        <Chapter>
            <Heading>
                Presentations of Numerical Semigroups
            </Heading>
            In this chapter we explain how to compute a minimal presentation of a numerical
            semigroup. There are three functions involved in this process.

<#Include SYSTEM "Presentations_of_Numerical_Semigroups.xml">

</Chapter>


        <Chapter>
            <Heading>
                Constructing numerical semigroups from others
            </Heading>

<#Include SYSTEM "Adding_and_removing_elements_of_a_numerical_semigroup.xml">
<#Include SYSTEM "Constructing_sets_of_numerical_semigroups.xml">

</Chapter>


        <Chapter>
            <Heading>
                Irreducible numerical semigroups
            </Heading>

<#Include SYSTEM "Irreducible_numerical_semigroups.xml">

</Chapter>


        <Chapter>
            <Heading>
                Ideals of numerical semigroups
            </Heading>

<#Include SYSTEM "Ideals_of_numerical_semigroups.xml">

</Chapter>


        <Chapter>
            <Heading>
                Numerical semigroups with maximal embedding dimension
            </Heading>

<#Include SYSTEM "Numerical_semigroups_with_maximal_embedding_dimension.xml">
<#Include SYSTEM "Numerical_semigroups_with_the_Arf_property_and_Arf_closures.xml">

</Chapter>


<Chapter>
	<Heading>
		Catenary and Tame degrees of numerical semigroups
	</Heading>

	<#Include SYSTEM "catenary-tame.xml">

</Chapter>


</Body>

<#Include SYSTEM "generalstuff.xml">

<#Include SYSTEM "random.xml">

<#Include SYSTEM "xnumericalsemigroup.xml">


<Bibliography Databases="NumericalSgpsMan" />

<TheIndex/>

</Book>

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