<?xml version="1.0" encoding="ISO-8859-1"?>
<!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> ©right; 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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