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Numerical Semigroups

( Version 0.96 )

Manuel Delgado
Email: mdelgado@fc.up.pt
Homepage: http://www.fc.up.pt/cmup/mdelgado

Pedro A. García-Sánchez
Email: pedro@ugr.es
Homepage: http://www.ugr.es/~pedro

José João Morais
Email: josejoao@fc.up.pt

Copyright

© 2005 by Manuel Delgado, Pedro A. García-Sánchez and José João Morais

We adopt the copyright regulations of GAP as detailed in the copyright notice in the GAP manual.

Acknowledgements

The first author's work was (partially) supported by the Centro de Matemática da Universidade do Porto (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.

The second author was supported by the project MTM2004-01446 and FEDER founds.

The third author acknowledges financial support of FCT and the POCTI program through a scholarship given by Centro de Matemática da Universidade do Porto.

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.

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.

Contents

1 Introduction
2 Numerical Semigroups
3 Basic operations with numerical semigroups
4 Presentations of Numerical Semigroups
5 Constructing numerical semigroups from others
6 Irreducible numerical semigroups
7 Ideals of numerical semigroups
8 Numerical semigroups with maximal embedding dimension
9 Catenary and Tame degrees of numerical semigroups
A Generalities
B Random functions
C A graphical interface

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