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numericalsgps-- a package for numerical semigroups

Version 1.3.1

Manuel Delgado

Pedro A. García-Sánchez

José João Morais


© 2005--2015 Centro de Matemática da Universidade do Porto, Portugal and Universidad de Granada, Spain

Numericalsgps is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the file 'GPL' included in the package or see the FSF's own site.


The authors wish to thank the contributors of the package. A full list with the help received is available in Appendix C. We are also in debt with H. Schönemann, C. Söeger and M. Barakat for their fruitful advices concerning SingularInterface, Singular, Normaliz, NormalizInterface and GradedModules.

The maintainers want to thank the organizers of GAPDays in their several editions.

The authors also thank the Centro de Servicios de Informática y Redes de Comunicaciones (CSIRC), Universidad de Granada, for providing the computing time, specially Rafael Arco Arredondo for installing this package and the extra software needed in, and Santiago Melchor Ferrer for helping in job submission to the cluster.

The first and second authors warmly thank María Burgos for her support and help.


The first author's work was (partially) supported by the Centro de Matemática da Universidade do Porto (CMUP), financed by FCT (Portugal) through the programs 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 projects MTM2004-01446 and MTM2007-62346, the Junta de Andalucía group FQM-343, 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 first author was (partially) supported by the FCT project PTDC/MAT/65481/2006 and also by the Centro de Matemática da Universidade do Porto (CMUP), funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2011.

Both maintainers were (partially) supported by the projects MTM2010-15595 and MTM2014-55367-P, which were funded by Ministerio de Economía y Competitividad and the Fondo Europeo de Desarrollo Regional FEDER.

Both maintainers want to acknowledge partial support by CMUP (UID/MAT/00144/2013 and UID/MAT/00144/2019), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.

Both maintainers were also partially supported by the project MTM2017-84890-P, which is funded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER.

The first author acknowledges a sabbatical grant from the FCT: SFRH/BSAB/142918/2018.

The second author was supported in part by Grant PGC2018-096446-B-C21 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe".

Both maintainers were partially supported by CMUP, member of LASI, which is financed by Portuguese national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020.


This work started when (in 2004) the first author visited the University of Granada in part of a sabbatical year. Since Version 0.96 (released in 2008), the package is maintained by the first two authors. Bug reports, suggestions and comments are, of course, welcome. Please use our email addresses to this effect.

If you have benefited from the use of the numerigalsgps GAP package in your research, please cite it in addition to GAP itself, following the scheme proposed in

If you have predominantly used the functions in the Appendix, contributed by other authors, please cite in addition these authors, referring "software implementations available in the GAP package NumericalSgps".


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 Nonunique invariants for factorizations in numerical semigroups
10 Polynomials and numerical semigroups
11 Affine semigroups
12 Good semigroups
13 External packages
14 Dot functions
A Generalities
B "Random" functions
C Contributions

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