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A GAP package to deal with numerical semigroups and affine semigroups
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NumericalSgps is a GAP package for computing with Numerical Semigroups.


The features of the package NumericalSgps include

  • defining numerical semigroups;
  • computing several properties of numerical semigroups, namely: multiplicity, Frobenius number, (minimal) system of generators, Apéry set, gaps, fundamental gaps, etc.;
  • perform several operations on numerical semigroups and ideals, namely: intersection, quotient by an integer, decompose into irreducible semigroups, add a special gap, ...; -computing and testing membership to relevant families of numerical semigroups.

There is a manual in the sub-directory doc written using the GAP package gapdoc which describes the available functions in detail. The pdf, html versions of the manual are also available there.

If you have used this package, please let us know by sending us an email. If you have found important features missing or if there is a bug, we would appreciate it very much if you send us an email.

The current maintainers of the package are:

Manuel Delgado

Pedro A. García-Sánchez

For the full list of contributors (and contributions), please refer to to the contributions appendix in the manual.


This package consists only of GAP code, so for its installation please refer to the GAP manual.

Acknowledgements and funding

Please refer to the acknowledgements section in the manual.

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