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  3. numericalsgps



The GAP 4 package `NumericalSgps' to compute with Numerical Semigroups


This is release 1.0 of the package NumericalSgps.

The features of this package 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 dvi, 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 mdelgado@fc.up.pt

Pedro A. García-Sánchez pedro@ugr.es


With this version you should have obtained the following files and directories:

File/directory Description
README this file
EXAMPLES some examples
CHANGES changelog
doc the manual
gap the GAP code
init.g the file that initializes this package
read.g the file that reads in the package
PackageInfo.g information file for automatic processing
version the version number


The package is distributed with the main GAP archive. In order to use it you just have to start GAP and type

  LoadPackage( "numericalsgps" );

For updates between releases of GAP itself check the package web page



You may get NumericalSgps as a compressed tar archive (file name ends with .tar.gz). Use the appropriate command on your system to unpack the archive.

On UNIX systems the compressed tar archive may be unpacked by

tar xzf numericalsgps-<version>.tar.gz

or, if tar on your system does not understand the option z, by

gunzip numericalsgps-<version>.tar.gz
tar xf numericalsgps-<version>.tar

which will in each case unpack the code into a directory 'numericalsgps' in the current directory. We assume that the current directory is the directory /usr/local/lib/gap4r7/pkg/.


Copy the folder 'numericalsgp' to your pkg gap folder (for instance /usr/local/lib/gap4r7/pkg). You can also place it somewhere else and then use the command SetPackagePath:


or add this line to your gaprc.

In order to check the installation, launch gap:


Then try the following

gap> LoadPackage( "numericalsgps" );

Good luck!

You can also add the line

LoadPackage( "numericalsgps" );

to your gaprc file.

In other systems, there are equivalent ways to do the same.