Set-Theoretic Computations with Residue Classes

Stefan Kohl


ResClasses is a little GAP 4 package for computing with set-theoretic unions of residue classes of the ring of integers.

The class of sets which ResClasses can deal with includes the open and the closed sets in the topology on the integers which is induced by taking the set of all residue classes as a basis, as far as the usual restrictions imposed by the finiteness of computing resources permit this.

Similar functionality as for the ring of integers is provided for its (semi-)localizations at one or several prime ideals as well as for polynomial rings in one variable over a finite field. Special methods are available for unions of residue classes with distinguished (`fixed') representatives.

The functionality of this package is used in a group theoretical context by the RCWA package.


The ResClasses manual is available in the following formats:

Requirements and Installation

ResClasses can be used on any platform for which GAP is available. It requires only a recent GAP installation. For details see the README file. The installation requires only extracting the archive file in the pkg/ subdirectory of the GAP root directory. To load the package, enter LoadPackage("resclasses"); at the GAP prompt.


Download the recent version of this package from here. To install an older version, download one of the following archives:

The .tar.gz files are for all operating systems except for Windows, while the file is the Windows version. ResClasses is redistributed on the GAP website here. Note that the redistribution may take a while to pick up the recent version.

If you have problems with this package, if you wish to make comments or suggestions or if you find bugs, then please send me an e-mail. Also please let me know if you use ResClasses in some of your work.