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# ResClasses

## Set-Theoretic Computations with Residue Classes

Version 2.3.5

September 29, 2006

Stefan Kohl
e-mail: kohl@mathematik.uni-stuttgart.de
WWW: http://www.cip.mathematik.uni-stuttgart.de/~kohlsn
Address:
Institut für Geometrie und Topologie
Pfaffenwaldring 57
Universität Stuttgart
70550 Stuttgart
Germany

### Abstract

ResClasses is a package for GAP 4, which provides a fully-featured and easy-to-use implementation of residue classes of Z and a few other rings as sets. The package further provides slightly more specialized functionality for unions of residue classes with distinguished representatives and signed moduli. The ResClasses package is used in a group theoretical context by the RCWA package [K05].

### Copyright

(C) 2003 - 2006 by Stefan Kohl

This package is distributed under the GNU General Public License.

### Contents

1. Unions of Residue Classes
1.1 Entering residue classes and unions thereof
1.1-1 ResidueClass
1.1-2 ResidueClassUnion
1.1-3 AllResidueClassesModulo
1.2 Methods for unions of residue classes
1.2-1 SplittedClass
1.2-2 AsUnionOfFewClasses
1.2-3 Density
1.2-4 RandomPartitionIntoResidueClasses
1.3 The categories and families of unions of residue classes
1.3-1 IsUnionOfResidueClasses
1.3-2 ResidueClassUnionsFamily
2. Unions of Residue Classes with Fixed Representatives
2.1 Entering unions of residue classes with fixed representatives
2.1-1 ResidueClassWithFixedRep
2.1-2 ResidueClassUnionWithFixedReps
2.1-3 AllResidueClassesWithFixedRepsModulo
2.2 Methods for unions of residue classes with fixed representatives
2.2-1 Multiplicity
2.2-2 Union
2.2-3 Intersection
2.2-4 Difference
2.3 The invariant Delta
2.3-1 Delta
2.3-2 RepresentativeStabilizingRefinement
2.4 The categories of unions of residue classes with fixed rep's
3. Semilocalizations of the Integers
3.1 Entering semilocalizations of the integers
3.1-1 Z_pi
3.2 Methods for semilocalizations of the integers
4. Installation and auxiliary functions
4.1 Requirements
4.2 Installation
4.3 The testing routine
4.3-1 ResClassesTest
4.4 Building the manual
4.4-1 ResClassesBuildManual

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