Goto Chapter: Top 1 2 3 4 Bib Ind
Top of Book Next Chapter

# ResClasses

## Set-Theoretic Computations with Residue Classes

Version 2.5.1

June 1, 2007

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 set-theoretic unions of residue classes of the integers and of a few other rings.

The class of sets which ResClasses can deal with includes the open and the closed sets in the topology on the respective ring 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.

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 [Koh07].

### Copyright

© 2003 - 2007 by Stefan Kohl

This package is distributed under the GNU General Public License.

### Contents

1. Set-Theoretic Unions of Residue Classes
1.1 Entering residue classes and set-theoretic unions thereof
1.1-1 ResidueClass
1.1-2 ResidueClassUnion
1.1-3 AllResidueClassesModulo
1.2 Methods for residue class unions
1.2-1 SplittedClass
1.2-2 AsUnionOfFewClasses
1.2-3 PartitionsIntoResidueClasses
1.2-4 RandomPartitionIntoResidueClasses
1.2-5 Density
1.3 The categories and families of residue class unions
1.3-1 IsResidueClassUnion
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 ResidueClassWithFixedRepresentative
2.1-2 UnionOfResidueClassesWithFixedReps
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
Top of Book Next Chapter
Goto Chapter: Top 1 2 3 4 Bib Ind

generated by GAPDoc2HTML