  
  
                                   [1X[5XResClasses[0X[0X
  
  
                [1XSet-Theoretic Computations with Residue Classes[0X
  
  
                                 Version 2.5.3
  
  
                               September 26, 2007
  
  
                                  Stefan Kohl
  
  
  
  Stefan Kohl
      Email:    [7Xmailto:kohl@mathematik.uni-stuttgart.de[0X
      Homepage: [7Xhttp://www.cip.mathematik.uni-stuttgart.de/~kohlsn/[0X
      Address:  Institut für Geometrie und Topologie
                Pfaffenwaldring 57
                Universität Stuttgart
                70550 Stuttgart
                Germany
  
  
  
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  [1XAbstract[0X
  [5XResClasses[0X  is  a  package  for  [5XGAP[0X  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 [5XResClasses[0X 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  [5XResClasses[0X  package  is used in a group theoretical context by the [5XRCWA[0X
  package [Koh07].
  
  
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  [1XCopyright[0X
  © 2003 - 2007 by Stefan Kohl
  
  This package is distributed under the GNU General Public License.
  
  
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  [1XContent (ResClasses)[0X
  
  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
    4.5 SendEmail and EmailLogFile
      4.5-1 SendEmail
      4.5-2 EmailLogFile
  
  
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