  
  
                                   [1m[4m[31mResClasses[0m
  
  
        [1m[4m[31mComputations with Residue Classes and their Set-Theoretic Unions[0m
  
  
                               ( Version 2.1.2 )
  
  
                                January 12, 2006
  
  
                                  Stefan Kohl
  
  
  
  Stefan Kohl
      Email:    [34mmailto:kohl@mathematik.uni-stuttgart.de[0m
      Homepage: [34mhttp://www.cip.mathematik.uni-stuttgart.de/~kohlsn[0m
      Address:  Institut für Geometrie und Topologie
                Universität Stuttgart
                70550 Stuttgart
                Germany
  
  
  
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  [1m[4m[31mAbstract[0m
  This  package  for  [1mGAP[0m  4  (at  least version 4.4) implements set-theoretic
  unions   of  residue  classes  of  the  ring  Z  of  the  integers,  of  its
  semilocalisations  Z_(pi)  at  some  finite  set  of  primes  pi  and of the
  polynomial rings GF(q)[x] for some prime power q as [1mGAP[0m domains.
  
  It  provides basic functionality for computing with these sets, like forming
  intersections,  unions and differences. Any of this is also supported in the
  case  that one of the operands is a finite set of elements. The package also
  implements the mentioned rings Z_(pi) as [1mGAP[0m domains.
  
  
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  [1m[4m[31mCopyright[0m
  (C) 2003 - 2006 by Stefan Kohl
  
  This package is distributed under the same conditions as the [1mGAP[0m system.
  
  
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  [1m[4m[31mContent (ResClasses)[0m
  
  1. Preface
  2. Semilocalizations of the Integers
    2.1 Entering semilocalizations of the integers
      2.1-1 Z_pi
      2.1-2 IsZ_pi
      2.1-3 NoninvertiblePrimes
    2.2 Methods for semilocalizations of the integers
  3. Unions of Residue Classes
    3.1 Entering residue classes and unions thereof
      3.1-1 ResidueClass
      3.1-2 IsResidueClass
      3.1-3 ResidueClassUnion
      3.1-4 AllResidueClassesModulo
      3.1-5 AllResidues
    3.2 Methods for unions of residue classes
      3.2-1 Union
      3.2-2 Intersection
      3.2-3 Difference
      3.2-4 SplittedClass
      3.2-5 AsUnionOfFewClasses
      3.2-6 \+
      3.2-7 \-
      3.2-8 \*
      3.2-9 \/
      3.2-10 Density
    3.3 The categories and families of unions of residue classes
      3.3-1 IsUnionOfResidueClasses
      3.3-2 ResidueClassUnionsFamily
  4. Unions of Residue Classes with Fixed Representatives
    4.1 About unions of residue classes with fixed representatives
    4.2 Entering unions of residue classes with fixed representatives
      4.2-1 ResidueClassWithFixedRepresentative
      4.2-2 ResidueClassUnionWithFixedRepresentatives
      4.2-3 AllResidueClassesWithFixedRepresentativesModulo
    4.3 Methods for unions of residue classes with fixed representatives
      4.3-1 Multiplicity
      4.3-2 IsOverlappingFree
      4.3-3 AsOrdinaryUnionOfResidueClasses
      4.3-4 \in
      4.3-5 AsListOfClasses
      4.3-6 IsSubset
      4.3-7 Density
      4.3-8 Union
      4.3-9 Intersection
      4.3-10 Difference
      4.3-11 \+
      4.3-12 \-
      4.3-13 \*
      4.3-14 \/
    4.4 The invariant Delta
      4.4-1 RepresentativeStabilizingRefinement
      4.4-2 Delta
      4.4-3 Rho
    4.5 The categories of unions of residue classes with fixed rep's
  5. Installation and auxiliary functions
    5.1 Installation
    5.2 Building the manual
      5.2-1 ResClassesBuildManual
    5.3 The testing routine
      5.3-1 ResClassesTest
    5.4 Changing the viewing format for residue class unions
      5.4-1 ResidueClassUnionViewingFormat
  
  
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