  
  
                                   [1m[4m[31mResClasses[0m
  
  
        [1m[4m[31mComputations with Residue Classes and their Set-Theoretic Unions[0m
  
  
                               ( Version 1.1.1 )
  
  
                                February 3, 2004
  
  
                                  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 and provides
  basic  functionality  for  computing  with  these sets (intersection, union,
  difference  etc., any of these also when one of the operands is a finite set
  of  elements).  It  also  implements the above-mentioned rings Z_(pi) as [1mGAP[0m
  domains.
  
  
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  [1m[4m[31mCopyright[0m
  (C) 2003 by Stefan Kohl
  
  We  adopt  the  copyright  regulations  of  [1mGAP[0m as detailed in the copyright
  notice in the [1mGAP[0m manual.
  
  
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  [1m[4m[31mContent (ResClasses)[0m
  
  1. Preface
  2. Semilocalizations of the Integers
    2.1 Defining 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
      2.2-1 \in
      2.2-2 Intersection
      2.2-3 IsSubset
      2.2-4 StandardAssociate
      2.2-5 GcdOp
      2.2-6 LcmOp
      2.2-7 Factors
      2.2-8 IsUnit
  3. Unions of Residue Classes
    3.1 Defining unions of residue classes
      3.1-1 ResidueClass
      3.1-2 ResidueClassUnion
      3.1-3 Modulus
      3.1-4 Residues
      3.1-5 IncludedElements
      3.1-6 ExcludedElements
    3.2 Methods for unions of residue classes
      3.2-1 String
      3.2-2 Print
      3.2-3 Display
      3.2-4 \in
      3.2-5 IsSubset
      3.2-6 Density
      3.2-7 Union
      3.2-8 Intersection
      3.2-9 Difference
      3.2-10 Iterator
      3.2-11 NextIterator
      3.2-12 \+
      3.2-13 \-
      3.2-14 \*
      3.2-15 \/
    3.3 The categories and families of unions of residue classes
      3.3-1 IsUnionOfResidueClasses
      3.3-2 IsUnionOfResidueClassesOfZ
      3.3-3 IsUnionOfResidueClassesOfZ_pi
      3.3-4 IsUnionOfResidueClassesOfZorZ_pi
      3.3-5 IsUnionOfResidueClassesOfGFqx
      3.3-6 ResidueClassUnionsFamily
  4. Installation and auxiliary functions
    4.1 Installation
    4.2 Building the manual
      4.2-1 ResClassesBuildManual
    4.3 The testing routine
      4.3-1 ResClassesTest
    4.4 Changing the viewing format for residue class unions
      4.4-1 ResidueClassUnionViewingFormat
  
  
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