  
  
                                    [1X utils [101X
  
  
                           [1X Utility functions in [5XGAP[105X [101X
  
  
                                      0.96
  
  
                                  6 June 2026
  
  
                                 Thomas Breuer
  
                               Sebastian Gutsche
  
                                    Max Horn
  
                                Alexander Hulpke
  
                              Pedro García-Sánchez
  
                             Christopher Jefferson
  
                                  Stefan Kohl
  
                                  Frank Lübeck
  
                                 Chris Wensley
  
  
  
  Thomas Breuer
      Email:    [7Xmailto:sam@math.rwth-aachen.de[107X
      Homepage: [7Xhttps://www.math.rwth-aachen.de/~Thomas.Breuer[107X
  Sebastian Gutsche
      Email:    [7Xmailto:gutsche@mathematik.uni-siegen.de[107X
      Homepage: [7Xhttps://sebasguts.github.io/[107X
  Max Horn
      Email:    [7Xmailto:mhorn@rptu.de[107X
      Homepage: [7Xhttps://github.com/mhorn[107X
  Alexander Hulpke
      Email:    [7Xmailto:hulpke@math.colostate.edu[107X
      Homepage: [7Xhttps://www.math.colostate.edu/~hulpke[107X
  Pedro García-Sánchez
      Email:    [7Xmailto:pedro@ugr.es[107X
      Homepage: [7Xhttp://www.ugr.es/local/pedro[107X
  Christopher Jefferson
      Email:    [7Xmailto:caj21@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://caj.host.cs.st-andrews.ac.uk/[107X
  Stefan Kohl
      Email:    [7Xmailto:stefan@mcs.st-and.ac.uk[107X
      Homepage: [7Xhttps://www.gap-system.org/DevelopersPages/StefanKohl/[107X
  Frank Lübeck
      Email:    [7Xmailto:Frank.Luebeck@Math.RWTH-Aachen.De[107X
      Homepage: [7Xhttps://www.math.rwth-aachen.de/~Frank.Luebeck[107X
  Chris Wensley
      Email:    [7Xmailto:cdwensley.maths@btinternet.com[107X
      Homepage: [7Xhttps://github.com/cdwensley[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe [5XUtils[105X package provides a space for utility functions in a variety of [5XGAP[105X
  packages  to  be collected together into a single package. In this way it is
  hoped that they will become more visible to package authors.[133X
  
  [33X[0;0YAny  package  author who transfers a function to [5XUtils[105X will become an author
  of [5XUtils[105X.[133X
  
  [33X[0;0YIf  deemed  appropriate,  functions  may  also  be transferred from the main
  library.[133X
  
  [33X[0;0YBug  reports,  suggestions  and  comments  are,  of  course, welcome. Please
  contact  the  last author at [7Xmailto:cdwensley.maths@btinternet.com[107X or submit
  an          issue          at          the         GitHub         repository
  [7Xhttps://github.com/gap-packages/utils/issues/[107X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2015-2026, The GAP Group.[133X
  
  [33X[0;0YThe [5XUtils[105X package is free software; you can redistribute it and/or modify it
  under  the  terms of the GNU General Public License as published by the Free
  Software  Foundation;  either  version 2 of the License, or (at your option)
  any later version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis  documentation  was prepared using the [5XGAPDoc[105X [LN17] and [5XAutoDoc[105X [GH16]
  packages.[133X
  
  [33X[0;0YThe   procedure   used   to   produce   new   releases   uses   the  package
  [5XGitHubPagesForGAP[105X [Hor17] and the package [5XReleaseTools[105X.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Utils)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YInformation for package authors[133X
  2 [33X[0;0YPrinting Lists and Iterators[133X
    2.1 [33X[0;0YPrinting selected items[133X
      2.1-1 PrintSelection
  3 [33X[0;0YLists, Sets and Strings[133X
    3.1 [33X[0;0YFunctions for lists[133X
      3.1-1 DifferencesList
      3.1-2 QuotientsList
      3.1-3 SearchCycle
      3.1-4 RandomCombination
    3.2 [33X[0;0YDistinct and Common Representatives[133X
      3.2-1 DistinctRepresentatives
    3.3 [33X[0;0YFunctions for strings[133X
      3.3-1 BlankFreeString
  4 [33X[0;0YNumber-theoretic functions[133X
    4.1 [33X[0;0YFunctions for integers[133X
      4.1-1 AllSmoothIntegers
      4.1-2 AllProducts
      4.1-3 RestrictedPartitionsWithoutRepetitions
      4.1-4 NextProbablyPrimeInt
      4.1-5 PrimeNumbersIterator
  5 [33X[0;0YGroups and homomorphisms[133X
    5.1 [33X[0;0YFunctions for groups[133X
      5.1-1 Comm
      5.1-2 IsCommuting
      5.1-3 ListOfPowers
      5.1-4 GeneratorsAndInverses
      5.1-5 UpperFittingSeries
    5.2 [33X[0;0YLeft Cosets for Groups[133X
      5.2-1 LeftCoset
      5.2-2 [33X[0;0YInverse[133X
    5.3 [33X[0;0YFunctions for group homomorphisms[133X
      5.3-1 EpimorphismByGenerators
      5.3-2 Pullback
      5.3-3 CentralProduct
      5.3-4 IdempotentEndomorphisms
      5.3-5 DirectProductOfFunctions
      5.3-6 DirectProductOfAutomorphismGroups
  6 [33X[0;0YMatrices[133X
    6.1 [33X[0;0YSome operations for matrices[133X
      6.1-1 DirectSumDecompositionMatrices
  7 [33X[0;0YIterators[133X
    7.1 [33X[0;0YSome iterators for groups and their isomorphisms[133X
      7.1-1 AllIsomorphismsIterator
      7.1-2 AllSubgroupsIterator
    7.2 [33X[0;0YOperations on iterators[133X
      7.2-1 CartesianIterator
      7.2-2 UnorderedPairsIterator
  8 [33X[0;0YRecords[133X
    8.1 [33X[0;0YFunctions for records[133X
      8.1-1 AssignGlobals
    8.2 [33X[0;0YOption records for functions[133X
      8.2-1 OptionRecordWithDefaults
  9 [33X[0;0YWeb Downloads[133X
    9.1 [33X[0;0YFunctions for downloading files from the web[133X
      9.1-1 Download
      9.1-2 [33X[0;0YUser preference [10XDownloadVerifyCertificate[110X[133X
      9.1-3 [33X[0;0YUser preference [10XDownloadMaxTime[110X[133X
  10 [33X[0;0YGeneralized Straight Line Programs[133X
    10.1 [33X[0;0YFunctions for Generalized Straight Line Programs[133X
      10.1-1 IsGeneralizedStraightLineProgram
      10.1-2 [33X[0;0YGeneralizedStraightLineProgram[133X
      10.1-3 DataOfGeneralizedStraightLineProgram
      10.1-4 NrInputsOfGeneralizedStraightLineProgram
      10.1-5 NrOutputsOfGeneralizedStraightLineProgram
      10.1-6 ResultOfGeneralizedStraightLineProgram
      10.1-7 EquivalentStraightLineProgram
      10.1-8 IsInternallyConsistent
  11 [33X[0;0YVarious other functions[133X
    11.1 [33X[0;0YFile operations[133X
      11.1-1 Log2HTML
    11.2 [33X[0;0YLaTeX strings[133X
      11.2-1 IntOrInfinityToLaTeX
      11.2-2 LaTeXStringFactorsInt
    11.3 [33X[0;0YConversion to [22XMagma[122X strings[133X
      11.3-1 ConvertToMagmaInputString
  12 [33X[0;0YObsolete functions[133X
    12.1 [33X[0;0YOperations from AutoDoc[133X
    12.2 [33X[0;0YFunctions for printing[133X
    12.3 [33X[0;0YOther obsolete functions[133X
      12.3-1 [33X[0;0YApplicable Methods[133X
      12.3-2 [33X[0;0YExponentOfPrime[133X
  13 [33X[0;0YThe transfer procedure[133X
  
  
  [32X
