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AtlasRep — A GAP 4 Package

(Version 2.1.8)

Robert A. Wilson
Email: R.A.Wilson@qmul.ac.uk
Homepage: http://www.maths.qmw.ac.uk/~raw

Richard A. Parker
Email: richpark@gmx.co.uk

Simon Nickerson
Homepage: http://nickerson.org.uk/groups

John N. Bray
Email: J.N.Bray@qmul.ac.uk
Homepage: http://www.maths.qmw.ac.uk/~jnb

Thomas Breuer
Email: sam@Math.RWTH-Aachen.De
Homepage: https://www.math.rwth-aachen.de/~Thomas.Breuer

Copyright

© 2002–2024

This package may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see http://www.gnu.org/licenses.

Contents

1 Introduction to the AtlasRep Package

1.1 The ATLAS of Group Representations

1.2 The GAP Interface to the ATLAS of Group Representations

1.3 What's New in AtlasRep, Compared to Older Versions?

  1.3-1 What's New in Version 2.1.8? (January 2024)
  1.3-2 What's New in Version 2.1.7? (August 2023)
  1.3-3 What's New in Version 2.1.6? (October 2022)
  1.3-4 What's New in Version 2.1.5? (August 2022)
  1.3-5 What's New in Version 2.1.4? (August 2022)
  1.3-6 What's New in Version 2.1.3? (August 2022)
  1.3-7 What's New in Version 2.1.2? (March 2022)
  1.3-8 What's New in Version 2.1.1? (February 2022)
  1.3-9 What's New in Version 2.1.0? (May 2019)
  1.3-10 What's New in Version 1.5.1? (March 2016)
  1.3-11 What's New in Version 1.5? (July 2011)
  1.3-12 What's New in Version 1.4? (June 2008)
  1.3-13 What's New in Version 1.3.1? (October 2007)
  1.3-14 What's New in Version 1.3? (June 2007)
  1.3-15 What's New in Version 1.2? (November 2003)
  1.3-16 What's New in Version 1.1? (October 2002)

1.4 Acknowledgements

2 Tutorial for the AtlasRep Package

2.1 Accessing a Specific Group in AtlasRep

2.1-1 Accessing a Group in AtlasRep via its Name
2.1-2 Accessing a Maximal Subgroup of a Group in AtlasRep

2.2 Accessing Specific Generators in AtlasRep

2.3 Basic Concepts used in AtlasRep

2.3-1 Groups, Generators, and Representations
2.3-2 Straight Line Programs

2.4 Examples of Using the AtlasRep Package

  2.4-1 Example: Class Representatives
  2.4-2 Example: Permutation and Matrix Representations
  2.4-3 Example: Outer Automorphisms
  2.4-4 Example: Using Semi-presentations and Black Box Programs
  2.4-5 Example: Using the GAP Library of Tables of Marks
  2.4-6 Example: Index \(770\) Subgroups in \(M_{22}\)
  2.4-7 Example: Index \(462\) Subgroups in \(M_{22}\)

3 The User Interface of the AtlasRep Package

3.1 Accessing vs. Constructing Representations

3.2 Group Names Used in the AtlasRep Package

3.3 Standard Generators Used in the AtlasRep Package

3.4 Class Names Used in the AtlasRep Package

  3.4-1 Definition of ATLAS Class Names
  3.4-2 AtlasClassNames
  3.4-3 AtlasCharacterNames

3.5 Accessing Data via AtlasRep

  3.5-1 DisplayAtlasInfo
  3.5-2 Examples for DisplayAtlasInfo
  3.5-3 AtlasGenerators
  3.5-4 AtlasProgram
  3.5-5 AtlasProgramInfo
  3.5-6 OneAtlasGeneratingSetInfo
  3.5-7 AllAtlasGeneratingSetInfos
  3.5-8 AtlasGroup
  3.5-9 AtlasSubgroup
  3.5-10 AtlasRepInfoRecord
  3.5-11 EvaluatePresentation
  3.5-12 StandardGeneratorsData

3.6 Browse Applications Provided by AtlasRep

3.6-1 BrowseMinimalDegrees
3.6-2 BrowseBibliographySporadicSimple

4 Customizations of the AtlasRep Package

4.1 Installing the AtlasRep Package

4.2 User Preferences of the AtlasRep Package

  4.2-1 User preference AtlasRepAccessRemoteFiles
  4.2-2 User preference AtlasRepDataDirectory
  4.2-3 User preference AtlasRepTOCData
  4.2-4 User preference CompressDownloadedMeatAxeFiles
  4.2-5 User preference FileAccessFunctions
  4.2-6 User preference AtlasRepLocalServerPath
  4.2-7 User preference HowToReadMeatAxeTextFiles
  4.2-8 User preference WriteHeaderFormatOfMeatAxeFiles
  4.2-9 User preference WriteMeatAxeFilesOfMode2
  4.2-10 User preference BaseOfMeatAxePermutation
  4.2-11 User preference DisplayFunction
  4.2-12 User preference AtlasRepMarkNonCoreData
  4.2-13 User preference DebugFileLoading
  4.2-14 User preference AtlasRepJsonFilesAddresses

4.3 Web Contents for the AtlasRep Package

4.4 Extending the ATLAS Database

5 Extensions of the AtlasRep Package

5.1 Notify Additional Data

  5.1-1 AtlasOfGroupRepresentationsNotifyData
  5.1-2 AtlasOfGroupRepresentationsForgetData
  5.1-3 StringOfAtlasTableOfContents

5.2 The Effect of Extensions on the User Interface

5.3 An Example of Extending the AtlasRep Data

6 New GAP Objects and Utility Functions provided by the AtlasRep Package

6.1 Straight Line Decisions

  6.1-1 IsStraightLineDecision
  6.1-2 LinesOfStraightLineDecision
  6.1-3 NrInputsOfStraightLineDecision
  6.1-4 ScanStraightLineDecision
  6.1-5 StraightLineDecision
  6.1-6 ResultOfStraightLineDecision
  6.1-7 Semi-Presentations and Presentations
  6.1-8 AsStraightLineDecision
  6.1-9 StraightLineProgramFromStraightLineDecision

6.2 Black Box Programs

  6.2-1 IsBBoxProgram
  6.2-2 ScanBBoxProgram
  6.2-3 RunBBoxProgram
  6.2-4 ResultOfBBoxProgram
  6.2-5 AsBBoxProgram
  6.2-6 AsStraightLineProgram

6.3 Representations of Minimal Degree

  6.3-1 MinimalRepresentationInfo
  6.3-2 MinimalRepresentationInfoData
  6.3-3 SetMinimalRepresentationInfo
  6.3-4 Criteria Used to Compute Minimality Information

6.4 A JSON Interface

  6.4-1 Why JSON?
  6.4-2 AGR.JsonText
  6.4-3 AGR.GapObjectOfJsonText

7 Technicalities of the AtlasRep Package

7.1 Global Variables Used by the AtlasRep Package

  7.1-1 InfoAtlasRep
  7.1-2 InfoCMeatAxe
  7.1-3 InfoBBox
  7.1-4 AGR
  7.1-5 AtlasOfGroupRepresentationsInfo

7.2 How to Customize the Access to Data files

7.3 Reading and Writing MeatAxe Format Files

  7.3-1 ScanMeatAxeFile
  7.3-2 MeatAxeString
  7.3-3 FFList
  7.3-4 CMtxBinaryFFMatOrPerm
  7.3-5 FFMatOrPermCMtxBinary

7.4 Reading and Writing ATLAS Straight Line Programs

7.4-1 ScanStraightLineProgram
7.4-2 AtlasStringOfProgram

7.5 Data Types Used in the AtlasRep Package

7.5-1 AGR.DeclareDataType

7.6 Filenames Used in the AtlasRep Package

7.6-1 AGR.ParseFilenameFormat
7.6-2 AGR.FileContents

7.7 The record component identifier used by the AtlasRep Package

7.7-1 AtlasRepIdentifier

7.8 The Tables of Contents of the AtlasRep Package

7.9 Sanity Checks for the AtlasRep Package

7.9-1 Sanity Checks for a Table of Contents
7.9-2 Other Sanity Checks

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