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AtlasRep — A GAP 4 Package

(Version 1.5.1)

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: http://www.math.rwth-aachen.de/~Thomas.Breuer

Copyright

© 2002–2016

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 1.5.1? (March 2016)
  1.3-2 What's New in Version 1.5? (July 2011)
  1.3-3 What's New in Version 1.4? (June 2008)
  1.3-4 What's New in Version 1.3.1? (October 2007)
  1.3-5 What's New in Version 1.3? (June 2007)
  1.3-6 What's New in Version 1.2? (November 2003)
  1.3-7 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

4 Customizations of the AtlasRep Package

4.1 Installing the AtlasRep Package

4.2 Maintaining the Local Data of the AtlasRep Package

  4.2-1 ReloadAtlasTableOfContents
  4.2-2 StoreAtlasTableOfContents
  4.2-3 ReplaceAtlasTableOfContents
  4.2-4 AtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates

4.3 User Parameters for the AtlasRep Package

  4.3-1 Local or Remote Access
  4.3-2 Adding and Removing Servers
  4.3-3 Accessing Data Files with the GAP Package IO or with wget
  4.3-4 Compressed or Uncompressed Data Files
  4.3-5 Customizing DisplayAtlasInfo
  4.3-6 Customizing the Access to Data Files
  4.3-7 Reading Large Matrices over Finite Fields
  4.3-8 AtlasOfGroupRepresentationsUserParameters
  4.3-9 User preference AtlasRepDataDirectory
  4.3-10 User preference WriteMeatAxeFilesOfMode2
  4.3-11 User preference BaseOfMeatAxePermutation

4.4 Web Services for the AtlasRep Package

4.5 Extending the ATLAS Database

5 Private Extensions of the AtlasRep Package

5.1 Adding a Private Data Directory

5.1-1 AtlasOfGroupRepresentationsNotifyPrivateDirectory
5.1-2 AtlasOfGroupRepresentationsForgetPrivateDirectory

5.2 The Effect of Private Extensions on the User Interface

5.3 An Example of Extending the AtlasRep Package

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

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 CMeatAxe.FastRead
  7.1-5 AGR
  7.1-6 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 ATLAS of Group Representations

7.5-1 AGR.DeclareDataType

7.6 Filenames Used in the ATLAS of Group Representations

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

7.7 The Tables of Contents of the ATLAS of Group Representations

7.8 Sanity Checks for the ATLAS of Group Representations

7.8-1 Sanity Checks for a Table of Contents
7.8-2 Other Sanity Checks

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