chap1.txt

  
  1 Introduction to the AtlasRep Package
  
  The  aim  of the GAP 4 package AtlasRep is to provide a link between GAP and
  the  ATLAS  of  Group  Representations  [ATLAS],  a  database that comprises
  generating  permutations  and  matrices  for  many almost simple groups, and
  information  about  their  maximal  subgroups.  This  database  is available
  independent of GAP at
  
  http://brauer.maths.qmul.ac.uk/Atlas
  
  The  AtlasRep  package consists of this database (see Section 1.1) and a GAP
  interface  (see  Section 1.2); the latter is extended by further information
  available via the internet (see Section 4.4).
  
  This package manual has the following parts.
  
  A tutorial
        gives  an  overview  how the functions of the package can be used, see
        Chapter 2.
  
  User interface functions
        are described in Chapter 3.
  
  Customizations of the package
        are described in Chapter 4.
  
  Information how to extend the database
        can be found in Chapter 5.
  
  More technical information
        can  be  found  in  the  chapters 6  (concerning  GAP objects that are
        introduced  by  the  package)  and 7  (concerning global variables and
        sanity checks).
  
  
  1.1 The ATLAS of Group Representations
  
  The  ATLAS of Group Representations consists of matrices over various rings,
  permutations,  and  shell scripts encoding so-called black box programs (see
  [Nic06]  and  Section 6.2). Many of these scripts are straight line programs
  (see [BSWW01],   [SWW00],   and 'Reference:  Straight  Line  Programs')  and
  straight  line  decisions  (see  Section 6.1). These programs can be used to
  compute  certain  elements  in  a  group  G  from  its  standard  generators
  (see [Wil96] and Section 3.3) for example generators of maximal subgroups of
  G or representatives of conjugacy classes of G.
  
  The ATLAS of Group Representations has been prepared by Robert Wilson, Peter
  Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker, Simon Norton, Simon
  Nickerson,   Steve   Linton,  John  Bray,  and  Rachel  Abbott  (in  reverse
  alphabetical order).
  
  The  information  was  computed  and composed using computer algebra systems
  such  as  MeatAxe  (see [Rin]),  Magma  (see [CP96]),  and  GAP  (in reverse
  alphabetical  order).  Part of the constructions have been documented in the
  literature  on  almost  simple groups, or the results have been used in such
  publications, see for example the references in [CCNPW85] and [BN95].
  
  If you use the ATLAS of Group Representations to solve a problem then please
  send  a  short  email to mailto:[email protected] about it. The ATLAS of
  Group  Representations  database should be referenced with the entry [ATLAS]
  in the bibliography of this manual.
  
  If  your  work  made use of functions of the GAP interface (see Section 1.2)
  then you should also reference this interface, as follows.
  
  
    @misc{ AtlasRep1.5.1,
      author =       {Wilson, R. A. and Parker, R. A. and Nickerson, S. and
                      Bray, J. N. and Breuer, T.},
      title =        {{AtlasRep}, A \textsf{GAP} Interface to the Atlas of
                      Group Representations,
                      {V}ersion 1.5.1},
      month =        {March},
      year =         {2016},
      note =         {\textsf{GAP} package},
      howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/atlasrep}
    }
  
  
  For  referencing  the  GAP  system  in  general,  use the entry [GAP] in the
  bibliography of this manual, see also
  
  http://www.gap-system.org.
  
  
  1.2 The GAP Interface to the ATLAS of Group Representations
  
  The  GAP  interface  to  the  ATLAS  of  Group  Representations  consists of
  essentially two parts.
  
      First,  there  is  the  user interface which allows the user to get an
        overview  of  the  contents of the database, and to access the data in
        GAP  format;  this  is  described in Chapter 3. Advanced users may add
        their own data to the database, this is described in Chapter 5.
  
      Second,  there  is administrational information, which covers also the
        declaration  of  GAP objects such as straight line decisions and black
        box  programs.  This  is  important mainly for users interested in the
        actual  implementation  (e. g., for modifying the package) or in using
        it  together  with  the  C-MeatAxe  standalone  (see [Rin]);  this  is
        described in Chapter 7.
  
  Information  concerning  the  C-MeatAxe,  including the manual [Rin], can be
  found at
  
  http://www.math.rwth-aachen.de/LDFM/homes/MTX
  
  The  interface  and  this manual have been provided by Thomas Breuer, except
  for  the  interpreter for black box programs (see Section 6.2), which is due
  to  Simon  Nickerson.  Comments,  bug  reports,  and hints for improving the
  interface can be sent to mailto:[email protected].
  
  
  1.3 What's New in AtlasRep, Compared to Older Versions?
  
  
  1.3-1 What's New in Version 1.5.1? (March 2016)
  
      The  paths  of  the directories where downloaded data files get stored
        are  now  customizable,  see  Section  4.3-9. Up to now, the data were
        stored  in  subdirectories of the package directory, which might cause
        problems  with write permissions, depending on the installation of the
        package. (Note that choosing other data directories can be useful also
        in  order  to keep existing local data files when a new version of GAP
        or  of  the AtlasRep package gets installed.) Thanks to Bill Allombert
        for pointing out this problem.
  
      The   information   about   data   files   from  the  ATLAS  of  Group
        Representations  has  been  extended  by  CrcFile (Reference: CrcFile)
        values.  These  values  are checked whenever data from such a file are
        read,  and  an  error is signalled if the checksum does not fit to the
        expected  one. Note that several users may access the same data files,
        and  a  user  should not suffer from perhaps corrupted files that have
        been downloaded by other users. Thanks to Frank Lübeck for the idea to
        introduce this consistency test.
  
      Whenever StringFile (GAPDoc: StringFile) is called by functions of the
        package, this happens in the wrapper function AGR.StringFile, in order
        to  replace  occasional  line  breaks  of  the  form  "\r\n"  by "\n".
        Apparently  it  may  happen that the "\r" is silently smuggled in when
        data  files  get  copied to the local computer. Thanks to Marek Mitros
        for help with detecting and fixing this problem.
  
      The   function   FFMatOrPermCMtxBinary   (7.3-5)  can  now  read  also
        permutations  stored  in  binary  files  that  have  been created with
        version  2.4 of the C-MeatAxe; note that this format is different from
        the    one    that    is   written   by   version   2.3.   Conversely,
        CMtxBinaryFFMatOrPerm  (7.3-4)  has  been  generalized  such that both
        formats  can  be written. The reference to the C-MeatAxe documentation
        now  points  to  that  of  version  2.4.  Thanks  to Jürgen Müller for
        pointing out this problem.
  
      The function MeatAxeString (7.3-2) can now encode permutation matrices
        in  different  ways. The mode (the first header entry) can be either 2
        (then the positions of the nonzero entries are listed) or 1 or 6 (then
        all  entries  of  the  matrix  are  listed). In previous versions, the
        function  produced  a matrix of mode 2 whenever this was possible, but
        this  behaviour  is  not  useful if the result is not processed by the
        C-MeatAxe. Thanks to Klaus Lux for pointing out this problem.
  
      Depending   on   the   terminal   capabilities   and   the   value  of
        AtlasOfGroupRepresentationsInfo.displayFunction,     some    non-ASCII
        characters may appear in the output shown by DisplayAtlasInfo (3.5-1).
  
  
  1.3-2 What's New in Version 1.5? (July 2011)
  
      The function AtlasSubgroup (3.5-8) now admits also the return value of
        OneAtlasGeneratingSetInfo  (3.5-5)  or  the return value of AtlasGroup
        (3.5-7)  as  its first argument. The latter is implemented via the new
        attribute  AtlasRepInfoRecord  (3.5-9),  which  is  set  in the groups
        constructed by AtlasGroup (3.5-7).
  
      Information   about   transitivity,   rank,   primitivity,  and  point
        stabilizers  of  many permutation representations is now available. If
        applicable  then  this  information appears in the records returned by
        OneAtlasGeneratingSetInfo (3.5-5), it is part of the overview shown by
        DisplayAtlasInfo (3.5-1), and it is shown also in the data overview in
        the web, see Section 4.4.
  
        Two  new  manual sections about point stabilizers have been added, see
        the sections 2.4-6 and 2.4-7.
  
      Information   about   the  characters  afforded  by  many  matrix  and
        permutation  representations is now available. If applicable then this
        information     appears     in     the     records     returned     by
        OneAtlasGeneratingSetInfo  (3.5-5),  for  matrix representations it is
        part  of  the  overview  shown  by DisplayAtlasInfo (3.5-1), and it is
        shown also in the data overview in the web, see Section 4.4.
  
      The  functions  Character (Reference: Character (for a character table
        and   a  list)),  Identifier  (Reference:  Identifier  (for  character
        tables)),    IsPrimitive    (Reference:   IsPrimitive),   IsTransitive
        (Reference: IsTransitive), Transitivity (Reference: Transitivity), and
        RankAction   (Reference:   RankAction)  are  now  supported  as  input
        conditions   in  DisplayAtlasInfo  (3.5-1),  OneAtlasGeneratingSetInfo
        (3.5-5), etc..
  
      It  is  now  possible  to  restrict the data shown by DisplayAtlasInfo
        (3.5-1)  to  private  or  non-private  data. Also the data returned by
        OneAtlasGeneratingSetInfo  (3.5-5)  can  be  restricted  to private or
        non-private data.
  
      A  tutorial  for beginners was added to the manual, see Chapter 2, and
        the manual was restructured.
  
      In  the  overview  shown  by  DisplayAtlasInfo (3.5-1) and in the data
        overview  in  the  web  (see  Section 4.4), the ordering of groups was
        improved such that, e.g., "A9" precedes "A10".
  
      The function AtlasClassNames (3.4-2) now admits also a Brauer table as
        its  argument,  and  works  also  for  character  tables  of  bicyclic
        extensions of simple groups.
  
      The   group  names  that  are  entered  in  DisplayAtlasInfo  (3.5-1),
        OneAtlasGeneratingSetInfo (3.5-5), etc., are now case insensitive, and
        if  the  package  CTblLib is available then the admissible group names
        for  the  GAP  character table of the group in question can be used in
        these functions.
  
      In  order  to reduce the number of global variables, several functions
        have  been  turned  into  components  of  the  new global variable AGR
        (7.1-5).  A few of these functions had been documented in the previous
        version,  the  old  values  are  still  available  if the package file
        gap/obsolete.g has been read. This file is read automatically when the
        package  gets  loaded if GAPInfo.UserPreferences.ReadObsolete is true,
        see 'Reference: The gap.ini file'.
  
      A  few  nicer  characters  are  used  by  DisplayAtlasInfo  (3.5-1) if
        GAPInfo.TermEncoding     has     the     value    "UTF-8"    and    if
        AtlasOfGroupRepresentationsInfo.displayFunction   is   different  from
        Print (Reference: Print), see Section 4.3-5.
  
      A  bug  in  the function ReloadAtlasTableOfContents (4.2-1) was fixed.
        Thanks to Jack Schmidt for reporting this bug.
  
  
  1.3-3 What's New in Version 1.4? (June 2008)
  
      In  addition  to  the group orders that were added in version 1.3 (see
        Section  1.3-5),  also  many  orders  of  maximal  subgroups  are  now
        available.  These values occur in the records returned by AtlasProgram
        (3.5-3)  (for  the  case  of  "maxes"  type programs) and of the three
        argument  version of AtlasGenerators (3.5-2); now a size component may
        be bound. In these cases, the groups returned by AtlasSubgroup (3.5-8)
        have the Size (Reference: Size) attribute set.
  
      The  information  about the number of maximal subgroups, if available,
        is now used in DisplayAtlasInfo (3.5-1).
  
      In  many  cases,  straight  line  programs for computing generators of
        maximal  subgroups  of  a group G, say, can in fact be used to compute
        also  generators  of maximal subgroups of downward extensions of G; if
        not  then it may suffice to extend the given straight line programs by
        additional generators.
  
        Currently  this  yields  more  than  200  new possibilities to compute
        maximal  subgroups,  this  means  a  growth  by  about 25 percent. For
        example,  all  maximal  subgroups  of  12.M_22  and 2.Fi_22 can now be
        accessed via AtlasGenerators (3.5-2).
  
        (Of  course this extension means only that one can access the straight
        line  programs  in  question  automatically  via the GAP interface. In
        principle  one  could  have  used  them  already before, by explicitly
        applying a straight line program for a factor group to generators of a
        group,  and  perhaps  adding some element in the kernel of the natural
        epimorphism.)
  
        For  this  feature,  information  about  the compatibility of standard
        generators of groups and their factor groups was added.
  
      The  bibliographies  contained in the ATLAS of Finite Groups [CCNPW85]
        and  in the ATLAS of Brauer Characters [JLPW95] are now available, see
        BrowseBibliographySporadicSimple (3.6-2).
  
      If  the  GAP  package  Browse  (see  [BL14])  is  loaded  then the new
        functions           BrowseMinimalDegrees          (3.6-1)          and
        BrowseBibliographySporadicSimple    (3.6-2)   are   available;   these
        functions  can  be  called  also  by  choosing  the corresponding menu
        entries    of    the   Browse   application   BrowseGapData   (Browse:
        BrowseGapData).
  
      The  function  AtlasGroup  (3.5-7) now admits also the return value of
        OneAtlasGeneratingSetInfo (3.5-5) as its argument.
  
  
  1.3-4 What's New in Version 1.3.1? (October 2007)
  
  This  version  was  mainly  released in order to fix a few problems. Now one
  does not get warnings about unbound variables when the package is loaded and
  the  GAP package IO [Neu14] is not available, and pathological situations in
  FFMatOrPermCMtxBinary  (7.3-5)  (concerning  extremely  short corrupted data
  files  and  different  byte  orderings  in  binary  files)  are handled more
  carefully.
  
  Besides this, the two functions AtlasGroup (3.5-7) and AtlasSubgroup (3.5-8)
  were  introduced,  and  the  extended function QuaternionAlgebra (Reference:
  QuaternionAlgebra)  of  GAP 4.4.10 can now be used for describing base rings
  in OneAtlasGeneratingSetInfo (3.5-5) and AllAtlasGeneratingSetInfos (3.5-6).
  (This  is  the  reason  why  this  version  of the package requires at least
  version 4.4.10 of GAP.)
  
  
  1.3-5 What's New in Version 1.3? (June 2007)
  
      The  database  was extended, see Section 4.3-4 for the number and size
        of files.
  
      New data types and corresponding GAP objects have been introduced, for
        representing   semi-presentations,  presentations,  and  programs  for
        finding  standard  generators.  For details, see AtlasProgram (3.5-3),
        Chapter 6, and Section 7.6.
  
      The   records  returned  by  the  functions  AtlasGenerators  (3.5-2),
        OneAtlasGeneratingSetInfo   (3.5-5),   and  AllAtlasGeneratingSetInfos
        (3.5-6)  now contain the name and (if known) the order of the group in
        question,  and  also  components  describing the degree in the case of
        permutation  representations or the dimension and the base ring of the
        natural module in the case of matrix representations.
  
      For  many  of  the  groups,  information  about  the minimal degree of
        faithful  permutation  representations  and  the minimal dimensions of
        faithful   matrix   representations   in  various  characteristics  is
        available   for  DisplayAtlasInfo  (3.5-1),  OneAtlasGeneratingSetInfo
        (3.5-5), and AllAtlasGeneratingSetInfos (3.5-6), see also Section 6.3.
        For  these  functions,  also properties such as IsPrimeInt (Reference:
        IsPrimeInt)  can  be  used to describe the intended restriction of the
        output.
  
      One   can   now   use   Pager   (Reference:  Pager)  functionality  in
        DisplayAtlasInfo (3.5-1), see Section 4.3-5.
  
        An  interactive alternative to DisplayAtlasInfo (3.5-1) is provided by
        the  function  BrowseAtlasInfo  (Browse: BrowseAtlasInfo) from the new
        (recommended) GAP package Browse [BL14].
  
      The      functions      OneAtlasGeneratingSetInfo      (3.5-5)     and
        AllAtlasGeneratingSetInfos  (3.5-6)  now  admit  also  a list of group
        names as the first argument.
  
      The  functions  for actually accessing the data are more flexible now,
        see Section 4.3-6.
  
      For  transferring  remote  data, the GAP package IO [Neu14] can now be
        used   (and   is   recommended)   as   an  alternative  to  wget,  see
        Section 4.3-3.
  
      The  address  of  the data server has changed. Since the access to the
        server  is no longer possible via ftp, the mechanim used up to version
        1.2, which was based on ftp, had to be rewritten.
  
        The  main consequence of this change is that information about updates
        of  the  table  of contents is now provided at the package's homepage.
        This  means that on the one hand, now package users cannot compute the
        table of contents directly from the server data, but on the other hand
        the  update  information  can  be  downloaded without the necessity to
        install perl.
  
        Another consequence is that the system program ls is no longer needed,
        see Section 1.3-7.
  
      The package manual has been restructured, extended and improved. It is
        now based on the package GAPDoc [LN12].
  
  
  1.3-6 What's New in Version 1.2? (November 2003)
  
  Not much.
  
  The release of Version 1.2 became necessary first of all in order to provide
  a   package   version   that   is   compatible   with  GAP 4.4,  since  some
  cross-references into the GAP Reference Manual were broken due to changes of
  section  names.  Additionally,  several web addresses concerning the package
  itself were changed and thus had to be adjusted.
  
  This opportunity was used
  
      to  upgrade  the  administrational part for loading the package to the
        mechanism that is recommended for GAP 4.4,
  
      to  extend  the  test  suite, which now covers more consistency checks
        using the GAP Character Table Library [Bre13],
  
      to  make  the function ScanMeatAxeFile (7.3-1) more robust, due to the
        fact  that the GAP function PermList (Reference: PermList) now returns
        fail instead of raising an error,
  
      to  change  the way how representations with prescribed properties are
        accessed  (the  new  function OneAtlasGeneratingSetInfo (3.5-5) is now
        preferred     to     the     former     OneAtlasGeneratingSet,     and
        AllAtlasGeneratingSetInfos  (3.5-6) has been added in order to provide
        programmatic  access  in  parallel  to the human readable descriptions
        printed by DisplayAtlasInfo (3.5-1)),
  
      and last but not least to include the current table of contents of the
        underlying database.
  
  For  AtlasRep  users, the new feature of GAP 4.4 is particularly interesting
  that due to better kernel support, reading large matrices over finite fields
  is now faster than it was in GAP 4.3.
  
  
  1.3-7 What's New in Version 1.1? (October 2002)
  
  The  biggest change w.r.t. Version 1.1 is the addition of private extensions
  (see  Chapter 5).  It  includes a new free format for straight line programs
  (see  Section 5.2).  Unfortunately, this feature requires the system program
  ls,  so  it  may  be  not  available  for example under MS Windows operating
  systems. [But see Section 1.3-5.]
  
  In order to admit the addition of other types of data, the implementation of
  several functions has been changed. Data types are described in Section 7.5.
  An  example  of  a  new  data  type  are  quaternionic  representations (see
  Section 7.6). The user interface itself (see Chapter 3) remained the same.
  
  As  an alternative to perl, one can use wget now for transferring data files
  (see 4.3).
  
  Data  files can be read much more efficiently in GAP 4.3 than in GAP 4.2. In
  Version 1.1  of  the  AtlasRep  package,  this  feature  is used for reading
  matrices  and  permutations  in  MeatAxe  text  format  with ScanMeatAxeFile
  (7.3-1).  As  a  consequence,  (at  least)  GAP 4.3 is required for AtlasRep
  Version 1.1.
  
  The     new     compress     component     of     the     global    variable
  AtlasOfGroupRepresentationsInfo  (7.1-6)  allows  one  to  store  data files
  automatically in gzipped form.
  
  For  matrix  representations  in  characteristic  zero,  invariant forms and
  generators for the centralizer algebra are now accessible in GAP if they are
  contained  in  the  source  files  --this  information  had  been ignored in
  Version 1.0 (see AtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates
  (4.2-4) for necessary updates).
  
  Additional information is now available via the internet (see 4.4).
  
  The update facilities have been extended (see 4.2).
  
  The  manual  is  now  distributed  also in pdf and HTML format; on the other
  hand, the PostScript format manual is no longer contained in the archives.
  
  Apart  from these changes, a few minor bugs in the handling of MeatAxe files
  have  been  fixed,  typos  in the documentation have been corrected, and the
  syntax checks for ATLAS straight line programs (see 7.4) have been improved.
  
  
  1.4 Acknowledgements
  
      Frank  Lübeck  and Max Neunhöffer kindly provided the perl script that
        had  been used for fetching remote data until version 1.2. Thanks also
        to  Greg  Gamble  and  Alexander Hulpke for technical hints concerning
        standard perl.
  
      Ulrich Kaiser helped with preparing the package for MS Windows.
  
      Klaus  Lux  had the idea to support private extensions of the package,
        see Chapter 5 and helped to fix several bugs.
  
      Frank  Lübeck  contributed the functions CMtxBinaryFFMatOrPerm (7.3-4)
        and FFMatOrPermCMtxBinary (7.3-5).
  
      Frank Lübeck and Max Neunhöffer wrote the GAPDoc package [LN12], which
        is  used  for processing the documentation of the AtlasRep package and
        for  processing  the  bibliographies  included  in  this  package (see
        BrowseBibliographySporadicSimple (3.6-2)),
  
      Max  Neunhöffer wrote the GAP package IO [Neu14], which is recommended
        for transferring data.
  
      Max has also suggested the generalization of the data access described
        in  Section 7.2,  and  the  admissibility  of  the  function Character
        (Reference:  Character (for a character table and a list)) as a filter
        in  DisplayAtlasInfo  (3.5-1),  OneAtlasGeneratingSetInfo (3.5-5), and
        AllAtlasGeneratingSetInfos (3.5-6).
  
      Gunter  Malle  suggested to make the information about representations
        of minimal degree accessible, see Section 6.3.
  
      Andries Brouwer suggested to add a tutorial (see Chapter 2), Klaus Lux
        suggested several improvements of this chapter.